Research On Image Denoising Based On Wavelet Analysis And Partial Differential Equations

Image is a comprehensive science subject, The successful application of the subject has agreat relationship with many related subject,especially with the subject of mathematics has greatrelevance. In image processing, image restoration in both image denoising or imageoptimization.Ultimately,it can be attributed to a related theoretical problem of a subject,especially associated with the knowledge of mathematical theory. In recent years, as people onthe reunderstanding and reuse of the traditional mathematical theory, new mathematical theoryget gradually developed and become mature. Mainly it is represented by the wavelet analysis andpartial differential equations as the mathematical tools, actively in the field of image processingin various research.The combination of Wavelet analysis and partial differential equations in thefield of image denoising has a good foundation for the establishment of a image scientific systemand broad application prospects.Denoising effect good or not directly impact on the effect of subsequent image processing.This thesis mainly use wavelet analysis and partial differential equations as the main tool for theproblems of image denoising studied in image processing,and explore their combined applicationof image denoising problem. The main content and the achievements of the research are asfollows：(1) Researched wavelet theoretical knowledge and Wavelet analysis method characteristicsin image denoising. Summarized several of the continuous wavelet transform based on imagedenoising, mainly focusing on two kinds of wavelet threshold denoising method, that is the hardthreshold and soft threshold, And to compare them, combined with the advantages, proposed asemi-hard and semi-soft thresholding.(2) Researched several of model of anisotropic diffusion denoising based on the partialdifferential equation, the spreading noise can be a good noise suppression. Studying these typesof models are Linear filtering, TV models and P-M equation model. Comparing these types ofmodels could obtained that using PM-equation model can be achieved not only protect the edge and remove noise,but also relatively high signal to noise ratio.(3) Researched the links between wavelet analysis and partial differential equations. that is,Besov space. it is the link between these models in the partial differential equations and thewavelet threshold. And compared the wavelet denoising in the Besov space to the waveletdenoising in Spatial domain,it can effectively improve the denoising results. And studied waveletedge detection and wavelet reconstruction.(4) Based on the presented theory above, presented a new image denoising algorithm, that isP-M equation model which has the advantage of protected by the edge in partial differentialequations low-frequency denoising,then reconstructed low and high frequency part ofwavelet,finaly low and high frequency part of wavelet.