Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm

Nicki Holighaus; Günther Koliander; Zdeněk Průša; Luis Daniel Abreu

We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a byproduct of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only coefficients. The cornerstone of our analysis is an expression of the partial derivatives of the continuous WT, which results in phase-magnitude relationships similar to the short-time Fourier transform setting and valid for the generalized family of Cauchy wavelets. We show that the existence of such relations is equivalent to analyticity of the WT up to a multiplicative weight and a scaling of the mother wavelet. The implementation of the new phaseless reconstruction method is considered in detail and compared to previous methods. It is shown that the proposed method provides significant performance gains and a great flexibility regarding accuracy versus complexity. In addition, we discuss the relation between scalogram reassignment operators and the wavelet transform phase gradient and present an observation on the phase around zeros of the WT.

SPS on Twitter

  • On 15 September 2022, we are excited to partner with and to bring you a webinar and roundtable,…
  • The SPS Webinar Series continues on Monday, 22 August when Dr. Yu-Huan Wu and Dr. Shanghua Gao present “Towards Des…
  • CALL FOR PAPERS: The IEEE/ACM Transactions on Audio, Speech, and Language Processing is now accepting submissions f…
  • DEADLINE EXTENDED: The IEEE Journal of Selected Topics in Signal Processing is now accepting submissions for a Spec…
  • Our Information Forensics and Security Webinar Series continues on Tuesday, 23 August when Dr. Anderson Rocha prese…

SPS Videos

Signal Processing in Home Assistants


Multimedia Forensics

Careers in Signal Processing             


Under the Radar