Partial Differential Equations as a Tool for Evaluation of the Continuous Wavelet Transform, pp. 1-36
Authors: (Eugene B. Postnikov, Humboldt Univ., Berlin/Kursk Univ.)
Abstract: The presented review is dedicated to the consideration of the Continuous Wavelet tarsnsform from the diffusion signal and image processing point of view. Such an approach is based on the consideration of diffusion smoothing via the solution of proper partial diferential equations. Within this group of methods the real and complex wavelet transform with the wavelets of Gauss and Morlet families are considered. Especial attention is concentrated on the variety of numerical examples considering the processing of regular and irregular (random samples, chaotic ODE solutions etc.) signals. All of them are graphically illustrated.