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arXiv · 1103.3317

Uniqueness for the continuous wavelet transform

H. -Q. Bui·R. S. Laugesen
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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.

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H. -Q. Bui, R. S. Laugesen. 2011-03-16. Uniqueness for the continuous wavelet transform. https://arxiv.org/abs/1103.3317

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