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Uniqueness for the continuous wavelet transform

By H. -Q. Bui and R. S. Laugesen

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.Comment: 7 page

Topics: Mathematics - Classical Analysis and ODEs, 42C40
Year: 2011
OAI identifier: oai:arXiv.org:1103.3317
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