Augmented-Lagrangian regularization of matrix-valued maps

Augmented-lagrangian Regularization of Matrix-valued Maps

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 matrixvalued image regularization. We demonstrate the applicability of the framework for various problems, such as motion ana...

Fast Regularization of Matrix-Valued Images

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 a...

Total Variation Regularization of Matrix-Valued Images

We generalize the total variation restoration model, introduced by Rudin, Osher, and Fatemi in 1992, to matrix-valued data, in particular, to diffusion tensor images (DTIs). Our model is a natural extension of the color total variation model proposed by Blomgren and Chan in 1998. We treat the diffusion matrix D implicitly as the product D = LL(T), and work with the elements of L as variables, i...

Diffusion and Regularization of Vector- and Matrix-Valued Images

Partially Augmented Lagrangian Method for Matrix Inequality Constraints

We discuss a partially augmented Lagrangian method for optimization programs with matrix inequality constraints. A global convergence result is obtained. Applications to hard problems in feedback control are presented to validate the method numerically.