Uniqueness for the continuous wavelet transform
Classical Analysis and ODEs
2011-03-18 v1
Abstract
Injectivity of the continuous wavelet transform acting on a square integrable signal is proved under weak conditions on the Fourier transform of the wavelet, namely that it is nonzero somewhere in almost every direction. For a bounded signal (not necessarily square integrable), we show that if the continuous wavelet transform vanishes identically, then the signal must be constant.
Keywords
Cite
@article{arxiv.1103.3317,
title = {Uniqueness for the continuous wavelet transform},
author = {H. -Q. Bui and R. S. Laugesen},
journal= {arXiv preprint arXiv:1103.3317},
year = {2011}
}
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7 pages