An approximate l0 norm based signal reconstruction algorithm in the compressive sampling theory

In the compressive sampling theory, a small number of random linear projections of a sparse or compressible signal have contained sufficient information and the original signal can be accurately reconstructed by taking advantage of modern optimization algorithms. We proposed an approximate l₀ norm based signal reconstruction algorithm in this paper. It not only can convert the classical constrained l₀ minimization problem of the compressive sampling theory into an unconstrained optimization problem, but also can reduce the dimension of the search space substantially. The experiment results have shown that our proposed algorithm can improve the sparse signal reconstruction performance while maintaining appropriate signal reconstruction efficiency.