This work proposes an evolution-operator-based single-time-stepmethod for image and signal processing. The key component of theproposed method is a local spectral evolution kernel (LSEK) thatanalytically integrates a class of evolution partial differentialequations (PDEs). From the point of view PDEs, the LSEK providesthe analytical solution in a single time step, and is of spectralaccuracy, free of instability constraint. From the point ofimage/signal processing, the LSEK gives rise to a family oflowpass filters. These filters contain controllable time delay andamplitude scaling. The new evolution operator-based method isconstructed by pointwise adaptation of anisotropy to thecoefficients of the LSEK. The Perona-Malik-type of anisotropicdiffusion schemes is incorporated in the LSEK for image denoising.A forward-backward diffusion process is adopted to the LSEK forimage deblurring or sharpening. A coupled PDE system is modifiedfor image edge detection. The resulting image edge is utilized forimage enhancement. Extensive computer experiments are carried outto demonstrate the performance of the proposed method. The majoradvantages of the proposed method are its single-step solution andreadiness for multidimensional data analysis.
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