A Fast Algorithm Based on a Sylvester-like Equation for LS Regression with GMRF Prior
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.
Cite
@article{arxiv.1709.06178,
title = {A Fast Algorithm Based on a Sylvester-like Equation for LS Regression with GMRF Prior},
author = {Qi Wei and Emilie Chouzenoux and Jean-Yves Tourneret and Jean-Christophe Pesquet},
journal= {arXiv preprint arXiv:1709.06178},
year = {2017}
}