I'm new to multi scale transformations. I was wondering if there is a special case where wave atom converts to curvelet transform? Can I use wave atom parameters to have curvelet properties?

  • $\begingroup$ Thank you for this question. A natural interrogation would be: why would you want to use wave atoms instead of curvelets, and what curvelet properties are you interested in? $\endgroup$ – Laurent Duval Jul 24 '17 at 8:45
  • $\begingroup$ @LaurentDuval Because I could not handle 3D curvelet code to use under windows 64-bit and MATLAB environment. $\endgroup$ – M.Jalali Jul 25 '17 at 4:54
  • 1
    $\begingroup$ Understood. Being closer to packets, and less elongated, they may behave a little differently. However, the reduced sparsity of wave atoms can be useful to tune in practice $\endgroup$ – Laurent Duval Jul 25 '17 at 8:18

In their 2007 paper, Wave atoms and sparsity of oscillatory patterns, Demanet and Ying draw connections between wave atoms and other types of wavelets:

Wave atoms,

In plain words:

We introduce “wave atoms” as a variant of 2D wavelet packets obeying the parabolic scaling wavelength

with a better spatial localization, meant for texture analysis. Their choice ($\alpha=\beta=1/2$) was a compromise between two types of sparsification (preservation under warping, sparsity of oscillations). Yet, one could built different collections of such wave packets, with alternative choices of $\alpha$ and $\beta$, bridging the gap between the different transform choices.

Yet, their natural redundancy is 2, with an orthonormal variant, and a complex one with redundancy 4, different from that of the curvelets. So I do no think they can be used as a special case of curvelets.

A tutorial on 2D geometric transformation can be obtain in A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity, 2011.

| improve this answer | |
  • $\begingroup$ Thank you for your response, I meant "is there a parameter in wave atom formulation to convert it to curvelet transform?" $\endgroup$ – M.Jalali Jul 25 '17 at 5:05
  • 1
    $\begingroup$ So the global answer is no. From the paper, this is a fixed transformation (ie non-parametric) $\endgroup$ – Laurent Duval Jul 25 '17 at 8:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.