Gibbs diffusion (GDiff): a new Bayesian blind denoising method with applications in image denoising and cosmology

With the recent advancement of deep generative models, the challenge of denoising has also become apparent. Diffusion models are trained and designed similarly to denoisers, and their modeled distributions agree with denoising priors when applied in a Bayesian setting. However, blind denoising, when these parameters are unknown, is difficult since conventional diffusion-based denoising techniques require prior knowledge of the noise level and covariance.

In a recent study, a team of researchers from the Ecole Polytechnique, the Institut Polytechnique de Paris, and the Flatiron Institute proposed a unique method called Gibbs Diffusion (GDiff) to overcome the limitations. This method allows for post-sampling of noise parameters in addition to signal parameters simultaneously. The creation of a Gibbs method specifically designed for situations involving arbitrary parametric Gaussian noise is the main feature here. The two types of sampling phases that the algorithm uses in alternation are as follows.

1. Conditional Diffusion Model Sampling: In this stage, a trained diffusion model is used to map the prior distribution of the signal to a family of noise distributions. This model considers the peculiarities of the noise and helps in signal inference.

1. Monte Carlo sampling: Inferring noise parameters is the main objective of the Monte Carlo sampling stage. The method allows estimating the parameters that characterize the noise distribution using a Monte Carlo sampler.

The team has shared that the theoretical evaluation of the Gibbs diffusion method quantifies the defects in the stationary Gibbs distribution resulting from the diffusion model. It also offers recommendations for diagnostic applications. Two applications have been highlighted to illustrate the effectiveness of this method.

1. Blind noise removal from natural images: In this application, color noise is used to blur images, but its amplitude and spectral index are unknown. The GDiff method recovers the clean image and characterizes the noise at the same time, which enables it to successfully solve the blind noise removal problem.

1. Cosmological problem: The second application deals with the processing of data related to the cosmic microwave background (CMB). In this framework, constraining models of the universe evolution are achieved by Bayesian inference of noise parameters. The GDiff approach can be used to improve the understanding of cosmological models by inference of noise parameters.

The team has shared its main contributions, which are as follows.

1. To address the difficulties of modeling the sample-based prior distribution and sampling the posterior, the team introduced Gibbs Diffusion (GDiff), a unique approach to blind denoising.

1. The team has provided a solid theoretical framework for GDiff by establishing requirements for the presence of a stationary distribution within the method and quantifying the propagation of inference errors.

1. The effectiveness of this approach has been demonstrated in two domains: cosmology, where it supports Bayesian inference of noise parameters to constrain models of the evolution of the Universe, and blind denoising of natural photographs with arbitrary color noise, where GDiff outperforms traditional baselines.

In conclusion, Gibbs scattering is a major advance in noise removal that allows for more complete and accurate signal recovery in situations where noise parameters are unknown.

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