Operator-Like Wavelet Bases of L-2(R-d)

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a stochastic model: signals are tempered distributions such that the application of a whitening (differential) operator results in a realization of a sparse white noise. Using wavelets constructed from these operators, the sparsity of the white noise can be inherited by the wavelet coefficients. In this paper, we specify such wavelets in full generality and determine their properties in terms of the underlying operator.


Published in:
Journal Of Fourier Analysis And Applications, 19, 6, 1294-1322
Year:
2013
Publisher:
New York, Springer Birkhauser
ISSN:
1069-5869
Keywords:
Laboratories:




 Record created 2014-01-09, last modified 2018-09-13


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