Linear and Nonlinear Generative Models for ‘Zero-Shot’ Image Denoising in the Limit of Few Photons

Abstract Images acquired in very low-light conditions have (on average) just few photons recorded per image pixel. Consequently, such images are very noisy, and any image enhancement is considered difficult. In this work, we study denoising of very low-light images, and we consider approaches that are applicable when solely the noisy image itself is available for training. While applicability in such a ‘zero-shot’ setting is attractive in domains with few data and high noise, suitable methods have to overcome considerable challenges. Here, we primarily investigate two methods. Both assume observed data to follow a Poisson distribution, which canonically models photon counts at low lights, and both assume a prior which can flexibly model sparsity. However, one of the used probabilistic generative models assumes a linear superposition to reconstruct image patches, while the other assumes a fixed nonlinear superposition more aligned with occlusions. For both models, parameters are estimated based on an approximate maximum likelihood approach. Concretely, we derive iterative fixed-point equations for parameter updates, which are combined with a recently suggested variational optimization approach. We are specifically interested in the differences between the two approaches as well as in their performance compared to other ‘zero-shot’ algorithms that can operate in the considered setting. In numerical experiments, we found both models to be very competitive for denoising benchmarks. Moreover, the nonlinear model was observed to be preferable to the linear one in most cases. For some settings, we here report new state-of-the-art results, which also recommends the investigated methods for count data beyond low-light images.