SNIPS: Solving Noisy Inverse Problems Stochastically
This addresses uncertainty in inverse problems for applications such as image processing, though it appears incremental as it builds on existing methods like Langevin dynamics and denoisers.
The authors tackled the problem of sampling from the posterior distribution in linear inverse problems with additive white Gaussian noise, introducing SNIPS, a stochastic algorithm that produces multiple high perceptual quality samples for tasks like image deblurring, super-resolution, and compressive sensing.
In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise. Our solution incorporates ideas from Langevin dynamics and Newton's method, and exploits a pre-trained minimum mean squared error (MMSE) Gaussian denoiser. The proposed approach relies on an intricate derivation of the posterior score function that includes a singular value decomposition (SVD) of the degradation operator, in order to obtain a tractable iterative algorithm for the desired sampling. Due to its stochasticity, the algorithm can produce multiple high perceptual quality samples for the same noisy observation. We demonstrate the abilities of the proposed paradigm for image deblurring, super-resolution, and compressive sensing. We show that the samples produced are sharp, detailed and consistent with the given measurements, and their diversity exposes the inherent uncertainty in the inverse problem being solved.