Wavelet transform and diffusion equations: applications to the   processing of the "Cassini" spacecraft observations
  We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of this approach is that the initial data can be represented by non-uniform sample of an arbitrary node number. We apply the proposed method to the processing of the image of the Saturn A-ring obtained from the Cassini spacecraft. Also we have got via the wavelet transform using PDE, the local correlation coefficient of the signal and the harmonic function. 
E.B. Postnikov, A.Loskutov