【作者】 赵敏；

【导师】 谢胜利；

【作者基本信息】 华南理工大学 ， 信号与信息处理， 2010， 博士

【摘要】 盲源分离是上世纪80年代初在信号处理领域诞生的备受学术界关注的新生学科,在许多新兴领域都有着重要的应用。盲分离按照其混叠方式的不同,可分为瞬时线性混叠和非线性混叠。本文着重研究主要针对盲分离瞬时线性混叠模型的适定、欠定情形以及卷积混叠模型,具体的工作包括如下几个方面:1.针对适定线性混叠的情形,深入研究了如何把联合对角化技术应用于解决盲信号分离问题。利用信号时序结构的二阶统计量方法通常需要解决一个联合对角化问题。首先对一类特殊的矩阵束——良态矩阵束给出了一个新算法。由于采用了共轭梯度算法优化目标函数,算法不仅收敛快,而且收敛性有保证。然后,给出了可完美对角化的判别定理。同时,还把对角化问题转化为含有R-正交约束的一类优化问题,给出了统一的优化框架。2.在线性欠定混叠盲分离以及稀疏分量分析中,如果信号是非严格稀疏时,通常的两步法将失去作用,前人提出了源信号非严格稀疏下的k-SCA条件,并给出了在此条件下,混叠矩阵能被估计以及源信号可恢复的理论证明,但目前甚少相关的具体实现算法。文中首先提出了一种针对k-SCA条件,利用超平面聚类转化为其法线聚类来估计混叠矩阵的有效算法,在源信号重建上,还提出了一种简化l1范数解的新算法,弥补了该领域研究的一个缺失。3.同样是针对线性欠定混叠的情形,提出利用基于单源区间的盲分离算法。采用Bofill的两步法,第一步估计混叠矩阵,第二步恢复源信号。首次发现了暂时非混叠性这一混叠信号的物理性质,并定义了单源区间,提出了一个基于最小相关系数的统计稀疏分解准则(SSDP)。并在此基础上,提出了非完全稀疏性的问题。现有的最短路径法、l1范数解和SSDP算法仅适用于稀疏源而不适宜非完全稀疏源。针对两个观测信号的情形,提出了统计非稀疏准则(SNSDP)。该准则将信号分成若干区间,用源的相关性判断各区间是否非完全稀疏,并在非完全稀疏和稀疏的区间采取不同的源恢复策略。它改善了估计的源信号。最后,语音信号的仿真实验显示它的性能和实用性。4.针对卷积混叠模型。提出了一种自适应盲解卷算法,该算法不要求源信号独立同分布、也不要求源信号平稳。特别是,对于混叠信号数目少于源信号数目情况下,算法能够实现卷积盲分离,扩大了卷积盲分离的应用范围。仿真与分析表明,本文所提出的算法能有效地解决线性混叠和卷积混叠的部分问题,巩固了盲分离理论和方法的基础,展现了盲分离研究领域的发展前景。更多还原

【Abstract】 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.更多还原