An adaptive regularized smoothed ℓ° norm algorithm for sparse signal recovery in noisy environments

The smoothed ℓ° norm (SL0) algorithm as one of the fastest implementations of sparse signal recovery suffers from significant performance degradation in noisy environments due to the inaccurate equality constraint involved in the optimization problem. Based on the regularized SL0 (ReSL0) algorithm adopting the regularization term to tolerate error, we propose an improved algorithm termed “adaptive regularized SL0 (AReSL0) algorithm” for making the sparse solution more robust against noise. The AReSL0 algorithm adaptively generates the efficient and reliable regularization parameter to balance the fit of the sparsity and residual error in the ReSL0-based objective function during the iteration process, and then exhibits higher immunity to noise than both the SL0 and ReSL0 algorithms. In an attempt to accelerate the AReSL0 algorithm, the SVD-based approach is employed for fast computing the inverse of the successive updated large matrices, thus increasing the execution speed of AReSL0 without loss of accuracy. Simulation results are presented to verify the effectiveness of the proposed method.