A Mixture Autoregressive Image Generative Model on Quadtree Regions for Gaussian Noise Removal via Variational Bayes and Gradient Methods

TL;DR

This paper introduces a probabilistic quadtree-based mixture autoregressive model for grayscale image denoising, utilizing variational Bayes and gradient methods to optimize noise removal.

Contribution

It presents a novel combination of quadtree partitioning with mixture autoregressive modeling and a variational framework for efficient image denoising.

Findings

The proposed algorithm effectively removes Gaussian noise from grayscale images.

Gradient updates can be computed analytically without numerical approximation.

Experiments confirm the model's capability in noise reduction and suggest future improvements.

Abstract

This paper addresses the problem of image denoising for grayscale images. We propose a probabilistic image generative model that combines a quadtree region-partitioning model with a mixture autoregressive model, and propose a framework that reduces MAP (maximum a posteriori)-estimation-based denoising to the maximization of a variational lower bound. To maximize this lower bound, we develop an algorithm that alternately applies variational Bayes and gradient methods. We particularly demonstrate that the gradient-based update rule can be computed analytically without numerical computation or approximation. We carried out some experiments to verify that the proposed algorithm actually removes image noise and to identify directions for future improvement.