Tight wavelet frames for irregular multiresolution analysis |
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Authors: | Maria Charina Joachim Stckler |
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Institution: | aFachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany |
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Abstract: | An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourier-domain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of bounded L-shaped domains, refinements of subdivision surfaces around irregular vertices, and nonstationary subdivision. We consider the case of nonnegative refinement coefficients and develop a fully local construction method for tight frames. Especially, in the shift-invariant setting, our construction produces the same tight frame generators as the Unitary Extension Principle. |
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Keywords: | Wavelet frames Unitary Extension Principle Irregular MRA Nonstationary MRA |
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