Complex Successive Concave Sparsity Approximation

Fast, Efficient, and Viable Compressed Sensing, Low-Rank, and Robust Principle Component Analysis Algorithms for Radar Signal Processing

“…Among the smoothed 0 -approaches, successive concave sparsity approximation (SCSA) appeals through its simplicity and efficiency due to the availability of closed form solutions of subsequent optimization steps. This algorithm was extended to the complex case named CSCSA [54] and serves, in the algorithm collection presented in this work, as the final refinement approach of CS applications. In the work presented here, a similar approach is applied to the smoothed rank approximation (SRA) algorithm from [64] to extend it into the complex case and to improve its efficiency due to the use of closed form solutions of subsequent minimization steps.…”

“…The CSCSA algorithm does so, which is the author's extension of the SCSA algorithm from [63], capable of handling complex numbers. The CSCSA algorithm was published in [54] and is summarized in the following in brevity. Simulation results illustrating the performance of CSCSA in combination with the TST, SPGL1, and FISTA algorithms are presented in the following.…”

“…and W 0 (•) denotes the upper branch of the multi-valued Lambert W function [54]. It should be noted that T…”

“…Furthermore, the initial value γ 0 is set to γ 0 = max(|s 0 |)/10, where s 0 denotes the convex relaxed initial solution. More details regarding the CSCSA algorithm and the special selections of λ γ and γ 0 are given in [54]. Finally, to further improve the convergence speed of the applied IT approach, a FISTA-like technique can be used as in [53], which does not increase the computational complexity but boosts the convergence rate from O( 1 /i) up to O( 1 /i 2 ).…”