"Qualitative" Bayesian estimation of digital signals and images

Bayesian estimation of digital signals is ordinarily concerned with the problem of estimating an ideal signal, given a noisy signal. The problem of partial or "qualitative" Bayesian description is considered, rather than complete estimation, of the ideal signal. Only the case of a piecewise constant signal is considered; instead of estimating the value of the ideal signal, only a piecewise symbolic description of the signal is sought-e.g. is the value high or low, where these descriptors are defined by probability densities on the possible signal values. This task is computationally less costly than that of complete Bayesian estimation of the signal; moreover, it is found that the descriptions can be estimated robustly. This approach is illustrated both for digital signals and for a simple class of digital images.