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A two-dimensional least-mean-square (TDLMS) adaptive algorithm based on the method of steepest decent is proposed and applied to noise reduction in images. The adaptive property of the TDLMS algorithm enables the filter to have an improved tracking performance in nonstationary images. The results presented show that the TDLMS algorithm can be used successfully to reduce noise in images. The algorithm complexity is 2(N*N) multiplications and the same number of additions per image sample, where N is the parameter-matrix dimension. Analysis and convergence properties of the LMS algorithm in the one-dimensional case presented by other authors is shown to be applicable to this algorithm. The algorithm can be used in a number of two-dimensional applications such as image enhancement and image data processing.>
Hadhoud et al. (1988) studied this question.