Recovery analysis of log-sum minimization under mutual coherence condition

The log-sum minimization has been widely employed in signal and image processing. In this paper, in order to analyze its applicable conditions and achievable boundary for compressed sensing scenario, some theoretical derivations of the log-sum function are studied based on the mutual coherence (MC) of measurement matrix. Firstly, the existence condition of the global minimum is demonstrated for the log-sum minimization without noise perturbation. Secondly, for the iterative threshold log-sum (ITL) algorithm, the theoretical performance guarantee of recovering sparse signal disturbed by noise is proposed. Additionally, comprehensive experimental results verify the theoretical analysis for the log-sum one and display the advantages and disadvantages of four sparse estimation algorithms, i.e., the ITL algorithm, ℓ_1/2 regularization, ℓ₁ regularization and orthogonal matching pursuit (OMP).