, Volume 95, Supplement 1, pp 771–784 | Cite as

GPU-accelererated regularisation of large diffusion-tensor volumes

  • Tuomo Valkonen
  • Manfred Liebmann


We discuss the benefits, difficulties, and performance of a GPU implementation of the Chambolle–Pock algorithm for TGV (total generalised variation) denoising of medical diffusion tensor images. Whereas we have previously studied the denoising of 2D slices of \(2 \times 2\) and \(3 \times 3\) tensors, attaining satisfactory performance on a normal CPU, here we concentrate on full 3D volumes of data, where each 3D voxel consists of a symmetric \(3 \times 3\) tensor. One of the major computational bottle-necks in the Chambolle–Pock algorithm for these problems is that on each iteration at each voxel of the data set, a tensor potentially needs to be projected to the positive semi-definite cone. This in practise demands the QR algorithm, as explicit solutions are not numerically stable. For a \(128 \times 128 \times 128\) data set, for example, the count is 2 megavoxels, which lends itself to massively parallel GPU implementation. Further performance enhancements are obtained by parallelising basic arithmetic operations and differentiation. Since we use the relatively recent OpenACC standard for the GPU implementation, the article includes a study and critique of its applicability.


DTI Regularisation Medical imaging GPU Open ACC 

Mathematics Subject Classification (2010)

92C55 94A08 26B30 49M29 



T. Valkonen has been financially supported by the SFB research program “Mathematical Optimization and Applications in Biomedical Sciences” of the Austrian Science Fund (FWF). The original diffusion-MRI measurement data on which Fig. 1 is based on, is courtesy of Karl Koschutnig.


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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Institute for Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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