BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Operator-Like Wavelet Bases of L2(ℝd)

I. Khalidov, M. Unser, J.P. Ward

The Journal of Fourier Analysis and Applications, vol. 19, no. 6, pp. 1294-1322, December 2013.

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. 

@ARTICLE(http://bigwww.epfl.ch/publications/khalidov1301.html,
AUTHOR="Khalidov, I. and Unser, M. and Ward, J.P.",
TITLE="Operator-Like Wavelet Bases of $L_{2}({\mathbb{R}}^{d})$",
JOURNAL="The Journal of {F}ourier Analysis and Applications",
YEAR="2013",
volume="19",
number="6",
pages="1294--1322",
month="December",
note="")

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