An Extended Log-Sum Regularization Threshold Iteration Algorithm for Complex-Domain Signal Processing

Traditional sparse reconstruction algorithms, such as Matching Pursuit (MP), Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), Iterative Hard Thresholding, and Iterative Soft Thresholding—have been widely adopted in engineering applications like radar signal processing and medical imaging. However, these methods suffer from high computational complexity and limited reconstruction accuracy. In contrast, the log-sum thresholding iteration algorithm has obtained superior performance in both computational efficiency and recovery precision. Notably, engineering applications, including radar signals and image processing, often involve complex-valued signals. In this paper, we firstly extend the log-sum thresholding iteration algorithm,originally designed for real-valued signals—to the complex domain. Secondly, we analyze the convergence of the algorithm. Finally, a systematic MSE analysis is conducted to compare the performance between the proposed complex-domain algorithm (C-Log) and the direct application of the real-domain algorithm to complex cases (CR-Log) under different signal-to-noise ratio (SNR) conditions. the results exhibit that the proposed extended algorithm enhances the applicability of sparse reconstruction in complex-valued scenarios, offering improved performance for practical engineering applications.