Research On Sparse Optimization Algorithm Based On Brainstorming

Compressive sensing theory shows that if a signal is sparse or compressive,the original signal can be reconstructed by sampling a few measured values.In fact,this problem can be converted into a multi-obj ective optimization problem,which considers sparsity and measurement error.And this thesis proposes the multi-objective brainstorm algorithm based on objective space to optimize these two competing terms.Meanwhile,the local searchability of the proposed algorithm is enhanced by introducing iterative half-thresholding operator under the frame of l1/2 regulation.Based on the Pareto-solution set,the knee point is selected without prior signal information.According to the results on the eighteen test functions compared with several state-of-the-art compressive sensing recover methods,the effectiveness of multi-objective brainstorm algorithm based on objective space is verified for sparse optimization problems,achieving higher recover and smaller error.Although the multi-objective brainstorm algorithm based on objective space has certain advantages in solving the sparse optimization problem,it costs a large number of calculations.Therefore,a two-phase driven multi-obj ective brainstorm optimization algorithm is proposed to solve l0-regularized sparse reconstruction problem.To reduce the consumption of computing resources,the proposed algorithm focuses on exploiting the solutions near the true sparsity.In the first phase,the center of K-means in each group is determined by the improved Bayesian Information Criterion.With a cluster,the statistical features of solutions are extracted and solutions with similar characteristics are defined as one class.In the second phase,the global-best guidance mechanism outside the group is conducted to further update new idea and locate the true sparsity more precisely in the Pareto-optimal set without prior signal information.Meanwhile,the iterative half-threshold operator also performs fine searching and improves the local searching ability of the brainstorm optimization algorithm.In a coarse-to-fine manner,the proposed algorithm has a certain tolerance to noise.Compared with several state-of-the-art compressive sensing recover methods on 29 test functions/instances,the proposed algorithm shows great potential in reconstructing signals,though these long signals contain noise.Finally,the potential effectiveness of the proposed algorithm is confirmed by applying on practical application instances.The main contents of this thesis are as follows:It first shows the research background and the framework of sparse optimization.And the relevant concepts and literature review are also included.At the same time,it also describes the steps of brainstorm optimization algorithm according to group/cluster,the generation of new solutions,and selection.Then the research status of sparse optimization is introduced.Due to the shortcomings and deficiencies in the current state of research,two multi-objective optimization algorithms based on brainstorm optimization are proposed.Second,it introduces the multi-objective brainstorm optimization algorithm in detail and also emphatically describes the model of multi-objective optimization and the method of the selection of knee point.Besides,the evaluation index,test function,comparison algorithms,and parameter setting are explained,respectively.Finally,the influence of noise on the proposed algorithm is analyzed.Third,the motivation and main process of two-phase driven multi-objective brainstorm optimization algorithm are showed.For solving the sparse optimization problem,a series of experimental description,parameter setting,the analysis of the guidance mechanism,and comparisons under evaluation indexes are given.In addition,some factors or proposed strategies which may have a remarkable influence on the proposed algorithm are analyzed thoroughly.Then,the proposed algorithm is successfully used in the reconstruction of the image.At last,the work of this thesis is summarized and the direction of future work is described.In addition,the shortcomings in the current work and the expectations for the future are also described.