Maximum-a-posteriori Restoration of Images - an Application of the Viterbi Algorithm to Two-dimensional Filtering

In many restoration problems, the a-priori knowledge of a finite number of pixel amplitudes of the original image is available (e.g. blurred blackand-white images). It is shown how to incorporate this information into optimal image reconstruction. The degradation of a discrete image is modeled as a two-dimensional, finite-state Markov process. Dynamic programming is then applied to get an optimal estimate of the state sequence of that process observed in memoryless noise, a technique which is known as Viterbi algorithm. This leads to a nonlinear recursive filter providing superior performance over optimal linear filtering. Examples are given in comparison with inverse filtering.