Recursive deconvolution of Bernoulli-Gaussian processes using a MA representation

The authors deal with the problem of deconvolution of Bernoulli-Gaussian random processes observed through linear systems. This corresponds to situations frequently encountered in areas such as geophysics, ultrasonic imaging, and nondestructive evaluation. Deconvolution of such signals is a detection-estimation problem that does not allow purely linear data processing, and the nature of the difficulties greatly depends on the type of representation chosen for the linear system. A MA degenerate state-space representation is used. It presents interesting algorithmic properties and simplifies implementation problems. To obtain a globally recursive procedure, a detection step is inserted in an estimation loop by Kalman filtering. Two recursive detectors based on maximum a posteriori and maximum-likelihood criteria, respectively, are derived and compared