Study On Blind Signal Separation Methods Under Various Mixture Models

Blind Signal Separation (BSS) is defined as retrieving the potential unobservablemultidimensional source signals just from a set of observation signals received by a group ofsensors, without knowing a prior knowledge of the transmitting system. Recently, BlindSignal Separation has become a hot issue in the scientific fields of statistics, neural networksand signal proeessing, due to its wide and important application perspective in wirelesscommunication, speech identification and enhancement, image recognition and featureextraction, etc. For the BSS problems under different mixing models, the main contributionsof this dissertation are as follows:First, for the typical linear determined mixing model, i.e., the number of the observationsignals is equal to the number of the source signals, two adaptive blind signal separationmethods are proposed separately based on the Minimum Mutual Information principle. Forthe relatively slow convergence problem of the traditional gradient-type algorithm in thereal-time computation, a new BSS algorithm is presented with the momentum technology.The proposed algorithm adopts the mutual information of the separation signals as the costfunction. The momentum is incorporated into the natural gradient updating rules foroptimizing the cost function, and then an adaptive learning algorithm for searching theoptimal separating matrix is derived. In order to enable the proposed algorithm to separate thesource signals with different statistical properties, in each updating step, an online scorefunction estimation method based on the Gram-Charlier expansion is employed. Simulationresults validate the fast convergent speed and the appealing behavior in separating the sourceswith both Super-Gaussian and the Sub-Gaussian signals of the proposed adaptive BSSmethod.In consideration of the appealing performance of the conjugate gradient optimizationalgorithm in the neural network training, a new adaptive blind signal separation algorithm isproposed based on the conjugate gradient. On the basis of the stochastic gradient algorithmand the natural gradient one, the proposed BSS algorithm introduces the conjugate gradientsearching principle to calculate the expected separating matrix, combining the mutualinformation criterion. In other words, the separating matrix always updates along the directionconjugate to the current searching direction. As a keypoint of the algorithm, a kernel densityfunction estimation method is exploited to estimate probability density function and itsderivative of the separating signals, instead of choosing a certain non-linear functionempirically. Simulation results confirm the effectiveness of the proposed conjugate gradientbased BSS method.For the case, when there are more observation signals than the source signals, and themixing matrix has full column rank, an over-determined BSS algorithm is presented. Thealgorithm first introduces an over-determined BSS cost function based on the singular valuedecomposition on the separating matrix. Then the learning algorithm of the separating matrixis derived with the conjugate gradient searching principle. The score functions are estimated by the kernel density function estimation. Simulations demonstrate the superior performanceof the proposed algorithm through comparison with the traditional stochastic gradient and thenatural algorithm.For the problem of the insufficient number of the observation signals under theunderdetermined mixing model, a new underdetermined BSS method is proposed based onthe local mean decomposition technology. The BSS problem for non-sparse signals under theunderdetermined mixing model is studied. The propsoed BSS method firstly introduces thelocal mean decomposition algorithm into the underdetermined BSS model to generate severalproduct functions, which are then filtrated in the light of a certain criterion. The selectedproduct functions are then combined with the initial mixtures such that the underdeterminedBSS problem is transformed into a determined one which is much easier to cope with, and thedifficulty of the deficiency of the mixtures is overcome. For the rebuilt mixtures and thenewly formed determined BSS problem, two BSS algorithms are proposed to recover thesources. Theoretically, there is no limit to the object of the LMD algorithm, so the proposedunderdetermined BSS method is supposed to be able to break the sparse constraint included inmost existed methods. On the other hand, the proposed BSS method separates the sourcesignals directly, instead of estimating the underdetermined mixing matrix primarily, avoidingthe unnecessary computation. Simulations results show the good performance of the proposedmethod.In addition to the above mentioned linear mixing model, the non-linear BSS problem isalso investigated. A non-linear BSS method based on perceptron network is proposed. Themethod employs a three layer perceptron network as the non-linear separating system. TheInformax principle is exploited as the basis to search for the optimal parameters of thenon-linear separating system. The conjugate gradient algorithm is used to update the weightmatrices of the hide layer and the output layer of the perceptron system to speed up theconvergence of the BSS algorithm. Additionally, the probability density function is chosen asthe Sigmoid function in the algorithm, and is estimated adaptively by a parametric method.Simulations results confirm the appealing performance of the proposed non-linear BSSmethod.Finally, a new blind signal separation method based on joint approximate diagonalizationis proposed for the linear convolutive mixing model. If the mixing process is notinstantaneous, i.e., the time delay is also considered during the transmitting process from thesources to the sensors, the BSS problem will become a multidimensional convolutive mixingmodel. In the proposed BSS method, the convolutive mixing model is first transformed intoan instantaneous mixing model; then a joint approximate diagonalization method is applied tothe transformed model in order to computing out the separating matrix. Meanwhile, in theprocess of diagonalization, a constraint condition is introduced for the limitation of the classof the separating matrices such that the singular solutions are avoided. Simulation resultsshow that the proposed method can realize the blind separation of convolutive mixture signals successfully.