Fast Regularization of Matrix-Valued Images

  • Guy Rosman
  • Yu Wang
  • Xue-Cheng Tai
  • Ron Kimmel
  • Alfred M. Bruckstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7574)


Regularization of images with matrix-valued data is important in medical imaging, motion analysis and scene understanding. We propose a novel method for fast regularization of matrix group-valued images.

Using the augmented Lagrangian framework we separate total- variation regularization of matrix-valued images into a regularization and a projection steps. Both steps are computationally efficient and easily parallelizable, allowing real-time regularization of matrix valued images on a graphic processing unit.

We demonstrate the effectiveness of our method for smoothing several group-valued image types, with applications in directions diffusion, motion analysis from depth sensors, and DT-MRI denoising.


Matrix-valued Regularization Total-variation Optimization Motion understanding DT-MRI Lie-groups 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Guy Rosman
    • 1
  • Yu Wang
    • 1
  • Xue-Cheng Tai
    • 2
  • Ron Kimmel
    • 1
  • Alfred M. Bruckstein
    • 1
  1. 1.Dept. of Computer ScienceTechnion - IITHaifaIsrael
  2. 2.Dept. of MathematicsUniversity of BergenBergenNorway

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