Studies On Algorithms For Multiple-sets Splitting Feasibility Problem Based On Selection Technique

Multiple-sets split feasibility problem is a generalization and extension of split feasibility problem,which has a wide application background in the real world,such as medical care,image reconstruction,signal processing and so on.Over the years,many numerical algorithms have been designed for this problem.In this thesis,some classical algorithms are reviewed,and several improved algorithms based on selection technology are proposed.In addition,some new improved algorithms are presented for the phase recovery problem,which is an application of multiple-sets split feasibility problem.Firstly,in order to solve the multiple-sets split feasibility problem,three new improved algorithms are proposed based on the classical CQ algorithm,projection gradient method and adaptive step-size projection gradient method.These three algorithms can transform the multiple-sets split feasibility problem into split feasibility problem at each step,which improves the solving efficiency.The convergence analysis of finite dimensional Euclidean space is also given.Secondly,aiming at the multiple-sets split feasibility problem,some greedy random projection gradient algorithms based on selection technology is proposed,and the convergence analysis is given.This kind of algorithms make the sets selected in each step of algorithm iteration have randomness according to probability,which can alleviate the problem of the three algorithms descending too much in the deviated descending direction,and increase the robustness and generalization ability of the algorithm.Finally,based on classical ER algorithm,HIO algorithm and Shrinkwrap algorithm,two hybrid adaptive step size algorithms are proposed for phase recovery.The new algorithms overcome the shortcoming of premature stagnation after a certain number of iterations,make the reconstruction error further decrease rapidly,and improve the definition of the reconstructed image.A series of numerical experiments are carried out based on several text and face images to verify the excellence of the two new algorithms in image reconstruction.