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Analysis of singularities from modulus maxima of complex wavelets

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3 Author(s)
Chun-Liang Tu ; Comput. & Commun. Res. Labs., Taiwan ; Wen-Liang Hwang ; Jinn Ho

Complex-valued wavelets are normally used to measure instantaneous frequencies, while real wavelets are normally used to detect singularities. We prove that the wavelet modulus maxima with a complex-valued wavelet can detect and characterize singularities. This is an extension of the previous wavelet work of Mallat and Hwang on modulus maxima using a real wavelet. With this extension, we can simultaneously detect instantaneous frequencies and singularities from the wavelet modulus maxima of a complex-valued wavelet. Some results of singularity detection with the modulus maxima from a real wavelet and an analytic complex-valued wavelet are compared. We also demonstrate that singularity detection methods can be employed to detect the corners of a planar object.

Published in:

IEEE Transactions on Information Theory  (Volume:51 ,  Issue: 3 )