Sobolev Spaces Of Negative Index Of Adaptive Multi-scale Denoising Model And Algorithm

Image denoising models and algorithms are the core contents of image processing, It is important to preserve the fine scale features in the processing of denoising. New models and algorithms for image denoising will provide new methods and tools to promote these areas of research and development, such as image segmentation, image restoration, super-resolution reconstruction and will be widely used in military surveillance, video surveillance, remote sensing imaging, medical imaging, fingerprint recognition, iris recognition and other fields .In this paper, the existed image denoising models are summarized at first, particularly the ROF model which can preserve edges and the models in negative Sobolev space which are propitious to preserve finer scale features are summarized, compared and analyzed. Based on these works, the adaptive multi-scale model and algorithm for image denoising in negative Sobolev space well be talked in this paper.Firstly, for the multi-scale model in negative Sobolev space using the equivalent norm of negative Sobolev space based on orthogonal wavelet decomposition, the mechanism and effect on noise removing and texture preserving of the space parameters are analyzed. An alternating projection algorithm for the multi-scale model is proposed, and finally we compare and analyze the proposed multi-scale model and algorithm by numerical experimentsSecondly, the choice of parameters in multi-scale model is studied. Based on the Euler-Lagrange equation of the multi-scale model and making use of the statistics characteristics such as the local variance of image and variance estimates of noise, we give an adaptive selection method of the regularization parameter. Based on the relationship between modulus maxima of wavelet coefficients and the regularity of function, we give an adaptive selection method of space parameters of Sobolev space. Based on these works, we study an adaptive multi-scale variation model and algorithm in negative Sobolev space. Numerical experiments show that the adaptive multi-scale variation model and algorithm in the negative Sobolev space can distinguish between image texture region and non-texture regions. The proposed method can remove noise effectively in non-texture regions of image. Using the proposed method, the PSNR the denoised image has been improved significantly and the denoised image has a good visual effect.