PPR: Plug-and-Play Regularization Model for Solving Nonlinear Imaging Inverse Problems

Abstract The problem of recovering an image of interest from nonlinear measured data is challenging. To address this nonlinear imaging inverse problem, we propose a novel Plug-and-Play Regularization (PPR) approach that can exploit multiple priors. The underlying image and its filtered image by a denoiser should have similar structures. To exploit this similarity, we enforce the similarity of their sparse coefficients with respect to a tight frame. We formulate a PPR-based nonlinear imaging optimization problem and solve it by using the alternating optimization strategy that consists of filtering step, sparse coding step and image updating step. To avoid the finely-tuned regularization parameter, the epigraph concept is employed in the image updating step. Multiple priors, including the priors employed by the denoiser and the sparsity in the sparsifying transform domain, can be utilized in the proposed PPR model. Under the coded diffraction imaging scenario, we show that the proposed algorithm of exploiting a deep denoiser can achieve higher quality images, compared to the previous imaging algorithms. A public demo code of the proposed PPR framework is available at https://github.com/shibaoshun/PPR .