Score-Based Denoising Diffusion Models for Photon-Starved Image Restoration Problems

Score-based denoising diffusion models have recently emerged as a powerful strategy to solve image restoration problems. Early diffusion models required problem-specific training. However, modern approaches can combine a likelihood function that is specified during test-time with a foundational pretrained diffusion model, which is used as an implicit prior in a Plug-and-Play (PnP) manner. This approach has been shown to deliver state-of-the-art performance in a wide range of image restoration problems involving Gaussian and mild Poisson noise. With extreme computer vision applications in mind, this paper presents the first PnP denoising diffusion method for photon-starved imaging problems. These problems arise in new quantum-enhanced imaging systems that exploit the particle nature of light to exceed the limitations of classical imaging. The problems involve highly challenging noise statistics, such as binomial, geometric, and low-intensity Poisson noise, which are difficult because of high uncertainty about the solution and because the models exhibit poor regularity properties (e.g., exploding scores, constraints). The proposed method is demonstrated on a series of challenging photon-starved imaging experiments with as little as 1 photon per pixel, where it delivers remarkably accurate solutions and outperforms alternative strategies from the state-of-the-art.