A method of two-dimensional filter image with a nonseparable autocovariance function

Recently, various methods have been reported for two-dimensional image enhancement with the development of satellite image and medical image processing. This paper proposes a two-dimensional filter for the image with a nonseparable autocovariance function in order to reduce the memory storage and processing time. Also, a simple method of estimating the necessary statistics to compose the filter is considered. The proposed two-dimensional filter is a stable one which satisfies an estimation criterion of unbiasness and minimum variance. Also, the filter introduced here is completely equivalent to the Kalman filter algorithm when the filter parameters a1, a2, a3 are such that a3 = 0 and a1 or a2 = 0. Thus, the proposed filter is a natural extension of a classical Kalman filter into a two-dimensional system. Finally, we compare existing methods with the proposed method by simulation, and examine qualitatively the contention that the estimation accuracy and computation time of the proposed method are superior to the others.