On Multivariate Compactly Supported Bi-Frames |
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Authors: | Martin Ehler |
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Institution: | (1) Department of Mathematics and Computer Science, Hans-Meerwein-Strasse, 35032 Marburg, Germany |
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Abstract: | In this article, we construct compactly supported multivariate pairs of dual wavelet frames, shortly called bi-frames, for
an arbitrary dilation matrix. Our construction is based on the mixed oblique extension principle, and it provides bi-frames
with few wavelets. In the examples, we obtain optimal bi-frames, i.e., primal and dual wavelets are constructed from a single
fundamental refinable function, whose mask size is minimal w.r.t. sum rule order and smoothness. Moreover, the wavelets reach
the maximal approximation orderw.r.t. the underlying refinable function. For special dilation matrices, we derive very simple
but optimal arbitrarily smooth bi-frames in arbitrary dimensions with only two primal and dual wavelets. |
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Keywords: | |
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