用四叉树分区与混合自回归模型，高效去除灰度图噪声。
A Mixture Autoregressive Image Generative Model on Quadtree Regions for Gaussian Noise Removal via Variational Bayes and Gradient Methods
- 四叉树分区+混合自回归建模图像结构
- 通过变分下界最大化实现最优去噪
- 梯度更新可解析计算，无需数值近似
本文针对灰度图像去噪问题，提出一种概率生成模型，结合四叉树区域划分与混合自回归结构。将最大后验估计（MAP）去噪转化为变分下界最大化问题，并设计交替使用变分贝叶斯与梯度方法的算法。特别证明梯度更新可通过解析方式计算，无需数值求解或近似。实验验证了该方法有效去除图像噪声，并指出了未来改进方向。
原文摘要 · Abstract (English)
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.
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