Detection and estimation of superimposed signals

The problem of fitting 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 l₁-norm of the weights. Different equivalent formulations of the criterion are presented. They lead to appealing physical interpretations. Due to limited space, we only sketch an analysis of the performance of the algorithm that has been successfully applied to different classes of problems