Local spectral analysis of images via the wavelet transform based on partial differential equations

We propose method for the local spectral analysis of images via the two-dimensional continuous wavelet transform with the Morlet wavelet based on its representation as a solution of the partial differential equation. It has been shown that a transformed function uniquely determines an initial value for the equation, i.e. a Cauchy problem is stated. Its solving implies that scale parameter a plays a role of “time variable” and two translation parameters bx, by are spatial independent variables. Numerical examples are given to illustrate the efficiency of the proposed method.

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