Optimal smoothing of binary Markov sequences by genetic algorithm and its application to image restoration

Two-state Markov models play important roles in analysis of physical and engineering phenomena. When the Markov sequence cannot be observed directly but through some noisy observation system, a “most likely” estimate of the underlying Markov sequence should be estimated from its noise-corrupted observation sequence. Although the estimate can be obtained by the integer programming approach, it is too tedious for long sequences. In this paper, a simple approach based on the genetic algorithm is proposed to obtain the estimate. A numerical example illustrates its applicability. The restoration of noisy binary images composed by N×M pixels is considered as an application of the proposed smoothing method