Research On Algorithms Of Image Restoration Based On ι₁Optimization Model And Bregman Iteration

In this paper, based on the linearized Bregman iteration, the algorithms of the l1optimization about image deblurring and sparse signal reconstruction are investigated.Image restored is a kind of practical problems, which is widely used in various fields of science and technology as well as daily life. Because of its great practical significance and broad applications, it has drawn considerable attention in recent years. The image denoise has many methods and models, also has achieved better results. Due to the relative complex of the existence of the convolution, the realization of calculation method mostly has difficulties in implementation. On the other hand, the sparse signal reconstruction is often needed in many advanced technology, especially it is required less information obtained by the measurement as little as possible through the sensor to recover; these are definitely of great importance in the applications.This paper aims to improve the calculation efficiency of the image deblurring and the sparse signal reconstruction. The main work is as follows:First of all, a family of generalized inverse iteration scheme is proposed, the conver-gence results are proved and the efficiency of the scheme is demonstrated by numerical experiments.Secondly, based on linearized Bregman iteration, combined with iterative formulas of generalized inverse together with the computational efficiency and recovery effect ad-equately, especially on the recovery of the image and signal details characteristics, the new simplified iteration and the new chaotic iteration are presented. The new simplified iteration replaces the SVD decomposition method with the purpose of solving the gener-alized inverse iteration. The calculation is achieved based on inner-outer loop. Under the inner and outer loop relative balance situation, the satisfactory effect could be obtained. In contract, after translating inner-outer loop to the unified single loop, the new chaotic iteration can not only further simplify the calculation but also ensure that all the iterative information of the image or signal could be used in the recovery of the next step. In this way, not only the workload is reduced, but also the lost detailed information and feature in the image recovery or signal reconstruction process could be substituted again, this will improve the computational efficiency and recovery effects. At the same time, the convergence proof is presented and numerical examples are provided to demonstrate the theoretical results.Again, after the proposing of the new chaotic iteration, reweighted l1minimization method is put forward combined with the repeat reweighted thought. Based on the new chaotic iteration, this method is obtained by introducing the weighted coefficient in the each step of the update. In the theory, reweighted l1minimization method is equiva-lent to modify the l1minimization problem into the weighted l1optimization problem. So generalized weighted soft threshold operator is defined during the calculation. This method modifies each step calculation results with repeat reweighted. The characteristics of image restoration could be made up in time especially in the texture sensitive cases, eventually making effect to achieve an ideal state. The calculation efficiency is not affect-ed by the introduction of the weight coefficient, and at the same time, the recovery effect is improved.Finally, according to the linearized Bregman iteration procedure for the l1optimiza-tion model and taking into account the problem itself, the equivalence relationship be-tween iteration schemes is presented.In short, based on the linearized Bregman iteration for l1optimization model, the new competitive simplified iteration method, chaotic iteration method and reweighted l1minimization method are presented; both the theoretical and numerical aspects show the efficiency of these methods.