2-D fast Kalman algorithms for adaptive parameter estimation ofnonhomogeneous Gaussian Markov random field model

摘要

In this paper, a two-dimensional (2-D) nonhomogeneous GaussiannMarkov Random Field (GMRF) model is presented and the problem ofnadaptive parameter estimation for this model is addressed. Two 2-D fastnKalman algorithms are proposed as extensions of the 1-D fast Kalmannalgorithm, which utilize the shift-invariant and near-to-Toeplitznproperties of the coefficient matrix of the normal equation resultingnfrom the least squares (LS) criterion. In the first algorithm thenspace-varying model parameters are updated by sliding a data window withna constant size. By first shifting the data window from left to rightnand then from top to bottom, the spatial adaptive algorithm covers anwhole image. In the second algorithm the model parameters are updated bynabsorbing new pixel data or deleting old pixel data. The computationalncomplexities of the proposed two algorithms are O(Lm2)+O(Ln2m) MADPR (Multiplications And Divisions Per Recursion) acidnO(m3/2) MADPR respectively, compared with O(L2mn2)+O(m3) and O(m3) needed in thencorresponding direct least squares method, m and L being respectivelynthe total number of model parameters to be estimated and the size ofndata window. For computer simulation two sample images which obey twonsets of known parameters are first synthesized, and are then merged,nresulting in a non-homogeneous image. It is shown that the 2-D fastnKalman algorithms developed in the paper reduce the computationalncomplexity significantly and can track the model parameters very well.nThe estimated model parameters are as same as those obtained by usingndirect LS method. The algorithms derived in this paper can be used innmany applications where an image is considered as a nonstationary one