Image assimilation by geometric wavelet based reaction-diffusion equation
Jianwei Ma · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
Denoising is always a challenge problem in natural image and geophysical data processing. From the point of view of data assimilation, in this paper we consider the denoising of texture images in a scale space using a geometric wavelet based nonlinear reaction-diffusion equation, in which a curvelet shrinkage is used as a regularization of the diffusivity to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as a pseudo-observation in the reaction for enhancement of interesting oriented textures. We named the general framework as image assimilation. The goal of the image assimilation is to link together these rich information such as sparse constraint in multiscale geometric space in order to retrieve the state of images. As a byproduct, we proposed a 2D wavelet-inspired numerical scheme for solving of the nonlinear diffusion. Experimental results show the performance of the proposed model for texture-preserving denoising and enhancement.