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Suboptimality of the Karhunen-Loève transform for transform coding

Effros, Michelle and Feng, Hanying and Zeger, Kenneth (2004) Suboptimality of the Karhunen-Loève transform for transform coding. IEEE Transactions on Information Theory, 50 (8). pp. 1605-1619. ISSN 0018-9448. doi:10.1109/TIT.2004.831787.

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We examine the performance of the Karhunen-Loeve transform (KLT) for transform coding applications. The KLT has long been viewed as the best available block transform for a system that orthogonally transforms a vector source, scalar quantizes the components of the transformed vector using optimal bit allocation, and then inverse transforms the vector. This paper treats fixed-rate and variable-rate transform codes of non-Gaussian sources. The fixed-rate approach uses an optimal fixed-rate scalar quantizer to describe the transform coefficients; the variable-rate approach uses a uniform scalar quantizer followed by an optimal entropy code, and each quantized component is encoded separately. Earlier work shows that for the variable-rate case there exist sources on which the KLT is not unique and the optimal quantization and coding stage matched to a "worst" KLT yields performance as much as 1.5 dB worse than the optimal quantization and coding stage matched to a "best" KLT. In this paper, we strengthen that result to show that in both the fixed-rate and the variable-rate coding frameworks there exist sources for which the performance penalty for using a "worst" KLT can be made arbitrarily large. Further, we demonstrate in both frameworks that there exist sources for which even a best KLT gives suboptimal performance. Finally, we show that even for vector sources where the KLT yields independent coefficients, the KLT can be suboptimal for fixed-rate coding.

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Additional Information:“©2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.” Manuscript received April 25, 2002; revised November 6, 2003. Posted online: 2004-07-26. This material is based upon work supported in part by the National Science Foundation under Grants CCR-9909026, CCR-0073489, and CCR-0105734, an Intel equipment grant, the UCSD Center for Wireless Communications, and the Lee Center for Advanced Networking. The material in this paper was presented in part at the IEEE Data Compression Conference, Snowbird, UT, March 2003. The authors are grateful to the anonymous reviewers and the Associate Editor Ram Zamir for their detailed suggestions and comments and to Vivek Goyal and Tamás Linder for pointing out citations [10] and [8], respectively.
Subject Keywords:Bit allocation, lossy source coding, quantization, transform coding; source code design; transforms for source coding
Issue or Number:8
Record Number:CaltechAUTHORS:EFFieeetit04b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1332
Deposited By: Archive Administrator
Deposited On:10 Jan 2006
Last Modified:08 Nov 2021 19:09

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