Reconstruction of sparse signals using smoothed ℓ0 norm via the Mittag-Leffler function

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.