Image Denoising Algorithm Based On Variational Partial Differential Equation

Total variation(TV)model diffuses only along the direction perpendicular to the image gradient at every point of the image,that is,along the edge direction,but not in the gradient direction,which solves the problem of over-smoothing and effectively protects the information of the image edge.therefore,the model can better retain the edge details of the image.But for the flat region of the image,its edge direction is actually not obvious or even does not exist,and diffusion along the edge direction of the image at this time will lead to the lack of denoising ability of the flat region,so it is easy to mistake the noise of the flat region as image edge processing resulting in false edges resulting in a ladder effect.The image denoising method based on variational method and partial differential equation can effectively balance the contradiction between removing noise and maintaining image structure information,so that the restored image can get a good visual effect.In this paper,the variational partial differential equation is applied to remove additive Gaussian noise in gray image.With the help of the theoretical advantages of the variational method and partial differential equation,two improved algorithms are proposed for image denoising,namely HNHOTV-OGS(hybrid non-convex higher total variation over mapping group space)algorithm and LNLTV(local and local total variation)algorithm.Both algorithms are built based on the composite regularization model,the aim is to achieve the balance between noise removal and image edge details,and to some extent eliminate the ladder effect.HNHOTV-OGS algorithm uses both overlapping group sparse(overlapping group sparsity,OGS)regular terms and non-convex higher-order full-variable regular terms for step effect elimination.OGS regular terms tend to smooth artifacts in restored images in a global range,while non-convex higher-order terms tend to smooth local texture parts and maintain sharp edges.LNLTV arithmetic this is a local and non-local total variational composite regularization image denoising model.at the same time,the image local structure and non-local similarity are used to combine the TV model and the NLTV model to alleviate their disadvantages,and the advantages of the two models are fully utilized to de-noise the image.the method first uses the TV spectrum transformation to decompose the original noisy image into cartoon components(constant region and edge)and detail components(texture and weak edge).Then local total variation(TV)and nonlocal total variation(NLTV)methods are used respectively to regularize the cartoon component and detail component,the model retains the structure edge and effectively restores the image details,and can better suppress the generation of ladder effect in the smooth region of the image.Finally,the simulation experiments of classical gray-level images in digital image processing by MATLAB platform show that the two algorithms proposed in this paper can make the restored images obtain higher peak signal-to-noise ratio(peak-signal-to-noiseratio,PSNR)and structural similarity(structured similarity index measurement,SSIM),and outperform several other full-variant algorithms in subjective visual effects,and can effectively suppress the generation of ladder effects.