The Research On The Image Denoising Method Based On Total Variation

Total variation has good theoretical basis and high degree of flexibility, so the imageprocessing method which based on total variation combines mathematics and imageprocessing more closely. The image processing method based on total variation is that deduceone or a set of partial differential equations and solve the partial differential equations usingnumerical methods to get the numerical solution, and that is the final image.To avoid the problems in traditional image denoising algorithms such as that are prone toblur edges, difficult to preserve details, and so on, the nonlinear structure tensors are employedto calculate norm parameter since they can provide more information, and the absolute valuesof the second-order directional derivatives are employed to calculate fidelity term parametersince they can well distinguish details of images, a novel adaptive total variation denoisingalgorithm based on the second-order directional derivatives in the local coordinate system andnonlinear structure tensors is proposed in this thesis, which can improve the ability to avoidstaircase effect and preserve details. At the same time, the total variational denoising model isapplied in image inpainting, in order to restore the missing information in image such as thesmall targets, a novel adaptive total variation image inpainting hybrid model based on thesecond-order directional derivatives in the local coordinate system and is gave in this thesis,which can improve the ability of image inpainting, strengthen the diffusion behavior of flatarea and the approximation behavior of detail information.The properties and effects of the eigenvalues of nonlinear structure tensors are similar tothe absolute values of the second-order directional derivatives respectively while they are usedto detect an image. Both of them can detect the information about edges, corners and flatregions, but there are still differences between them because that nonlinear structure tensorsare produced by the first-order derivatives, and this causes some differences between abilitiesto reveal details. Although more information about edges and corners can be detected out bymeans of the eigenvalues of nonlinear structure tensors, they are not all effective. By contrast,less information about edges and corners can be detected out by means of absolute values ofthe second-order directional derivatives, but they are more accurate. Thus in the algorithm, thenonlinear structure tensors are employed to control the diffusion behavior of equation since they can provide more information. This is a way to enhance the ability of denoising. And theabsolute values of the second-order directional derivatives are employed to decide the fidelitydegree since they can well distinguish details of images. By constructing some correspondingcalculation rules, the norm parameters and fidelity term parameters can be calculated in properforms adaptively, and a proper balance between diffusion operation and fidelity operation areyielded. At the same time, to analyse the advantages and disadvantages of harmonic modeland adaptive inpainting model, the absolute values of the second-order directional derivativesare employed to decide the weight function since they can well distinguish details of images,in order to distribute of the proportion of hybrid inpainting model.In the numerical experiments, compare several typical algorithms with the new algorithm.Subjective and objective evaluations are given according to visual effect, peak signal to noiseratio and mean absolute error, respectively. Numerical results show that the new denoisingalgorithm can avoid staircase effect and preserve details effectively, the new image inpaintingalgorithm can approximate details well. At the same time, the new denoising algorithm canreach a higher peak signal to noise ratio and better denoising ability, the new image inpaintingalgorithm can reach a higher peak signal to noise ratio and better image inpainting ability.