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This paper presents a fast approach for penalized least squares (LS)regression problems using a 2D Gaussian Markov random field (GMRF) prior. Moreprecisely, the computation of the proximity operator of the LS criterionregularized by different GMRF potentials is formulated as solving aSylvester-like matrix equation. By exploiting the structural properties ofGMRFs, this matrix equation is solved columnwise in an analytical way. Theproposed algorithm can be embedded into a wide range of proximal algorithms tosolve LS regression problems including a convex penalty. Experiments carriedout in the case of a constrained LS regression problem arising in amultichannel image processing application, provide evidence that an alternatingdirection method of multipliers performs quite efficiently in this context.

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