An improved smoothed ℓ⁰ approximation algorithm for sparse representation

ℓ⁰ norm based algorithms have numerous potential applications where a sparse signal is recovered from a small number of measurements. The direct ℓ⁰ norm optimization problem is P-hard. In this paper we work with the the smoothed ℓ⁰ (SL0) approximation algorithm for sparse representation. We give an upper bound on the run-time estimation error. This upper bound is tighter than the previously known bound. Subsequently, we develop a reliable stopping criterion. This criterion is helpful in avoiding the problems due to the underlying discontinuities of the ℓ⁰ cost function. Furthermore, we propose an alternative optimization strategy, which results in a Newton like algorithm.