Computational neuroscience and medical imaging

- Application oriented research topic of WIAS -




Images are often characterized by qualitative properties of their spatial structure, e.g. spatially extended regions of homogeneity that are separated by discontinuities. Images or image data with such a property are the target of the methods considered in this research. The methods summarized under the term structural adaptive smoothing try to employ a qualitative assumption on the spatial structure of the data. This assumption is used to simultaneously describe the structure and efficiently estimate parameters like image intensities. Structural adaptive smoothing generalizes several concepts in non-parametric regression. The methods are designed to provide intrinsic balance between variability and bias of the reconstruction results.

A first attempt to use the idea of structural adaptive smoothing for image processing was proposed in Polzehl and Spokoiny (2000) under the name adaptive weights smoothing. This was generalized and refined especially in Polzehl and Spokoiny (2006) providing a theory for the case of one-parameter exponential families. This has become known under the name propagation-separation approach. Several extentions have been made to cover locally smooth images, color images (Polzehl and Tabelow, 2007) and applications from the neurosciences like functional Magnetic Resonance Imaging (fMRI) and diffusion-weighted Magnetic Resonance Imaging (dMRI).

Poster on fMRI at HBM 2009 Poster on R at HBM 2013 Poster on msPOAS at HBM 2013 Poster on local estimation of noise level in MRI at HBM 2014
Figure 1. (Left to right) Selected posters on results for a) functional Magnetic Resonance Imaging (fMRI) and b) Activities on medical imaging and R. c) Smoothing diffusion weighted MR data in orientation spaces (msPOAS). d) Local estimation of noise level in MRI.

Applications to fMRI

In a series of publications we develop dedicated methods for noise reduction and signal inference in functional MRI based on the propagation-separation approach: In Tabelow et al. 2006 we proposed a new adaptive method for noise reduction of the statistical parametric map in a single-subject fMRI dataset. The properties of this map after smoothing allow for the application of Random Field theory for signal detection. We demonstrated that the method is able to recover the signal-to-noise loss when increasing the spatial resolution of the MRI acquisition (Tabelow et al. 2009) and its applicability for pre-surgical planning (Tabelow et al. 2008). Later, we were able to include the signal detection into a coherent statistical framework for adaptive fMRI analysis in a structural adaptive segmentation method (Polzehl et al. 2010), see Figure 2.

Signal detection with Gaussian filter Signal detection with structural adaptive smoothing and RFT Signal detection with structural adaptive segmentation
Figure 2. Signal detection in a single-subject finger-tapping experiment using (Left to right) a) Gaussian filter b) structural adaptive smoothing and Random field theory (RFT) (Tabelow et al. 2006), c) structural adaptive segmentation (Polzehl et al. 2010).

All adaptive methods for fMRI are implemented in the R software environment for statistical computing and graphics as a free contributed package fmri. It can be downloaded from the CRAN server. It is also listed at NITRC and part of the WIAS R packages for neuroimaging. The structural adaptive segmentation algorithm is available as Adaptive Smoothing Plugin for the neuroimaging software BrainVoyager QX.

Applications to dMRI

The signal attenuation by the diffusion weighting in dMRI makes this imaging modality vulnerable to noise. We developed a structural adaptive smoothing method for Diffusion Tensor Imaging data (Tabelow et al. 2008; Polzehl and Tabelow 2009). The method uses local comparisons of the estimated diffusion tensor to define the local homogeneity regions for the propagation-separation approach. We developed a position-orientation adaptive smoothing algorithm for denoising of diffusion-weigthed MR data (POAS). This algorithm works in the orientation space of the measurement and does not refer to a model for the spherical distribution of the data like the diffusion tensor (Becker et. al 2012). Recently, the method could be extended for multi-shell dMRI data as multi-shell POAS (msPOAS) (Becker et al. 2014), see Figure 3.

All adaptive methods for dMRI are implemented in the R software environment for statistical computing and graphics as a free contributed package dti. It can be downloaded from the CRAN server. It is also listed at NITRC and part of the WIAS R packages for neuroimaging. The msPOAS method is also implemented in Matlab as part on the ACID-Toolbox for SPM (Tabelow et al. 2015). The method has shown to be an essential part of an improved processing pipeline for Diffusion Kurtosis Imaging (DKI) in Mohammadi et al. 2015.

The application of many processing methods to neuroimaging data, like the denoising method msPOAS, requires knowledge on the (local) noise level in the data. In Tabelow et al. 2015 we provide a new method LANE for the corresponding estimation problem.


Figure 3. Color-coded fractional anisotropy (FA) from dMRI data at 7T. (Left to right) a) Original data b) reconstruction after applying POAS (Becker et. al 2012) to the data which achieve almost the quality of c) reconstruction using four repeated measurements from the same session.

The R package dti is capable of performing a full analysis of dMRI data and implements a large number of diffusion models for the data, e.g. the DTI model, the diffusion kurtosis model (DKI), and the orientation distribution function. We proposed a computationally feasible and interpretable tensor mixture model for the modelling of dMRI data (Tabelow et al. 2012), see Figure 4.


Figure 4. Crossing fibres detected by the mixed tensor model proposed in Tabelow et al. (2012). Left we show the color coded FA, the partial volume corrected FA and the estimated efficient order of the model.

Clinical applications

The importance of adequate processing of neuroimaging data for diagnostic sensitivity became obvious in two publications together with colleagues from Universitätsklinikum Münster concerning multiple sclerosis (Deppe et al. 2015 [epub ahead]) and EHEC (Krämer et al. 2015).

Applications to learning research

In collaboration with the Leibniz Institut for Neurobiology we aim at the identification and description of neuronal changes in learning experiments. First results have been published at HBM 2014 and 2015.


Highlights

Many of the image processing tools especially in the context of neuroimaging are developed in the MATHEON project F10 "Image and signal processing in the biomedical sciences".

Methods developed in this project have been successfully applied in several high-ranked papers, e.g.:

  • Functional MRI of the zebra finch brain during song stimulation suggests a lateralized response topography (Voss et al., PNAS, 2007)
  • Dissociations between behavioral and fMRI-based evaluations of cognitive function after brain injury (Bardin et al., Brain, 2011)

The research activity of many international groups with respect to R and Medical Imaging has been recently summarized in a Special Volume of the Journal of Statistical Software "Magnetic Resonance Imaging in R" vol. 44 (2011) edited by K. Tabelow and B. Whitcher, see also Tabelow et al. 2011.

Software has been developed within the framework of the R Environment for Statistical Computing:

  • adimpro - Adaptive Smoothing of Digital Images
  • dti - DTI/DWI Analysis
  • fmri - Analysis of fMRI Experiments

Further software packages and plugins are

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Contributing Groups of WIAS

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Mathematical Context

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Related main application areas

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Contact

Dr. Polzehl, Jörg

Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstrasse 39
10117 Berlin
 
tel: +49 30 20372-481
fax: +49 30 20372-303
e-mail: Joerg.Polzehl@wias-berlin.de

Dr. Tabelow, Karsten

Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstrasse 39
10117 Berlin
 
tel: +49 30 20372-564
fax: +49 30 20372-303
e-mail: Karsten.Tabelow@wias-berlin.de

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Publications

  Monographs

  • 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. 65--81, (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

  • 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, non-lesional cerebellar damage in patients with multiple sclerosis: DTI measures correlate with disability, atrophy, and disease duration, Multiple Sclerosis Journal, 22 (2016) pp. 73--84.

  • 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.

  • K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, POAS4SPM --- A toolbox for SPM to denoise diffusion MRI data, Neuroinformatics, 13 (2015) pp. 19--29.
    Abstract

    We present an implementation of a recently developed noise reduction algorithm for dMRI data, called multi-shell 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 non-adaptive smoothing. We give examples for the usage of the toolbox and explain the determination of experiment-dependent 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. 76--86.
    Abstract

    We present a method for local estimation of the signal-dependent noise level in magnetic resonance images. The procedure uses a multi-scale approach to adaptively infer on local neighborhoods with similar data distribution. It exploits a maximum-likelihood estimator for the local noise level. The validity of the method was evaluated on repeated diffusion data of a phantom and simulated data using T1-data corrupted with artificial noise. Simulation results are compared with a recently proposed estimate. The method was applied to a high-resolution 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 2-associated hemolytic-uremic syndrome, Journal of the Neurological Sciences, 356 (2015) pp. 175--183.

  • G.N. Milstein, J.G.M. Schoenmakers, Uniform approximation of the Cox--Ingersoll--Ross process, Advances in Applied Probability. Sheffield Univ. (GB). Dept. of Probability and Statistics. Applied Probability Trust, Sheffield., 47 (2015) pp. 1132--1156.
    Abstract

    The Doss-Sussmann (DS) approach is used for simulating the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows for expressing trajectories of the CIR process by solutions of some ordinary differential equation (ODE) that depend on realizations of the Wiener process involved. Via simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving an ODE, we approximately construct the trajectories of the CIR process. From a conceptual point of view the proposed method may be considered as an exact simulation approach.

  • S. Mohammadi, K. Tabelow, L. Ruthotto, Th. Feiweier, J. Polzehl, N. Weiskopf, High-resolution diffusion kurtosis imaging at 3T enabled by advanced post-processing, Frontiers in Neuroscience, 8 (2015) pp. 427/1--427/14.

  • S. Becker, K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS, NeuroImage, 95 (2014) pp. 90--105.
    Abstract

    In this article we present a noise reduction method (msPOAS) for multi-shell diffusion-weighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. 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 position-orientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted 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. 435--445.
    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 non-adaptive 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, Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS), Medical Image Analysis, 16 (2012) pp. 1142--1155.
    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 three-dimensional Euclidean motion SE(3). Subsequently, pairwise comparisons of the values of the diffusion weighted signal are used for adaptation. The position-orientation adaptive smoothing preserves the edges of the observed fine and anisotropic structures. The POAS-algorithm 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. 200--211.
    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. 1686--1693.
    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 contrast-enhanced 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. 1--21.
    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 publication-ready 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 fMRI-based evaluations of cognitive function after brain injury, Brain, 134 (2011) pp. 769--782.
    Abstract

    Functional neuroimaging methods hold promise for the identification of cognitive function and communication capacity in some severely brain-injured patients who may not retain sufficient motor function to demonstrate their abilities. We studied seven severely brain-injured 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) blood-oxygen-level-dependent responses without exception, the brain-injured subjects showed a wide variation in the correlation of blood-oxygen-level-dependent responses and overt behavioural responses. Specifically, the brain-injured subjects dissociated bedside and functional magnetic resonance imaging-based command following and communication capabilities. These observations reveal significant challenges in developing validated functional magnetic resonance imaging-based methods for clinical use and raise interesting questions about underlying brain function assayed using these methods in brain-injured subjects.

  • J. Polzehl, K. Tabelow, Beyond the Gaussian model in diffussion-weighted imaging: The package dti, Journal of Statistical Software, 44 (2011) pp. 1--26.
    Abstract

    Diffusion weighted imaging is a magnetic resonance based method to investigate tissue micro-structure 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.

  • E. Diederichs, A. Juditsky, V. Spokoiny, Ch. Schütte, Sparse non-Gaussian component analysis, Institute of Electrical and Electronics Engineers. Transactions on Information Theory, 56 (2010) pp. 3033--3047.

  • J. Polzehl, H.U. Voss, K. Tabelow, Structural adaptive segmentation for statistical parametric mapping, NeuroImage, 52 (2010) pp. 515--523.
    Abstract

    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 signal-to-noise 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, High-resolution fMRI: Overcoming the signal-to-noise problem, Journal of Neuroscience Methods, 178 (2009) pp. 357--365.
    Abstract

    Increasing the spatial resolution in functional Magnetic Resonance Imaging (fMRI) inherently lowers the signal-to-noise ratio (SNR). In order to still detect functionally significant activations in high-resolution images, spatial smoothing of the data is required. However, conventional non-adaptive 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 high-resolution fMRI experiments regardless of the lower SNR. The procedure is evaluated on human visual and sensory-motor mapping experiments. In these applications, the higher resolution could be fully utilized and high-resolution 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. 1--24.
    Abstract

    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 Propagation-Separation 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. 531--537.
    Abstract

    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 Propagation-Separation 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. 1763--1773.
    Abstract

    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 Propagation-Separation 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.

  • D. Divine, J. Polzehl, F. Godtliebsen, A propagation-separation approach to estimate the autocorrelation in a time-series, Nonlinear Processes in Geophysics, 15 (2008) pp. 591--599.

  • V. Katkovnik, V. Spokoiny, Spatially adaptive estimation via fitted local likelihood techniques, IEEE Transactions on Signal Processing, 56 (2008) pp. 873--886.
    Abstract

    This paper offers a new technique for spatially adaptive estimation. The local likelihood is exploited for nonparametric modelling of observations and estimated signals. The approach is based on the assumption of a local homogeneity of the signal: for every point there exists a neighborhood in which the signal can be well approximated by a constant. The fitted local likelihood statistics is used for selection of an adaptive size of this neighborhood. The algorithm is developed for quite a general class of observations subject to the exponential distribution. The estimated signal can be uni- and multivariable. We demonstrate a good performance of the new algorithm for Poissonian image denoising and compare of the new method versus the intersection of confidence interval (ICI) technique that also exploits a selection of an adaptive neighborhood for estimation.

  • O. Minet, H. Gajewski, J.A. Griepentrog, J. Beuthan, The analysis of laser light scattering during rheumatoid arthritis by image segmentation, Laser Physics Letters, 4 (2007) pp. 604--610.

  • H.U. Voss, K. Tabelow, J. Polzehl, O. Tchernichovski, K. Maul, D. Salgado-Commissariat, 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. 10667--10672.
    Abstract

    Electrophysiological and activity-dependent 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 level-dependent 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 left-right 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. 1--17.
    Abstract

    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 non-adaptive 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 Propagation-Separation 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. 13--17.

  • K. Tabelow, J. Polzehl, H.U. Voss, V. Spokoiny, Analyzing fMRI experiments with structural adaptive smoothing procedures, NeuroImage, 33 (2006) pp. 55--62.
    Abstract

    Data from functional magnetic resonance imaging (fMRI) consists of time series of brain images which are characterized by a low signal-to-noise 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 propagation-separation 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 non-adaptive smoothing are illustrated by artificial examples and an analysis of experimental data.

  • G. Blanchard, M. Kawanabe, M. Sugiyama, V. Spokoiny, K.-R. Müller, In search of non-Gaussian components of a high-dimensional distribution, Journal of Machine Learning Research (JMLR). MIT Press, Cambridge, MA. English, English abstracts., 7 (2006) pp. 247--282.
    Abstract

    Finding non-Gaussian components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new em linear method to identify the ``non-Gaussian subspace'' within a very general semi-parametric framework. Our proposed method, called NGCA (Non-Gaussian Component Analysis), is essentially based on the fact that we can construct a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector which belongs to the low dimensional non-Gaussian target subspace up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family. Numerical examples demonstrate the usefulness of our method.

  • H. Gajewski, J.A. Griepentrog, A descent method for the free energy of multicomponent systems, Discrete and Continuous Dynamical Systems, 15 (2006) pp. 505--528.

  • A. Goldenshluger, V. Spokoiny, Recovering convex edges of image from noisy tomographic data, Institute of Electrical and Electronics Engineers. Transactions on Information Theory, 52 (2006) pp. 1322--1334.

  • J. Polzehl, V. Spokoiny, Propagation-separation approach for local likelihood estimation, Probability Theory and Related Fields, 135 (2006) pp. 335--362.
    Abstract

    The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including, e.g., regression, density, Poisson and binary response models. The method extends the adaptive weights smoothing (AWS) procedure introduced by the authors [Adaptive weights smoothing with applications to image sequentation. J. R. Stat. Soc., Ser. B 62, 335-354 (2000)] in the context of image denoising. The main idea of the method is to describe a greatest possible local neighborhood of every design point in which the local parametric assumption is justified by the data. The method is especially powerful for model functions having large homogeneous regions and sharp discontinuities. The performance of the proposed procedure is illustrated by numerical examples for density estimation and classification. We also establish some remarkable theoretical non-asymptotic results on properties of the new algorithm. This includes the ``propagation'' property which particularly yields the root-$n$ consistency of the resulting estimate in the homogeneous case. We also state an ``oracle'' result which implies rate optimality of the estimate under usual smoothness conditions and a ``separation'' result which explains the sensitivity of the method to structural changes.

  • J. Griepentrog, On the unique solvability of a nonlocal phase separation problem for multicomponent systems, Banach Center Publications, 66 (2004) pp. 153-164.

  • A. Goldenshluger, V. Spokoiny, On the shape-from-moments problem and recovering edges from noisy Radon data, Probability Theory and Related Fields, 128 (2004) pp. 123--140.

  • J. Polzehl, V. Spokoiny, Image denoising: Pointwise adaptive approach, The Annals of Statistics, 31 (2003) pp. 30--57.
    Abstract

    A new method of pointwise adaptation has been proposed and studied in Spokoiny (1998) in context of estimation of piecewise smooth univariate functions. The present paper extends that method to estimation of bivariate grey-scale images composed of large homogeneous regions with smooth edges and observed with noise on a gridded design. The proposed estimator $, hatf(x) ,$ at a point $, x ,$ is simply the average of observations over a window $, hatU(x) ,$ selected in a data-driven way. The theoretical properties of the procedure are studied for the case of piecewise constant images. We present a nonasymptotic bound for the accuracy of estimation at a specific grid point $, x ,$ as a function of the number of pixel $n$, of the distance from the point of estimation to the closest boundary and of smoothness properties and orientation of this boundary. It is also shown that the proposed method provides a near optimal rate of estimation near edges and inside homogeneous regions. We briefly discuss algorithmic aspects and the complexity of the procedure. The numerical examples demonstrate a reasonable performance of the method and they are in agreement with the theoretical issues. An example from satellite (SAR) imaging illustrates the applicability of the method.

  • J. Polzehl, V. Spokoiny, Functional and dynamic Magnetic Resonance Imaging using vector adaptive weights smoothing, Journal of the Royal Statistical Society. Series C. Applied Statistics, 50 (2001) pp. 485--501.
    Abstract

    We consider the problem of statistical inference for functional and dynamic Magnetic Resonance Imaging (MRI). A new approach is proposed which extends the adaptive weights smoothing (AWS) procedure from Polzehl and Spokoiny (2000) originally designed for image denoising. We demonstrate how the AWS method can be applied for time series of images, which typically occur in functional and dynamic MRI. It is shown how signal detection in functional MRI and analysis of dynamic MRI can benefit from spatially adaptive smoothing. The performance of the procedure is illustrated using real and simulated data.

  • J. Polzehl, V. Spokoiny, Adaptive Weights Smoothing with applications to image restoration, Journal of the Royal Statistical Society. Series B. Statistical Methodology, 62 (2000) pp. 335--354.
    Abstract

    We propose a new method of nonparametric estimation which is based on locally constant smoothing with an adaptive choice of weights for every pair of data-points. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on some simulated univariate and bivariate examples and compare it with other nonparametric methods. Finally we discuss applications of this procedure to magnetic resonance and satellite imaging.

  Contributions to Collected Editions

  • K. Tabelow, J. Polzehl, SHOWCASE 21 -- Towards in-vivo 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. 378--379.

  • 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. 359--376.

  • K. Tabelow, Viele Tests --- viele Fehler, in: Besser als Mathe --- Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen, K. Biermann, M. Grötschel, B. Lutz-Westphal, eds., Reihe: Populär, Vieweg+Teubner, Wiesbaden, 2010, pp. 117--120.

  • H. Gajewski, J.A. Griepentrog, A. Mielke, J. Beuthan, U. Zabarylo, O. Minet, Image segmentation for the investigation of scattered-light images when laser-optically diagnosing rheumatoid arthritis, in: Mathematics -- Key Technology for the Future, W. Jäger, H.-J. Krebs, eds., Springer, Heidelberg, 2008, pp. 149--161.

  Preprints, Reports, Technical Reports

  • M. Hintermüller, C.N. Rautenberg, T. Wu, A. Langer, Optimal selection of the regularization function in a generalized total variation model. Part II: Algorithm, its analysis and numerical tests, Preprint no. 2236, WIAS, Berlin, 2016.
    Abstract, PDF (6570 kByte)

    Based on the generalized total variation model and its analysis pursued in part I (WIAS Preprint no. 2235), in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.

  • M. Hintermüller, C.N. Rautenberg, Optimal selection of the regularization function in a generalized total variation model. Part I: Modelling and theory, Preprint no. 2235, WIAS, Berlin, 2016.
    Abstract, PDF (417 kByte)

    A generalized total variation model with a spatially varying regularization weight is considered. Existence of a solution is shown, and the associated Fenchel-predual problem is derived. For automatically selecting the regularization function, a bilevel optimization framework is proposed. In this context, the lower-level problem, which is parameterized by the regularization weight, is the Fenchel predual of the generalized total variation model and the upper-level objective penalizes violations of a variance corridor. The latter object relies on a localization of the image residual as well as on lower and upper bounds inspired by the statistics of the extremes.

  • J. Polzehl, K. Tabelow, Modeling high resolution MRI: Statistical issues with low SNR, Preprint no. 2179, WIAS, Berlin, 2015.
    Abstract, PDF (2940 kByte)

    Noise is a common issue for all Magnetic Resonance Imaging (MRI) techniques and obviously leads to variability of the estimates in any model describing the data. A number of special MR sequences as well as increasing spatial resolution in MR experiments further diminish the signal-to-noise ratio (SNR). However, with low SNR the expected signal deviates from its theoretical 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 quasi-likelihood 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 that the problem is relevant even for data from the Human Connectome Project, one of the highest quality diffusion MRI data available so far.

  • M. Deliano, K. Tabelow, R. König, J. Polzehl, Improving accuracy and temporal resolution of learning curve estimation for within- and across-session analysis, Preprint no. 2170, WIAS, Berlin, 2015.
    Abstract, PDF (829 kByte)

    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 shuttle-box 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.

  • L. Lücken, O.V. Popovych, P.A. Tass, S. Yanchuk, Noise enhanced coupling between two oscillators with long-term plasticity, Preprint no. 2124, WIAS, Berlin, 2015.
    Abstract, PDF (1749 kByte)

    Spike time-dependent plasticity is a fundamental adaptation mechanism of the nervous system. It induces structural changes of synaptic connectivity by regulation of coupling strengths between individual cells depending on their spiking behavior. As a biophysical process its functioning is constantly subjected to natural fluctuations. We study theoretically the influence of noise on a microscopic level by considering only two coupled neurons. Adopting a phase description for the neurons we derive a two-dimensional system which describes the averaged dynamics of the coupling strengths. We show that a multistability of several coupling configurations is possible, where some configurations are not found in systems without noise. Intriguingly, it is possible that a strong bidirectional coupling, which is not present in the noise-free situation, can be stabilized by the noise. This means that increased noise, which is normally expected to desynchronize the neurons, can be the reason for an antagonistic response of the system, which organizes itself into a state of stronger coupling and counteracts the impact of noise. This mechanism, as well as a high potential for multistability, is also demonstrated numerically for a coupled pair of Hodgkin-Huxley neurons.

  • L. Lücken, S. Yanchuk, Detection and storage of multivariate temporal sequences by spiking pattern reverberators, Preprint no. 2122, WIAS, Berlin, 2015.
    Abstract, PDF (876 kByte)

    We consider networks of spiking coincidence detectors in continuous time. A single detector is a finite state machine that emits a pulsatile signal whenever the number incoming inputs exceeds a threshold within a time window of some tolerance width. Such finite state models are well-suited for hardware implementations of neural networks, as on integrated circuits (IC) or field programmable arrays (FPGAs) but they also reflect the natural capability of many neurons to act as coincidence detectors. We pay special attention to a recurrent coupling structure, where the delays are tuned to a specific pattern. Applying this pattern as an external input leads to a self-sustained reverberation of the encoded pattern if the tuning is chosen correctly. In terms of the coupling structure, the tolerance and the refractory time of the individual coincidence detectors, we determine conditions for the uniqueness of the sustained activity, i.e., for the funcionality of the network as an unambiguous pattern detector. We also present numerical experiments, where the functionality of the proposed pattern detector is demonstrated replacing the simplistic finite state models by more realistic Hodgkin-Huxley neurons and we consider the possibility of implementing several pattern detectors using a set of shared coincidence detectors. We propose that inhibitory connections may aid to increase the precision of the pattern discrimination.

  Talks, Poster

  • J. Polzehl, Modeling high resolution MRI: Statistical issues, Mathematical and Statistical Challenges in Neuroimaging Data Analysis, January 31 - February 5, 2016, Banff International Research Station (BIRS), Banff, Canada, Banff, Canada, February 1, 2016.

  • N. Buzun, Multiscale parametric approach for change point detection, Information Technologies and Systems 2015, September 6 - 11, 2015, Russian Academy of Sciences, Institute for Information Transmission Problems, Sochi, Russian Federation, September 9, 2015.

  • J. Krämer, M. Deppe, K. Göbel, K. Tabelow, H. Wiendl, S. Meuth, Recovery of thalamic microstructural damage after Shiga toxin 2-associated hemolytic-uremic 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, Analysing dMRI data: Consequences of low SNR, SAMSI Working group ``Structural Connectivity'', Statistical and Applied Mathematical Sciences Institute (SAMSI), Research Triangle Park, USA, December 8, 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.

  • J. Polzehl, Statistical problems in diffusion weighted MR, University of Minnesota, Biostatistics-Statistics Working Group in Imaging, Minneapolis, USA, January 30, 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 post-processing 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.

  • J. Polzehl, Estimation of sparse precision matrices, MMS-Workshop ``large p small n'', WIAS-Berlin, April 15, 2014.

  • J. Polzehl, Quantification of noise in MR experiments, Statistical Challenges in Neuroscience, September 3 - 5, 2014, University of Warwick, Centre for Research in Statistical Methodology, UK, September 4, 2014.

  • J. Polzehl, Quantification of noise in MR experiments, International Workshop ``Advances in Optimization and Statistics'', May 15 - 16, 2014, Russian Academy of Sciences, Institute of Information Transmission Problems (Kharkevich Institute), Moscow, May 16, 2014.

  • J. Polzehl, Statistical problems in diffusion weighted MR, CoSy Seminar, University of Uppsala, Department of Mathematics, Sweden, November 11, 2014.

  • K. Tabelow, S. Mohammadi, N. Weiskopf, J. Polzehl, Adaptive noise reduction in multi-shell 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 Ultra-Highfield MRI Scientific Symposium, Max Delbrück Center, Berlin, June 20, 2014.

  • K. Tabelow, High-resolution 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, Multi-shell position-orientation 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, Assessing the structure of the brain, WIAS-Day, WIAS Berlin, February 18, 2013.

  • K. Tabelow, Noise in diffusion MRI -- Impact and treatment, Strukturelle MR-Bildgebung 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, High-resolution diffusion kurtosis imaging (DKI) improves detection of gray-white matter boundaries, 19th Annual Meeting of the Organization for Human Brain Mapping, Seattle, USA, June 16 - 20, 2013.

  • J. Polzehl, Diffusion weighted magnetic resonance imaging -- Data, models and problems, Statistics Seminar, University of Minnesota, School of Statistics, USA, June 6, 2013.

  • J. Polzehl, Position-orientation adaptive smoothing (POAS) in diffusion weighted imaging, Neuroimaging Data Analysis, June 9 - 14, 2013, Statistical and Applied Mathematical Sciences Institute (SAMSI), Durham (NC), USA, June 9, 2013.

  • J. Polzehl, Position-orientation adaptive smoothing -- Noise reduction in dMRI, Strukturelle MR-Bildgebung in der Neuropsychiatrischen Forschung, September 13 - 14, 2013, Philipps-Universität Marburg, Klinik für Psychiatrie und Psychotherapie, Zentrum für Psychische Gesundheit, September 14, 2013.

  • J. Polzehl, dMRI modeling: An intermediate step to fiber tracking and connectivity, Neuroimaging Data Analysis, June 9 - 14, 2013, Statistical and Applied Mathematical Sciences Institute (SAMSI), Durham (NC), USA, June 9, 2013.

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

  • S. Becker, Diffusion weighted imaging: Modeling and analysis beyond the diffusion tensor, Methodological Workshop: Structural Brain Connectivity: Diffusion Imaging---State of the Art and Beyond, October 30 - November 2, 2012, Humboldt-Universität zu Berlin, November 2, 2012.

  • S. Becker, Image processing via orientation scores, Workshop ``Computational Inverse Problems'', October 23 - 26, 2012, Mathematisches Forschungsinstitut Oberwolfach, October 25, 2012.

  • S. Becker, Revisiting: Propagation-separation approach for local likelihood estimation, PreMoLab: Moscow-Berlin-Stochastic and Predictive Modeling, May 29 - June 1, 2012, Russian Academy of Sciences, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, May 31, 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: Moscow-Berlin 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, Position-orientation 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.

  • J. Polzehl, Adaptive methods for noise reduction in diffusion weighted MR, BRIC Seminar Series, University of North Carolina, School of Medicine, Chapel Hill, NC, USA, July 10, 2012.

  • J. Polzehl, Medical image analysis in R (tutorial), The 8th International R User Conference (Use R!2012), June 11 - 15, 2012, Vanderbilt University, Department of Biostatics, Nashville, TN, USA, June 12, 2012.

  • J. Polzehl, Modeling dMRI data: An introduction from a statistical viewpoint, Workshop on Neurogeometry, November 15 - 17, 2012, Masaryk University, Department of Mathematics and Statistics, Brno, Czech Republic, November 16, 2012.

  • J. Polzehl, Statistical issues in diffusion weighted MR (dMRI), PreMoLab: Moscow-Berlin 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, 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'', Karl-Franzens-Universität 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.

  • J. Polzehl, Statistical issues in modeling diffusion weighted magnetic resonance data, 3rd International Conference on Statistics and Probability 2011 (IMS-China), July 8 - 11, 2011, Institute of Mathematical Statistics, Xian, China, July 10, 2011.

  • J. Polzehl, Modeling the orientation distribution function by mixtures of angular central Gaussian distributions, Workshop on Statistics and Neuroimaging 2011, November 23 - 25, 2011, WIAS, November 24, 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, Georg-August-Universität Göttingen, Fakultät für Mathematik und Informatik, September 11, 2010.

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

  • J. Polzehl, Medical image analysis for structural and functional MRI, The R User Conference 2010, July 20 - 23, 2010, National Institute of Standards and Technology (NIST), Gaithersburg, USA, July 20, 2010.

  • J. Polzehl, Statistical issues in accessing brain functionality and anatomy, The R User Conference 2010, July 20 - 23, 2010, National Institute of Standards and Technology (NIST), Gaithersburg, USA, July 22, 2010.

  • J. Polzehl, Statistical problems in functional and diffusion weighted magnetic resonance, Uppsala University, Dept. of Mathematics, Graduate School in Mathematics and Computing, Sweden, May 27, 2010.

  • J. Polzehl, Structural adaptive smoothing in neuroscience applications, Statistische Woche Nürnberg 2010, September 14 - 17, 2010, Friedrich-Alexander-Universität Erlangen-Nürnberg, Naturwissenschaftliche Fakultät, September 16, 2010.

  • V. Spokoiny, Local parametric estimation, October 18 - 22, 2010, École Nationale de la Statistique et de l'Analyse de l'Information (ENSAI), Rennes, France.

  • V. Spokoiny, Semidefinite non-Gaussian component analysis, Bivariate Penalty Choice in Model Selection, Deutsches Diabetes Zentrum Düsseldorf, June 17, 2010.

  • K. Tabelow, J. Polzehl, H.U. Voss, Structural adaptive smoothing methods for high-resolution 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 Sloan-Kettering 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 R-package dti, 15th Annual Meeting of the Organization for Human Brain Mapping (HBM 2009), San Francisco, USA, June 18 - 22, 2009.

  • N. Serdyukova, Local parametric estimation under noise misspecification in regression problem, Workshop on structure adapting methods, November 6 - 8, 2009, WIAS, November 7, 2009.

  • V. Spokoiny, Adaptive local parametric estimation, Université Joseph Fourier Grenoble I, Équipe de Statistique et Modélisation Stochastique, Laboratoire Jean Kuntzmann, France, February 26, 2009.

  • V. Spokoiny, Adaptive local parametric methods in imaging, Technische Universität Kaiserslautern, Fachbereich Mathematik, January 23, 2009.

  • V. Spokoiny, Modern nonparametric statistics (block lecture), October 2 - 13, 2009, École Nationale de la Statistique et de l'Analyse de l'Information (ENSAI), Rennes, France.

  • V. Spokoiny, Modern nonparametric statistics (block lecture), October 18 - 29, 2009, Yale University, New Haven, USA.

  • V. Spokoiny, Modern nonparametric statistics (block lecture), January 13 - 16, 2009, École Nationale de la Statistique et de l'Analyse de l'Information (ENSAI), Rennes, France.

  • V. Spokoiny, Parameter tuning in statistical inverse problem, European Meeting of Statisticians (EMS2009), July 20 - 22, 2009, Université Paul Sabatier, Toulouse, France, July 21, 2009.

  • V. Spokoiny, Saddle point model selection, Université Toulouse 1 Capitole, Toulouse School of Economics, France, November 24, 2009.

  • V. Spokoiny, Saddle point model selection, Workshop on structure adapting methods, November 6 - 8, 2009, WIAS, November 7, 2009.

  • V. Spokoiny, Sparse non-Gaussian component analysis, Workshop ``Sparse Recovery Problems in High Dimensions: Statistical Inference and Learning Theory'', March 15 - 21, 2009, Mathematisches Forschungsinstitut Oberwolfach, March 16, 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.

  • J. Polzehl, New developments in structural adaptive smoothing: Images, fMRI and DWI, University of Tromsoe, Norway, May 27, 2008.

  • J. Polzehl, Smoothing fMRI and DWI data using the propagation-separation approach, University of Utah, Computing and Scientific Imaging Institute, Salt Lake City, USA, September 11, 2008.

  • J. Polzehl, Structural adaptive smoothing in diffusion tensor imaging, Workshop on ``Locally Adaptive Filters in Signal and Image Processing'', November 24 - 26, 2008, EURANDOM, Eindhoven, Netherlands, November 25, 2008.

  • J. Polzehl, Structural adaptive smoothing using the propagation-separation approach, University of Chicago, Department of Statistics, USA, September 3, 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, A-Day des sc Matheon, Konrad-Zuse-Zentrum 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 imaging, Seminar ``Visualisierung und Datenanalyse'', Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), January 30, 2007.

  • J. Polzehl, Propagation-separation procedures for image processing, 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.

  • J. Polzehl, Structural adaptive smoothing in imaging problems, Spring Seminar Series, University of Minnesota, School of Statistics, College of Liberal Arts, USA, May 24, 2007.

  • J. Polzehl, Structural adaptive smoothing procedures by propagation-separation methods, Final meeting of the DFG Priority Program 1114, November 7 - 9, 2007, Freiburg, November 7, 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.

  • J. Polzehl, Structural adaptive smoothing by propagation-separation, 69th Annual Meeting of the IMS and 5th International Symposium on Probability and its Applications, July 30 - August 4, 2006, Rio de Janeiro, Brazil, July 30, 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, Ludwig-Maximilians-Universität 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.

  • J. Polzehl, Adaptive smoothing by propagation-separation, Australian National University, Center of Mathematics and its Applications, Canberra, March 31, 2005.

  • J. Polzehl, Image reconstruction and edge enhancement by structural adaptive smoothing, 55th Session of the International Statistical Institute (ISI), April 5 - 12, 2005, Sydney, Australia, April 8, 2005.

  • J. Polzehl, Propagation-separation at work: Main ideas and applications, National University of Singapore, Department of Probability Theory and Statistics, March 24, 2005.

  • J. Polzehl, Spatially adaptive smoothing: A propagation-separation approach for imaging problems, Joint Statistical Meetings, August 7 - 11, 2005, Minneapolis, USA, August 11, 2005.

  • J. Polzehl, Structural adaptive smoothing by propagation-separation methods, Ludwig-Maximilians-Universität München, SFB 386, December 7, 2005.

  • J. Polzehl, Local likelihood modeling by structural adaptive smoothing, University of Minnesota, School of Statistics, Minneapolis, USA, September 9, 2004.

  • J. Polzehl, Smoothing by adaptive weights: An overview, Chalmers University of Technology, Department of Mathematical Statistics, Gothenburg, Sweden, May 11, 2004.

  • J. Polzehl, Structural adaptive smoothing methods, Georg-August-Universität Göttingen, Institut für Mathematische Stochastik, January 14, 2004.

  • J. Polzehl, Structural adaptive smoothing methods, Tandem-Workshop on Non-linear Optimization at the Crossover of Discrete Geometry and Numerical Analysis, July 15 - 16, 2004, Technische Universität Berlin, Institut für Mathematik, July 15, 2004.

  • J. Polzehl, Structural adaptive smoothing methods and possible applications in imaging, Charité Berlin, NeuroImaging Center, Berlin, July 1, 2004.

  • J. Polzehl, Structural adaptive smoothing methods for imaging problems, Annual Conference of Deutsche Mathematiker-Vereinigung (DMV), September 13 - 17, 2004, Heidelberg, September 14, 2004.

  • J. Polzehl, Structural adaptive smoothing methods for imaging problems, German-Israeli Binational Workshop, October 20 - 22, 2004, Ollendorff Minerva Center for Vision and Image Sciences, Technion, Haifa, Israel, October 21, 2004.

  • A. Hutt, J. Polzehl, Spatial adaptive signal detection in fMRT, Human Brain Mapping Conference, New York, USA, June 17 - 22, 2003.

  • J. Polzehl, Adaptive smoothing procedures for image processing, Workshop on Nonlinear Analysis of Multidimensional Signals, February 25 - 28, 2003, Teistungenburg, February 25, 2003.

  • J. Polzehl, Image processing using Adaptive Weights Smoothing, Uppsala University, Department of Mathematics, Sweden, May 7, 2003.

  • J. Polzehl, Local likelihood modeling by Adaptive Weights Smoothing, Joint Statistical Meetings, August 3 - 7, 2003, San Francisco, USA, August 6, 2003.

  • J. Polzehl, Local modeling by structural adaptation, The Art of Semiparametrics, October 19 - 21, 2003, Berlin, October 20, 2003.

  • J. Polzehl, Structural adaptive smoothing methods and applications in imaging, Magnetic Resonance Seminar, Physikalisch-Technische Bundesanstalt, March 13, 2003.

  • J. Polzehl, Structural adaptation I: Pointwise adaptive smoothing and imaging, University of Tromso, Department of Mathematics, Norway, April 11, 2002.

  • J. Polzehl, Structural adaptation I: Varying coefficient regression modeling by adaptive weights smoothing, Workshop on Nonparametric Smoothing in Complex Statistical Models, April 27 - May 4, 2002, Ascona, Switzerland, April 30, 2002.

  • J. Polzehl, Structural adaptation methods in imaging, Joint Statistical Meetings 2002, August 11 - 15, 2002, New York, USA, August 12, 2002.

  • J. Polzehl, Structural adaptive smoothing and its applications in imaging and time series, Uppsala University, Department of Mathematics, Sweden, May 2, 2002.

  • J. Polzehl, Structural adaptive estimation, Bayer AG, Leverkusen, November 29, 2001.

  • J. Polzehl, Adaptive weights smoothing with applications in imaging, Universität Essen, Fachbereich Mathematik, Sfb 475, November 6, 2000.

  • J. Polzehl, Adaptive weights smoothing with applications to image denoising and signal detection, Université Catholique de Louvain-la-Neuve, Institut de Statistique, Belgium, September 29, 2000.

  • J. Polzehl, Functional and dynamic Magnet Resonance Imaging using adaptive weights smoothing, Workshop "`Mathematical Methods in Brain Mapping"', Université de Montréal, Centre de Recherches Mathématiques, Canada, December 11, 2000.

  • J. Polzehl, Spatially adaptive procedures for signal detection in fMRI, Tagung "`Controlling Complexity for Strong Stochastic Dependencies"', September 10 - 16, 2000, Mathematisches Forschungsinstitut Oberwolfach, September 11, 2000.

  • J. Polzehl, Spatially adaptive smoothing techniques for signal detection in functional and dynamic Magnet Resonance Imaging, Human Brain Mapping 2000, San Antonio, Texas, USA, June 12 - 16, 2000.

  • J. Polzehl, Spatially adaptive smoothing techniques for signal detection in functional and dynamic Magnet Resonance Imaging, MEDICA 2000, Düsseldorf, November 22 - 25, 2000.

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