An approximate L0 norm minimization algorithm for compressed sensing

ℓ⁰ Norm based signal recovery is attractive in compressed sensing as it can facilitate exact recovery of sparse signal with very high probability. Unfortunately, direct ℓ⁰ norm minimization problem is NP-hard. This paper describes an approximate ℓ⁰ norm algorithm for sparse representation which preserves most of the advantages of ℓ⁰ norm. The algorithm shows attractive convergence properties, and provides remarkable performance improvement in noisy environment compared to other popular algorithms. The sparse representation algorithm presented is capable of very fast signal recovery, thereby reducing retrieval latency when handling high dimensional signal.