Methods and Applications of Analysis
Volume 21 (2014)
Augmented-Lagrangian regularization of matrix-valued maps
Pages: 105 – 122
We propose a novel framework for fast regularization of matrix-valued images. The resulting algorithms allow a unified treatment for a broad set of matrix groups and manifolds. Using an augmented-Lagrangian technique, we formulate a fast and highly parallel algorithm for matrix-valued image regularization.
We demonstrate the applicability of the framework for various problems, such as motion analysis and diffusion tensor image reconstruction, show the formulation of the algorithm in terms of split-Bregman iterations and discuss the convergence properties of the proposed algorithms.
regularization, Lie-groups, total-variation, split-Bregman, matrix-manifolds, diffusion-imaging, rotations, articulated motion
2010 Mathematics Subject Classification