Stochastic Deep Restoration Priors for Imaging Inverse Problems

Deep neural networks trained as image denoisers are widely used as priors for solving imaging inverse problems. We introduce Stochastic deep Restoration Priors (ShaRP), a novel framework that stochastically leverages an ensemble of deep restoration models beyond denoisers to regularize inverse problems. By using generalized restoration models trained on a broad range of degradations beyond simple Gaussian noise, ShaRP effectively addresses structured artifacts and enables self-supervised training without fully sampled data. We prove that ShaRP minimizes an objective function involving a regularizer derived from the score functions of minimum mean square error (MMSE) restoration operators. We also provide theoretical guarantees for learning restoration operators from incomplete measurements. ShaRP achieves state-of-the-art performance on tasks such as magnetic resonance imaging reconstruction and single-image super-resolution, surpassing both denoiser- and diffusion-model-based methods without requiring retraining.