Robust Computational Methods for Smoothed L0 Approximation
Wang Feng①② Xiang Xin② Yi Ke-chu① Xiong Lei②
①(State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China) ②(Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi'an 710038, China)
Computational framework using surrogate functions and prior probability density functions, for smoothed L0 minimization approximation is studied in this paper, for the purpose of improving the recovery performance of non-convex compressed sensing. Firstly, a simple parameter adjusting strategy and modified SL0 and FOCUSS are presented, based on the convex-concave property analysis of approximation functions. Secondly, since L0 approximation problem can be viewed as a L0-Regularized Least Squares problem in noisy setting,a new computational framework called IRSL0 (Iteratively Reweighted SL0) is derived from the Newton direction, furthermore, a new surrogate function is also given. Finally, extensive numerical simulations demonstrate the robustness and applicability of the new theory and algorithms.
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