Tight wavelet frames for irregular multiresolution analysis
نویسندگان
چکیده
An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourierdomain 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. © 2007 Elsevier Inc. All rights reserved.
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