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

Qi Wei (1) , Emilie Chouzenoux (2, 3) , Jean-Yves Tourneret (4, 5) , Jean-Christophe Pesquet (2, 3)

1 CAM - University of Cambridge [UK]
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 GALEN - Organ Modeling through Extraction, Representation and Understanding of Medical Image Content
4 IRIT-MINDS - CoMputational imagINg anD viSion
5 Toulouse INP - Institut National Polytechnique (Toulouse)

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 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.

Domaines: Traitement du signal et de l'image [eess.SP]

Qi Wei, Emilie Chouzenoux, Jean-Yves Tourneret, Jean-Christophe Pesquet. A Fast Algorithm Based on a Sylvester-like Equation for LS Regression with GMRF Prior. CAMSAP 2017- IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Dec 2017, Curaçao, Netherlands Antilles. ⟨hal-01635601⟩