Section: New Results

Fast Algorithm for Least-Squares Regression with GMRF Prior

Participants: Emilie Chouzenoux and Jean-Christophe Pesquet (in collaboration with J.Y. Tourneret, IRIT, Toulouse, and Q. Wei, Duke Univ.)

The paper [29] 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 column-wise 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.