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 ℓ
₀
norm. Contrary to the previous algorithms such as smoothed ℓ
₀
norm algorithm(SL0), ℓ
₁
-magic and iteratively re-weighted algorithm, our approach yields improved signal reconstruction performance for compressible signal. When compared to smoothed ℓ
₀
norm algorithm, the improved signal reconstruction performance is always achieved although the amount of computation is increased somewhat.