Sparse And Low-rank Methods For Subspace Clustering And CT Image Reconstruction

With the development of science and technology,the Information technology is constantly updated.The ubiquity of the Internet and mobile communications has created huge amounts of data.Big data has become the most important feature of today.How to make full use of these massive data has spawned data analysis and data mining.Subspace clustering is one of the key techniques in data analysis and data mining.And subspace clustering is an effective way for high-dimensional data clustering.In this paper,sparse subspace clustering,low-rank subspace clustering and few-view CT image reconstruction are studied.Based on the reweighted sparse subspace clustering,us-ing the geometric relationship between data,the geometrically-structure-information induced reweighted sparse subspace clustering is established,which is called Side-information-induced Reweighted Sparse Subspace Clustering（SRSSC）.Inspired by structured sparse subspace clus-tering,we introduced the influence of data clustering label on data representation.Based on the SRSSC,geometrically-structure-information induced iterative reweighted sparse sub-space clustering is further proposed,which is referred as Side-information-induced Iterative Reweighted Sparse Subspace Clustering（SIRSSC）.The alternate direction multiplier method（ADMM）is used to solve these models,and the experiment results show that the proposed methods can effectively improve the performance of data clustering.In popular subspace clustering methods,Self-representation is key role.Through observation,it is found that the block diagonal structure of the self-representation coefficient matrix of the independent subspaces is beneficial to the accurate clustering of data.A relaxed block diagonal repre-sentation model（RBDR）is established for subspace clustering by using the block diagonal regularization of the self-representation coefficient matrix and an orthogonal transformation,which improves the block diagonal performance of self-representation coefficient matrix and has obvious clustering effect on the disordered data which not arranged in clusters in prac-tice.Multi-view data is widespread in practice.For multi-view data clustering,the similarity matrix learning and label indication matrix learning of a specific perspective are unified into a minimization problem framework.The similarity matrix learning and cluster label indica-tor matrix learning are mutually guided and constrained by block diagonal regularization to provide double guarantee for improving the accuracy of data clustering,which is called Cou-pled Block Diagonal Regularization for Mulit-view Subspace Clustering（CBDMSC）.Based on alternating minimization,an effective algorithm is proposed to solve the problem.Exper-iments show that the algorithm has great advantages in most indexes of common data sets.Regularization is an effective method for reconstruction of projection data with few-view.In this paper,l_1/2regularization is used to solve the ill-conditioned problem of few-view pro-jection CT image reconstruction.Half-threshold algorithm is used to solve this problem.The convergence and stability of this method are analyzed and the theoretical proof is given in this article.Numerical experiments show that the proposed method has more advantages than traditional classical algorithms in noise suppression and image detail preservation during CT image reconstruction.At the end of this paper,the author briefly introduces the main problems and challenges of the subspace clustering.A further research plan combining deep learning with subspace cluster-ing is proposed.In the future,the problem of clustering with missing data features,clustering of large-scale data or dynamic data,and the adaptive problem of the number of subspace clus-ters will be studied.The author also wants to find more applications for subspace clustering and solve more practical problems.