Image denoising with generalized Gaussian mixture model patch priors

TL;DR

This paper enhances image denoising by replacing the Gaussian mixture model with a generalized Gaussian mixture model in the EPLL framework, improving patch distribution modeling and denoising performance.

Contribution

It introduces efficient approximations for integrating GGMM priors into EPLL, enabling practical application despite computational challenges.

Findings

GGMM better models patch distribution than GMM

Proposed approximations enable fast computation with GGMM

GGMM-based denoising outperforms GMM-based methods

Abstract

Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular Expected Patch Log-Likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture model (GMM) prior learned on clean image patches as a way to regularize degraded patches. In this paper, we show that a generalized Gaussian mixture model (GGMM) captures the underlying distribution of patches better than a GMM. Even though GGMM is a powerful prior to combine with EPLL, the non-Gaussianity of its components presents major challenges to be applied to a computationally intensive process of image restoration. Specifically, each patch has to undergo a patch classification step and a shrinkage step. These two steps can be efficiently solved with a GMM prior but are computationally impractical when using a GGMM prior. In this paper, we provide approximations and computational recipes for fast evaluation of these two steps, so that EPLL can embed a GGMM prior on an image with more than tens of thousands of patches. Our main contribution is to analyze the accuracy of our approximations based on thorough theoretical analysis. Our evaluations indicate that the GGMM prior is consistently a better fit formodeling image patch distribution and performs better on average in image denoising task.