Dr. Karsten Tabelow  Publications
Monographs

J. Polzehl, K. Tabelow, Magnetic Resonance Brain Imaging: Modeling and Data Analysis using R, 2nd Revised Edition, Series: Use R!, Springer International Publishing, Cham, 2023, 258 pages, (Monograph Published), DOI 10.1007/9783031389498 .
Abstract
This book discusses the modeling and analysis of magnetic resonance imaging (MRI) data acquired from the human brain. The data processing pipelines described rely on R. The book is intended for readers from two communities: Statisticians who are interested in neuroimaging and looking for an introduction to the acquired data and typical scientific problems in the field; and neuroimaging students wanting to learn about the statistical modeling and analysis of MRI data. Offering a practical introduction to the field, the book focuses on those problems in data analysis for which implementations within R are available. It also includes fully worked examples and as such serves as a tutorial on MRI analysis with R, from which the readers can derive their own data processing scripts. The book starts with a short introduction to MRI and then examines the process of reading and writing common neuroimaging data formats to and from the R session. The main chapters cover three common MR imaging modalities and their data modeling and analysis problems: functional MRI, diffusion MRI, and MultiParameter Mapping. The book concludes with extended appendices providing details of the nonparametric statistics used and the resources for R and MRI data.The book also addresses the issues of reproducibility and topics like data organization and description, as well as open data and open science. It relies solely on a dynamic report generation with knitr and uses neuroimaging data publicly available in data repositories. The PDF was created executing the R code in the chunks and then running LaTeX, which means that almost all figures, numbers, and results were generated while producing the PDF from the sources. 
L. Starke, K. Tabelow, Th. Niendorf, A. Pohlmann, Chapter 34: Denoising for Improved Parametric MRI of the Kidney: Protocol for Nonlocal Means Filtering, in: Preclinical MRI of the Kidney: Methods and Protocols, A. Pohlmann, Th. Niendorf, eds., 2216 of Methods in Molecular Biology, Springer Nature Switzerland AG, Cham, 2021, pp. 565576, (Chapter Published), DOI 10.1007/9781071609781_34 .

J. Polzehl, K. Tabelow, Magnetic Resonance Brain Imaging: Modeling and Data Analysis using R, Series: Use R!, Springer International Publishing, Cham, 2019, 231 pages, (Monograph Published), DOI 10.1007/9783030291846 .
Abstract
This book discusses the modeling and analysis of magnetic resonance imaging (MRI) data acquired from the human brain. The data processing pipelines described rely on R. The book is intended for readers from two communities: Statisticians who are interested in neuroimaging and looking for an introduction to the acquired data and typical scientific problems in the field; and neuroimaging students wanting to learn about the statistical modeling and analysis of MRI data. Offering a practical introduction to the field, the book focuses on those problems in data analysis for which implementations within R are available. It also includes fully worked examples and as such serves as a tutorial on MRI analysis with R, from which the readers can derive their own data processing scripts. The book starts with a short introduction to MRI and then examines the process of reading and writing common neuroimaging data formats to and from the R session. The main chapters cover three common MR imaging modalities and their data modeling and analysis problems: functional MRI, diffusion MRI, and MultiParameter Mapping. The book concludes with extended appendices providing details of the nonparametric statistics used and the resources for R and MRI data.The book also addresses the issues of reproducibility and topics like data organization and description, as well as open data and open science. It relies solely on a dynamic report generation with knitr and uses neuroimaging data publicly available in data repositories. The PDF was created executing the R code in the chunks and then running LaTeX, which means that almost all figures, numbers, and results were generated while producing the PDF from the sources. 
J. Polzehl, K. Tabelow, Chapter 4: Structural Adaptive Smoothing: Principles and Applications in Imaging, in: Mathematical Methods for Signal and Image Analysis and Representation, L. Florack, R. Duits, G. Jongbloed, M.C. VAN Lieshout, L. Davies, eds., 41 of Computational Imaging and Vision, Springer, London et al., 2012, pp. 6581, (Chapter Published).

K. Tabelow, B. Whitcher, eds., Magnetic Resonance Imaging in R, 44 of Journal of Statistical Software, American Statistical Association, 2011, 320 pages, (Monograph Published).
Articles in Refereed Journals

J.M. Oeschger, K. Tabelow, S. Mohammadi, Investigating apparent differences between standard DKI and axisymmetric DKI and its consequences for biophysical parameter estimates, Magnetic Resonance in Medicine, 92, pp. 6981, DOI 10.1002/mrm.30034 .

I.F. Tellez Ceja, Th. Gladytz, L. Starke, K. Tabelow, Th. Niendorf, H.M. Reiman, Precision fMRI and clusterfailure in the individual brain, Human Brain Mapping, 45, pp. e26813/1 e26813/20, DOI 10.1002/hbm.26813 .

F. Galarce Marín, K. Tabelow, J. Polzehl, Ch.P. Papanikas, V. Vavourakis, L. Lilaj, I. Sack, A. Caiazzo, Displacement and pressure reconstruction from magnetic resonance elastography images: Application to an in silico brain model, SIAM Journal on Imaging Sciences, 16 (2023), pp. 9961027, DOI 10.1137/22M149363X .
Abstract
This paper investigates a data assimilation approach for noninvasive quantification of intracranial pressure from partial displacement data, acquired through magnetic resonance elastography. Data assimilation is based on a parametrizedbackground data weak methodology, in which the state of the physical system tissue displacements and pressure fields is reconstructed from partially available data assuming an underlying poroelastic biomechanics model. For this purpose, a physicsinformed manifold is built by sampling the space of parameters describing the tissue model close to their physiological ranges, to simulate the corresponding poroelastic problem, and compute a reduced basis. Displacements and pressure reconstruction is sought in a reduced space after solving a minimization problem that encompasses both the structure of the reducedorder model and the available measurements. The proposed pipeline is validated using synthetic data obtained after simulating the poroelastic mechanics on a physiological brain. The numerical experiments demonstrate that the framework can exhibit accurate joint reconstructions of both displacement and pressure fields. The methodology can be formulated for an arbitrary resolution of available displacement data from pertinent images. It can also inherently handle uncertainty on the physical parameters of the mechanical model by enlarging the physicsinformed manifold accordingly. Moreover, the framework can be used to characterize, in silico, biomarkers for pathological conditions, by appropriately training the reducedorder model. A first application for the estimation of ventricular pressure as an indicator of abnormal intracranial pressure is shown in this contribution. 
S. Mohammadi, T. Streubel, L. Klock, A. Lutti, K. Pine, S. Weber, L. Edwards, P. Scheibe, G. Ziegler, J. Gallinat, S. Kuhn, M. Callaghan, N. Weiskopf, K. Tabelow, Error quantification in multiparameter mapping facilitates robust estimation and enhanced group level sensitivity, NeuroImage, 262 (2022), pp. 119529/1119529/14, DOI 10.1016/j.neuroimage.2022.119529 .
Abstract
MultiParameter Mapping (MPM) is a comprehensive quantitative neuroimaging protocol that enables estimation of four physical parameters (longitudinal and effective transverse relaxation rates R1 and R2*, proton density PD, and magnetization transfer saturation MTsat) that are sensitive to microstructural tissue properties such as iron and myelin content. Their capability to reveal microstructural brain differences, however, is tightly bound to controlling random noise and artefacts (e.g. caused by head motion) in the signal. Here, we introduced a method to estimate the local error of PD, R1, and MTsat maps that captures both noise and artefacts on a routine basis without requiring additional data. To investigate the method's sensitivity to random noise, we calculated the modelbased signaltonoise ratio (mSNR) and showed in measurements and simulations that it correlated linearly with an experimental rawimagebased SNR map. We found that the mSNR varied with MPM protocols, magnetic field strength (3T vs. 7T) and MPM parameters: it halved from PD to R1 and decreased from PD to MT_sat by a factor of 34. Exploring the artefactsensitivity of the error maps, we generated robust MPM parameters using two successive acquisitions of each contrast and the acquisitionspecific errors to downweight erroneous regions. The resulting robust MPM parameters showed reduced variability at the group level as compared to their singlerepeat or averaged counterparts. The error and mSNR maps may better inform powercalculations by accounting for local data quality variations across measurements. Code to compute the mSNR maps and robustly combined MPM maps is available in the opensource hMRI toolbox. 
J.M. Oeschger, K. Tabelow, S. Mohammadi, Axisymmetric diffusion kurtosis imaging with Rician bias correction: A simulation study, Magnetic Resonance in Medicine, 89 (2023), pp. 787799 (published online on 05.10.2022), DOI 10.1002/mrm.29474 .

A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, Th. Koprucki, Numerical simulation of TEM images for In(Ga)As/GaAs quantum dots with various shapes, Optical and Quantum Electronics, 52 (2020), pp. 257/1257/11, DOI 10.1007/s1108202002356y .
Abstract
We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the DarwinHowieWhelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gallium arsenide QDs with different shapes and compare the resulting TEM images to experimental ones. This tool chain can be applied to generate a database of simulated TEM images, which is a key element of a novel concept for modelbased geometry reconstruction of semiconductor QDs, involving machine learning techniques. 
J. Polzehl, K. Papafitsoros, K. Tabelow, Patchwise adaptive weights smoothing in R, Journal of Statistical Software, 95 (2020), pp. 127, DOI 10.18637/jss.v095.i06 .
Abstract
Image reconstruction from noisy data has a long history of methodological development and is based on a variety of ideas. In this paper we introduce a new method called patchwise adaptive smoothing, that extends the PropagationSeparation approach by using comparisons of local patches of image intensities to define local adaptive weighting schemes for an improved balance of reduced variability and bias in the reconstruction result. We present the implementation of the new method in an R package aws and demonstrate its properties on a number of examples in comparison with other stateofthe art image reconstruction methods. 
M.F. Callaghan, A. Lutti, J. Ashburner, E. Balteau, N. Corbin, B. Draganski, G. Helms, F. Kherif, T. Leutritz, S. Mohammadi, Ch. Phillips, E. Reimer, L. Ruthotto, M. Seif, K. Tabelow, G. Ziegler, N. Weiskopf, Example dataset for the hMRI toolbox, Data in Brief, 25 (2019), pp. 104132/1104132/6, DOI 10.1016/j.dib.2019.104132 .

K. Tabelow, E. Balteau, J. Ashburner, M.F. Callaghan, B. Draganski, G. Helms, F. Kherif, T. Leutritz, A. Lutti, Ch. Phillips, E. Reimer, L. Ruthotto, M. Seif, N. Weiskopf, G. Ziegler, S. Mohammadi, hMRI  A toolbox for quantitative MRI in neuroscience and clinical research, NeuroImage, 194 (2019), pp. 191210, DOI 10.1016/j.neuroimage.2019.01.029 .
Abstract
Quantitative magnetic resonance imaging (qMRI) finds increasing application in neuroscience and clinical research due to its sensitivity to microstructural properties of brain tissue, e.g. axon, myelin, iron and water concentration. We introduce the hMRItoolbox, an easytouse opensource tool for handling and processing of qMRI data presented together with an example dataset. This toolbox allows the estimation of highquality multiparameter qMRI maps (longitudinal and effective transverse relaxation rates R1 and R2*, proton density PD and magnetisation transfer MT) that can be used for calculation of standard and novel MRI biomarkers of tissue microstructure as well as improved delineation of subcortical brain structures. Embedded in the Statistical Parametric Mapping (SPM) framework, it can be readily combined with existing SPM tools for estimating diffusion MRI parameter maps and benefits from the extensive range of available tools for highaccuracy spatial registration and statistical inference. As such the hMRItoolbox provides an efficient, robust and simple framework for using qMRI data in neuroscience and clinical research. 
TH. Koprucki, M. Kohlhase, K. Tabelow, D. Müller, F. Rabe, Model pathway diagrams for the representation of mathematical models, Optical and Quantum Electronics, 50 (2018), pp. 70/170/9, DOI 10.1007/s1108201813217 .
Abstract
Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machineactionable as well as humanunderstandable representation of the mathematical knowledge they contain and the domainspecific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the van Roosbroeck system describing the carrier transport in semiconductors by drift and diffusion. We introduce an approach for the blockbased composition of models from simpler components. 
M. Deppe, K. Tabelow, J. Krämer, J.G. Tenberge, P. Schiffler, S. Bittner, W. Schwindt, F. Zipp, H. Wiendl, S.G. Meuth, Evidence for early, nonlesional cerebellar damage in patients with multiple sclerosis: DTI measures correlate with disability, atrophy, and disease duration, Multiple Sclerosis Journal, 22 (2016), pp. 7384, DOI 10.1177/1352458515579439 .

K. Schildknecht, K. Tabelow, Th. Dickhaus, More specific signal detection in functional magnetic resonance imaging by false discovery rate control for hierarchically structured systems of hypotheses, PLOS ONE, 11 (2016), pp. e0149016/1e0149016/21, DOI 10.1371/journal.pone.0149016 .

H.U. Voss, J.P. Dyke, K. Tabelow, N. Schiff, D. Ballon, Magnetic resonance advection imaging of cerebrovascular pulse dynamics, Journal of Cerebral Blood Flow and Metabolism, 37 (2017), pp. 12231235 (published online on 24.05.2016), DOI 10.1177/0271678x16651449 .

M. Deliano, K. Tabelow, R. König, J. Polzehl, Improving accuracy and temporal resolution of learning curve estimation for within and acrosssession analysis, PLOS ONE, 11 (2016), pp. e0157355/1e0157355/23, DOI 10.1371/journal.pone.0157355 .
Abstract
Estimation of learning curves is ubiquitously based on proportions of correct responses within moving trial windows. In this approach, it is tacitly assumed that learning performance is constant within the moving windows, which, however, is often not the case. In the present study we demonstrate that violations of this assumption lead to systematic errors in the analysis of learning curves, and we explored the dependency of these errors on window size, different statistical models, and learning phase. To reduce these errors for single subjects as well as on the population level, we propose adequate statistical methods for the estimation of learning curves and the construction of confidence intervals, trial by trial. Applied to data from a shuttlebox avoidance experiment with Mongolian gerbils, our approach revealed performance changes occurring at multiple temporal scales within and across training sessions which were otherwise obscured in the conventional analysis. The proper assessment of the behavioral dynamics of learning at a high temporal resolution clarified and extended current descriptions of the process of avoidance learning. It further disambiguated the interpretation of neurophysiological signal changes recorded during training in relation to learning. 
J. Polzehl, K. Tabelow, Low SNR in diffusion MRI models, Journal of the American Statistical Association, 111 (2016), pp. 14801490, DOI 10.1080/01621459.2016.1222284 .
Abstract
Noise is a common issue for all magnetic resonance imaging (MRI) techniques such as diffusion MRI and obviously leads to variability of the estimates in any model describing the data. Increasing spatial resolution in MR experiments further diminish the signaltonoise ratio (SNR). However, with low SNR the expected signal deviates from the true value. Common modeling approaches therefore lead to a bias in estimated model parameters. Adjustments require an analysis of the data generating process and a characterization of the resulting distribution of the imaging data. We provide an adequate quasilikelihood approach that employs these characteristics. We elaborate on the effects of typical data preprocessing and analyze the bias effects related to low SNR for the example of the diffusion tensor model in diffusion MRI. We then demonstrate the relevance of the problem using data from the Human Connectome Project. 
K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, POAS4SPM  A toolbox for SPM to denoise diffusion MRI data, Neuroinformatics, 13 (2015), pp. 1929.
Abstract
We present an implementation of a recently developed noise reduction algorithm for dMRI data, called multishell position orientation adaptive smoothing (msPOAS), as a toolbox for SPM. The method intrinsically adapts to the structures of different size and shape in dMRI and hence avoids blurring typically observed in nonadaptive smoothing. We give examples for the usage of the toolbox and explain the determination of experimentdependent parameters for an optimal performance of msPOAS. 
K. Tabelow, H.U. Voss, J. Polzehl, Local estimation of the noise level in MRI using structural adaptation, Medical Image Analysis, 20 (2015), pp. 7686.
Abstract
We present a method for local estimation of the signaldependent noise level in magnetic resonance images. The procedure uses a multiscale approach to adaptively infer on local neighborhoods with similar data distribution. It exploits a maximumlikelihood estimator for the local noise level. The validity of the method was evaluated on repeated diffusion data of a phantom and simulated data using T1data corrupted with artificial noise. Simulation results are compared with a recently proposed estimate. The method was applied to a highresolution diffusion dataset to obtain improved diffusion model estimation results and to demonstrate its usefulness in methods for enhancing diffusion data. 
J. Krämer, M. Deppe, K. Göbel, K. Tabelow, H. Wiendl, S.G. Meuth, Recovery of thalamic microstructural damage after Shiga toxin 2associated hemolyticuremic syndrome, Journal of the Neurological Sciences, 356 (2015), pp. 175183.

S. Mohammadi, K. Tabelow, L. Ruthotto, Th. Feiweier, J. Polzehl, N. Weiskopf, Highresolution diffusion kurtosis imaging at 3T enabled by advanced postprocessing, Frontiers in Neuroscience, 8 (2015), pp. 427/1427/14.

S. Becker, K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, Adaptive smoothing of multishell diffusionweighted magnetic resonance data by msPOAS, NeuroImage, 95 (2014), pp. 90105.
Abstract
In this article we present a noise reduction method (msPOAS) for multishell diffusionweighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all qshells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed positionorientation adaptive smoothing (POAS) procedure to multishell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusionweighted data measured on a single shell and on multiple shells. 
M. Welvaert, K. Tabelow, R. Seurinck, Y. Rosseel, Adaptive smoothing as inference strategy: More specificity for unequally sized or neighboring regions, Neuroinformatics, 11 (2013), pp. 435445.
Abstract
Although spatial smoothing of fMRI data can serve multiple purposes, increasing the sensitivity of activation detection is probably its greatest benefit. However, this increased detection power comes with a loss of specificity when nonadaptive smoothing (i.e. the standard in most software packages) is used. Simulation studies and analysis of experimental data was performed using the R packages neuRosim and fmri. In these studies, we systematically investigated the effect of spatial smoothing on the power and number of false positives in two particular cases that are often encountered in fMRI research: (1) Single condition activation detection for regions that differ in size, and (2) multiple condition activation detection for neighbouring regions. Our results demonstrate that adaptive smoothing is superior in both cases because less false positives are introduced by the spatial smoothing process compared to standard Gaussian smoothing or FDR inference of unsmoothed data. 
S. Becker, K. Tabelow, H.U. Voss, A. Anwander, R.M. Heidemann, J. Polzehl, Positionorientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS), Medical Image Analysis, 16 (2012), pp. 11421155.
Abstract
We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both space and diffusion direction. The method, called POAS, does not refer to a specific model for the data, like the diffusion tensor or higher order models. It works by embedding the measurement space into a space with defined metric and group operations, in this case the Lie group of threedimensional Euclidean motion SE(3). Subsequently, pairwise comparisons of the values of the diffusion weighted signal are used for adaptation. The positionorientation adaptive smoothing preserves the edges of the observed fine and anisotropic structures. The POASalgorithm is designed to reduce noise directly in the diffusion weighted images and consequently also to reduce bias and variability of quantities derived from the data for specific models. We evaluate the algorithm on simulated and experimental data and demonstrate that it can be used to reduce the number of applied diffusion gradients and hence acquisition time while achieving similar quality of data, or to improve the quality of data acquired in a clinically feasible scan time setting. 
K. Tabelow, H.U. Voss, J. Polzehl, Modeling the orientation distribution function by mixtures of angular central Gaussian distributions, Journal of Neuroscience Methods, 203 (2012), pp. 200211.
Abstract
In this paper we develop a tensor mixture model for diffusion weighted imaging data using an automatic model selection criterion for the order of tensor components in a voxel. We show that the weighted orientation distribution function for this model can be expanded into a mixture of angular central Gaussian distributions. We show properties of this model in extensive simulations and in a high angular resolution experimental data set. The results suggest that the model may improve imaging of cerebral fiber tracts. We demonstrate how inference on canonical model parameters may give rise to new clinical applications. 
K. Tabelow, J.D. Clayden, P. Lafaye DE Micheaux, J. Polzehl, V.J. Schmid, B. Whitcher, Image analysis and statistical inference in neuroimaging with R, NeuroImage, 55 (2011), pp. 16861693.
Abstract
R is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost every major operating system currently available. We highlight several R packages built specifically for the analysis of neuroimaging data in the context of functional MRI, diffusion tensor imaging, and dynamic contrastenhanced MRI. We review their methodology and give an overview of their capabilities for neuroimaging. In addition we summarize some of the current activities in the area of neuroimaging software development in R. 
K. Tabelow, J. Polzehl, Statistical parametric maps for functional MRI experiments in R: The package fmri, Journal of Statistical Software, 44 (2011), pp. 121.
Abstract
The package fmri is provided for analysis of single run functional Magnetic Resonance Imaging data. It implements structural adaptive smoothing methods with signal detection for adaptive noise reduction which avoids blurring of edges of activation areas. fmri provides fmri analysis from time series modeling to signal detection and publicationready images. 
J. Bardin, J. Fins, D. Katz, J. Hersh, L. Heier, K. Tabelow, J. Dyke, D. Ballon, N. Schiff, H. Voss, Dissociations between behavioral and fMRIbased evaluations of cognitive function after brain injury, Brain, 134 (2011), pp. 769782.
Abstract
Functional neuroimaging methods hold promise for the identification of cognitive function and communication capacity in some severely braininjured patients who may not retain sufficient motor function to demonstrate their abilities. We studied seven severely braininjured patients and a control group of 14 subjects using a novel hierarchical functional magnetic resonance imaging assessment utilizing mental imagery responses. Whereas the control group showed consistent and accurate (for communication) bloodoxygenleveldependent responses without exception, the braininjured subjects showed a wide variation in the correlation of bloodoxygenleveldependent responses and overt behavioural responses. Specifically, the braininjured subjects dissociated bedside and functional magnetic resonance imagingbased command following and communication capabilities. These observations reveal significant challenges in developing validated functional magnetic resonance imagingbased methods for clinical use and raise interesting questions about underlying brain function assayed using these methods in braininjured subjects. 
J. Polzehl, K. Tabelow, Beyond the Gaussian model in diffussionweighted imaging: The package dti, Journal of Statistical Software, 44 (2011), pp. 126.
Abstract
Diffusion weighted imaging is a magnetic resonance based method to investigate tissue microstructure especially in the human brain via water diffusion. Since the standard diffusion tensor model for the acquired data failes in large portion of the brain voxel more sophisticated models have bee developed. Here, we report on the package dti and how some of these models can be used with the package. 
J. Polzehl, H.U. Voss, K. Tabelow, Structural adaptive segmentation for statistical parametric mapping, NeuroImage, 52 (2010), pp. 515523.
Abstract, PreprintPDF (1015 kByte), PreprintPostscript (9284 kByte)
Functional Magnetic Resonance Imaging inherently involves noisy measurements and a severe multiple test problem. Smoothing is usually used to reduce the effective number of multiple comparisons and to locally integrate the signal and hence increase the signaltonoise ratio. Here, we provide a new structural adaptive segmentation algorithm (AS) that naturally combines the signal detection with noise reduction in one procedure. Moreover, the new method is closely related to a recently proposed structural adaptive smoothing algorithm and preserves shape and spatial extent of activation areas without blurring the borders. 
K. Tabelow, V. Piëch, J. Polzehl, H.U. Voss, Highresolution fMRI: Overcoming the signaltonoise problem, Journal of Neuroscience Methods, 178 (2009), pp. 357365.
Abstract, PreprintPDF (2578 kByte), PreprintPostscript (5888 kByte)
Increasing the spatial resolution in functional Magnetic Resonance Imaging (fMRI) inherently lowers the signaltonoise ratio (SNR). In order to still detect functionally significant activations in highresolution images, spatial smoothing of the data is required. However, conventional nonadaptive smoothing comes with a reduced effective resolution, foiling the benefit of the higher acquisition resolution. We show how our recently proposed structural adaptive smoothing procedure for functional MRI data can improve signal detection of highresolution fMRI experiments regardless of the lower SNR. The procedure is evaluated on human visual and sensorymotor mapping experiments. In these applications, the higher resolution could be fully utilized and highresolution experiments were outperforming normal resolution experiments by means of both statistical significance and information content. 
J. Polzehl, K. Tabelow, Structural adaptive smoothing in diffusion tensor imaging: The R package dti, Journal of Statistical Software, 31 (2009), pp. 124.
Abstract, PDF (2809 kByte)
Diffusion Weighted Imaging has become and will certainly continue to be an important tool in medical research and diagnostics. Data obtained with Diffusion Weighted Imaging are characterized by a high noise level. Thus, estimation of quantities like anisotropy indices or the main diffusion direction may be significantly compromised by noise in clinical or neuroscience applications. Here, we present a new package dti for R, which provides functions for the analysis of diffusion weighted data within the diffusion tensor model. This includes smoothing by a recently proposed structural adaptive smoothing procedure based on the PropagationSeparation approach in the context of the widely used Diffusion Tensor Model. We extend the procedure and show, how a correction for Rician bias can be incorporated. We use a heteroscedastic nonlinear regression model to estimate the diffusion tensor. The smoothing procedure naturally adapts to different structures of different size and thus avoids oversmoothing edges and fine structures. We illustrate the usage and capabilities of the package through some examples. 
K. Tabelow, J. Polzehl, A.M. Uluğ, J.P. Dyke, R. Watts, L.A. Heier, H.U. Voss, Accurate localization of brain activity in presurgical fMRI by structure adaptive smoothing, IEEE Transactions on Medical Imaging, 27 (2008), pp. 531537.
Abstract, PreprintPDF (746 kByte), PreprintPostscript (12 MByte)
An important problem of the analysis of fMRI experiments is to achieve some noise reduction of the data without blurring the shape of the activation areas. As a novel solution to this problem, the PropagationSeparation approach (PS), a structure adaptive smoothing method, has been proposed recently. PS adapts to different shapes of activation areas by generating a spatial structure corresponding to similarities and differences between time series in adjacent locations. In this paper we demonstrate how this method results in more accurate localization of brain activity. First, it is shown in numerical simulations that PS is superior over Gaussian smoothing with respect to the accurate description of the shape of activation clusters and and results in less false detections. Second, in a study of 37 presurgical planning cases we found that PS and Gaussian smoothing often yield different results, and we present examples showing aspects of the superiority of PS as applied to presurgical planning. 
K. Tabelow, J. Polzehl, V. Spokoiny, H.U. Voss, Diffusion tensor imaging: Structural adaptive smoothing, NeuroImage, 39 (2008), pp. 17631773.
Abstract, PreprintPDF (887 kByte), PreprintPostscript (3191 kByte)
Diffusion Tensor Imaging (DTI) data is characterized by a high noise level. Thus, estimation errors of quantities like anisotropy indices or the main diffusion direction used for fiber tracking are relatively large and may significantly confound the accuracy of DTI in clinical or neuroscience applications. Besides pulse sequence optimization, noise reduction by smoothing the data can be pursued as a complementary approach to increase the accuracy of DTI. Here, we suggest an anisotropic structural adaptive smoothing procedure, which is based on the PropagationSeparation method and preserves the structures seen in DTI and their different sizes and shapes. It is applied to artificial phantom data and a brain scan. We show that this method significantly improves the quality of the estimate of the diffusion tensor and hence enables one either to reduce the number of scans or to enhance the input for subsequent analysis such as fiber tracking. 
H.U. Voss, K. Tabelow, J. Polzehl, O. Tchernichovski, K. Maul, D. SalgadoCommissariat, D. Ballon, S.A. Helekar, Functional MRI of the zebra finch brain during song stimulation suggests a lateralized response topography, Proceedings of the National Academy of Sciences of the United States of America, 104 (2007), pp. 1066710672.
Abstract
Electrophysiological and activitydependent gene expression studies of birdsong have contributed to the understanding of the neural representation of natural sounds. However, we have limited knowledge about the overall spatial topography of song representation in the avian brain. Here, we adapt the noninvasive functional MRI method in mildly sedated zebra finches (Taeniopygia guttata) to localize and characterize song driven brain activation. Based on the blood oxygenation leveldependent signal, we observed a differential topographic responsiveness to playback of bird's own song, tutor song, conspecific song, and a pure tone as a nonsong stimulus. The bird's own song caused a stronger response than the tutor song or tone in higher auditory areas. This effect was more pronounced in the medial parts of the forebrain. We found leftright hemispheric asymmetry in sensory responses to songs, with significant discrimination between stimuli observed only in the right hemisphere. This finding suggests that perceptual responses might be lateralized in zebra finches. In addition to establishing the feasibility of functional MRI in sedated songbirds, our results demonstrate spatial coding of song in the zebra finch forebrain, based on developmental familiarity and experience. 
J. Polzehl, K. Tabelow, Adaptive smoothing of digital images: The R package adimpro, Journal of Statistical Software, 19 (2007), pp. 117.
Abstract, PDF (14 MByte)
Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used nonadaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the PropagationSeparation approach by Polzehl and Spokoiny (2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples. 
J. Polzehl, K. Tabelow, fmri: A package for analyzing fmri data, Newsletter of the R Project for Statistical Computing, 7 (2007), pp. 1317.
PDF (1620 kByte) 
K. Tabelow, J. Polzehl, H.U. Voss, V. Spokoiny, Analyzing fMRI experiments with structural adaptive smoothing procedures, NeuroImage, 33 (2006), pp. 5562.
Abstract, PreprintPDF (396 kByte), PreprintPostscript (1091 kByte)
Data from functional magnetic resonance imaging (fMRI) consists of time series of brain images which are characterized by a low signaltonoise ratio. In order to reduce noise and to improve signal detection the fMRI data is spatially smoothed. However, the common application of a Gaussian filter does this at the cost of loss of information on spatial extent and shape of the activation area. We suggest to use the propagationseparation procedures introduced by Polzehl and Spokoiny (2006) instead. We show that this significantly improves the information on the spatial extent and shape of the activation region with similar results for the noise reduction. To complete the statistical analysis, signal detection is based on thresholds defined by random field theory. Effects of ad aptive and nonadaptive smoothing are illustrated by artificial examples and an analysis of experimental data.
Contributions to Collected Editions

L. Kastner, K. Tabelow, Ach ja  Forschungsdatenmanagement, 32 of Mitteilungen der Deutschen MathematikerVereinigung, Walter de Gruyter GmbH, Berlin/Boston, 2024, pp. 102104, DOI 10.1515/dmvm20240031 .

R. Danabalan, M. Hintermüller, Th. Koprucki, K. Tabelow, MaRDI: Building research data infrastructures for mathematics and the mathematical sciences, in: 1st Conference on Research Data Infrastructure (CoRDI)  Connecting Communities, Y. SureVetter, C. Goble, eds., 1 of Proceedings of the Conference on Research Data Infrastructure, TIB Open Publishing, Hannover, 2023, pp. 69/169/4, DOI 10.52825/cordi.v1i.397 .
Abstract
MaRDI is building a research data infrastructure for mathematics and beyond based on semantic technologies (metadata, ontologies, knowledge graphs) and data repositories. Focusing on the algorithms, models and workflows, the MaRDI infrastructure will connect with other disciplines and NFDI consortia on data processing methods, solving real world problems and support mathematicians on research datamanagement 
T. Boege, R. Fritze, Ch. Görgen, J. Hanselman, D. Iglezakis, L. Kastner, Th. Koprucki, T. Krause, Ch. Lehrenfeld, S. Polla, M. Reidelbach, Ch. Riedel, J. Saak, B. Schembera, K. Tabelow, M. Weber, Researchdata management planning in the German mathematical community, 130 of EMS Magazine, European Mathematical Society, 2023, pp. 4047, DOI 10.4171/MAG/152 .

F. Galarce Marín, K. Tabelow, J. Polzehl, Ch. Panagiotis, V. Vavourakis, I. Sack, A. Caiazzo, Assimilation of magnetic resonance elastography displacement data in brain tissues, in: 7th International Conference on Computational & Mathematical Biomedical Engineering (CMBE22), 27th  29th June, 2022, Milan, Italy, P. Nithiarasu, C. Vergara, eds., 2, CMBE, Cardiff, UK, 2022, pp. 648651.

TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2019, J. Piprek, K. Hinze, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 1314, DOI 10.1109/NUSOD.2019.8807025 .

TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Towards modelbased geometry reconstruction of quantum dots from TEM, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 115116.

TH. Koprucki, M. Kohlhaase, D. Müller, K. Tabelow, Mathematical models as research data in numerical simulation of optoelectronic devices, in: Numerical Simulation of Optoelectronic Devices (NUSOD), 2017, pp. 225 226, DOI 10.1109/NUSOD.2017.8010073 .
Abstract
Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machineactionable as well as humanunderstandable representation of the mathematical knowledge they contain and the domainspecific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the stationary onedimensional driftdiffusion equations (van Roosbroeck system). 
M. Kohlhase, Th. Koprucki, D. Müller, K. Tabelow, Mathematical models as research data via flexiformal theory graphs, in: Intelligent Computer Mathematics: 10th International Conference, CICM 2017, Edinburgh, UK, July 1721, 2017, Proceedings, H. Geuvers, M. England, O. Hasan, F. Rabe , O. Teschke, eds., 10383 of Lecture Notes in Artificial Intelligence and Lecture Notes in Computer Science, Springer International Publishing AG, Cham, 2017, pp. 224238, DOI 10.1007/9783319620756_16 .
Abstract
Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines. It is common to categorize the involved numerical data and to some extent the corresponding scientific software as research data. But both have their origin in mathematical models, therefore any holistic approach to research data in MMS should cover all three aspects: data, software, and models. While the problems of classifying, archiving and making accessible are largely solved for data and first frameworks and systems are emerging for software, the question of how to deal with mathematical models is completely open. In this paper we propose a solution  to cover all aspects of mathematical models: the underlying mathematical knowledge, the equations, boundary conditions, numeric approximations, and documents in a flexiformal framework, which has enough structure to support the various uses of models in scientific and technology workflows. Concretely we propose to use the OMDoc/MMT framework to formalize mathematical models and show the adequacy of this approach by modeling a simple, but nontrivial model: van Roosbroeck's driftdiffusion model for onedimensional devices. This formalization  and future extensions  allows us to support the modeler by e.g. flexibly composing models, visualizing Model Pathway Diagrams, and annotating model equations in documents as induced from the formalized documents by flattening. This directly solves some of the problems in treating MMS as "research data” and opens the way towards more MKM services for models. 
TH. Koprucki, K. Tabelow, Mathematical models: A research data category?, in: Mathematical Software  ICMS 2016: 5th International Conference, Berlin, Germany, July 1114, 2016, Proceedings, G.M. Greuel, Th. Koch, P. Paule, A. Sommese, eds., Lecture Notes in Computer Science, Springer International Publishing AG Switzerland, Cham, 2016, pp. 423428.
Abstract
Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines and application areas. It is common to categorize the involved numerical data and to some extend the corresponding scientific software as research data. Both have their origin in mathematical models. In this contribution we propose a holistic approach to research data in MMS by including the mathematical models and discuss the initial requirements for a conceptual data model for this field. 
K. Tabelow, J. Polzehl, SHOWCASE 21  Towards invivo histology, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 378379.

H. Lamecker, H.Ch. Hege, K. Tabelow, J. Polzehl, F2  Image processing, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 359376.

K. Tabelow, Viele Tests  viele Fehler, in: Besser als Mathe  Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen, K. Biermann, M. Grötschel, B. LutzWestphal, eds., Reihe: Populär, Vieweg+Teubner, Wiesbaden, 2010, pp. 117120.
Preprints, Reports, Technical Reports

G. Dong, M. Flaschel, M. Hintermüller, K. Papafitsoros, C. Sirotenko, K. Tabelow, Datadriven methods for quantitative imaging, Preprint no. 3105, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3105 .
Abstract, PDF (7590 kByte)
In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as quantitative Magnetic Resonance Imaging (qMRI), where quantitative maps of biophysical parameters can characterize the imaged tissue and thus lead to more accurate diagnoses. Such quantitative values can also be useful in subsequent, automatized classification tasks in order to discriminate normal from abnormal tissue, for instance. The accurate reconstruction of these quantitative maps is typically achieved by solving two coupled inverse problems which involve a (forward) measurement operator, typically illposed, and a physical process that links the wanted quantitative parameters to the reconstructed qualitative image, given some underlying measurement data. In this review, by considering qMRI as a prototypical application, we provide a mathematicallyoriented overview on how datadriven approaches can be employed in these inverse problems eventually improving the reconstruction of the associated quantitative maps. 
A. Neumann, N. Peitek, A. Brechmann, K. Tabelow, Th. Dickhaus, Utilizing anatomical information for signal detection in functional magnetic resonance imaging, Preprint no. 2806, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2806 .
Abstract, PDF (2995 kByte)
We are considering the statistical analysis of functional magnetic resonance imaging (fMRI) data. As demonstrated in previous work, grouping voxels into regions (of interest) and carrying out a multiple test for signal detection on the basis of these regions typically leads to a higher sensitivity when compared with voxelwise multiple testing approaches. In the case of a multisubject study, we propose to define the regions for each subject separately based on their individual brain anatomy, represented, e.g., by socalled Aparc labels. The aggregation of the subjectspecific evidence for the presence of signals in the different regions is then performed by means of a combination function for pvalues. We apply the proposed methodology to real fMRI data and demonstrate that our approach can perform comparably to a twostage approach for which two independent experiments are needed, one for defining the regions and one for actual signal detection. 
S. Mohammadi, Ch. D'alonzo, L. Ruthotto, J. Polzehl, I. Ellerbrock, M.F. Callaghan, N. Weiskopf, K. Tabelow, Simultaneous adaptive smoothing of relaxometry and quantitative magnetization transfer mapping, Preprint no. 2432, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2432 .
Abstract, PDF (3888 kByte)
Attempts for invivo histology require a high spatial resolution that comes with the price of a decreased signaltonoise ratio. We present a novel iterative and multiscale smoothing method for quantitative Magnetic Resonance Imaging (MRI) data that yield proton density, apparent transverse and longitudinal relaxation, and magnetization transfer maps. The method is based on the propagationseparation approach. The adaptivity of the procedure avoids the inherent bias from blurring subtle features in the calculated maps that is common for nonadaptive smoothing approaches. The characteristics of the methods were evaluated on a highresolution data set (500 μ isotropic) from a single subject and quantified on data from a multisubject study. The results show that the adaptive method is able to increase the signaltonoise ratio in the calculated quantitative maps while largely avoiding the bias that is otherwise introduced by spatially blurring values across tissue borders. As a consequence, it preserves the intensity contrast between white and gray matter and the thin cortical ribbon. 
V. Avanesov, J. Polzehl, K. Tabelow, Consistency results and confidence intervals for adaptive l1penalized estimators of the highdimensional sparse precision matrix, Preprint no. 2229, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2229 .
Abstract, PDF (522 kByte)
In this paper we consider the adaptive l1penalized estimators for the precision matrix in a finitesample setting. We show consistency results and construct confidence intervals for the elements of the true precision matrix. Additionally, we analyze the bias of these confidence intervals. We apply the estimator to the estimation of functional connectivity networks in functional Magnetic Resonance data and elaborate the theoretical results in extensive simulation experiments. 
D. Hoffmann, K. Tabelow, Structural adaptive smoothing for singlesubject analysis in SPM: The aws4SPMtoolbox, Technical Report no. 11, WIAS, Berlin, 2008, DOI 10.20347/WIAS.TECHREPORT.11 .
Abstract
There exists a variety of software tools for analyzing functional Magnetic Resonance Imaging data. A very popular one is the freely available SPM package by the Functional Imaging Laboratory at the Wellcome Department of Imaging Neuroscience. In order to enhance the signaltonoise ratio it provides the possibility to smooth the data in a preprocessing step by a Gaussian filter. However, this comes at the cost of reducing the effective resolution. In a series of recent papers it has been shown, that using a structural adaptive smoothing algorithm based on the PropagationSeparation method allows for enhanced signal detection while preserving the shape and spatial extent of the activation areas. Here, we describe our implementation of this algorithm as a toolbox for SPM.
Talks, Poster

C. Cárcamo Sanchez, F. Galarce Marín, A. Caiazzo, I. Sack, K. Tabelow, Quantitative tissue pressure imaging via PDEinformed assimilation of MRdata, MATH+ Day, HumboldtUniversität zu Berlin, October 20, 2023.

K. Tabelow, MaRDI: Building research data infrastructures for mathematics and the mathematical science, 1st Conference on Research Data Infrastructure (CoRDI), September 12  14, 2023, Karlsruhe Institute of Technology (KIT), September 12, 2023.

K. Tabelow, Mathematical research data management in interdisciplinary research, Workshop on Biophysicsbased Modeling and Data Assimilation in Medical Imaging (Hybrid Event), WIAS Berlin, August 31, 2023.

TH. Koprucki, K. Tabelow, HackMD (online talk), ECoffeeLecture (Online Event), WIAS Berlin, March 25, 2022.

K. Tabelow, Neural MRI, Tandem tutorial ``Mathematics of Imaging' ', Berlin Mathematics Research Center MATH+, February 18, 2022.

A. Caiazzo, F. Galarce Marín, J. Polzehl, I. Sack, K. Tabelow, Physics based assimilation of displacements data from magnetic resonance elastography, Kickoff Workshop of the MATH+ Thematic Einstein Semester on Mathematics of Imaging in RealWorld Challenges (Hybrid Event), Berlin, October 6  8, 2021.

K. Tabelow, MaRDI  The mathematical research data Initiative within the NFDI (online talk), SFB 1294 Colloquium (Online Event), Universität Potsdam, Institut für Mathematik, April 16, 2021.

TH. Koprucki, K. Tabelow, T. Streckenbach, T. Niermann, A. Maltsi, Modelbased geometry reconstruction of TEM images, MATH+ Day 2020 (Online Event), Berlin, November 6, 2020.

K. Tabelow, MaRDI: Mathematical research data initiative, Leibniz NFDIKonferenz (Online Event), August 19, 2020.

A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Modelbased geometry reconstruction of quantum dots from TEM, Microscopy Conference 2019, Poster session IM 4, Berlin, September 1  5, 2019.

A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Modelbased geometry reconstruction of quantum dots from TEM, BMS Summer School 2019: Mathematics of Deep Learning, Berlin, August 19  30, 2019.

J. Polzehl, K. Tabelow, Analyzing neuroimaging experiments within R, 2019 OHBM Annual Meeting, Organization for Human Brain Mapping, Rome, Italy, June 9  13, 2019.

K. Tabelow, Adaptive smoothing data from multiparameter mapping, 7th NordicBaltic Biometric Conference, June 3  5, 2019, Vilnius University, Faculty of Medicine, Lithuania, June 5, 2019.

K. Tabelow, Modelbased imaging for quantitative MRI, KoMSO ChallengeWorkshop Mathematical Modeling of Biomedical Problems, December 12  13, 2019, FriedrichAlexanderUniversität ErlangenNürnberg, December 12, 2019.

K. Tabelow, Quantitative MRI for invivo histology, Neuroimmunological Colloquium, CharitéUniversitätsmedizin Berlin, November 11, 2019.

K. Tabelow, Quantitative MRI for invivo histology, Doktorandenseminar, Berlin School of Mind and Brain, April 1, 2019.

K. Tabelow, Speaker of Neuroimaging Workshop, Workshop in Advanced Statistics: Good Scientific Practice for Neuroscientists, February 13  14, 2019, University of Zurich, Center for Reproducible Science, Switzerland.

K. Tabelow, Version control using git / Dynamic documents in R, Leibniz MMS Summer School 2019, October 28  November 1, 2019, Mathematisches Forschungsinstitut Oberwolfach.

A. Maltsi, Th. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Computing TEM images of semiconductor nanostructures, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8  10, 2018.

K. Tabelow, Structural adaptation for noise reduction in magnetic resonance imaging, SIAM Conference on Imaging Science, Minisymposium MS5 ``Learning and Adaptive Approaches in Image Processing'', June 5  8, 2018, Bologna, Italy, June 5, 2018.

K. Tabelow, Ch. D'alonzo, L. Ruthotto, M.F. Callaghan, N. Weiskopf, J. Polzehl, S. Mohammadi, Removing the estimation bias due to the noise floor in multiparameter maps, The International Society for Magnetic Resonance in Medicine (ISMRM) 25th Annual Meeting & Exhibition, Honolulu, USA, April 22  27, 2017.

K. Tabelow, Ch. D'alonzo, J. Polzehl, Toward invivo histology of the brain, 2nd Leibniz MMs Days 2017, Technische Informationsbibliothek, Hannover, February 22  24, 2017.

K. Tabelow, Adaptive smoothing of multiparameter maps, Berlin Symposium 2017: Modern Statistical Methods From Data to Knowledge, December 14  15, 2017, organized by Indiana Laboratory of Biostatistical Analysis of Large Data with Structure (ILBALDS), Berlin, December 14, 2017.

K. Tabelow, High resolution MRI by variance and bias reduction, Channel Network Conference 2017 of the International Biometric Society (IBS), April 24  26, 2017, Hasselt University, Diepenbeek, Belgium, April 25, 2017.

K. Tabelow, MRI data models at low SNR, 2nd Leibniz MMs Days2017, February 22  24, 2017, Leibniz Informationszentrum Technik und Naturwissenschaften Technische Informationsbibliothek, Hannover, February 24, 2017, DOI 10.5446/21910 .

K. Tabelow, To smooth or not to smooth in fMRI, Cognitive Neuroscience Seminar, Universitätsklinikum HamburgEppendorf, Institut für Computational Neuroscience, April 4, 2017.

K. Tabelow, V. Avanesov, M. Deliano, R. König, A. Brechmann, J. Polzehl, Assessing dynamics in learning experiments, Challenges in Computational Neuroscience: Transition Workshop, Research Triangle Park, North Carolina, USA, May 4  6, 2016.

K. Tabelow, Ch. D'alonzo, J. Polzehl, M.F. Callaghan, L. Ruthotto, N. Weiskopf, S. Mohammadi, How to achieve very high resolution quantitative MRI at 3T?, 22th Annual Meeting of the Organization of Human Brain Mapping (OHBM 2016), Geneva, Switzerland, June 26  30, 2016.

K. Tabelow, Adaptive smoothing in quantitative imaging, Invivo histology/VBQ meeting, Max Planck Institute for Human Cognitinve and Brain Sciences, Leipzig, April 13, 2016.

K. Tabelow, Denoising brain images: A clinical need and a mathematical idea, LeibnizKolleg for Young Researchers: Challenges and Chances of Interdisciplinary Research, November 9  11, 2016, LeibnizGemeinschaft, Berlin, November 9, 2016.

K. Tabelow, Functional magnetic resonance imaging: Processing large dataset, AG DANK Autumn Meeting 2016, November 18  19, 2016, Gesellschaft für Klassifikation, Arbeitsgruppe ``Datenanalyse und Numerische Klassifikation'', WIAS Berlin, November 18, 2016.

K. Tabelow, Mathematical models: A research data category?, The 5th International Congress on Mathematical Software, July 11  14, 2016, KonradZuseZentrum für Informationstechnik Berlin (ZIB), July 13, 2016.

J. Krämer, M. Deppe, K. Göbel, K. Tabelow, H. Wiendl, S. Meuth, Recovery of thalamic microstructural damage after Shiga toxin 2associated hemolyticuremic syndrome, 21th Annual Meeting of the Organization for Human Brain Mapping, Honolulu, USA, June 14  18, 2015.

H.U. Voss, J. Dyke, D. Ballon, N. Schiff, K. Tabelow, Magnetic resonance advection imaging (MRAI) depicts vascular anatomy, 21th Annual Meeting of the Organization for Human Brain Mapping, Honolulu, USA, June 14  18, 2015.

J. Polzehl, K. Tabelow, H.U. Voss, Towards higher spatial resolution in DTI using smoothing, 21th Annual Meeting of the Organization for Human Brain Mapping, Honolulu, USA, June 14  18, 2015.

J. Polzehl, K. Tabelow, Bias in low SNR diffusion MRI experiments: Problems and solution, 21th Annual Meeting of the Organization for Human Brain Mapping, Honolulu, USA, June 14  18, 2015.

K. Tabelow, M. Deliano, M. Jörn, R. König, A. Brechmann, J. Polzehl, Towards a population analysis of behavioral and neural state transitions during associative learning, 21th Annual Meeting of the Organization for Human Brain Mapping, Honolulu, USA, June 14  18, 2015.

K. Tabelow, To smooth or not to smooth in fMRI, Seminar ``Bildgebende Verfahren in den Neurowissenschaften: Grundlagen und aktuelle Ergebnisse'', Universitätsklinikum Jena, IDIR, Medical Physics Group, April 17, 2015.

K. Tabelow, msPOAS  An adaptive denoising procedure for dMRI data, Riemannian Geometry in Shape Analysis and Computational Anatomy, February 23  27, 2015, Universität Wien, Erwin Schrödinger International Institute for Mathematical Physics, Austria, February 25, 2015.

S. Mohammadi, L. Ruthotto, K. Tabelow, T. Feiweier, J. Polzehl, N. Weiskopf, ACID  A postprocessing toolbox for advanced diffusion MRI, 20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, June 8  12, 2014.

N. Angenstein, J. Polzehl, K. Tabelow, A. Brechmann, Categorical versus sequential processing of sound duration, 20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, June 8  12, 2014.

K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, Adaptive noise reduction in multishell dMRI data with SPM by POAS4SPM, 20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, June 8  12, 2014.

K. Tabelow, H.U. Voss, J. Polzehl, Local estimation of noise standard deviation in MRI images using propagation separation, 20th Annual Meeting of the Organization for Human Brain Mapping, Hamburg, June 8  12, 2014.

K. Tabelow, H.U. Voss, J. Polzehl, Local estimation of the noise level in MRI images using structural adaptation, 5th UltraHighfield MRI Scientific Symposium, Max Delbrück Center, Berlin, June 20, 2014.

K. Tabelow, Highresolution diffusion MRI by msPOAS, Statistical Challenges in Neuroscience, September 3  5, 2014, University of Warwick, Centre for Research in Statistical Methodology, UK, September 4, 2014.

K. Tabelow, S. Becker, S. Mohammadi, N. Weiskopf, J. Polzehl, Multishell positionorientation adaptive smoothing (msPOAS), 19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, USA, June 16  20, 2013.

K. Tabelow, H.U. Voss, J. Polzehl, Analyzing fMRI and dMRI experiments with R, 19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, USA, June 16  20, 2013.

K. Tabelow, Advanced statistical methods for noisy and highdimensional medical (and nonmedical) data, Innovation Days 2013, December 9  10, 2013, HelmholtzGemeinschaft, Geschäftsstelle Berlin, December 9, 2013.

K. Tabelow, Assessing the structure of the brain, WIASDay, WIAS Berlin, February 18, 2013.

K. Tabelow, Diffusion MRI  news on adaptive processing, PreMoLab Workshop on: Advances in predictive modeling and optimization, May 16  17, 2013, WIASBerlin, May 17, 2013.

K. Tabelow, Noise in diffusion MRI  Impact and treatment, Strukturelle MRBildgebung in der neuropsychiatrischen Forschung, September 13  14, 2013, Philipps Universität Marburg, September 13, 2013.

M. Welvaert, K. Tabelow, R. Seurinck, Y. Rosseel, Defining ROIs based on localizer studies: More specific localization using adaptive smoothing, 19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, USA, June 16  20, 2013.

S. Mohammadi, K. Tabelow, Th. Feiweier, J. Polzehl, N. Weiskopf, Highresolution diffusion kurtosis imaging (DKI) improves detection of graywhite matter boundaries, 19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, USA, June 16  20, 2013.

S. Becker, K. Tabelow, H.U. Voss, A. Anwander, R.M. Heidemann, J. Polzehl, Positionorientation adaptive smoothing (POAS) at 7T dMRI, UltraHighfield MRI Scientific Symposium, Max Delbrück Communication Center, Berlin, June 8, 2012.

K. Tabelow, Adaptive methods for noise reduction in diffusion weighted MRI  Position orientation adaptive smoothing (POAS), University College London, Wellcome Trust Centre for Neuroimaging, UK, November 1, 2012.

K. Tabelow, Functional magnetic resonance imaging: Estimation and signal detection, PreMoLab: MoscowBerlin Stochastic and Predictive Modeling, May 31  June 1, 2012, Russian Academy of Sciences, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, May 31, 2012.

K. Tabelow, Positionorientation adaptive smoothing (POAS) diffusion weighted imaging data, Workshop on Neurogeometry, November 15  17, 2012, Masaryk University, Department of Mathematics and Statistics, Brno, Czech Republic, November 16, 2012.

K. Tabelow, S. Keller , S. Mohammadi, H. Kugel, J.S. Gerdes, J. Polzehl, M. Deppe, Structural adaptive smoothing increases sensitivity of DTI to detect microstructure alterations, 17th Annual Meeting of the Organization on Human Brain Mapping (HBM 2011), Quebec City, Canada, June 26  30, 2011.

K. Tabelow, H. Voss, J. Polzehl , Package dti: A framework for HARDI modeling in R, 17th Annual Meeting of the Organization on Human Brain Mapping (HBM 2011), Quebec City, Canada, June 26  30, 2011.

K. Tabelow, H. Voss, J. Polzehl , Structural adaptive smoothing methods for fMRI and its implementation in R, 17th Annual Meeting of the Organization on Human Brain Mapping (HBM 2011), Quebec City, Canada, June 26  30, 2011.

K. Tabelow, B. Whitcher, J. Polzehl, Performing tasks in medical imaging with R, 17th Annual Meeting of the Organization on Human Brain Mapping (HBM 2011), Quebec City, Canada, June 26  30, 2011.

K. Tabelow, Diffusion weighted imaging (DTI and beyond) using dti, The R User Conference 2011, August 15  18, 2011, University of Warwick, Department of Statistics, Coventry, UK, August 15, 2011.

K. Tabelow, Functional MRI using fmri, The R User Conference 2011, August 15  18, 2011, University of Warwick, Department of Statistics, Coventry, UK, August 15, 2011.

K. Tabelow, Modeling the orientation distribution function by mixtures of angular central Gaussian distributions, Cornell University, New York, Weill Medical College, USA, June 23, 2011.

K. Tabelow, Statistical parametric maps for functional MRI experiments in R: The package fmri, The R User Conference 2011, August 15  18, 2011, University of Warwick, Department of Statistics, Coventry, UK, August 18, 2011.

K. Tabelow, Structural adaptive smoothing fMRI and DTI data, SFB Research Center ``Mathematical Optimization and Applications in Biomedical Sciences'', KarlFranzensUniversität Graz, Institut für Mathematik und Wissenschaftliches Rechnen, Austria, June 8, 2011.

K. Tabelow, Structural adaptive smoothing fMRI and DTI data, Maastricht University, Faculty of Psychology and Neuroscience, Netherlands, September 28, 2011.

K. Tabelow, J.D. Clayden, P. Lafaye DE Micheaux, J. Polzehl, V.J. Schmid, B. Whitcher, Image analysis and statistical inference in NeuroImaging with R., Human Brain Mapping 2010, Barcelona, Spain, June 6  10, 2010.

K. Tabelow, J. Polzehl, S. Mohammadi, M. Deppe, Impact of smoothing on the interpretation of FA maps, Human Brain Mapping 2010, Barcelona, Spain, June 6  10, 2010.

K. Tabelow, Structural adaptive smoothing fMRI and DTI data, Workshop on Novel Reconstruction Strategies in NMR and MRI 2010, September 9  11, 2010, GeorgAugustUniversität Göttingen, Fakultät für Mathematik und Informatik, September 11, 2010.

J. Polzehl, K. Tabelow, Image and signal processing in the biomedical sciences: Diffusionweighted imaging modeling and beyond, 1st Annual Scientific Symposium ``Ultrahigh Field Magnetic Resonance'', Max Delbrück Center, Berlin, April 16, 2010.

K. Tabelow, J. Polzehl, H.U. Voss, Structural adaptive smoothing methods for highresolution fMRI, 15th Annual Meeting of the Organization for Human Brain Mapping (HBM 2009), San Francisco, USA, June 18  22, 2009.

K. Tabelow, A3  Image and signal processing in the biomedical sciences: diffusion weighted imaging  modeling and beyond, Center Days 2009 (DFG Research Center scshape Matheon), March 30  April 1, 2009, Technische Universität Berlin, March 30, 2009.

K. Tabelow, Structural adaptive methods in fMRI and DTI, Biomedical Imaging Research Seminar Series, Weill Cornell Medical College, Department of Radiology & Citigroup Biomedical Imaging Center, New York, USA, June 25, 2009.

K. Tabelow, Structural adaptive methods in fMRI and DTI, Memorial SloanKettering Cancer Center, New York, USA, June 25, 2009.

K. Tabelow, Structural adaptive smoothing in fMRI and DTI, Workshop on Recent Developments in fMRI Analysis Methods, Bernstein Center for Computational Neuroscience Berlin, January 23, 2009.

J. Polzehl, K. Tabelow, Structural adaptive smoothing diffusion tensor imaging data: The Rpackage dti, 15th Annual Meeting of the Organization for Human Brain Mapping (HBM 2009), San Francisco, USA, June 18  22, 2009.

K. Tabelow, A3  Image and signal processing in medicine and biosciences, Center Days 2008 (DFG Research Center scshape Matheon), April 7  9, 2008, Technische Universität Berlin, April 7, 2008.

K. Tabelow, Structure adaptive smoothing medical images, 22. Treffpunkt Medizintechnik: Fortschritte in der medizinischen Bildgebung, Charité, Campus Virchow Klinikum Berlin, May 22, 2008.

K. Tabelow, Strukturadaptive Bild und Signalverarbeitung, Workshop of scshape Matheon with Siemens AG (Health Care Sector) in cooperation with Center of Knowledge Interchange (CKI) of Technische Universität (TU) Berlin and Siemens AG, TU Berlin, July 8, 2008.

K. Tabelow, J. Polzehl, H.U. Voss, Increasing SNR in high resolution fMRI by spatially adaptive smoothing, Human Brain Mapping Conference 2007, Chicago, USA, June 10  14, 2007.

K. Tabelow, J. Polzehl, H.U. Voss, Reducing the number of necessary diffusion gradients by adaptive smoothing, Human Brain Mapping Conference 2007, Chicago, USA, June 10  14, 2007.

K. Tabelow, A3: Image and signal processing in medicine and biosciences, ADay des sc Matheon, KonradZuseZentrum für Informationstechnik Berlin (ZIB), December 5, 2007.

K. Tabelow, Improving data quality in fMRI and DTI by structural adaptive smoothing, Cornell University, Weill Medical College, New York, USA, June 18, 2007.

K. Tabelow, Structural adaptive signal detection in fMRI and structure enhancement in DTI, International Workshop on Image Analysis in the Life Sciences, Theory and Applications, February 28  March 2, 2007, Johannes Kepler Universität Linz, Austria, March 2, 2007.

K. Tabelow, Structural adaptive smoothing in medical imagine, WIAS Day, WIAS Berlin, February 22, 2007.

K. Tabelow, Structural adaptive smoothing in medical imaging, Seminar ``Visualisierung und Datenanalyse'', KonradZuseZentrum für Informationstechnik Berlin (ZIB), January 30, 2007.

K. Tabelow, J. Polzehl, H.U. Voss, V. Spokoiny, Analyzing fMRI experiments with structural adaptive smoothing methods, Human Brain Mapping Conference, Florence, Italy, June 12  15, 2006.

K. Tabelow, J. Polzehl, V. Spokoiny, J.P. Dyke, L.A. Heier, H.U. Voss, Accurate localization of functional brain activity using structure adaptive smoothing, ISMRM 14th Scientific Meeting & Exhibition, Seattle, USA, May 10  14, 2006.

K. Tabelow, Analyzing fMRI experiments with structural adaptive smoothing methods, BCCN PhD Symposium 2006, June 7  8, 2006, Bernstein Center for Computational Neuroscience Berlin, Bad Liebenwalde, June 8, 2006.

K. Tabelow, Image and signal processing in medicine and biosciences, Evaluation Colloquium of the DFG Research Center sc Matheon, Berlin, January 24  25, 2006.

K. Tabelow, Structure adaptive smoothing in statistical fMRI analysis, Workshop ``Highfield MRI and MRS3T and Beyond'', PhysikalischTechnische Bundesanstalt Berlin, February 20  21, 2006.

K. Tabelow, J. Polzehl, Structure adaptive smoothing procedures in medical imaging, 19. Treffpunkt Medizintechnik ``Imaging und optische Technologien für die Medizin'', Berlin, June 1, 2005.

K. Tabelow, Adaptive weights smoothing in the analysis of fMRI data, LudwigMaximiliansUniversität München, SFB 386, December 8, 2005.

K. Tabelow, Detecting shape and borders of activation areas infMRI data, Forschungsseminar ''Mathematische Statistik'', WIAS, Berlin, November 23, 2005.

K. Tabelow, Spatially adaptive smoothing infMRI analysis, Neuroimaging Center, Cahrité, Berlin, November 10, 2005.
External Preprints

J.M. Oeschger, K. Tabelow, S. Mohammadi, Investigating apparent differences between standard DKI and axisymmetric DKI and its consequences for biophysical parameter estimates, Preprint no. bioRxiv:2023.06.21.545891, Cold Spring Harbor Laboratory, bioRxiv, , DOI 10.1101/2023.06.21.545891 .

D. Gergely, B. Fricke, J.M. Oeschger, L. Ruthotto, P. Freund, K. Tabelow, S. Mohammadi, ACID: A comprehensive toolbox for image processing and modeling of brain, spinal cord, and ex vivo diffusion MRI data, Preprint no. bioRxiv:2023.10.13.562027, Cold Spring Harbor Laboratory, 2023, DOI 10.1101/2023.10.13.562027 .

J.M. Oeschger, K. Tabelow, S. Mohammadi, Investigating apparent differences between standard DKI and axisymmetric DKI and its consequences for biophysical parameter estimates, Preprint no. bioRxiv:2023.06.21.545891, Cold Spring Harbor Laboratory, 2023, DOI 10.1101/2023.06.21.545891 .

T. Boege, R. Fritze, Ch. Görgen, J. Hanselman, D. Iglezakis, L. Kastner, Th. Koprucki, T. Krause, Ch. Lehrenfeld, S. Polla, M. Reidelbach, Ch. Riedel, J. Saak, B. Schembera, K. Tabelow, M. Weber, Researchdata management planning in the German mathematical community, Preprint no. arXiv:2211.12071, Cornell University, 2022, DOI 10.48550/arXiv.2211.12071 .
Abstract
In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of researchdata management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring researchdata management plans to mathematicians' research processes and discuss their usage all along the data life cycle. 
S. Mohammadi, T. Streubel, L. Klock, A. Lutti, K. Pine, S. Weber, L. Edwards, P. Scheibe, G. Ziegler, J. Gallinat, S. Kuhn, M. Callaghan, N. Weiskopf, K. Tabelow, Error quantification in multiparameter mapping facilitates robust estimation and enhanced group level sensitivity, Preprint no. bioRxiv: 2022.01.11.475846, Cold Spring Harbor Laboratory, 2022, DOI 10.1101/2022.01.11.475846 .
Abstract
MultiParameter Mapping (MPM) is a comprehensive quantitative neuroimaging protocol that enables estimation of four physical parameters (longitudinal and effective transverse relaxation rates R1 and R2*, proton density PD, and magnetization transfer saturation MTsat) that are sensitive to microstructural tissue properties such as iron and myelin content. Their capability to reveal microstructural brain differences, however, is tightly bound to controlling random noise and artefacts (e.g. caused by head motion) in the signal. Here, we introduced a method to estimate the local error of PD, R1, and MTsat maps that captures both noise and artefacts on a routine basis without requiring additional data. To investigate the method's sensitivity to random noise, we calculated the modelbased signaltonoise ratio (mSNR) and showed in measurements and simulations that it correlated linearly with an experimental rawimagebased SNR map. We found that the mSNR varied with MPM protocols, magnetic field strength (3T vs. 7T) and MPM parameters: it halved from PD to R1 and decreased from PD to MT_sat by a factor of 34. Exploring the artefactsensitivity of the error maps, we generated robust MPM parameters using two successive acquisitions of each contrast and the acquisitionspecific errors to downweight erroneous regions. The resulting robust MPM parameters showed reduced variability at the group level as compared to their singlerepeat or averaged counterparts. The error and mSNR maps may better inform powercalculations by accounting for local data quality variations across measurements. Code to compute the mSNR maps and robustly combined MPM maps is available in the opensource hMRI toolbox. 
J.M. Oeschger, K. Tabelow, S. Mohammadi, Axisymmetric diffusion kurtosis imaging with Rician bias correction: A simulation study, Preprint no. bioRxiv2022.03.15.484442, Cold Spring Harbor Laboratory, bioRxiv, 2022, DOI 10.1101/2022.03.15.484442 .
Articles in Refereed Journals related to high energy physics

C. BOROS,
T. MENG,
R. RITTEL,
K. TABELOW,
Y. ZHANG,
Formation of ColorSinglet GluonCluster and Inelastic Diffractive Scattering, Phys. Rev. D 61, 094010 (2000).

J. FU,
T. MENG,
R. RITTEL,
K. TABELOW,
Criticality in quark gluon systems far beyond thermal and chemical equilibrium, Phys. Rev. Lett. 86, 1961 (2001).

K. TABELOW,
Gap function in the finite BakSneppen model, Phys. Rev. E 63, 047101 (2001).
Preprints related to high energy physics
 T. MENG,
R. RITTEL,
K. TABELOW,
Y. ZHANG,
Formation of colorsinglet gluonclusters and inelastic diffractive scattering. Part II: Derivation of the $t$ and $M_x^2/s$dependence of crosssections in the SOCapproach,
hepph/9807314 (1998).
 T. MENG,
R. RITTEL,
K. TABELOW,
Gluons in small$x_B$ deepinelastic scattering,
hepph/9905538 (1999).
 T. MENG,
R. RITTEL,
K. TABELOW,
Y. ZHANG,
Inelastic diffraction and meson radii
hepph/9910331 (1999).
Talks/Proceedings related to high energy physics
 K. TABELOW, Formation of ColorSinglets GluonClusters
and Inelastic Diffractive Scattering 7th
International Workshop on Deep Inelastic Scattering and QCD,
DIS99, Zeuthen, Germany, 1923 April 1999, Nucl. Phys. B
(Proc. Suppl.) 79, 393395 (1999).
 K. TABELOW, Selforganized criticality in gluon systems
and its consequences invited talk at the XXXth International
Symposium on Multiparticle Dynamics, ISMD2000, Tihany, Hungary,
915 Oct 2000, published in Proceedings of ISMD2000 (World
Scientific), 9398 (2001).
WeierstraßInstitut für Angewandte Analysis und
Stochastik, Mohrenstraße 39, 10117 Berlin, phone: +493020372564, fax: +493020372303
last reviewed: Aug 19, 2016, Karsten Tabelow