high performance computing on graphics processing units: hgpu.org

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.