Bayesian deconvolution of Bernoulli-Gaussian processes

We present some Bayesian algorithms for the detection and estimation of Bernoulli-Gaussian processes, when just a filtered and noise-corrupted version of the original sequence is available. In a Bayesian framework, reconstruction is obtained from the posterior distribution of this sequence. Then, we conventionally define the likelihood of a Bernoulli-Gaussian process and show that this prior definition allows one to control the errors of detection, as well as the maximum intensity value that can be detected. Some of the traditional algorithms, generally used in image restoration, as MAP, MPM or ICM, are shown to be very efficient for the deconvolution of Bernoulli-Gaussian processes. Simulations and applications to real data are presented.