Research On Nonconvex And Nonsmooth Variational Image Restoration

Image restoration is a very important processing technology in the field of image processing.Its main purpose is to remove the degradation phenomena such as noise and blur in the image,so as to improve the visual quality of the image.Image restoration technology is widely used in many scientific and technical fields,such as remote sensing technology,medical imaging,pattern recognition,image understanding,big data and so on.Image restoration is actually an estimation process,which needs to estimate the clear image according to some specific image degradation models.Although there are a lot of methods to realize image restoration,the contradiction between image information preservation and noise removal is still an urgent problem to be solved by these image restoration technologies.Variational method is widely used in image denoising,image restoration and image segmentation because of its good theoretical foundation,high flexibility and accurate experimental results.Variational method in image restoration is to minimize the corresponding energy functional,and the obtained value is the restoration result of degraded image.Total variation(TV)model is the most widely used subject of variational method.TV model can preserve image edges well,but there will be serious staircase artifacts.Based on this,this paper studies the variational method in detail,and proposes two variational models to alleviate the ladder effect.The main research contents are as follows:1.A nonconvex nonsmooth anisotropic total variation(NNATV)model is propossed for image denoising and deblurring.The model provides sparse representation of directional derivatives of restored images in horizontal and vertical directions by using nonconvex nonsmooth potential functions.The graduated nonconvexity(GNC)algorithm is used to solve the proposed model.The experimental results show that the model can effectively preserve the edges and contours,and alleviate the staircase artifacts that often appears in TV models.2.A generalized mixed nonconvex variational regularization(HNVR)model is proposed.The model uses nonconvex TV and nonconvex Laplacian regularization to apply a priori to two different components of the image.A first-order algorithm based on alternating direction multiplier method(ADMM)combined with majorization-minimization(MM)scheme is adopted to effectively solve this nonconvex minimization problem.Because the proposed model adopts the combination of piecewise constant and piecewise smooth component,the new model inherits the advantages of nonconvex regularization and first-order and second-order mixed variational regularization.Experimental simulation shows that the model is effective in removing noise,preserving image contour and reducing staircase artifacts.