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Abstract. In this paper, a region-based shock-diffusion equation is presented for image denoising and edge sharpening. An image is divided into three-type different regions according to image features: edges, textures and details, and flat areas. For edges, a shock-type backward diffusion is performed in the gradient direction to the isophote line (edge), incorporating a forward diffusion in the isophote line direction; while for textures and details, a soft backward diffusion is done to enhance image features preserving a natural transition. Moreover, an isotropic diffusion is used to smooth flat areas simultaneously. Finally, a shock capturing scheme with a special limiter function is developed to speed the process with numerical stability. Experiments on real images show that this method produces better visual results of the enhanced images than some related equations.

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SUMMARYA group of new Saul'yev-type asymmetric difference schemes to approach the dispersive equation are given here. On the basis of these schemes, an alternating difference scheme with intrinsic parallelism for solving the dispersive equation is constructed. The scheme is unconditionally stable. Numerical experiments show that the method has high accuracy.