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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 presents for the first time the application of order recursive least squares algorithm to estimate Gaussian Markov random field model parameters. Using the symmetry properties of the model parameters with respect to the field, we transform a Gaussian Markov random field model supported by a non-causal symmetric neighborhood into a model supported by a causal asymmetric half-plane region, thus making recursive computation possible. By using the approximate Toeplitz property of the coefficient matrix in the canonical equations, the order recursive least squares algorithm with the MADP of O (m ~ 3) + O (M ~ 2m) is derived. The direct calculation using the solution equation is O m ~ 3) + O (M ~ 2m ~ 2), where M ~ 2 represents the size of one image and m represents the number of model parameters.