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ENGINEERING Information Technology & Electronic Engineering

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A reversibility-gain model for integer Karhunen-Loève transform design in video coding

Author(s): Xing-guo Zhu, Lu Yu
Affiliation(s): Zhejiang Provincial Key Laboratory of Information Network Technology, Institute of Information and Communication Engineering, Zhejiang University, Hangzhou 310027, China
Corresponding email(s): yul@zju.edu.cn
Key Words: Integer transform, Karhunen-Loève transform (KLT), Integer-KLT, Transform coding, Video coding

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Xing-guo Zhu, Lu Yu. A reversibility-gain model for integer Karhunen-Loève transform design in video coding[J]. Frontiers of Information Technology & Electronic Engineering,in press.https://doi.org/10.1631/FITEE.1500071

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Abstract
Chinese Summary
Academic Network
Reviewer Comment

Abstract: karhunen-Loève transform (KLT) is the optimal transform that minimizes distortion at a given bit allocation for Gaussian source. As a KLT matrix usually contains non-integers, integer-KLT design is a classical problem. In this paper, a joint reversibility-gain (R-G) model is proposed for integer-KLT design in video coding. Specifically, the ‘reversibility’ is modeled according to distortion analysis in using forward and inverse integer transform without quantization. It not only measures how invertible a transform is, but also bounds the distortion introduced by the non-orthonormal integer transform process. The ‘gain’ means transform coding gain (TCG), which is a widely used criterion for transform design in video coding. Since KLT maximizes the TCG under some assumptions, here we define the TCG loss ratio (LR) to measure how much coding gain an integer-KLT loses when compared with the original KLT. Thus, the R-G model can be explained as follows: subject to a certain TCG LR, an integer-KLT with the best reversibility is the optimal integer transform for a given non-integer-KLT. Experimental results show that the R-G model can guide the design of integer-KLTs with good performance.

Abstract: The paper proposes a model (R-G) to select from a set that contains a large number of integer-KLTs, the one that better performs for video coding. All candidates integer transforms are generated from the same original KLT by scaling the coefficients, applying a rounding operation and expanding the coefficients using a parameter k. The selection model is based on two criteria: the first one is Loss Ratio TCG and the second is reversibility. This model is compared with two other integerization models. Overall, the paper is organized well.

视频编码中指导整数Karhunen-Loève变换设计的可逆-增益模型

目的：Karhunen-Loève变换（KLT）核矩阵含有无理数而需要整数化。但整数化过程通常会削弱KLT对视频信号去相关能力，同时整数KLT的非正交性也会带来失真。因而需要一个评价模型来指导整数KLT的设计。
创新点：综合考虑KLT在视频压缩中所起作用，分别对整数KLT矩阵的可逆程度和其变换编码增益（TCG）进行建模，并形成可逆-增益模型。用该模型进行KLT的整数化设计，得到的整数KLT矩阵在视频压缩效率上都高于其他整数化方法得到的矩阵。
方法：首先，充分考虑KLT的正交性，分析无量化情形下整数变换编码过程中失真的来源及其与整数变换核矩阵的解析关系，并利用此解析关系为整数KLT矩阵的可逆程度进行建模（式15）。然后，由于KLT可以最大化TCG，我们对KLT在整数化过程中的TCG损失率进行建模（式16），并分析整数余弦变换的TCG损失率（表1），以作为参考。最后，联合变换的可逆程度和TCG损失率，形成一个指导整数KLT设计的可逆-增益模型（式18）：在给定TCG损失率约束下，具有最佳可逆程度的整数KLT即是对给定KLT进行整数化的最优结果。
结论：在视频压缩中，给定任意KLT矩阵和倍乘因子下，利用本文提出的可逆-增益模型指导该KLT的整数化，能得到在压缩效率上最优的整数KLT矩阵。

关键词组：整数变换；KLT；变换编码；视频编码

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视频编码中指导整数Karhunen-Loève变换设计的可逆-增益模型

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