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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。
Objective: The Karhunen-Loeve Transform (KLT) kernel matrix contains an irrational number and requires integerization. However, the process of integerization usually weakens the KLT de-correlation of the video signal, and the non-orthonormality of the integer KLT also causes distortion. Therefore, an evaluation model is needed to guide the design of the integer KLT. Innovative point: Considering KLT plays a role in video compression, the reversibility of integer KLT matrix and its transform coding gain (TCG) are respectively modeled and the reversible-gain model is formed. With this model, the integer KLT is designed, and the resulting integer KLT matrix is higher in video compression efficiency than those obtained by other integer methods. Methods: Firstly, considering the orthogonality of KLT, the source of distortion in integer transform coding without quantization and its analytical relationship with integer transform kernel matrix are analyzed, and the relationship between the KLT matrix and the integer transform kernel matrix is analyzed. (Equation 15). Then, since the KLT can maximize the TCG, we model the TCG loss rate of KLT during integerization (Equation 16) and analyze the TCG loss rate of the integer cosine transform (Table 1) for reference. Finally, the degree of reversibility of the joint transformation and the TCG loss rate form a reversible-gain model that directs the integer KLT design (Eq. 18): The integer KLT with the best reversible degree for a given TCG loss rate constraint KLT optimal integer results. Conclusion: In the video compression, given the arbitrary KLT matrix and the multiplication factor, the integer KLT matrix with the best compression efficiency can be obtained by using the reversible-gain model proposed in this paper.