The Research On The Image Denoising Method Based On The Total Variation Partial Differential Equations

As the image pre-processing,the presence of the image denoising has a veryimportant significance.Its main purpose is to remove the interfering information of theimage, to protect the local characteristics of the image,and to improve the quality of theimage,it provides a reliable guarantee to the subsequent processing of the image such asedge detection, image segmentation and feature extraction, etc.It plays a vital role forthe entire image processing.Because the denoising method which based on PDE (partialdifferential equation, PDE) combines Mathematics and Engineering more closely andhas the characteristic of adaptivity,flexibility and accommodation,it gets a rapiddevelopment in the aspect of the protection of the inherent characteristics of the imageand the image noise’s removing in recent years.The denoising method based on PDE mainly derives from unconstrainedoptimization, energy minimization and variational method,Its basic thinking istransforming our research problem to the functional minimum based on the Bayesiantheoretical model. And then deduce one or a set of partial differential equations usingthe variational method and solve the partial differential equations using numericalmethods to get the numerical solution,and that is the final image.In recent years, the denoising model which based on variational PDE was usedwidely. This model takes the image gradient as its edge indicator,through detecting thegradient magnitude in the flat area and an edge area,it selects TV model and lineardiffusion model adaptively,combining the two originally separate processing of theimage edge detection and image denoising organically.These models include ROF totalvariation model,generalized TV model and the adaptive TV model based on gradientmodulus values.However,because of taking the gradient modulus values as edgedetector,the model has two shortcomings:One is that it can not effectively distinguishthe edges of the image and the isolated noise which has large gradient values in the flatarea.The other is the gradient operator we used cannot effectively distinguish betweenedges and ramps which has "moderate gradient".Thus,Even the model we selected isvery reasonable,the denoising can also not achieve the desired effect because theparameters of the model (edge detection operator) is inaccurate.In view of this, the paper takes the source of the problem as its starting point,improving the edge indicators which decide to select the model parameters.developing a new edge indicator which based on the quadratic differential in the local coordinatesystem.This indicator can effectively overcome those shortcomings,and itsregularization term and fidelity term can be weighted by the image fine information，getting good results.And in the aspect of the numerical implementation, a new methodbased on the variation of the image gradient direction is adopted to discrete the gradientfunction’s divergence term of the gradient descent flow to better preserve fine detailseffectively. Each pixel points’ neighborhood4points from the "main direction" anddiagonal direction can be weighted by the change of the image gradient vector’sdirection in the process of the divergence’s discrete.Numerical experiments demonstratethat the new algorithm is superior to the traditional ones in the aspect of preservingfine details.