Robust compressed sensing with bounded and structured uncertainties

The robust compressed sensing problem subject to a bounded and structured perturbation in the sensing matrix is solved in two steps. The alternating direction method of multipliers (ADMM) is first applied to obtain a robust support set. Unlike the existing robust signal recovery solutions, the proposed optimisation problem is convex. The ADMM algorithm that every subproblem has a global minimum is employed to solve the optimisation problem. Then, the standard robust regularised least-squares problem restrained to the support is solved to reduce the recovery error. The numerical tests show that the proposed approach provides a robust estimation of support set, although it is conservative to recover signal magnitudes as a result of minimising the worst-cast data error across all bounded perturbations.