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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 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.
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https://hal.archives-ouvertes.fr/hal-01635601
Contributor : Emilie Chouzenoux <>
Submitted on : Wednesday, November 15, 2017 - 1:57:19 PM
Last modification on : Wednesday, April 8, 2020 - 4:02:56 PM
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  • HAL Id : hal-01635601, version 1

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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⟩

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