L1-norm noisy Tauberian deconvolution

We propose a method to model a signal as the output of an all-pole linear system, with noncausal impulse response, driven by a mixed signal (sparse impulses plus noise sequence). The filter parameters and the excitation sequences are obtained by separating the output of a forward-backward predictor into two signals. The mean absolute value of the first one is minimized and the absolute values of the second one are hounded. Its features and advantages with respect to other techniques are pointed out.