Structured vector quantization using linear transforms

This paper presents novel structured vector quantization (VQ) techniques characterized by the use of linear transformations for the input VQ. The first technique is called the affine transformations VQ, in which the quantized vector is formed by adding the transformed outputs of a multistage codebook rather than just adding the outputs of the stages as in regular multistage vector quantization (MSVQ). The name of the VQ technique comes from the fact that in the two-stage case, the quantized vector is obtained as the result of an affine transformation. This technique can be viewed as a generalized form of MSVQ. If the transformations are constrained to be the identity transformation, this technique becomes identical to the regular MSVQ. The transformations in the introduced technique are selected from a family of linear transformations, represented by a codebook of matrices. In order to I reduce the memory required for storing the matrices, the paper discusses a second technique called scaled rotation matrices VQ, where matrices are constrained to be scaled rotation matrices. Since rotation matrices can be stored by just storing the corresponding rotation angles, this approach enables efficient storage of linear transforms. The design algorithms are based on joint optimization of the linear transformation and the stage codebooks. Experimental results based on speech spectrum quantization show that the proposed VQ techniques outperform the MSVQ of the same bit rate.