Restoration of spiky signals: a new optimal estimate and a comparison

Discusses the restoration of spiky sequences distorted by a linear system and corrupted by additive noise. A (now) classical way of coping with this problem is to use a Bayesian approach with a Bernoulli-Gaussian (BG) prior model of the sequence. The authors refine this method using a Bernoulli-Gaussian plus Gaussian (BCG) prior model. This estimation method requires maximization of a posterior probability distribution, which cannot be performed optimally. Thus the authors propose a new non-Bayesian estimation scheme, derived from the Kullback-Leibler information or cross-entropy. This quite general method, called the maximum entropy on the mean method (MEMM) in Gamboa (1989) and le Besnerais (1995) is firmly based on convex analysis and yields a unique solution which can be efficiently calculated in practice, and which is, in this sense, truly optimal. As a conclusion, the authors present results obtained with both methods on a synthetic case