高斯马尔可夫随机场模型的递归最小二乘参数估计

Recursive Least Squares Parameter Estimation for Gaussian Markov Random Field Model

本文首次提出应用阶递归最小二乘算法来估计高斯马尔可夫随机场模型参数。利用模型参数关于领域的对称性质,我们将一个非因果对称邻域支持的高斯马尔可夫随机场模型转化成一个因果非对称半平面部域支持的模型,从而使递归计算成为可能。利用规范方程中系数矩阵的近似Toeplitz性质,导出了运算量为O(m^3)+O(M^2m)MADP的阶递归最小二乘算法,而直接采用解方程法的计算量为O(m^3)+O(M^2m^2),这里M^2表示一幅图象的尺寸,m代表模型参数的个数。

This paper, for the first time, presents an order recursive least squares(LS) algorithm for the parameter estimation of Gaussian Markov Random Field (GMRF) model. The symmetric property of the parameters about the neighbor set is used to change the noncausal GMRF model into a causal nonsym metric half-plane (NSHP) supported model. Based on the approximate Toeplitz structure of the coefficient matrix in the normal equation, we derive an order recursive LS algorithm with the computation complexity of O(m3) + O(M2m)MADP, While the direct LS method needs the computation complexity of O(m3) + O(M2m2), where M2 represents the size of an image and m is the total number of parameters to be estimated.