WIAS Preprint No. 1668, (2011)

Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)


  • Becker, Saskia
  • Tabelow, Karsten
    ORCID: 0000-0003-1274-9951
  • Voss, Henning U.
  • Anwander, Alfred
  • Heidemann, Robin M.
  • Polzehl, Jörg
    ORCID: 0000-0001-7471-2658

2010 Mathematics Subject Classification

  • 62P10 62G05 22E99


  • Diffusion weighted magnetic resonance imaging, POAS, Structural adaptive smoothing, Special Euclidean motion group, Lie groups


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.

Appeared in

  • Medical Image Analysis, 16 (2012) pp. 1142--1155

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