Research On Blind Source Separation Algorithms And Its Application

Blind source separation (BSS) is an important signal processing technology, which is widely used in biomedical signal processing, array signal processing, speech signal recognition, image processing and other fields. In practical applications, the BSS problem can be transformed into the optimization problem based on a mathematical model, then obtains the separable matrix by optimizing its objective function, and finally restores the source signal waveforms. In this sense, the optimization algorithm is an important part of the BSS algorithm, which determines the overall performance of the BSS algorithm. In this thesis, we delve into the BSS problem from mathematical model and optimization algorithm.In recent years, the BSS algorithm based on joint diagonalization(JD) becomes a research hotspot. However, these algorithms often occur a problem:the objective functions converge to the optimal value, but their solutions do not converge to separable matrices correspondingly. This is because the JD model does not consider the intrinsic relationship between the separation matrix and the mixing matrix. That leads to the algorithm’s search region to expand, therefore, a number of undesired solutions are included, and the convergent efficiency of the algorithm is ultimately reduced. We propose the following three improved models to overcome this drawback.It can be proved that, under these models, algorithm converges to the separable matrices so as to achieve the purpose of separation signals as long as its objective function converges to the optimal value.(1) Dual Matrix Model (DMM)。Introducing image matrices A and W, and structuring their quantitative relationships:AW-IN, from which it can be derived that the product of separating matrix and real mixing matrix is equal to the generalized switching matrix, i.e. algorithm converges to a separable matrix and achieves a separation of source signals. Simulation results show that the DMM-based blind source separation algorithm has higher efficiency than these algorithms based on JD model.(2) Variable Dual Matrix Model (VDMM). It is a generalization of DMM. In the DMM model, the matrix IN is an identity matrix, and its diagonal elements are constant 1. In fact, the condition is too strict to application, we can relax it as follows:AW=IN, where IN can be regarded as generalized matrix(its diagonal elements are nonzero variables). Obviously, VDMM model is more general, DMM is just a special case. Simulation results show that the separation algorithm based on VDMM model is more efficient.(3) Parallel Dual Matrix Model(PDMM). DMM algorithm converges to the separable matrices when its objective function converges to zero. However, the iterative algorithm performance generally involves the initial condition for the iterative method and the structure of the cost function itself. In the case of given the objective function, at several instances of initial conditions, the cost function does not necessarily converge to a small value. In addition to changing the initial point, but also changing the structure of the objective function can be used to improve the success rate of the algorithm. The numerical relation between the matrices A and W was fully considered in this dissertation. A completed was then constructed. The set is considered as a classifying operator of the search area. The very element of this set corresponds to a constrained term of the sub-algorithm. Thus, in the process of iterative computation, every sub-algorithm finds an optimizing solution in a given area of the BSS. In application, we can optimize several different parallel structures objective functions, since each objective function is able to convergence to optimal value in the sense of probability, therefore, this can improve the efficiency of the signal separation.When the blind source separation problem was abstracted into the mathematical model, its algorithm is converted into an unconstrained optimization problem. To further improve the efficiency of optimization, we propose two numerical algorithms:(1) Hybrid trust region method (HTRM). In this dissertation, we introduce a "hybrid" strategy into a trust-region framework. The hybrid method can be regarded as a combination of line search and trust region techniques. The primary aim of the method is to prevent from resolving the trust-region sub-problem when the current trial step is rejected. First, the proposed method solves the sub-problem in order to compute the trial step and then set updates next iterative point whenever the trial step is accepted. Otherwise, our method uses the gradient descent algorithm to compute new iteration points instead of resolving the trust-region sub-problem. Moreover, the computational cost of the gradient descent algorithm is much lower than the solving sub-problem. The analysis of the new approach shows that it inherits both stability of trust-region methods and low computational cost of line search methods. Theoretical analysis shows that hybrid trust region algorithm has strong robustness and super-linear convergence to the optimal value of the properties. Numerical simulations show that it is more efficient than some of the existing modified trust region algorithm.(2) Modified gradient descent algorithm (MGDA). Gradient descent algorithm is simple and easy to implement, it is widely used in the large-scale variable optimization problem. Most existing algorithms use Wolfe criterion to calculate iterative step length. But this criterion is inequalities, solving difficult and time-consuming. In order to improve computational efficiency, this paper proposes a new algorithm to determine the step length, the algorithm is more simple, and no requiring to solve inequalities. Theoretical analysis and numerical simulations show that the MGDA is more efficient than the Wolfe-criterion gradient descent algorithm.Finally, the MGDA is applied to the antenna array pattern synthesis, considering the single, multi-beam two cases. Firstly, inspired by the idea of penalty function, we transform the antenna array synthesis problem into an unconstrained optimization problem, and then use MGDA to optimize the objective function to obtain the solution. Simulation results show that both single and multi-beam pattern synthesis, the proposed algorithms have good synthesis capacity and are able to obtain better PSLL than those reported in some existing literatures.