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Convex Relaxation of Vectorial Problems with Coupled Regularization (2014)
BibTeX
@MISC{Strekalovskiy14convexrelaxation,
author = {Evgeny Strekalovskiy and Antonin Chambolle and Daniel Cremers},
title = {Convex Relaxation of Vectorial Problems with Coupled Regularization},
year = {2014}
}
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Abstract
We propose convex relaxations for non-convex energies on vector-valued functions which are both tractable yet as tight as possible. In contrast to existing relaxations, we can handle the combination of non-convex 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.
Keyphrases
coupled regularizers coupled l2-regularizers give systematic improvement non-convex energy non-convex data term entire functional key idea vector-valued function different functionals memory requirement data term theoretical analysis present run time optical flow estimation convex relaxation
