1 / 25

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

chappellm
Download Presentation

矢量量化 (Vector Quantization)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related