【作者】 张华；

【导师】 冯大政；

【作者基本信息】 西安电子科技大学 ， 信号与信息处理， 2010， 博士

【摘要】 盲源分离是在源信号与传输信道未知的情况下仅利用接收天线的观测数据提取或恢复统计独立的源信号。盲源分离具有非常重要的理论意义和实用价值,被广泛应用于无线通信领域、生物医学信号分析与处理、图像识别、数据挖掘、语音增强以及地球物理数据处理等方面,具有非常广阔的发展前景,极大地引发了信号处理和神经网络等学科众多研究者的共同关注。本文紧密围绕这一热点课题展开,并重点研究基于联合(块)对角化的盲分离算法。联合对角化(Joint Diagonalization,JD)和联合块对角化(Joint Block-Diagonalization, JBD)分别是解决瞬时和卷积混叠盲分离的重要技术,根据这两条主线,本文的主要工作可归纳如下:1.给出具有广泛适用性的非正交JD可辨识性定理,为基于非正交JD的盲分离算法提供了理论依据。用代数方法严格证明了,对于由共同的非正交(酉)混叠矩阵构成的具有可联合对角化结构的一组目标矩阵,从中提取(估计)出的混叠矩阵与真实的混叠矩阵本质相等,即仅相差一个广义置换矩阵。从而为基于非正交JD的盲分离算法提供了理论依据。2.根据盲分离算法固有的尺度和排列不定性,对经典的基于拟合误差最小二乘代价函数进行改进,提出三二次拟合代价函数,使原函数中关于混叠矩阵的四次函数转化为三组待定参数的二次函数。同时,给出了优化该代价函数的基于三二次迭代的非正交JD算法(Tri-quadratic Iterative Algorithm,TIA),该算法既不要求目标矩阵为对称或是共轭对称,也不要求混叠矩阵为(酉)正交矩阵。引入动力学理论中的李雅普诺夫函数以及LaSalle’s不变原则, 1)论证了在理想条件下,TIA算法收敛到三二次拟合函数的不变集; 2)验证了盲分离问题的可接受集合属于三二次拟合函数的不变集。3.提出一种基于二次优化的正交JBD方法:QJBD,该方法以非对角线上各子矩阵F-范数的平方和作为联合块对角化性能的评判准则,将原四次代价函数转化为一组较为简单的带约束的二次子代价函数,每一子代价函数用于估计酉分离矩阵的一个子矩阵。依次最小化各子函数,迭代搜索代价函数最小点,得到分离矩阵的估计。理论分析和实验结果表明,该方法收敛速度快,可直接在时域进行卷积盲分离;同时,该方法在不降低分离性能的基础上,克服了传统的基于类Jacobi旋转的JBD方法对于传输信道阶数和初始值较敏感的缺陷。4.研究表明,将适用于非正交JD的J-Di算法直接用于JBD所得到的分离矩阵,与真实的JBD分离矩阵之间,只相差一个置换矩阵。基于此,本文提出一种基于改进J-Di算法的非正交JBD方法:GH-NOJBD,直接在时域解决卷积盲分离问题。该方法不需要对观测信号进行预白化处理,从而不再要求至少存在一个目标矩阵为正定矩阵,也消除了白化误差的影响,具有比基于类Jacobi旋转的JBD方法更好的分离性能。5.分析接收信号相关矩阵组具有三因子(三矩阵)线性相乘的联合块对角化结构,通过对相关矩阵组构成的三维矩阵进行切片分割,并对切片矩阵各元素重新排列规划,得到关于三组待定矩阵的标准最小二乘解。进而提出了一种基于交替最小二乘的三因子分解算法(记作ALS-NOJBD),联合估计待定矩阵的所有参数,实现非正交JBD,克服了现有的非正交ZJBD算法易于产生奇异解以及本文所提出的GH-NOJBD算法对噪声敏感的不足。6.受到适用于非正交JD的TIA算法的启发,提出一种具有普遍适用性的基于三迭代的非正交JBD算法:TIA-NOJBD。与ALS-NOJBD算法相比,TIA-NOJBD继承了ALS-NOJBD收敛性能稳定的优点,同时避免了高阶矩阵运算,使得计算复杂度降低了至少一个数量级。与现有的(非)正交JBD算法(包括本文所提的QJBD,GH-NOJBD,ALS-NOJBD算法)相比,TIA-NOJBD在适用条件、计算复杂度和收敛性能这三个方面都更具优势。7.提出一种基于单分量追踪的多阶段时频卷积盲分离方法,MTD。该方法每次只分离一路信号的所有频率分量,有效地避免了由于单独处理各个频点而引入的频间排列不定性。该方法可认为是基于联合对角化的瞬时盲分离算法在时频域卷积盲分离问题中的推广应用。更多还原

【Abstract】 Blind source separation (BSS) aims to extract independent but unobservered source signals from their mixtures captured by a number of sensors without knowing the mixing coefficients. In the past two decades, BSS has received much attention in various fields, such as speech and audio processing, image enhancement and biomedical signal processing. This dissertation emphasizes on the theory and algorithm of BSS in both instantaneous case and convolutive case. The joint diagonalization (JD) and joint block-diagonalization (JBD) are the essential tools to resolve the instantaneous BSS and convolutive BSS, respectively. Accordingly, the main contributions of this dissertation are summarized as follows:1. An identifiability theorem of non-orthogonal (non-unitary) JD was given with wide applicability, which provides a theoretical basis for non-orthogonal (non-unitary) JD based BSS algorithms. It was shown with a strict algebraic proof that the extracted mixing matrix from a group of objective matrices constructed from a common mixing matric, is essentially equal to the real mixing matrix, i.e., there is only a difference of one generalized permutation matrix between the extracted and the real mixing matrices.2. Based on the permutation and scaling indeterminacies for the BSS problems, a novel tri-quadratic fitting function was proposed by improving the classical least squares cost function. The new fitting function is quadratic if any two of the three unknown parameter sets are fixed. Meanwhile, the corresponding non-orthogonal JD algorithm, tri-quadratic iterative algorithm (TIA), was given to optimize the new quadratic fitting function. Neither the (conjugate) symmetry of the objective matrix nor the orthogonality of the mixing function is required in the TIA algorithm. Convergence of TIA algorithm was analyzed by utilizing the definition of the Lyapunov function and the LaSalle’Invariance Principle. The analytical results indicate that the TIA converges to the invariant set of the tri-quadratic fitting function that contains the acceptable set of the BSS.3. Taking the sum of the F-norms of all off-diagonal sub-matrices as a criterion, a novel orthogonal JBD algorithm, QJBD (quadratic JBD), was proposed to estimate the whole mixing matrix through minimizing a sequence of restrictive quadratic subfunctions corresponding to mixing submatrices. Both theoretical analysis and simulation results show that QJBD has much lower complexity and faster convergence speed than that of the classical Jacobi-like methods without performance loss. Furthermore, different from Jacobi-like methods, QJBD is not sensitive to the channel order and initialization values.4. Analysis shows that there is only a difference of one permutation matrix between the estimated and the real separation matrices, if the J-Di algorithm that is used traditionally for non-orthogonal JD, is directly applied to JBD. Accordingly, a non-orthogonal JBD algorithm, GH-NOJBD, was proposed by improving the J-Di algorithm. GH-NOJBD solves the convolutive-mixture BSS directly in time domain and does not require pre-whitening of the observed signals. Then, obviously there is no extra error introduced by pre-whitening and as a result, there is no need to require at least one objective matrix to be positive definite. What is the most important is that the separation performance of the proposed GH-NOJBD algorithm is superior to that of the Jacobi-like JBD counterparts.5. To overcome the disadvantages of the existing ZJBD algorithm (easily generating singular solutions) and the proposed GH-NOJBD algorithm (sensitive to noise), an alternating and iterative approach (ALS-NOJBD) for non-orthogonal JBD was proposed to estimate all the parameters of the undetermined matrix jointly. Because the correlation matrix group of the received signals has a three-factor-product JBD structure, standard least-squares expressions could be deduced with respect to the three factorable matrices by cutting pieces and then reprogramming of the 3-D matrix composed of the correlation matrix group. This is just the motivation of the ALS-NOJBD algorithm. Simulation results show that compared with traditional JBD algorithms, ALS-NOJBD has better and more stable separation performance without limitation in initial parameter choosing, and effectively overcome the disadvantages of both ZJBD and GH-NOJBD algorithms.6. Inspired by the TIA for JD, its counterpart for JBD, TIA-NOJBD algorithm was proposed. In each sub-step, a closed solution is derived by minimizing the cost function associated with one parameter-group while fixing the others. Compared with ALS-NOJBD, TIA-NOJBD also has a stable separation performance but at least one order of magnitude lower computation complexity. Besides, TIA-NOJBD is superior to all other JBD algorithms (including those proposed in this thesis, QJBD,GH-NOJBD,ALS-NOJBD) in three aspects, i.e., application conditions, computation complexity and convergency performance.7. A multistage decomposition based on single component tracking (MTD) was proposed to resolve the convolutive BSS in time-frequency domain. Unlike the previous frequency-domain methods, MTD estimates one set of inverse FIR parameters corresponding to only one of the separated signals at a time. This feature of MTD makes there are no internal-permutation and internal-scaling ambiguities which are the inherent disadvantages of the frequency-domain convolutive BSS algorithms. From a certain point of view, MTD can be considered as an extential form of JD in time-frequency domain.更多还原