Research On The Algorithms For Nonnegative Blind Source Separation Based On Edge Features

With the development of science and technology and the progress of society,Nonnegative Blind Source Separation(NBSS)plays a more and more extensive role in the field of signal processing.Generally,the separation of signals is the basis for the subsequent identification and detection.NBSS commonly uses the geometric methods and the numerical method represented by Nonnegative Matrix Factorization(NMF).However,both the methods have restrictions:the geometric method has restrictions on the shape of the convex hull of the mixture scatterplot;The solution of NMF may not be unique,and certain restraints need to be added to constrict it.In addition,the existing algorithms can not resist ill conditions.These shortcomings affect the applicability and robustness of the existing algorithms.This dissertation takes NBSS as the research direction and edge features as the tool method to discuss the key technologies of NBSS algorithm based on edge features.The main research contents and innovations of this dissertation are as follows:(1)In this dissertation,a NBSS geometric method based on edge features is proposed.The existing geometric algorithms such as Minimum Volume Simplex(MVS)may have no solution due to the restriction of convex hull shape of mixture scatterplot.The geometric method proposed in this dissertation solves this problem.The edge feature scatterplot presents a structure of multiple line clusters.In this dissertation,a statistical algorithm for the slope or projection density distribution of edge feature scatters is proposed to solve the regression line equation of each cluster.This algorithm is faster and more stable than the existing clustering and regression algorithms,and can resist pathological conditions.(2)Focus on the problem that the solution of numerical algorithms such as NMF may not be unique,an NBSS numerical algorithm based on edge features is proposed.This method takes the proposed Minimum Jaccard Index(MJI)criterion as the evaluation standard.Under the MJI criterion,the numerical algorithm based on edge features only requires the source to meet the boundedness and nonnegativity assumptions,does not need to introduce additional constraints,including independence,smoothness,sparsity,full additivity and pure pixels,in particular,it can also resist ill conditions.(3)Aiming at the problem of large amount of calculation in high-order NBSS,the Partial Perfect Separation(PPS)theorem is proposed and proved.For geometric methods,PPS theorem can be used to effectively reduce the order of high-order mixing systems,and for numerical methods,the PPS theorem can be used to decompose the high-order mixing matrix into low-order blocks.Therefore,the introduction of PPS theorem can significantly reduce the amount of calculation in high-order NBSS.