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Abstract: karhunen-Loè;ve 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.

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

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