On Parseval wavelet frames via Multiresolution Analyses
A. San Antolin
TL;DR
This paper characterizes all Parseval wavelet frames derived from a specific frame multiresolution analysis, expanding understanding of wavelet frame construction using extension principles under certain Fourier transform conditions.
Contribution
It provides a comprehensive description of all Parseval wavelet frames linked to a given frame multiresolution analysis, utilizing a version of the Unitary and Oblique Extension Principles.
Findings
Complete characterization of Parseval wavelet frames from a frame multiresolution analysis.
Extension principles applied under Fourier transform continuity assumptions.
Framework for constructing wavelet frames with desired properties.
Abstract
We give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These results are based on a version of Unitary Extension Principle and Oblique Extension Principle with the assumption that the origin is a point of approximate continuity of the Fourier transform of the involved refinable functions.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Image and Signal Denoising Methods · Digital Filter Design and Implementation