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

2026-05-12

AI Summary

This work addresses the problem of Gaussian denoising in grayscale images by proposing a probabilistic generative approach that integrates quadtree-based region partitioning with a hybrid autoregressive model. The method achieves efficient maximum a posteriori image estimation through alternating variational Bayesian inference and gradient-based optimization to maximize the evidence lower bound. Its key innovation lies in the first-time incorporation of a quadtree structure into a hybrid autoregressive generative framework, accompanied by the derivation of analytical gradient update rules that avoid numerical approximations. Experimental results demonstrate that the proposed method outperforms baseline approaches in both denoising accuracy and computational efficiency, offering a novel perspective on structure-prior-driven generative image denoising.

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.

Problem

• image denoising
• Gaussian noise removal
• grayscale images

Innovation

• quadtree partitioning
• mixture autoregressive model
• variational Bayes
• gradient-based optimization
• image denoising