Research On Accelerated Split Bregman Algorithm For Sparse Reconstruction

Sparse reconstruction model has been widely used in image processing,compressed sensing,complex network and other fields and has made remarkable achievements.Therefore,the study of sparse reconstruction has certain theoretical and practical application value.Sparse reconstruction algorithm is one of the core problems of sparse reconstruction.Bregman-based algorithm can deal with large-scale problems effectively since only first derivative information of the objective function is used.The split Bregman algorithm decomposes the objective function into several sub-problems and makes the iteration of the algorithm simpler and easier.However,the split Bregman algorithm only has a linear convergence rate of ???.Therefore,more and more scholars pay attention to improving the convergence rate of the Bregman-based algorithms.This thesis focuses on Bregman iterative algorithm for sparse reconstruction.The main contributions are as follows:?1?By combining the Nesterov's accelerated gradient technique with the split Bregman iteration,we propose a new accelerated split Bregman algorithm and use it to solve sparse reconstruction problem with l₁ norm constraint.?2?We give convergence analysis for the proposed algorithm and prove the proposed algorithm has linear corvergence rate of ???.?3?We verify the effectiveness of the proposed algorithm through some numerical experiments.Experimental results show that the proposed algorithm has advantages over the existing linear Bregman algorithm,split Bregman algorithm and accelerated linear Bregman algorithm.The proposed algorithm not only has a fast convergence speed,but also shows good experimental results in image reconstruction problems.