Research On Image Resolution Enhancement Based On Partial Differential Equations

The partial differential equation(PDE)is a important branch of the methods for digital image processing.This paper studied on the application of the PDE in the image resolution enhancement(image enlargement).In the paper the processing image is from the photoelectric conversion device and the lowpass prefilter must be considering in the Degenerated model of the image.The image resolution enhancement algorithms are based on the research of high order PDE models,forward and backward diffusion model and complex diffusion model;the non-local PDE model is introduced and the PDE coupled directly to non-local means filters is provided.The corresponding resolution enhancement algorithms are proposed which are based on the non-local PDE model and PDE coupled by non-local means filters.The simulation proved that the algorithms of image resolution enhancement have better effect.The biorthogonal filter of the low pass filter with respect to sampling lattice in the Degenerated model and the low pass filter constitute a biorthogonal projection based on Laplacian Pyramid through which the constraint of the Degenerated model is realized.A framework of the image resolution enhancement algorithms is proposed,using the biorthogonal projection operator and nonlinear enhancement based on PDE.In the frame,the initial image which is interpolated linearly by the biorthogonal filter is nonlinearly processed by the PDE that is processed through regularization,and the regularized image is processed by the biorthogonal projection in order to make the image is fulfilled the Degenerated model completely.Under the frame,the following algorithms are proposed.Firstly,a method of the image enlargement is proposed that combines the isotropic forth order PDE and the improved TV model based on the analysis of the characteristic of forth order PDE avoiding the staircase effect;another method is that a anisotropic forth order PDE coupled to the improved TV model with the shock filters.The above two algorithms have the characteristic of faster computing speeding and more natural visual effect,therefore the algorithms are suit for natural scene image and photograph of human being.Secondly,based on the analysis of the forward and backward diffusion model,an improved model is performed for the image resolution enhancement and corresponding method is proposed.Based on the improved forward and backward model,a hybrid method combined the above method and the improved TV model coupling with the shock filters is provided,on the premise of enhancing the stronger edges,the method is able to enhance resolution of the weak edge,therefore the methods are suit for enlargement of the image with more edges and texture.Thirdly,the complex diffusion model is studied and improved.The improvements are performed in the diffusion coefficient through using a local variance to constrain the thareshold value and the imaginary part of the diffused image is divided by the diffusion time to avoid the linear diffusion at the beginning time of the diffusion.Based on the improved nonlinear complex diffusion coupled to the improved complex shock filters,the enlargement methods of noiseless and noise image are provided respectively.The method of noiseless image enlargement sharps the edges,containing the advantage of accurately locating the edges and preserving the ramp structure;The method of noise image enlargement enhances the edges of the image and remove the noise.The complex diffusion methods are proper for the image which requires accurate location of the edges and for the noise image.Lastly,based on the analysis of the non-local PDE,a algorithm of image enlargement is proposed under the biorthogonal projection,using the Bregman iteration.Another image enlargement algorithm is provided based on the non-local means filter coupled to the PDE containing the advantage of improved complex diffusion which sharps the edges and accurately locates the edges and the advantage of the non-local means filters which enhance the recurrence structures effectively.Comparing to the methods of above,the methods coupling with non-local ideal have more intensive computation,but the methods,especially the method of improved complex diffusion coupled to non-local means filter,have better effect of resolution enhancement for images with repeated structure and strong edges.