Methods And Applications Based On The Coupled Block Term Decomposition

The traditional tensor decomposition method,Canonical Polyadic Decomposition(CPD),is widely used in Blind Source Separation problems,such as cocktail parties,fetal heartbeat signal separation,and speech signal separation,because it uniquely writes a high-order tensor into the sum of a set of rank-1 tensors.In recent years,coupled Block Term Decomposition(C-BTD)has been proposed in the field of tensor decomposition,owing to the improvement of computer hardware technology and the more exacting actual scene.Compared with the traditional tensor decomposition methods,ones based on C-BTD solve multiple blind source separation problems simultaneously from the perspective of data fusion.Not only can it process several sets together while keeping correlation between different sets,but used to separate the multidimensional sources.Our discussed C-BTD in this paper mainly involves two innovative ones,the coupled I-type BTD(coupled rank-(L,L,1)block term decomposition)and the coupled II-type BTD(coupled rank-(L_m,L_n,·) block term decomposition).This paper mainly focuses on the related algorithms and some their latent practical application scenarios.The specific involved works and results are presented as follows:In this paper,coupled I-type BTD based methods are applied to multi-targets 3-D spatial localizing in multi-static-multi-pulse(MSMP)MIMO radar,and an iterative algorithm based on coupled I-type BTD,Coupled rank-(L,L,1)based Alternating Least Square,is proposed.We incorporate coupled I-type BTD into localizing targets in the MSMP-MIMO radar.The targets can be localized only by the extracted DOA information(Direction of Arrival).Our adopted methods do not require the probing signals to be orthogonal and its waveform to be known prior.Still in this paper,two algorithms achieving coupled II-type block term decomposition are proposed.The first is an algebraic algorithm called Coupled Exact Joint Block Decomposition(CE-JBD).The second is coupled II-type BTD based Alternating Least Square(CLLD-ALS)method.The CE-JBD proves fast in computing the factor matrices,which are relatively accurate.Therefore,it can provide a good starting point for the counterparts.It concludes that all estimates of the factor matrices can ensure alignment and have higher accuracy.The proposed CLLD-ALS is an iterative algorithm.At the beginning of the iteration,all factor matrices and factor tensors to be updated are randomly initialized,and then the factor matrices and factor tensors are updated alternately by using the cost function and the matricization methods of tensors.In the updating process,the factor matrix or factor tensor is regarded as unknown,while other factor matrices or factor tensors are considered as fixed,with their values being the old ones.Note that our proposed CLLD-ALS have more relaxed identifiability conditions over its predecessors.Furthermore,we establish several JISA(Joint Independent Subspace Analysis)signal models using different source signals and mixing matrices,and apply the proposed methods and some of their state-of-the-art counterparts to the constructed target tensors for comparison.The results show that our proposed methods dwarf the others in either speed or accuracy.