Research On Optimization Methods For Image Restoration Problem

Image restoration based on total variation of variational model is now a hotresearch point at home and abroad. In this paper, the primal model transferred into thedual problem. Some gradient projection algorithms are given. The main results are asfollows:Firstly, in this study, a spectral conjugate gradient projection method is presentedto solve total variation image restoration, which is transferred into the nonlinearconstrained optimization with closed set. The global convergence of the proposedscheme is analyzed. In the end, some numerical results illustrate the efficiency of thismethod.Secondly, we propose a new gradient projection algorithm for total variationimage restoration. The new proposed method exploits a nonmonotone line-search andan adaptive steplength selection based on recent strategies for the alternation of thewell-known Barzilai-Borwein rules. The convergence of the proposed schemeisproved. Numerical results illustrate the efficiency.Thirdly, we present a new algorithm to accelerate the Chambolle gradientprojection method for total variation image restoration. The new proposed methodconsiders an approximation of the Hessian based on the scent equation. Combinedwith the quasi-Cauchy equations and diagonal updating, we can get a positive definitediagonal matrix. In the proposed minimization method model, we use the positivedefinite diagonal matrix instead of the constant time stepsize in Chambolle’s method.The global convergence of the proposed scheme is proved. Some numerical resultsillustrate the efficiency of this method. Moreover, we also extend the quasi-Newtondiagonal updating method to solve the l1-norm regularized problems to decode asparse signal in compressive sensing. Performance comparisons show that theproposed method is efficient and competitive with the compared ones.