DocumentCode :
1464850
Title :
Results on principal component filter banks: colored noise suppression and existence issues
Author :
Akkarakaran, Sony ; Vaidyanathan, P.P.
Author_Institution :
Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA
Volume :
47
Issue :
3
fYear :
2001
fDate :
3/1/2001 12:00:00 AM
Firstpage :
1003
Lastpage :
1020
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
Keywords :
Wiener filters; channel bank filters; circuit optimisation; digital filters; filtering theory; principal component analysis; search problems; transform coding; white noise; colored noise suppression; compaction filter design; compression; concave function; concave objectives; filter optimization; minimization; noise spectra; noise subband variance; optimization search spaces; orthonormal filter banks; piecewise constant; progressive transmission; signal spectra; subband Wiener filtering; subband variances; transform coder; unconstrained orthonormal filter banks; variance maximization; white-noise suppression; Channel bank filters; Colored noise; Compaction; Filter bank; Finite impulse response filter; Geometry; Karhunen-Loeve transforms; Signal processing; White noise; Wiener filter;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.915656
Filename :
915656
Link To Document :
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