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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 NP-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. [ABSTRACT FROM AUTHOR]