Uniqueness for the continuous wavelet transform

Details Uniqueness for the continuous wavelet transform Uniqueness for the continuous wavelet transform

2011-03-16

arxiv.org/abs/1103.3317v1

Mathematics

Classical Analysis and ODEs

7 pages

Scientific paper

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.

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