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Author: Becker, Saskia × Subject: Structural adaptive smoothing ×

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    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.
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    The Propagation-Separation Approach: Consequences of model misspecification
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Becker, Saskia
    The article presents new results on the Propagation-Separation Approach by Polzehl and Spokoiny [2006]. This iterative procedure provides a unified approach for nonparametric estimation, supposing a local parametric model. The adaptivity of the estimator ensures sensitivity to structural changes. Originally, an additional memory step was included into the algorithm, where most of the theoretical properties were based on. However, in practice, a simplified version of the algorithm is used, where the memory step is omitted. Hence, we aim to justify this simplified procedure by means of a theoretical study and numerical simulations. In our previous study [Becker and Mathé, 2013], we analyzed the simplified Propagation-Separation Approach, supposing piecewise constant parameter functions with sharp discontinuities. Here, we consider the case of a misspecified model.
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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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    A new perspective on the propagation-separation approach: Taking advantage of the propagation condition
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Becker, Saskia; Mathé, Peter
    The Propagation-Separation approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean of the observations with data-driven weights. Within homogeneous regions it ensures a similar behavior as non-adaptive smoothing (propagation), while avoiding smoothing among distinct regions (separation). In order to enable a proof of stability of estimates, the authors of the original study introduced an additional memory step aggregating the estimators of the successive iteration steps. Here, we study theoretical properties of the simplified algorithm, where the memory step is omitted. In particular, we introduce a new strategy for the choice of the adaptation parameter yielding propagation and stability for local constant functions with sharp discontinuities