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Nonuniform principal component filter banks: definitions, existence, and optimality

Akkarakaran, Sony J. and Vaidyanathan, Palghat P. (2000) Nonuniform principal component filter banks: definitions, existence, and optimality. In: Wavelet Applications in Signal and Image Processing VIII. Proceedings of SPIE. No.4119. Society of Photo-optical Instrumentation Engineers (SPIE) , Bellingham, WA, pp. 768-779. ISBN 9780819437648. http://resolver.caltech.edu/CaltechAUTHORS:20181204-132725682

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Abstract

The optimality of principal component filter banks (PCFBs) for data compression has been observed in many works to varying extents. Recent work by the authors has made explicit the precise connection between the optimality of uniform orthonormal filter banks (FBs) and the principal component property: The PCFB is optimal whenever the minimization objective is a concave function of the subband variances of the FB. This gives a unified explanation of PCFB optimality for compression, denoising and progressive transmission. However not much is known for the case when the optimization is over a class of nonuniform Fbs. In this paper we first define the notion of a PCFB for a class of nonuniform orthonormal Fbs. We then show how it generalizes the uniform PCFBs by being optimal for a certain family of concave objectives. Lastly, we show that existence of nonuniform PCFBs could imply severe restrictions on the input power spectrum. For example, for the class of unconstrained orthonormal nonuniform Fbs with any given set of decimators that are not all equal, there is no PCFB if the input spectrum is strictly monotone.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1117/12.408666DOIArticle
ORCID:
AuthorORCID
Vaidyanathan, Palghat P.0000-0003-3003-7042
Additional Information:© 2000 Society of Photo-Optical Instrumentation Engineers (SPIE). Work supported in parts by the National Science Foundation under Grant MIP 0703755, and by Microsoft Research, Redmond, WA.
Funders:
Funding AgencyGrant Number
NSFMIP-0703755
Microsoft ResearchUNSPECIFIED
Subject Keywords:Principal Component Filter-Banks, nonuniform filter banks, optimal filter banks, majorization, convex objectives
Record Number:CaltechAUTHORS:20181204-132725682
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181204-132725682
Official Citation:Sony J. Akkarakaran, Palghat P. Vaidyanathan, } "Nonuniform principal component filter banks: definitions, existence, and optimality", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408666; https://doi.org/10.1117/12.408666
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91485
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:05 Dec 2018 16:14
Last Modified:05 Dec 2018 16:14

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