Stochastic Image Denoising by Sampling from the Posterior Distribution

TL;DR

This paper introduces a stochastic image denoising method using Langevin dynamics that samples from the posterior distribution, producing high-quality, diverse outputs and extending to inpainting tasks.

Contribution

It presents a novel stochastic denoising approach that maintains low MSE while enhancing perceptual quality and diversity of results, unlike traditional methods.

Findings

Produces diverse high-quality denoised images

Effectively samples from the posterior distribution

Extends to inpainting with missing data

Abstract

Image denoising is a well-known and well studied problem, commonly targeting a minimization of the mean squared error (MSE) between the outcome and the original image. Unfortunately, especially for severe noise levels, such Minimum MSE (MMSE) solutions may lead to blurry output images. In this work we propose a novel stochastic denoising approach that produces viable and high perceptual quality results, while maintaining a small MSE. Our method employs Langevin dynamics that relies on a repeated application of any given MMSE denoiser, obtaining the reconstructed image by effectively sampling from the posterior distribution. Due to its stochasticity, the proposed algorithm can produce a variety of high-quality outputs for a given noisy input, all shown to be legitimate denoising results. In addition, we present an extension of our algorithm for handling the inpainting problem, recovering missing pixels while removing noise from partially given data.