Abstract
This paper is devoted to a foreground/background joint estimation and separation problem. We first observe that this problem is modeled by a conditionally linear and Gaussian hidden Markov chain (CLGHMC). We next propose a filtering algorithm in the general non-linear and non Gaussian conditionally hidden Markov chain (CHMC), allowing the propagation of the filtering densities associated to the foreground and the background. We then focus on the particular case of our CLGHMC in which these filtering densities are weighted sums of Gaussian distributions; the parameters of each Gaussian are computed by using the Kalman filter algorithm, while the weights are computed by using the particle filter algorithm. We finally perform some simulations to highlight the interest of our method in both signals and images foreground/backgound joint estimation and separation.