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2001•Numerical Functional Analysis and OptimizationRequires access

BIORTHOGONAL UNCONDITIONAL BASES OF COMPACTLY SUPPORTED MATRIX VALUED WAVELETS

Konstantinos Slavakis, Isao Yamada

Open publisher page 7 citations

Abstract

In this paper, we introduce the concept of biorthogonal matrix valued wavelets. We elaborate on perfect reconstruction matrix filter banks which are assembled by matrix FIR fllters and we deduce that the resulting matrix valued wavelet functions have compact support. Moreover, we form biorthogonal unconditional bases for the space of matrix valued signals. To validate the theory, a class of biorthogonal and orthonormal matrix valued wavelets are given. The connection of the present scheme with the theory of multiwavelets are also explored.

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What this paper is about

In this paper, we introduce the concept of biorthogonal matrix valued wavelets. We elaborate on perfect reconstruction matrix filter banks which are assembled by matrix FIR fllters and we deduce that the resulting matrix valued wavelet functions have compact support. Moreover, we form biorthogonal unconditional bases for the space of matrix valued signals. To validate the theory, a class of biorthogonal and orthonormal matrix valued wavelets are given. The connection of the present scheme with the theory of multiwavelets are also explored.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we introduce the concept of biorthogonal matrix valued wavelets. We elaborate on perfect reconstruction matrix filter banks which are assembled by matrix FIR fllters and we deduce that the resulting matrix valued wavelet functions have compact support. Moreover, we form biorthogonal unconditional bases for the space of matrix valued signals. To validate the theory, a class of biorthogonal and orthonormal matrix valued wavelets are given. The connection of the present scheme with the theory of multiwavelets are also explored.

Key concepts: Biorthogonal system, Mathematics, Wavelet, Orthonormal basis, Matrix (chemical analysis), Pure mathematics, Biorthogonal wavelet, Connection (principal bundle)

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