A new signal recovery method based on optimal uncertainty quantification in compressed sensing

The existing signal recovery methods in compressed sensing (CS) viewed roughly noises or perturbations with statistical information as bounded constraints, which results in relatively poor recovery accuracy. This paper proposes a new signal recovery method based on optimal uncertainty quantification (OUQ) framework, which uses the statistical information of noises or perturbations. Firstly, we describe conventional CS problem using OUQ framework and form an equivalent finite-dimensional optimization problem. Then the solve approach of the finite-dimensional optimization problem is proposed. What is more, the partition method for high-dimensional signals is also proposed to solve the challenge that high-dimensional signals can not be solved effectively using OUQ framework. Finally, the simulation results are further presented to verify the effectiveness of the new signal recovery method.