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arXiv · 1709.06178

A Fast Algorithm Based on a Sylvester-like Equation for LS Regression with GMRF Prior

Qi Wei·Emilie Chouzenoux·Jean-Yves Tourneret·Jean-Christophe Pesquet
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Abstract

This paper presents a fast approach for penalized least squares (LS) regression problems using a 2D Gaussian Markov random field (GMRF) prior. More precisely, the computation of the proximity operator of the LS criterion regularized by different GMRF potentials is formulated as solving a Sylvester-like matrix equation. By exploiting the structural properties of GMRFs, this matrix equation is solved columnwise in an analytical way. The proposed algorithm can be embedded into a wide range of proximal algorithms to solve LS regression problems including a convex penalty. Experiments carried out in the case of a constrained LS regression problem arising in a multichannel image processing application, provide evidence that an alternating direction method of multipliers performs quite efficiently in this context.

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Qi Wei, Emilie Chouzenoux, Jean-Yves Tourneret, Jean-Christophe Pesquet. 2017-09-18. A Fast Algorithm Based on a Sylvester-like Equation for LS Regression with GMRF Prior. https://arxiv.org/abs/1709.06178

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