Egilmez Hilmi E, Chao Yung-Hsuan, Ortega Antonio
IEEE Trans Image Process. 2020 Sep 30;PP. doi: 10.1109/TIP.2020.3026627.
In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of transforms called graph-based transforms (GBTs) for video compression, and proposes two different techniques to design GBTs. In the first technique, we formulate an optimization problem to learn graphs from data and provide solutions for optimal separable and nonseparable GBT designs, called GL-GBTs. The optimality of the proposed GL-GBTs is also theoretically analyzed based on Gaussian-Markov random field (GMRF) models for intra and inter predicted block signals. The second technique develops edge-adaptive GBTs (EA-GBTs) in order to flexibly adapt transforms to block signals with image edges (discontinuities). The advantages of EA-GBTs are both theoretically and empirically demonstrated. Our experimental results show that the proposed transforms can significantly outperform the traditional Karhunen-Loeve transform (KLT).
在许多先进的压缩系统中，信号变换是编码和解码过程的一个组成部分，其中变换为感兴趣的信号提供紧凑表示。本文介绍了一类用于视频压缩的基于图的变换（GBT），并提出了两种不同的技术来设计GBT。在第一种技术中，我们制定了一个优化问题，以便从数据中学习图，并为最优可分离和不可分离GBT设计提供解决方案，称为GL-GBT。还基于帧内和帧间预测块信号的高斯-马尔可夫随机场（GMRF）模型对所提出的GL-GBT的最优性进行了理论分析。第二种技术开发了边缘自适应GBT（EA-GBT），以便灵活地使变换适应具有图像边缘（不连续性）的块信号。从理论和实验上都证明了EA-GBT的优点。我们的实验结果表明，所提出的变换可以显著优于传统的卡尔胡宁-洛伊夫变换（KLT）。
