Study On Blind Source Separation Algorithms And Its Related Theory

Blind source separation (BSS) or blind signal separation is the techniquewhich canseparate out original signals from some observed mixed signals according to certainconditions and assumptions without knowing any priori information on the all thesource signals themselves. In the past decades, the techniques of blind signal separationhavegainedmore and more attentions from domestic and foreign scholars, and haveobtained extremely rapid development because of its potential numerous applications.At the present, BSS methods have been applied to the areas of speech enhancement andrecognition, bio-engineering, information security, etc. The linear instantaneous mixtureblind source separation algorithms and its related theory which bewidely used in thearea of BSS isto be researched in this dissertation.This dissertation introduces the background of blind source separation and theresearch status of domestic and foreign at the beginning. And then, some basictheoretical knowledgeincluding the constraints,central processing and pre-whiteningprocessing are introduced. At the same time, theknowledge related to information theoryconsists of entropy, negative entropy,mutual information,kurtosis and higher-ordercumulants are presented.Some classical algorithms of BSS have also been provided.The main results of this thesis are as follows:1.A novel algorithm which can separate themixed smooth images by utilizing localsmoothness which attracts more and more attentions at the present is proposed. Thedegree of variations of pixels where a smaller area is very slowwhich can be discoveredby comparing image with wave signal. In other words, the image is of locally smooth.Based on this discovery, a proper like entropy function which can represent the localsmoothness of an image is formulated. The entropy of source images are the lowestbased on the like entropy function, at the same time, the entropy value of mixed imagesis between the highest entropy of the source images and the lowest entropy of the sourceimages. Accordingly, the separation weight vector associated with the lowest entropyvalues canbe obtained. Compared with the conventional independent componentanalysis algorithm, the original signals in theproposed algorithm are not required to be independent. Simulation results on mixed images are employed to furtherillustrate theadvantages of the proposed method.2.The blind separation algorithm based on second-order statistics is studied.Thedisadvantages existing in the method proposed by Duarte is analyzed.On that basis,areversed second-order frequency indentification algorithm is proposed. Bytheoreticalanalysis, the feasibility of the reversed algorithm is proven. However, the reversedalgorithm still has the shortcoming of cumulative errors. To overcome the disadvantagesof cumulative errors existing in the both of SOFI and RSOFI algorithm, an improvedmethod is proposed by using symmetric mode. Theoretical analysis and simulationresults show the effectiveness of the improved method compared with the originalalgorithm in both noisy and noise-free scenarios.3. Minor component analysis (MCA) are widely used in many applications such ascurve and surface fitting, robustbeamforming, and blind signal separation. Based on thegeneralized eigen-decomposition, completely different approach that leads to derive anovel MCA algorithm is presented. First, in the sense ofgeneralizedeigen-decomposition, by using gradient ascent approach, we derive analgorithm for extractingthe first minor eigenvector. Then, the algorithm used to extractmultiple minor eigenvectors is proposedby using the orthogonality property. The proofsand rigorous theoretical analysis show that the proposedalgorithm is convergent to theircorresponding minor eigenvectors. Three important characteristicsof these algorithmsare identified. The first is that the algorithm for extracting minor eigenvectors canbeextended to generalized minor eigenvectors easily. The second is that thecorresponding eigenvalues canbe computed simultaneously as a byproduct of thisalgorithm. The third is that the algorithm is globallyconvergent. The simulations havebeen conducted for illustration of the efficiency and effectiveness ofthe proposedalgorithm.This research of the thesis is closely linked with the present BSS theoreticalresearch, which has a certain instructional significance to the study of BSS theory andalgorithm.