Study On Image Processing Based On Variation And Partial Differential Equations

The theory based on variation and partial differential equation which used for imageprocessing has achieved developments greatly. In recent years, partial differential equationmethod has been widely used in image processing areas, especially in image restoration,image segmentation and edge detection, and image reconstruction areas. Partial differentialequations, which has good theoretical basis and high degree of flexibility has been widelyused in remote sensing, communication technology, medical diagnosis, aerospace and otherfields.The image processing based on variation and partial differential equations is studied in thisdissertation. Firstly, the dissertation introduces the research background and significance, thehistory and development of variation and partial differential equations, and then analysis andsummarizes the mainstream models of partial differential equation.Secondly, a variational image adaptive denoising model based on human visual system isproposed by introducing control parameter p which can determine the diffusion intensity tototal variation model. The model can adaptively select the value of parameter p accordingto human visual system noise visibility value of each pixel which makes diffusion intensityclose to edges smaller than those far away from edges. For this method is more consistentwith human perception, human eyes can perceive the improvement of image qualityintuitively. Numerical experiments show that the proposed method can overcome staircaseeffect, remove the noise while preserving significant image details and better performance hasbeen achieved.Thirdly, the dissertation investigates the relationship between local gradient and imagefrequency, gives the definition of image frequency based on local gradient, and then proposesa novel image frequency total variation (IFTV) method by introducing image frequencyinstead of gradient in traditional ROF model. Compared with other existing approaches, theIFTV model has a strong ability of denoising and can describe the image edge features andsmooth area more accurately.Lastly, according to the research of wavelet transforms, the dissertation proposes an imagedenoising method based on the modulus of wavelet transforms. The model can adaptivelychoose the denoising intensity according to the modulus of wavelet transforms. Numerical experiments show that the method can remove the noise while preserving significant imagedetails.