Regularized Generalized Inverse Accelerating Linearized Alternating Minimization Algorithm for Frame-Based Poissonian Image Deblurring

Abstract

Blurred images corrupted by Poisson noise frequently appear in medical and astronomical applications, and variational models based on sparsity priors such as the total variation and the framelet have been devoted to the problem of recovering the Poissonian images. However, developing efficient algorithms for solving the associated optimization problems is still an attractive research area due to the ill-posedness of the blurring operator and the complexity of the data-fidelity term. In this paper, we propose an accelerating linearized alternating minimization algorithm called GILAM for solving the frame-based variational model for Poissonian image deblurring. In the proposed method, a modification of the generalized inverse is introduced to overcome the negative effect of the ill-posed blurring operator, and, further, a discrepancy function is used to adjust the value of the regularization parameter automatically. The global convergence of the proposed algorithms is also investigated. Numerical experiments demonstrate that the proposed algorithms outperform the widely used ADMM (alternating direction method of multipliers) methods, especially in CPU time.