PG-DPIR: An efficient plug-and-play method for high-count Poisson-Gaussian inverse problems

Poisson-Gaussian noise describes the noise of various imaging systems thus the need of efficient algorithms for Poisson-Gaussian image restoration. Deep learning methods offer state-of-the-art performance but often require sensor-specific training when used in a supervised setting. A promising alternative is given by plug-and-play (PnP) methods, which consist in learning only a regularization through a denoiser, allowing to restore images from several sources with the same network. This paper introduces PG-DPIR, an efficient PnP method for high-count Poisson-Gaussian inverse problems, adapted from DPIR. While DPIR is designed for white Gaussian noise, a naive adaptation to Poisson-Gaussian noise leads to prohibitively slow algorithms due to the absence of a closed-form proximal operator. To address this, we adapt DPIR for the specificities of Poisson-Gaussian noise and propose in particular an efficient initialization of the gradient descent required for the proximal step that accelerates convergence by several orders of magnitude. Experiments are conducted on satellite image restoration and super-resolution problems. High-resolution realistic Pleiades images are simulated for the experiments, which demonstrate that PG-DPIR achieves state-of-the-art performance with improved efficiency, which seems promising for on-ground satellite processing chains.