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.

Deep priors for satellite image restoration with accurate uncertainties

Satellite optical images, upon their on-ground receipt, offer a distorted view of the observed scene. Their restoration, classically including denoising, deblurring, and sometimes super-resolution, is required before their exploitation. Moreover, quantifying the uncertainty related to this restoration could be valuable by lowering the risk of hallucination and avoiding propagating these biases in downstream applications. Deep learning methods are now state-of-the-art for satellite image restoration. However, they require to train a specific network for each sensor and they do not provide the associated uncertainties. This paper proposes a generic method involving a single network to restore images from several sensors and a scalable way to derive the uncertainties. We focus on deep regularization (DR) methods, which learn a deep prior on target images before plugging it into a model-based optimization scheme. First, we introduce VBLE-xz, which solves the inverse problem in the latent space of a variational compressive autoencoder, estimating the uncertainty jointly in the latent and in the image spaces. It enables scalable posterior sampling with relevant and calibrated uncertainties. Second, we propose the denoiser-based method SatDPIR, adapted from DPIR, which efficiently computes accurate point estimates. We conduct a comprehensive set of experiments on very high resolution simulated and real Pleiades images, asserting both the performance and robustness of the proposed methods. VBLE-xz and SatDPIR achieve state-of-the-art results compared to direct inversion methods. In particular, VBLE-xz is a scalable method to get realistic posterior samples and accurate uncertainties, while SatDPIR represents a compelling alternative to direct inversion methods when uncertainty quantification is not required.