Frame-based Poisson image restoration using a proximal linearized alternating direction method

The restoration problem for Poissonian images, arising in medical and astronomical applications, is an active research area. The associated optimization models are quite challenging since the fidelity term of the problem is not a quadratic function and the regularizer is usually nonsmooth. Recently, the augmented Lagrangian-based alternating direction method has been proposed to solve the total-variation-regularized convex model, frame-based analysis model and frame-based synthesis model. In this paper, we propose a frame-based balanced Poisson image restoration model and a proximal linearized alternating direction (PLAD) method to solve the proposed model. Unlike the augmented Lagrangian-based alternating direction method, the proposed PLAD algorithm does not require any inner iterations or inverses due to the replacement of the quadratic term of the augmented function by the sum of its linearization and the proximal function. We establish global convergence under mild conditions. The proposed method is highly parallelizable and it is thus suitable for large-scale image restoration problems. Numerical results show that the proposed framework, i.e., frame-based balanced model and the PLAD method outperforms analysis and synthesis models for Poisson image restoration problems in terms of the peak signal-to-noise ratio.