Miroslav Andrle and Laura Rebollo-Neira 2008 J. Phys. A: Math. Theor. 41 172001 doi:10.1088/1751-8113/41/17/172001
From cardinal spline wavelet bases to highly coherent dictionaries
FREE ARTICLEMiroslav Andrle and Laura Rebollo-Neira
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Wavelet families arise by scaling and translations of a prototype function, called the mother wavelet. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact interval, the identical effect can be achieved without changing the wavelet scale but reducing the translation parameter. By such a procedure we generate a redundant frame, called a dictionary, spanning the same spaces as a wavelet basis but with wavelets of broader support. We characterize the correlation of the dictionary elements by measuring their 'coherence' and produce examples illustrating the relevance of highly coherent dictionaries to problems of sparse signal representation.
- PACS
- MSC
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81R30 Coherent states (See also 22E45); squeezed states (See also 81V80)
- Subjects
- Dates
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Issue 17 (2 May 2008)
Received 24 January 2008, in final form 11 March 2008
Published 15 April 2008
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From cardinal spline wavelet bases to highly coherent dictionaries
Miroslav Andrle and Laura Rebollo-Neira 2008 J. Phys. A: Math. Theor. 41 172001
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