An information theoretic approach to hybrid deconvolution problems

Recovering the input of a system from a noisy lecture of the output is both a typical inverse ill-posed problem and a transmission paradigm. If the input-output relation is given by a convolution integral, we are concerned with the well-known deconvolution problem, which occurs in several scientific frameworks. In this paper, we develop an original information theoretic analysis and we design an encoding-decoding scheme for deconvolution. We propose different decoding algorithms to identify the input and we show both theoretic and simulations’ results.