The advancement of deep generative models has brought new challenges in denoising, specifically in blind denoising where noise level and covariance are unknown. To tackle this issue, a research team from Ecole Polytechnique, Institut Polytechnique de Paris, and Flatiron Institute developed a novel method called the Gibbs Diffusion (GDiff) approach.
The GDiff approach is a fresh possibility in blind denoising that introduces a Gibbs method specifically designed for scenarios involving arbitrary parametric Gaussian noise. This allows for the simultaneous sampling of the posterior of the noise and signal parameters. The process involves two alternating stages.
The first stage, Conditional Diffusion Model Sampling, uses a trained diffusion model to map the prior distribution of the signal to a family of noise distributions. This model considers the characteristics of the noise and assists in signal inference.
The second stage, Monte Carlo Sampling, aims at estimating the noise parameters. A Monte Carlo sampler is used in this case to estimate parameters that typify the noise distribution.
The Golay demonstrates the effectiveness of GDiff by highlighting its use in two areas. First, in the Blind Denoising of Natural Images, the algorithm outperforms traditional baselines by recovering clean images and characterizing the noise. Second, in cosmology, the GDiff algorithm enhances the understanding of cosmological models by helping to constrain models of the universe’s evolution through Bayesian inference of the noise parameters.
This study’s main contributions include introducing GDiff to address difficulties in modeling prior distribution based on samples and sampling the posterior. Additionally, the team provided a solid theoretical framework for GDiff by establishing requirements for a stationary distribution and quantifying inference error propagation within the method.
In conclusion, the Gibbs Diffusion method is a groundbreaking advancement in denoising that allows for more thorough and accurate signal recovery in scenarios where noise parameters are unknown. This innovative approach could significantly impact the fields of image analysis and cosmology, among others.
