Reconstruction of sparse signals by minimizing a re-weighted approximate ℓ0-norm in the null space of the measurement matrix

A new algorithm for signal reconstruction in a compressive sensing framework is presented. The algorithm is based on minimizing a re-weighted approximate ℓ₀-norm in the null space of the measurement matrix, and the unconstrained optimization involved is performed by using a quasi-Newton algorithm. Simulation results are presented which demonstrate that the proposed algorithm yields improved signal reconstruction performance and requires a reduced amount of computation relative to iteratively re-weighted algorithms based on the ℓ_p-norm with p <; 1. When compared with a known algorithm based on a smoothed ℓ₀-norm, improved signal reconstruction is achieved although the amount of computation is increased somewhat.