Abstract

Regularization of images with matrix-valued data is impor- tant 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 pro jection 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 sev- eral group-valued image types, with applications in directions diffusion, motion analysis from depth sensors, and DT-MRI denoising.