Convex relaxation of vectorial problems with coupled regularization

Strekalovskiy E, Chambolle A, Cremers D (2014)

Publication Type: Journal article

Publication year: 2014

Journal

Siam Journal on Imaging Sciences Society for Industrial and Applied Mathematics

Book Volume: 7

Pages Range: 294-336

Journal Issue: 1

DOI: 10.1137/130908348

Abstract

We propose convex relaxations for nonconvex energies on vector-valued functions which are tractable yet as tight as possible. In contrast to existing relaxations, we can handle the combination of nonconvex data terms with coupled regularizers such as l2-regularizers. The key idea is to consider a collection of hypersurfaces with a relaxation that takes into account the entire functional rather than separately treating the data term and the regularizers. We provide a theoretical analysis, detail the implementations for different functionals, present run time and memory requirements, and experimentally demonstrate that the coupled l2-regularizers give systematic improvements regarding denoising, inpainting, and optical flow estimation. © 2014 Society for Industrial and Applied Mathematics.

Involved external institutions

Technische Universität München (TUM) DE Germany (DE) École Polytechnique - Université Paris-Saclay FR France (FR)

How to cite

APA:

Strekalovskiy, E., Chambolle, A., & Cremers, D. (2014). Convex relaxation of vectorial problems with coupled regularization. Siam Journal on Imaging Sciences, 7(1), 294-336. https://dx.doi.org/10.1137/130908348

MLA:

Strekalovskiy, Evgeny, Antonin Chambolle, and Daniel Cremers. "Convex relaxation of vectorial problems with coupled regularization." Siam Journal on Imaging Sciences 7.1 (2014): 294-336.

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