Dr. Joerg Polzehl  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. 6581, (Chapter Published).
Articles in Refereed Journals

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 href="http://doi.org/10.1371/journal.pone.0157355" target="_blank">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, 11 (2016) pp. 14801490.
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. 
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. 
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. 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
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
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, S. Sperlich, A note on structural adaptive dimension reduction, Journal of Statistical Computation and Simulation, 79 (2009) pp. 805818.

J. Polzehl, K. Tabelow, Structural adaptive smoothing in diffusion tensor imaging: The R package dti, Journal of Statistical Software, 31 (2009) pp. 124.
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 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
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
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. 
D. Divine, J. Polzehl, F. Godtliebsen, A propagationseparation approach to estimate the autocorrelation in a timeseries, Nonlinear Processes in Geophysics, 15 (2008) pp. 591599.

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
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.

K. Tabelow, J. Polzehl, H.U. Voss, V. Spokoiny, Analyzing fMRI experiments with structural adaptive smoothing procedures, NeuroImage, 33 (2006) pp. 5562.
Abstract
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. 
B. RöhlKuhn, J. Polzehl, P. Klobes, Simultaneous confidence and prediction bands in the certification of pressurevolume curves for the pore size analysis of solids by means of mercury porosimetry, Accreditation and Quality Assurance, 11 (2006) pp. 107115.
Abstract
The pore size analysis of solids is widely applied in chemical industries, materials engineering, ceramic production, environmental engineering, catalysis, chromatography, nanotechnology, and many other fields. In spite of several new methods used for determining the pore size distribution of meso and macropores [see IUPAC Recommendations, 1994] mercury porosimetry has remained one of the most popular methods employed for the characterisation of porous materials. In this paper, a new way is described for the estimation of certified pressurevolume curves from experimental curves measured by different laboratories in connection with the certification of new reference materials for a comparatively low pressure range of mercury intrusion (< 2 MPa). Simultaneous confidence and prediction bands for the certified pressurevolume curves are constructed by bootstrapping. 
J. Polzehl, V. Spokoiny, Propagationseparation approach for local likelihood estimation, Probability Theory and Related Fields, 135 (2006) pp. 335362.
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, 335354 (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 nonasymptotic 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. Polzehl, S. Zwanzig, On a symmetrized simulation extrapolation estimator in linear errorsinvariables models, Computational Statistics & Data Analysis, 47 (2004) pp. 675688.
Abstract
Application of naive regression estimates in errorsinvariables models suffers from a severe bias. The simulation extrapolation estimator (SIMEX) was introduced by Cook and Stefanski as a correction method modeling the dependence of error variance in the regressors and bias of the regression method. Our symmetrized simulation extrapolation estimator (SYMEX), a generalization of SIMEX, allows to employ the symmetric structure of errorsinvariables models. Relations of both SIMEX and SYMEX to total least squares are investigated. 
J. Polzehl, V. Spokoiny, Image denoising: Pointwise adaptive approach, The Annals of Statistics, 31 (2003) pp. 3057.
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 greyscale 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 datadriven 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. 
M. Hristache, A. Juditsky, J. Polzehl, V. Spokoiny, Structure adaptive approach for dimension reduction, The Annals of Statistics, 29 (2001) pp. 15371566.
Abstract
We propose a new method of effective dimension reduction for a multiindex model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension $m$ of the index space does not exceed $3$, this space can be estimated with the rate $n^1/2$ under rather mild assumptions on the model. 
J. Polzehl, B. Grund, Semiparametric lackoffit tests in an additive hazard regression model, Statistics and Computing, 11 (2001) pp. 323335.
Abstract
In the semiparametric additive hazard regression model of McKeague and Sasieni (Biometrika 81: 501514), the hazard contributions of some covariates are allowed to change over time, without parametric restrictions (Aalen model), while the contributions of other covariates are assumed to be constant. In this paper, we develop tests that help to decide which of the covariate contributions indeed change over time. The remaining covariates may be modelled with constant hazard coefficients, thus reducing the number of curves that have to be estimated nonparametrically. Several bootstrap tests are proposed. The behavior of the tests is investigated in a simulation study. In a practical example, the tests consistently identify covariates with constant and with changing hazard contributions. 
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. 485501.
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. 335354.
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 datapoints. 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 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.

J. Franke, R. Dahlhaus, J. Polzehl, V. Spokoiny, G. Steidl, J. Weickert, A. Berdychevski, S. Didas, S. Halim, P. Mrázek, S.S. Rao, J. Tadjuidje, Structural adaptive smoothing procedures, in: Mathematical Methods in Time Series Analysis and Digital Image Processing, R. Dahlhaus, J. Kurths, P. Maass, J. Timmer, eds., Understanding Complex Systems, Springer, Berlin, Heidelberg, 2008, pp. 183229.

J. Polzehl, V. Spokoiny, Structural adaptive smoothing by propagationseparation methods, in: Handbook of Data Visualization, caps">Ch.h. Chen, W. Härdle, A. Unwin, eds., Springer Handbooks of Computational Statistics, Springer, Berlin, Heidelberg, 2008, pp. 471492.
Preprints, Reports, Technical Reports

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.
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.
Talks, Poster

K. Tabelow, Ch. D'alonzo, J. Polzehl, Toward invivo histology of the brain, 2nd Leibniz MMs Days2017, Hannover, February 22  24, 2017.

J. Polzehl, Assessing dynamics in learning experiments, Novel Statistical Methods in Neuroscience, June 22  24, 2016, OttovonGuerickeUniversität Magdeburg, Institut für Mathematische Stochastik, June 22, 2016.

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, February 1, 2016.

J. Polzehl, R in statistical neuroscience research, 1st Leibniz MMS Days, January 27  29, 2016, WIAS, January 27, 2016.

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.

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, Noise quantification in MR experiments, Joint Statistical Meetings 2015, August 10  13, 2015, Seattle, USA, August 12, 2015.

J. Polzehl, Statistical problems in diffusion weighted MR, University of Minnesota, BiostatisticsStatistics 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.

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.

J. Polzehl, Estimation of sparse precision matrices, MMSWorkshop ``large p small n'', WIASBerlin, 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 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, 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.

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.

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, Image processing with structural adaptive smoothing, XIV. Mathematika Tag, WIAS Berlin, February 26, 2013.

J. Polzehl, Positionorientation 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, Positionorientation adaptive smoothing  Noise reduction in dMRI, Strukturelle MRBildgebung in der Neuropsychiatrischen Forschung, September 13  14, 2013, PhilippsUniversität 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, Positionorientation adaptive smoothing (POAS) at 7T dMRI, UltraHighfield MRI Scientific Symposium, Max Delbrück Communication Center, Berlin, June 8, 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: 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.

J. Polzehl, Statistical problems in diffusion weighted MR (dMRI), 5th International Conference of the ERCIM Working Group on Computing & Statistics (ERCIM 2012), December 1  3, 2012, Universidad de Oviedo, Departamento de Estadística e Investigación Operativa y Didáctica de la Matemática, Spain, December 1, 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.

J. Polzehl, Statistical issues in modeling diffusion weighted magnetic resonance data, 3rd International Conference on Statistics and Probability 2011 (IMSChina), 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.

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.

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, FriedrichAlexanderUniversität ErlangenNürnberg, Naturwissenschaftliche Fakultät, September 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.

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.

J. Polzehl, Sequential multiscale procedures for adaptive estimation, The 1st Institute of Mathematical Statistics Asia Pacific Rim Meeting, June 28  July 1, 2009, Seoul National University, Institute of Mathematical Statistics, Korea (Republic of), July 1, 2009.

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 propagationseparation 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 propagationseparation 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.

J. Polzehl, Propagationseparation 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 methods, Gemeinsames Kolloquium des Fachbereichs Statistik und des SFB 475, Universität Dortmund, January 30, 2007.

J. Polzehl, Structural adaptive smoothing methods and related topics, Kickoff Meeting eVITA project, Tromsø, Norway, February 15, 2007.

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

J. Polzehl, Structural adaptive smoothing: Images, fMRI and DWI, Workshop on Algorithms in Complex Systems, September 24  26, 2007, EURANDOM, Eindhoven, Netherlands, September 24, 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.

J. Polzehl, Statistische Verfahren zur Bildrekonstruktion und Signalerkennung in Bildzeitreihen, Philips GmbH, Medizintechnik, Hamburg, December 15, 2006.

J. Polzehl, Statistische Verfahren, Bildrekonstruktion und Signalerkennung in Bildzeitreihen, Berlin, November 16, 2006.

J. Polzehl, Structural adaptive smoothing by propagationseparation, 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.

J. Polzehl, Adaptive smoothing by propagationseparation, 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, Propagationseparation 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 propagationseparation approach for imaging problems, Joint Statistical Meetings, August 7  11, 2005, Minneapolis, USA, August 11, 2005.

J. Polzehl, Structural adaptive smoothing by propagationseparation methods, LudwigMaximiliansUniversität München, SFB 386, December 7, 2005.

J. Polzehl, Adaptive estimation for a varying coefficient GARCH model, Karlsruher StochastikTage 2004, March 23  26, 2004, Universität Karlsruhe, March 23, 2004.

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

J. Polzehl, On a nonstationary structural adaptive approach to volatility estimation, University of Gothenburg, Centre for Finance, Sweden, May 5, 2004.

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

J. Polzehl, Spatially adaptive smoothing: A propagationseparation approach, Workshop on New Inference Concepts for Analysing Complex Data, November 14  19, 2004, Mathematisches Forschungszentrum Oberwolfach, November 15, 2004.

J. Polzehl, Structural adaptive smoothing methods, GeorgAugustUniversität Göttingen, Institut für Mathematische Stochastik, January 14, 2004.

J. Polzehl, Structural adaptive smoothing methods, TandemWorkshop on Nonlinear 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, 6th World Congress of the Bernoulli Society and the Institute of Mathematical Statistics, July 26  31, 2004, Universitat de Barcelona, Institut de Matemàtica, Spain, July 27, 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 MathematikerVereinigung (DMV), September 13  17, 2004, Heidelberg, September 14, 2004.

J. Polzehl, Structural adaptive smoothing methods for imaging problems, GermanIsraeli 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, Standards needs & VAMAS role in modeling and simulation, VAMAS Steering Committee and TWA Chairmen Meeting, May 12  14, 2003, Petten, Netherlands, May 13, 2003.

J. Polzehl, Structural adaptive smoothing methods and applications in imaging, Magnetic Resonance Seminar, PhysikalischTechnische Bundesanstalt, March 13, 2003.

J. Polzehl, Statistische Grundlagen der Zertifizierung von Kurven, Bundesanstalt für Materialforschung und prüfung, Zertifizierungskomitee der Abteilung I, Berlin, December 12, 2002.

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 II: Time series and estimation of dimension reduction spaces, University of Tromso, Department of Mathematics, Norway, April 17, 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, Structuraladaptive smoothing methods, FrenchGerman Seminar, Universität Potsdam, April 6, 2002.

J. Polzehl, Varying coefficient modeling using structural adaptation, Conference on Current Advances and Trends in Nonparametric Statistics, July 15  19, 2002, Crete, Greece, July 18, 2002.

J. Polzehl, Angewandte Statistik, Continuation Seminar for Engineers, November 12  13, 2001, Haus der Technik, Essen.

J. Polzehl, Can structural assumptions be used to improve nonparametric estimates?, University of Minnesota, School of Statistics, Minneapolis, USA, May 31, 2001.

J. Polzehl, Structural adaptation in nonparametric regression, Workshop on HighDimensional Nonlinear Statistical Modelling, September 15  19, 2001, Wulkow, September 16, 2001.

J. Polzehl, Structural adaption  A method to estimate the effective dimension reduction space, Closed Meeting of Sfb 373, May 17  19, 2001, Wulkow, May 18, 2001.

J. Polzehl, Structural adaption in nonparametric smoothing, Departamento de Estadistica y Econometria, Universidad Carlos III de Madrid, Spain, March 2, 2001.

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

J. Polzehl, Adaptive weights smoothing and applications in imaging, Hamburger StochastikTage 2000, March 21  24, 2000, Universität Hamburg, March 23, 2000.

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 LouvainlaNeuve, Institut de Statistique, Belgium, September 29, 2000.

J. Polzehl, Adaptive weights smoothing: What next?, HumboldtUniversität zu Berlin, Bereich Stochastik, December 19, 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, Räumlich adaptive Glättungsverfahren zur Signalerkennung in funktionellen und dynamischen MRI, Medica Research 2000, Berlin, May 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.

J. Polzehl, Statistical issues in functional Magnet Resonance Imaging, Seminar ParisBerlin, September 25  28, 2000, Garchy, France, September 25, 2000.
External Preprints

J. Polzehl, On a comparison of different simulation extrapolation estimators in errorsinvariables models, Preprint no. 17, Uppsala University, Department of Mathematics, 2003.
WeierstraßInstitut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, phone: +493020372481, fax: +493020372303, last reviewed: Mar 27, 2014, J. Polzehl