A recursive approach to reconstruction of sparse signals

Abstract

Compressive Sensing (CS) theory details how a sparsely represented signal in a known basis can be reconstructed using less number of measurements. In many practical systems, the observation signal has a sparse representation in a continuous parameter space. This situation rises the possibility of use of the CS reconstruction techniques in the practical problems. In order to utilize CS techniques, the continuous parameter space have to be discretized. This discritization brings the well-known off-grid problem. To prevent the off-grid problem, this study offers a recursive approach which discritizes the parameter space in an adaptive manner. The simulations show that the proposed approach can estimate the parameters with a high accuracy even if targets are closely spaced.