Research On Non-convex Hybrid Variational Regularization Image Restoration

Digital images can often intuitively describe and reflect external informa-tion,so the importance of images as the main medium for information exchange between humans and external systems is self-evident.However,the image qual-ity can be degraded during imaging,transmission,and storage because of image equipment failure or external environmental influences.Therefore,in order to ensure normal follow-up work such as image analysis,it is necessary to use im-age restoration technology to obtain the original clear image.Restoring a clear image from a degenerated image is a classic ill-posed inverse problem.Although there are a large number of existing techniques to restore the image well,it is still a worthwhile problem to preserve more image information while removing degradation.The variational image restoration models have received extensive attention due to its complete mathematical theory and effective experiment results.These types of models construct an energy functional based on the prior features of the image,and the restored image is the corresponding minimum point when the ener-gy functional obtains the minimum value.The non-convex total variation（NTV）model can restore the structural information such as image edge and contour well,but it will cause the staircase phenomenona in smooth regions of the restored im-age,thus losing some of the original image information.Based on this,in order to effectively reduce staircase phenomenons while improving the quality of the restored image,this paper proposes two non-convex hybrid regularization models for image restoration.The main research contents are as follows:1.A regularization model coupled with overlapping group sparse second-order TV and non-convex TV（OGSSO-NTV）is proposed for image restoration.The model uses overlapping group sparse second-order TV and non-convex TV regularizers to characterize the prior information of the image,so that the re-stored image is constrained to the intersection of two Sobolev spaces,i.e.,W^1,p∩W^2,1（p∈（0,1））.An alternating directional multiplier method（ADMM）is devel-oped to numerically solve proposed model,where the Majorize-Minimization（MM）and the iterative re-weighted l₁（IRL1）algorithm are used to solve the overlapping group and the non-convex minimization subproblem,respectively.This model in-herits the advantages of above two regularizers.The numerical experiment results show that the model can recover the image structure information and effectively alleviate the staircase effect.2.A weak space-hybrid non-convex regularization（WS-HNR）model is pro-posed in the framework of exponential Retinex theory,which uses weak space,non-convex first-order TV and non-convex second-order TV regularizers to mea-sure the oscillation information,reflectivity and illumination in the noisy image,respectively.Therefore,the model accurately decomposes the image into three disjoint components,and reconstruct the restored image through the reflection and illumination components.The model is solved by combining MM algorithm under the framework of ADMM.The numerical experiment results show that the model has excellent effect in image restoration.