A nonstationary accelerating alternating direction method for frame-based Poissonian image deblurring

Poissonian image deblurring problem has been an attractive research subject in many areas of imaging science and engineering. In order to obtain accurate restorations, one has to run several times to manually select a good value of a regularization parameter in many models. In this paper, we first propose an optimization model by combining a new data-fitting term with a frame-based analysis regularizer and a nonnegative constraint. A discrepancy principle based nonstationary accelerating alternating direction method, called DP-NAADM, is then proposed to solve the optimization model, without estimating the regularization parameter. Numerical results show that DP-NAADM provides competitive restoration results compared to the well-known Poisson image deconvolution by augmented Lagrangian method called PIDAL. Also, DP-NAADM provides better restorations in terms of both accuracy and visual quality than the discrepancy principle based PIDAL method. (C) 2018 Elsevier B.V. All rights reserved.