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Generalized Triangular Decomposition in Transform Coding

Weng, Ching-Chih and Chen, Chun-Yang and Vaidyanathan, P. P. (2010) Generalized Triangular Decomposition in Transform Coding. IEEE Transactions on Signal Processing, 58 (2). pp. 566-574. ISSN 1053-587X.

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A general family of optimal transform coders (TCs) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang This family includes the Karhunen-Loeve transform (KLT) and the generalized version of the prediction-based lower triangular transform (PLT) introduced by Phoong and Lin as special cases. The coding gain of the entire family, with optimal bit allocation, is equal to that of the KLT and the PLT. Even though the original PLT introduced by Phoong is not applicable for vectors that are not blocked versions of scalar wide sense stationary processes, the GTD-based family includes members that are natural extensions of the PLT, and therefore also enjoy the so-called MINLAB structure of the PLT, which has the unit noise-gain property. Other special cases of the GTD-TC are the geometric mean decomposition (GMD) and the bidiagonal decomposition (BID) transform coders. The GMD-TC in particular has the property that the optimum bit allocation is a uniform allocation; this is because all its transform domain coefficients have the same variance, implying thereby that the dynamic ranges of the coefficients to be quantized are identical.

Item Type:Article
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Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© 2010 IEEE. Manuscript received March 16, 2009; accepted August 18, 2009. First published September 09, 2009; current version published January 13, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Marcelo G. S. Bruno. This work was supported in part by the Office of Naval Research under Grant N00014-08-1-0709 and the National Science Council, Republic of China, under Taiwan TMS scholarship 94-2-A-018.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-08-1-0709
National Science Council (Taipei)94-2-A-018
Subject Keywords:Bit allocation; generalized triangular decomposition; geometric mean decomposition; linear prediction; majorization; Schur convexity
Issue or Number:2
Record Number:CaltechAUTHORS:20100208-082037409
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17409
Deposited By: Tony Diaz
Deposited On:11 Feb 2010 17:06
Last Modified:20 Nov 2020 23:47

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