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2019 - 2019212020 - 20221
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Author: Polzehl, Jörg × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik ×

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Now showing 1 - 10 of 22
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    Modeling high resolution MRI: Statistical issues with low SNR
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Polzehl, Jörg; Tabelow, Karsten
    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.
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    Improving accuracy and temporal resolution of learning curve estimation for within- and across-session analysis
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Deliano, Matthias; Tabelow, Karsten; König, Reinhard; Polzehl, Jörg
    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.
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    Structural adaptive smoothing in diffusion tensor imaging : the R package dti
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Polzehl, Jörg; Tabelow, Karsten
    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
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    Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Becker, Saskia; Tabelow, Karsten; Voss, Henning U.; Anwander, Alfred; Heidemann, Robin M.; Polzehl, Jörg
    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.
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    Consistency results and confidence intervals for adaptive l1-penalized estimators of the high-dimensional sparse precision matrix
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Avanesov, Valeriy; Polzehl, Jörg; Tabelow, Karsten
    In this paper we consider the adaptive '1-penalized estimators for the precision matrix in a finite-sample 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.
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    Adaptive smoothing of digital images : the R package adimpro
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Polzehl, Jörg; Tabelow, Karsten
    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.
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    Analysing fMRI experiments with the fmri package in R. version 1.0 : a user's guide
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Polzehl, Jörg; Tabelow, Karsten
    This document describes the usage of the R package fmri to analyse functional Magnetic Resonance Imaging (fMRI) data with structure adaptive smoothing procedures (Propagation-Separation (PS) approach) as described in [7].
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    Simultaneous adaptive smoothing of relaxometry and quantitative magnetization transfer mapping
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Mohammadi, Siawoosh; DAlonzo, Chiara; Ruthotto, Lars; Polzehl, Jörg; Ellerbrock, Isabel; Callaghan, Martina F.; Weiskopf, Nikolaus; Tabelow, Karsten
    Attempts for in-vivo histology require a high spatial resolution that comes with the price of a decreased signal-to-noise ratio. We present a novel iterative and multi-scale smoothing method for quantitative Magnetic Resonance Imaging (MRI) data that yield proton density, apparent transverse and longitudinal relaxation, and magnetization transfer maps. The method is based on the propagation-separation approach. The adaptivity of the procedure avoids the inherent bias from blurring subtle features in the calculated maps that is common for non-adaptive smoothing approaches. The characteristics of the methods were evaluated on a high-resolution data set (500 mym isotropic) from a single subject and quantified on data from a multi-subject study. The results show that the adaptive method is able to increase the signal-to-noise ratio in the calculated quantitative maps while largely avoiding the bias that is otherwise introduced by spatially blurring values across tissue borders. As a consequence, it preserves the intensity contrast between white and gray matter and the thin cortical ribbon.
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    Structural adaptive dimension reduction
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Polzehl, Jörg; Sperlich, Stefan
    The paper introduces and discusses different estimation methods for multi index models where the indices are parametric and the link function is nonparametric. More specific, the here introduced methods follow the idea of Hristache et al. (2001), modify and try to improve it. Moreover, they constitute alternatives to the so called MAVE-based methods (Xia et al, 2002). We concentrate on an intuitive presentation of what each procedure is doing to the data and its implementation. All methods considered here we have made freely available in R. We conclude with a comparative simulation study based on the provided package EDR.
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    Structural adaptive segmentation for statistical parametric mapping
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Polzehl, Jörg; Voss, Henning U.; Tabelow, Karsten
    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.