基于Sylvester-like方程的GMRF先验LS回归的快速算法
A Fast Algorithm Based on a Sylvester-like Equation for LS Regression with GMRF Prior
摘要：
提出了一种基于二维高斯马尔可夫随机场先验的惩罚最小二乘（LS）回归问题的快速算法。更准确地说，计算的邻近算子的LS准则正则化不同的GMRF潜力制定为解决Sylvester的矩阵方程。通过利用GMRF的结构特性，以解析方式逐列求解该矩阵方程。所提出的算法可以嵌入到广泛的近似算法，以解决LS回归问题，包括凸惩罚。在多通道图像处理应用中出现的约束LS回归问题的情况下进行的实验提供了证据，证明在这种情况下，交替方向的乘法器方法执行得相当有效。
英文摘要：
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.
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