Recovery Performance of LpLq-ADMM Algorithm under SαS impulse Noise

In the process of signal and image acquisition and transmission, there is not only the additive white Gaussian noise interference, but also the non-Gaussian noise interference. The performance of a standard reconstruction algorithm, known as compressed sensing, can be significantly reduced if it is used to recover the signal affected by non-Gaussian noise. In this paper, LpLq-ADMM algorithm (p ∈ ( 0, 2 ) , q ∈ ( 0, 1 )) based on alternating direction method of multipliers is proposed to improve the reconstruction accuracy and the robustness of signal and image restoration in impulsive SαS (symmetric α-stable) noise. Lp-norm is used as the loss function term to enhance the data restoration ability in SαS noise and Lq-norm is used as the generalized non-convex penalty term to guarantee the sparsity of the signal. In order to efficiently solve the cost function model with minimum non-convex and nonsmooth, reduce the computational complexity of the objective function and improve the processing ability of high-dimensional data, in this paper, the alternating direction method of multipliers (ADMM) is used to solve the cost function model. The appropriate p and q values are selected via numerical simulation experiments to achieve the optimal reconstruction accuracy and robustness of sparse signals in SαS noise. The reconstruction probability of sparse signals and image recovery performance are analyzed under the optimal p and q values. The simulation results show that LpLq-ADMM algorithm has great noise suppression ability to SαS noise, and its Peak Signal to Noise Ratio (PSNR) and signal recovery probability is higher than other recovery algorithms.