On criteria for periodic wavelet frame
Anastassia Gorsanova, Elena Lebedeva
TL;DR
This paper establishes comprehensive criteria for when a family of periodic wavelets forms a Parseval wavelet frame, extending existing principles and focusing on cases with polynomial refinable functions.
Contribution
It provides constructive necessary and sufficient conditions for periodic wavelet families to be Parseval frames, generalizing prior extension principles.
Findings
Criteria generalize unitary and oblique extension principles
Conditions are explicitly constructed for wavelet families
Special case analysis for polynomial refinable functions
Abstract
We provide constructive necessary and sufficient conditions for a family of periodic wavelets to be a Parseval wavelet frame. The criterion generalizes unitary and oblique extension principles. The case of one wavelet generator and refinable functions being trigonometric polynomials is discussed in details.
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Taxonomy
TopicsImage and Signal Denoising Methods · Image Processing Techniques and Applications