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矢量量化 (Vector Quantization)

矢量量化 (Vector Quantization). 赵胜辉. Scalar Quantization. Scalar Quantization v.s. Vector Quantization. VQ 系统. Why VQ?. x 2. x 2. x 1. x 1. Why VQ?. Why VQ?. Memory advantage Dependency between input samples Vanishes if the input samples are independent Shape advantage

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矢量量化 (Vector Quantization)

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  1. 矢量量化(Vector Quantization) 赵胜辉

  2. Scalar Quantization

  3. Scalar Quantization v.s. Vector Quantization

  4. VQ系统

  5. Why VQ? x2 x2 x1 x1

  6. Why VQ?

  7. Why VQ? • Memory advantage • Dependency between input samples • Vanishes if the input samples are independent • Shape advantage • Better adaptation of VQ quantization point density to the PDF of input • Vanishes in the case of entropy-constrained quantization • Space-filling advantage • Greater freedom of VQ in selecting quantization cell shapes • The advantage of an infinite-dimension VQ is 0.255 bits per dimension for the squared-error distortion

  8. How to do VQ? • S.P.Lloyd, “Least squares quantization in PCM,” IEEE Trans. Inform. Theory, vol.IT-28, pp.129-137,1982 • Lloyd algorithm (k-means algorithm) Generalized Lloyd algorithm (GLA) • Y.Linde, A.Buzo, and R.Gray, “An algorithm for vector quantizer design,” IEEE Trans. Comm., vol. COM-28, pp.84-95, 1980 • An iterative method that guarantee only local optimality

  9. How to do VQ? • Two optimality conditions • Optimizing the encoder • Optimizing the decoder 最近邻准则 Yi = argminE[d(X,Z)︱X∈Vi] Yi = E[X︱X∈Vi ] Z ∈Rk k-means Yi = 1/Ni∑X X∈Vi

  10. Discrete GLA

  11. 分裂法初始码本

  12. Some implementation problems • Large computational complexity due to the exhaustive codebook searching • Codebook storage • Large computational complexity due to codebook training Dimension (codeword length) Codebook size The size of training data

  13. Structured VQ • Tree-structured VQ • Multi-stage VQ • Split VQ • Gain-Shape VQ • Mean-Removed VQ

  14. Tree-structured VQ

  15. Multi-stage VQ

  16. Split VQ X1: (x1, x2,x3, x4) X: (x1, x2,x3,…, x8) X2: (x5, x6,x7, x8)

  17. Gain-Shape VQ

  18. Mean-Removed VQ Mean-removed vector codebook + Mean vector codebook

  19. 其它问题 • 特征矢量和失真准则的选择 • 快速码本搜索算法

  20. Rate-constrained VQ vs. Entropy-Constrained VQ • The optimal quantizer means minimizing the average distortion. • The resolution constraint limits the size of the codebook, i.e., fixed-rate. • The entropy constraint limits the entropy for the quantization indices, i.e., variable-rate.

  21. 课程设计2 • 矢量量化： • 对给定数据进行矢量量化。 • 要求用MATLAB或C语言实现码本训练和矢量量化算法，并给出量化结果（包括码本和平均量化失真）。 • 训练数据（128） ：training.dat • 待量化数据（64）: to_be_quantized.dat • 要求矢量为2维, 码本尺寸为4，失真准则采用均方误差。 • http://www.commlab.cn: • 北京理工大学现代通信实验室» 开设课程 • 5月15日前将算法描述、源程序、结果及其分析(打包压缩)通过E-MAIL发送到 wangjing@bit.edu.cn

  22. 下 课

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