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In this paper, a new algorithm for signal reconstruction in a compressive sensing framework is presented. The proposed algorithm is based on Mittag-Leffler function which approximates the ℓ0 norm. Contrary to the previous algorithms such as smoothed ℓ0 norm algorithm(SL0), ℓ1-magic and iteratively re-weighted algorithm, our approach yields improved signal reconstruction performance for compressible signal. When compared to smoothed ℓ0 norm algorithm, the improved signal reconstruction performance is always achieved although the amount of computation is increased somewhat.