Integer programming approach to optimal smoothing of two-state Markov sequences

This paper is concerned with the optimal smoothing problem of stationary two-state Markov sequences, which play important roles in analysis of physical and engineering phenomena. An optimal smoothing method is derived. The smoothing method provides a ´most likely´ estimate of underlying Markov sequence from its noise-corrupted observation. We first reduce the optimal smoothing problem to a 0-1 quadratic programming problem, and then derive the smoothing method using the game-theoretic equivalence relation. The method is characterized by the values of the stationary occurrence probability and the serial correlation coefficient of the Markov sequence, and the probability of the observation error in the observation system. The usefulness is exemplified by digital simulation studies. Reconstruction of noisy binary images is discussed briefly as an application of the proposed method.