Detection and estimation of superimposed signals

The problem of tting a model composed of a number of superimposed signals to noisy observations is addressed. An approach allowing us to evaluate both the number of signals and their characteristics is presented. The idea is to search for a parsimonious representation of the data. The parsimony is insured by adding to the maximum likelihood criterion a regularization term built upon the `1-norm of the weights. Di erent equivalent formulations of the criterion are presented. They lead to appealing physical interpretations. Due to limited space, we can only sketch here an analysis of the performance of the algorithm that has been successfully applied to di erent classes of problems [6],[7].