Fast Regularization of Matrix-Valued Images

Guy Rosman, Yu Wang, Xue-Cheng Tai, Ron Kimmel, Alfred M. Bruckstein
Computer Science Department, Techion – Israel Institute of Technology
Technical Report CIS-2011-03, 2011


   title={Fast Regularization of Matrix-Valued Images},

   author={Xue-Cheng, G.R.Y.W. and Bruckstein, T.R.K.A.M.},



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Regularization of matrix-valued data is of importance in medical imaging, motion analysis and scene understanding. In this report we describe a novel method for efficient regularization of matrix group-valued images. Using the augmented Lagrangian framework we separate the total-variation regularization of matrix-valued images into a regularization and projection steps, both of which are fast and parallelizable. We demonstrate the effectiveness of our method for denoising of several group-valued image types, with data in SO(n), SE(n), and SPD(n), and discuss its convergence properties.
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