Sparse Signal Recovery Using Iterative Proximal Projection

Abstract : —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.
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IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2018, 66 (4), pp.879 - 894. 〈10.1109/TSP.2017.2778695〉
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Fateme Ghayem, Mostafa Sadeghi, Massoud Babaie-Zadeh, Saikat Chatterjee, Mikael Skoglund, et al.. Sparse Signal Recovery Using Iterative Proximal Projection. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2018, 66 (4), pp.879 - 894. 〈10.1109/TSP.2017.2778695〉. 〈hal-01707062〉

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