Robust compressed sensing with side information based on Laplace mixtures models

In this paper, we propose a new method for the recovery of a sparse signal from few linear measurements using a reference signal as side information. Modeling the signal coefficients with a double Laplace mixture model, and assuming that the distribution of the components of the prior information differs slightly from the unknown signal, the problem is formulated as a weighted l1 minimization problem. We derive sufficient conditions for perfect recovery and we show that our method is able to reduce significantly the number of measurements required for reconstruction. Numerical experiments demonstrate that the proposed approach outperforms the best algorithms for compressed sensing with prior information and is robust in imperfect scenarios.