PDE Approaches to Evaluation of the Continuous Wavelet Transform
The talk presents an approach to calculate the CWT as a solution of a partial differential equations (PDE). This method uses the following facts:
1) The wavelet transform based on the Gaussian family of wavelets and Morlet wavelets admits specific PDEs.
2) It is possible to represent these wavelets as a combination of Dirac delta-functions in the limit of zero scale. Thus, the problem of calculating the wavelet transform is reduced to the problem of the solving the Cauchy problem for PDE. The advantages of this approach will be discussed. In the second part of the talk results of some applications (in Astrophysics and Biophysics) will be presented.