Fast image deconvolution using closed-form thresholding formulas of L _q (q = 1/2, 2/3) regularization

In this paper, we focus on the research of fast deconvolution algorithm based on the non-convex L_q(q=12,23) sparse regularization. Recently, we have deduced the closed-form thresholding formula for L1/2 regularization model (Xu (2010) [1]). In this work, we further deduce the closed-form thresholding formula for the L2/3 non-convex regularization problem. Based on the closed-form formulas for L_q(q=1/2,2/3) 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 L2/3 regularization is more effective than L₀,L1/2 or L₁ regularization in image deconvolution, andL1/2 regularization is competitive to L₁ regularization and better than L₀ regularization.