Sparse Signal Recovery Using Iterative Proximal Projection

Fatemeh Ghayyem (1, 2) , Mostafa Sadeghi (1) , Massoud Babaie-Zadeh (1) , Saikat Chatterjee (3) , Mikael Skoglund (3) , Christian Jutten (2)

1 EE department of SUT [Tehran] - Department of Electrical Engineering [Tehran]
2 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing
3 KTH - KTH Royal Institute of Technology [Stockholm]

—This paper is concerned with designing efficient algorithms for recovering sparse signals from noisy underdeter-mined measurements. More precisely, we consider minimization of a non-smooth and non-convex sparsity promoting function subject to an error constraint. To solve this problem, we use an alternating minimization penalty method, which ends up with an iterative proximal-projection approach. Furthermore, inspired by accelerated gradient schemes for solving convex problems, we equip the obtained algorithm with a so-called extrapolation step to boost its performance. Additionally, we prove its convergence to a critical point. Our extensive simulations on synthetic as well as real data verify that the proposed algorithm considerably outperforms some well-known and recently proposed algorithms.

Mots clés: Index Terms—Sparse signal recovery; compressed sensing; SL0; proximal splitting algorithms; iterative sparsification-projection

Domaines: Traitement du signal et de l'image [eess.SP]

Fatemeh Ghayyem, Mostafa Sadeghi, Massoud Babaie-Zadeh, Saikat Chatterjee, Mikael Skoglund, et al.. Sparse Signal Recovery Using Iterative Proximal Projection. IEEE Transactions on Signal Processing, 2018, 66 (4), pp.879 - 894. ⟨10.1109/TSP.2017.2778695⟩. ⟨hal-01707062⟩