L2/3L2/3 regularization: Convergence of iterative thresholding algorithm

• Under some condition, the sequence generated by the L2/3L2/3 algorithm converges to a local minimizer of L2/3L2/3 regularization.
• Under the same conditions, the asymptotical convergence rate of L2/3L2/3 algorithm is linear.
• Numerical experiments support our theoretical analysis.

The L2/3L2/3 regularization is a nonconvex and nonsmooth optimization problem. Cao et al. (2013) investigated that the L2/3L2/3 regularization is more effective in imaging deconvolution. The convergence issue of the iterative thresholding algorithm of L2/3L2/3 regularization problem (the L2/3L2/3 algorithm) hasn’t been addressed in Cao et al. (2013). In this paper, we study the convergence of the L2/3L2/3 algorithm. As the main result, we show that under certain conditions, the sequence {x(n)}{x(n)} generated by the L2/3L2/3 algorithm converges to a local minimizer of L2/3L2/3 regularization, and its asymptotical convergence rate is linear. We provide a set of experiments to verify our theoretical assertions and show the performance of the algorithm on sparse signal recovery. The established results provide a theoretical guarantee for a wide range of applications of the algorithm.