Robust minimax MMSE for sparse signal recovery against system perturbations

In this work, we develop a minimum mean square error (MMSE) estimator for the underdetermined systems when the signal of interest is sparse. To address the uncertainty issue introduced in the measurement system, robust approaches are developed based on stochastic and worst case optimization techniques under the minimax framework. To solve the optimization problem, different constraints on the unknown signal of interest are considered to transform the minimax optimization into semidefinite programming problem (SDP), which can be efficiently solved. Numerical studies are provided to demonstrate utilizing sparsity and robust approaches indeed improve MMSE estimator when the sparsity of the signal of interest is utilized and the system considered is underdetermined.