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Results on principal component filter banks: colored noise suppression and existence issues

Akkarakaran, Sony and Vaidyanathan, P. P. (2001) Results on principal component filter banks: colored noise suppression and existence issues. IEEE Transactions on Information Theory, 47 (3). pp. 1003-1020. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:AKKieeetit01

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Abstract

We have made explicit the precise connection between the optimization of orthonormal filter banks (FBs) and the principal component property: the principal component filter bank (PCFB) is optimal whenever the minimization objective is a concave function of the subband variances of the FB. This explains PCFB optimality for compression, progressive transmission, and various hitherto unnoticed white-noise, suppression applications such as subband Wiener filtering. The present work examines the nature of the FB optimization problems for such schemes when PCFBs do not exist. Using the geometry of the optimization search spaces, we explain exactly why these problems are usually analytically intractable. We show the relation between compaction filter design (i.e., variance maximization) and optimum FBs. A sequential maximization of subband variances produces a PCFB if one exists, but is otherwise suboptimal for several concave objectives. We then study PCFB optimality for colored noise suppression. Unlike the case when the noise is white, here the minimization objective is a function of both the signal and the noise subband variances. We show that for the transform coder class, if a common signal and noise PCFB (KLT) exists, it is, optimal for a large class of concave objectives. Common PCFBs for general FB classes have a considerably more restricted optimality, as we show using the class of unconstrained orthonormal FBs. For this class, we also show how to find an optimum FB when the signal and noise spectra are both piecewise constant with all discontinuities at rational multiples of π.


Item Type:Article
Additional Information:© Copyright 2001 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 December 13, 1999; revised September 29, 2000. This work was supported in part by the National Science Foundation under Grant MIP 0703755. The material in this paper was presented in part at the IEEE Workshop on Signal Processing Advances in Wireless Communications, Annapolis, MD, May 1999.
Subject Keywords:Filter bank (FB), majorization, noise suppression, optimal basis, principal component
Issue or Number:3
Record Number:CaltechAUTHORS:AKKieeetit01
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:AKKieeetit01
Alternative URL:http://dx.doi.org/10.1109/18.915656
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1283
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:08 Jan 2006
Last Modified:02 Oct 2019 22:41

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