Fast image deconvolution using closed-form thresholding formulas of Lq(q=12,23) regularization

In this paper, we focus on the research of fast deconvolution algorithm based on the non-convex Lq(q=12,23) sparse regularization. Recently, we have deduced the closed-form thresholding formula for L12 regularization model (Xu (2010) [1]). In this work, we further deduce the closed-form thresholding formula for the L23 non-convex regularization problem. Based on the closed-form formulas for Lq(q=12,23) regularization, we propose a fast algorithm to solve the image deconvolution problem using half-quadratic splitting method. Extensive experiments for image deconvolution demonstrate that our algorithm has a significant acceleration over Krishnan et al.’s algorithm (Krishnan et al. (2009) [3]). Moreover, the simulated experiments further indicate that L23 regularization is more effective than L0,L12 or L1L1 regularization in image deconvolution, andL12 regularization is competitive to L1L1 regularization and better than L0L0 regularization.

► We deduce the closed-form thresholding formula for linear model with L23 regularization.
► A fast deconvolution algorithm using Lq(12,23) regularization under half-quadratic splitting framework.
► L23 regularization is more powerful than L1,L12 or L0L0 regularization for image deconvolution.
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