Abstract
This work proposes an evolution-operator-based single-time-step method for image and signal processing. The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. From the point of image/signal processing, the LSEK gives rise to a family of lowpass filters. These filters contain controllable time delay and amplitude scaling. The new evolution operator-based method is constructed by pointwise adaptation of anisotropy to the coefficients of the LSEK. The Perona-Malik-type of anisotropic diffusion schemes is incorporated in the LSEK for image denoising. A forward-backward diffusion process is adopted to the LSEK for image deblurring or sharpening. A coupled PDE system is modified for image edge detection. The resulting image edge is utilized for image enhancement. Extensive computer experiments are carried out to demonstrate the performance of the proposed method. The major advantages of the proposed method are its single-step solution and readiness for multidimensional data analysis.
Highlights
Image denoising, restoration, edge detection, and enhancement are fundamental problems in image processing, computer vision, and artificial intelligence [1]
Partial-differential-equation- (PDE-) based approaches have great potential for the processing of images and multidimensional data because they can be made to be systematic and automatic for large-scale high-dimensional image data. Research in this direction is often hindered by problems in parameter optimization and extra computing time
By utilizing a local spectral evolution kernel (LSEK) that analytically integrates a class partial differential equations (PDEs), we show that a number of image processing operations, such as image deblurring, denoising, edge detection, and enhancement, can be effectively carried out in a single step of time integration
Summary
Restoration, edge detection, and enhancement are fundamental problems in image processing, computer vision, and artificial intelligence [1]. More sophisticated approaches, including variational methods, curvature, and active contours, have been extensively explored in the literature [21,22,23,24,25,26] Another problem with the original Perona-Malik equation concerns its efficiency in noisy removing and image enhancement. This problem was addressed by Wei [20] by introducing high-order edge-controlled diffusion operators. The second type of control was proposed by Wei and Jia [35] to stop the time evolution of their couple edge detection equations based on the difference in variance of two evolving images.
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