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.

Table of Contents:

TSP Featured Articles

SPS on Twitter

  • We are happy to welcome Prof. Jiebo Luo as the new Editor-in-Chief of IEEE Transactions on Multimedia beginning in…
  • wants your talents! Our tenure-track position in engineering applications of information and data science a…
  • If you’re missing out on , don’t worry - we’ll be tweeting all week long. Follow along with us to see the action!

SPS Videos

Signal Processing in Home Assistants


Multimedia Forensics

Careers in Signal Processing             


Under the Radar