On vector Karhunen-Loeve transforms and optimal vector transforms

Author

Xia, Xiang-Gen ; Suter, Bruce W.

Author_Institution

Dept. of Electr. & Comput. Eng., US Air Force Inst. of Technol., Wright-Patterson AFB, OH, USA

Volume

5

Issue

4

fYear

1995

fDate

8/1/1995 12:00:00 AM

Firstpage

372

Lastpage

374

Abstract

We first prove that the vector Karhunen-Loeve (VKL) transform for any finite many vector-valued signal, x₁,···,x_L, exists. The VKL transform is equivalent to the scalar KL transform for the scalar-valued signal X=(x₁^T,···,x_L^T)^T. Based on VKL transforms, we provide a necessary and sufficient condition for the existence of the optimal vector transforms (unitary). With the condition, one can see that the optimal unitary vector transforms do not exist in most cases, and therefore needs to use suboptimal unitary vector transforms. We then prove that the optimal nonunitary vector transform for x₁,···,x_L exists when all eigenvalues of the correlation matrix of the signal X are nonzero. We formulate the optimal vector transforms via the VKL transforms

Keywords

correlation methods; eigenvalues and eigenfunctions; matrix algebra; signal processing; transforms; vectors; correlation matrix; eigenvalues; finite many vector-valued signal; necessary and sufficient condition; optimal unitary vector transforms; optimal vector transforms; scalar KL transform; scalar-valued signal; suboptimal unitary vector transforms; vector Karhunen-Loeve transforms; Bit rate; Eigenvalues and eigenfunctions; Filter bank; Karhunen-Loeve transforms; Military computing; Sufficient conditions; Transform coding; Vector quantization; Wavelet transforms;

fLanguage

English

Journal_Title

Circuits and Systems for Video Technology, IEEE Transactions on

Publisher

ieee

ISSN

1051-8215

Type

jour

DOI

10.1109/76.465094

Filename

465094