Research On The Theory And Key Problems Of Blind Source Separation

Blind Source Separation (BSS) is a new research branch in signal processing that original developed in the 1980s. After that, BSS has gained much more attention. BSP has its potential applications in many key fields. According to the mixing form, BSS can be categorized into two main directions, such as instant linear mixing case and nonlinear mixing case. This dissertation focuses on well-determined case and under-determined case of linear mixture and convolutive mixture for blind source separation theorems, algorithms, and applications, including:1. For well-determined linear mixture, the joint diagonalization technique is used for solve BSS problem. Usually, the second order statistics method based on sequential structure must solve a joint diagonalization problem. Firstly, a new algorithm is given for a kind of sepecial matrix pencil (Well-Matrix Pencil). With objective function optimized by conjugated gradient algorithm, the new algorithm can convegent quickly. Then, the perfect diagonalization theorem is given. The joint diagonalization problem had been turned into a R-Orthogonal constraint problem. And a universal optimization framework is also put forward.2. In the under-determined linear mixing case and sparse component analysis, if the signal is not strictly sparse, the traditional"two steps"method cannot function. Some previous works proposed K-SCA condition, the prove of the estimation for mixing matrix and recoverable for source in non-strictly sparse case. But few works concern about the algorithm in detail. A new efficient algorithm is proposed in this paper based on mixing matrix estimated by normal clustering instead of hyperplane clustering. For the sources recovery, a algorithm of compact l1-norm solution is also proposed to make up the absence in this area.3. Also for underterminded linear mixture, a new bss algorithm based on single source interval is proposed. With Bofill two-step method, estimate the mixture matrix in the first step and then recover the source signal. For the first time, we discover the temporary unmixing physical property and define the single source interval. A sparse decomposition principle based on minimized correlative coefficient has been proposed and it is called statistical sparse decomposition principle (SSDP). Based on it, the incompletely sparsity problem is also put forward. The shorest path algorithm, l1-norm solution and SSDP algorithm is fit for sparse source but not incompletely sparse source. Statistically non-sparse decomposition principle (SNSDP) is proposed for two observed signals. The principle firstly divides the signals into many intervals, and then decides whether they are incompletely sparse using correlative of sources, and then utilizes different recovery strategy in the sparse and incompletely sparse intervals. It overcomes the shortcoming of these current algorithms and improves the estimated sources. Finally, mixed speech signals are used to show its performance for blind source separation in the simulations.4. For underdetermined convolutive mixture, a convolutive BSS algorithm in the frequency domain has been proposed. The algorithm does not imposes the condition that source signals are identically distributed(iid) and stable. Especially, the mixture signals'number is smaller than sources', the observed signals can also theoretically be separated. And it extends the application field of BSS in some degree.Simulations and analysis show that the proposed algorithms can partly solve the problems of linear or convolutive mixture. They make the basis of BSS theory and methods stronger and reveal the foreground of BSS's field.