A Variational Bayesian Approach for Image Restoration. Application to Image Deblurring with Poisson-Gaussian Noise

TL;DR

This paper introduces a variational Bayesian method for image restoration that automatically estimates regularization parameters and effectively handles non-Gaussian Poisson-Gaussian noise, demonstrating competitive performance.

Contribution

The paper presents a novel variational Bayesian framework for image deblurring with Poisson-Gaussian noise, eliminating the need for manual regularization parameter tuning.

Findings

The proposed method achieves performance comparable to state-of-the-art techniques.

It reliably estimates regularization parameters directly from observations.

The approach is computationally efficient and effective for non-Gaussian noise models.

Abstract

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is reliably estimated from the observations. As the posterior density of the unknown parameters is analytically intractable, the estimation problem is derived in a variational Bayesian framework where the goal is to provide a good approximation to the posterior distribution in order to compute posterior mean estimates. Moreover, a majorization technique is employed to circumvent the difficulties raised by the intricate forms of the non-Gaussian likelihood and of the prior density. We demonstrate the potential of the proposed approach through comparisons with state-of-the-art techniques that are specifically tailored to signal recovery in the presence of mixed Poisson-Gaussian noise. Results show that the proposed approach is efficient and achieves performance comparable with other methods where the regularization parameter is manually tuned from the ground truth.