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Storath, M.* ; Demaret, L. ; Massopust, P.*

Signal analysis based on complex wavelet signs.

Appl. Comput. Harmon. Anal. 42, 199-223 (2015)
Open Access Green as soon as Postprint is submitted to ZB.
We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of the signs of a signal's complex wavelet coefficients. We show that the signature equals zero at sufficiently regular points of a signal whereas at salient features, such as jumps or cusps, it is non-zero. At such feature points, the orientation of the signature in the complex plane can be interpreted as an indicator of local symmetry and antisymmetry. We establish that the signature rotates in the complex plane under fractional Hilbert transforms. We show that certain random signals, such as white Gaussian noise and Brownian motions, have a vanishing signature. We derive an appropriate discretization and show the applicability to signal analysis.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Complex Wavelets ; Feature Detection ; Hilbert Transform ; Phase ; Randomized Wavelet Coefficients ; Salient Feature ; Signal Analysis ; Wavelet Signature; Zero-crossings; Besov-spaces; Transform; Oscillation; Images; Phase
ISSN (print) / ISBN 1063-5203
e-ISSN 1096-603X
Quellenangaben Volume: 42, Issue: 2, Pages: 199-223 Article Number: , Supplement: ,
Publisher Academic Press
Publishing Place San Diego, Calif. [u.a.]
Reviewing status Peer reviewed