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

Zhu Xing-guo; Yu Lu

doi:10.1631/FITEE.1500071

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

Electrical & Electronic Engineering | Updated：2022-06-06

- A reversibility-gain model for integer Karhunen-Loève transform design in video coding*
- 视频编码中指导整数Karhunen-Loève变换设计的可逆-增益模型
- Frontiers of Information Technology & Electronic Engineering Vol. 16, Issue 10, Pages: 883-891(2015)
- Affiliations：
  
  Zhejiang Provincial Key Laboratory of Information Network Technology, Institute of Information and Communication Engineering, Zhejiang University, Hangzhou 310027, China
- Author bio：
  
  ‡Corresponding Author
- Funds：
- DOI：10.1631/FITEE.1500071
  CLC：
- Received：09 March 2015，
  
  Revised：2015-09-09，
  
  Accepted：31 July 2015，
  
  Published：2015-10
- Accepted：
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Zhu Xing-guo, Yu Lu. A reversibility-gain model for integer Karhunen-Loève transform design in video coding*[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(10): 883-891.
DOI：

Zhu Xing-guo, Yu Lu. A reversibility-gain model for integer Karhunen-Loève transform design in video coding*[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(10): 883-891. DOI： 10.1631/FITEE.1500071.

摘要

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。

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.

关键词

Keywords

references

N Ahmed , T Natarajan , KR Rao . Discrete cosine transform . IEEE Trans Comput , 1974 . C-23 ( 1 ): 90 - 93 . DOI: 10.1109/T-C.1974.223784 http://doi.org/10.1109/T-C.1974.223784 .

G Bjontegaard . Calculation of Average PSNR Differences Between RD-Curves . 2001 . Doc. VCEG-M33 ITU-T Q6/16, Austin, Texas, USA . .

J Chen . Reconstruction Image Distortion Model Considering the Quality of Reference Frame in Video Coding. MS T , 2012 . Zhejiang University, Hangzhou, China , (in Chinese) .

J Dong , KN Ngan , CK Fong , 等 . 2-D order-16 integer transforms for HD video coding . IEEE Trans Circ Syst Video Technol , 2009 . 19 ( 10 ): 1462 - 1474 . DOI: 10.1109/TCSVT.2009.2026792 http://doi.org/10.1109/TCSVT.2009.2026792 .

VK Goyal . High-rate transform coding: how high is high, and does it matter? . 2000 . Proc. IEEE Int. Symp. on Information Theory . 207 DOI: 10.1109/ISIT.2000.866505 http://doi.org/10.1109/ISIT.2000.866505 .

VK Goyal . Theoretical foundations of transform coding . IEEE Signal Process Mag , 2001 . 18 ( 5 ): 9 - 21 . DOI: 10.1109/79.952802 http://doi.org/10.1109/79.952802 .

J Han , A Saxena , V Melkeote , 等 . Jointly optimized spatial prediction and block transform for video and image coding . IEEE Trans Image Process , 2012 . 21 ( 4 ): 1874 - 1884 . DOI: 10.1109/TIP.2011.2169976 http://doi.org/10.1109/TIP.2011.2169976 .

AT Hinds , YA Reznik , L Yu , 等 . Drift analysis for integer IDCT . SPIE , 2007 . 6696 14.1 - 1416 . DOI: 10.1117/12.740220 http://doi.org/10.1117/12.740220 .

NS Jayant , P Noll . Digital Coding of Waveforms: Principles and Applications to Speech and Video , 1984 . Prentice-Hall, USA , .

A Saxena , FC Fernandes . Low latency secondary transforms for intra/inter prediction residual . IEEE Trans Image Process , 2013 . 22 ( 10 ): 4061 - 4071 . DOI: 10.1109/TIP.2013.2270087 http://doi.org/10.1109/TIP.2013.2270087 .

T Wiegand . H . 2001 . 26L Test Model Long-Term Number 9 (TML-9) draft0. Doc. VCEG-N83 ITU-T Q6/16, Santa Barbara, CA, USA . .

Y Ye , M Karczewicz . Improved H . 2008 . 264 intra coding based on bi-directional intra prediction, directional transform, and adaptive coefficient scanning. Proc. 15th IEEE Int. Conf. on Image Processing . 2116 - 2119 . DOI: 10.1109/ICIP.2008.4712205 http://doi.org/10.1109/ICIP.2008.4712205 .

C Yeo , YH Tan , Z Li , 等 . Mode-dependent transform for coding directional intra prediction residuals . IEEE Trans Circ Syst Video Technol , 2011 . 22 ( 4 ): 545 - 554 . DOI: 10.1109/TCSVT.2011.2168291 http://doi.org/10.1109/TCSVT.2011.2168291 .

C Zhang , J Wang , L Yu . Systematic approach of fixed point 8×8 IDCT and DCT design and implementation . 2006 . Proc. Picture Coding Symp . 1 - 6 . .

X Zhao , L Zhang , S Ma , 等 . Video coding with rate-distortion optimized transform . IEEE Trans Circ Syst Video Technol , 2011 . 22 ( 1 ): 138 - 151 . DOI: 10.1109/TCSVT.2011.2158363 http://doi.org/10.1109/TCSVT.2011.2158363 .

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