Researches On Non-convex TGV Regularization Method In Image Restoration

Due to the influence of imaging equipment and external factors,the acquired images are often unavoidably polluted by various noises or blurs,which has a bad impact on subsequent processing and analysis.Therefore,it is very significant to use image restoration technology to restore clear images from degraded images.Although the traditional total generalized variation(TGV)model can effectively suppress the staircase effect during image reconstruction,the recovered image often possesses blurred edges.For the purpose of better preserving the edge details of the image and based on the TGV model,this thesis combines the advantages of nonconvex potential functions,and studies the non-convex TGV regularized Poisson noise and impulse noise removal problems.The major contents of this work are outlined as follows.First,Chapter one briefly introduces the research background of image restoration and the research status at home and abroad.Next,the research contents and work arrangement of the full text are summarized.In Chapter two,we first briefly review the basic concepts and related properties of the TGV function.Then,several common numerical algorithms in image restoration are introduced,and some widely used image quality evaluation criteria are briefly reviewed.In the third Chapter,committed to removing the Poisson noise,this chapter introduces the non-convex potential function into the TGV regularization,and constructs an improved nonconvex variational model.Numerically,we propose an efficient alternating direction method of multipliers for resolving the objective problem by combining the iteratively reweighted L1 algorithm and the first-order primal-dual algorithm.Finally,a series of numerical experiments verify the excellent performance of the newly developed model in overcoming the staircase effect and preserving image edge details.In Chapter four,for the sake of removing impulse noise,this chapter uses non-convex TGV as the regularization term and combines non-convex data fidelity term to establish a novel non-convex variational model.Computationally,an improved alternating direction method of multipliers is proposed to solve the new model by integrating the iteratively reweighted L1 algorithm and the variable splitting approach.Finally,compared with other strategies,the provided numerical experiments show that the constructed model can not only preserve edge details of the image well,but also effectively overcome defects such as the staircasing effect while removing the impulse noise.The last Chapter summarizes the research contents and results of the full text.In addition,we propose some prospects and follow-up work for the aspects that can be improved in this thesis.