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 demonstrate that the proposed transforms can significantly outperform the traditional Karhunen-Loeve transform (KLT).
翻译:在许多最先进的压缩系统中,信号转换是编码和解码过程的一个组成部分,变换为感兴趣的信号提供了压缩的表示方式。本文介绍了一类变换,称为基于图形的变换(GBTs),用于视频压缩,并提出了两种不同的设计GBT的技术。在第一种技术中,我们设计了一个优化问题,从数据中学习图形,并为最佳可分离和不可分离的GBT设计提供解决方案,称为GL-GBTs。拟议的GL-GBTs的最佳性也是根据高山-马尔科夫随机场模型进行理论分析的。第二种技术开发了边缘适应性GBTs(EA-GBTs),以便灵活地将变换到图像边缘(不相干)的块状信号。EA-GBT的优点既有理论上的,也有经验性的。我们的实验结果表明,拟议的变换可以大大超过传统的Karhunen-Loeve变形(KLT)。