TL;DR
This paper explores the relationship between polynomial functions and refinement masks in wavelet theory, focusing on conversions and their uniqueness, expanding understanding beyond localized refinable functions.
Contribution
It investigates the conversions between refinement masks and polynomial functions and examines their uniqueness, providing new insights into polynomial refinability in wavelet theory.
Findings
Established conditions for conversions between masks and polynomials
Analyzed the uniqueness of polynomial refinability
Extended wavelet theory to include polynomial functions
Abstract
Research on refinable functions in wavelet theory is mostly focused to localized functions. However it is known, that polynomial functions are refinable, too. In our paper we investigate on conversions between refinement masks and polynomials and their uniqueness.
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