Filters

2011 - 201919

More filters

2019 - 2019142020 - 20225
Reset filters

Settings

Author: Tabelow, Karsten × End date: 2019 × Start date: 2011 ×

Search Results

Now showing 1 - 10 of 19
  • Thumbnail Image
    Item
    Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Becker, Saskia; Tabelow, Karsten; Mohammadi, Siawoosh; Weiskopf, Nikolaus; Polzehl, Jörg
    In this article we present a noise reduction method (msPOAS) for multi-shell diffusionweighted 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 positionorientation 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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    Adaptive smoothing as inference strategy: More specificity for unequally sized or neighboring regions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Welvaert, Marijke; Tabelow, Karsten; Seurinck, Ruth; Rosseel, Yves
    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 neu-Rosim 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.
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    More specific signal detection in functional magnetic resonance imaging by false discovery rate control for hierarchically structured systems of hypotheses
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Schildknecht, Konstantin; Tabelow, Karsten; Dickhaus, Thorsten
    Signal detection in functional magnetic resonance imaging (fMRI) inherently involves the problem of testing a large number of hypotheses. A popular strategy to address this multiplicity is the control of the false discovery rate (FDR). In this work we consider the case where prior knowledge is available to partition the set of all hypotheses into disjoint subsets or families, e. g., by a-priori knowledge on the functionality of certain regions of interest. If the proportion of true null hypotheses differs between families, this structural information can be used to increase statistical power. We propose a two-stage multiple test procedure which first excludes those families from the analysis for which there is no strong evidence for containing true alternatives. We show control of the family-wise error rate at this first stage of testing. Then, at the second stage, we proceed to test the hypotheses within each non-excluded family and obtain asymptotic control of the FDR within each family in this second stage. Our main mathematical result is that this two-stage strategy implies asymptotic control of the FDR with respect to all hypotheses. In simulations we demonstrate the increased power of this new procedure in comparison with established procedures in situations with highly unbalanced families. Finally, we apply the proposed method to simulated and to real fMRI data.
  • Thumbnail Image
    Item
    Mathematical models: A research data category?
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Koprucki, Thomas; Tabelow, Karsten
    Mathematical modeling and simulation (MMS) has now been established as an essential part of the scientific work in many disciplines and application areas. It is common to categorize the involved numerical data and to some extend the corresponding scientific software as research data. Both have their origin in mathematical models. In this contribution we propose a holistic approach to research data in MMS by including the mathematical models and discuss the initial requirements for a conceptual data model for this field.
  • Thumbnail Image
    Item
    POAS4SPM - A toolbox for SPM to denoise diffusion MRI data
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Tabelow, Karsten; Mohammadi, Siawoosh; Weiskopf, Nikolaus; Polzehl, Jörg
    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.
  • Thumbnail Image
    Item
    Model pathway diagrams for the representation of mathematical models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Koprucki, Thomas; Kohlhase, Michael; Tabelow, Karsten; Müller, Dennis; Rabe, Florian
    Mathematical models are the foundation of numerical simulation of optoelectronic devices. We present a concept for a machine-actionable as well as human-understandable representation of the mathematical knowledge they contain and the domain-specific knowledge they are based on. We propose to use theory graphs to formalize mathematical models and model pathway diagrams to visualize them. We illustrate our approach by application to the van Roosbroeck system describing the carrier transport in semiconductors by drift and diffusion. We introduce an approach for the block-based composition of models from simpler components.
  • Thumbnail Image
    Item
    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.