Methods and Applications of Analysis

Volume 21 (2014)

Number 1

Augmented-Lagrangian regularization of matrix-valued maps

Pages: 105 – 122

DOI: http://dx.doi.org/10.4310/MAA.2014.v21.n1.a5

Authors

Guy Rosman (Computer Science Department, Technion 32000, Haifa, Israel)

Xue-Cheng Tai (Department of Mathematics, University of Bergen, Norway)

Ron Kimmel (Computer Science Department, Technion 32000, Haifa, Israel)

Alfred M. Bruckstein (Computer Science Department, Technion 32000, Haifa, Israel)

Abstract

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.

Keywords

regularization, Lie-groups, total-variation, split-Bregman, matrix-manifolds, diffusion-imaging, rotations, articulated motion

2010 Mathematics Subject Classification

58Jxx, 65K10

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