【作者】 李炜；

【导师】 杨慧中；

【作者基本信息】 江南大学 ， 控制理论与控制工程， 2014， 博士

【摘要】 盲信号分离（Blind Signal Separation，BSS）是指仅通过对传感器上获取的一组观测信号进行分析和处理，从而在并不了解混合系统先验信息的情况下恢复出无法直接观测的多维源信号。盲信号分离在无线通信，语音的识别和增强，图像的重构和特征提取等方面都有着广泛而重要的应用价值，使得其已成为近年来人工神经网络，统计学以及信号处理等相关科研领域所研究的一个热点问题。本文围绕多种混合模型情况下的盲信号分离问题，做了以下几个方面的工作：首先，对于线性适定混合模型，即源信号数目与观测信号数目相等的情况，基于最小化互信息原理，分别提出了两种自适应BSS方法。针对传统的梯度类BSS算法在实时计算中收敛速度较慢的问题，提出了一种基于动量项技术的BSS算法。该算法采用分离信号的互信息量作为代价函数，并将动量项融入到了优化该代价函数的自然梯度学习规则中，推导了搜索期望分离矩阵的自适应算法。为了使得所提算法能够分离出包含不同统计特性的源信号，在分离算法的每一步迭代更新中，使用了基于Gram-Charlier展开式的分离信号评价函数的估计算法。仿真结果验证了所提BSS算法在收敛速度上的优越性，以及在源信号中同时包含超高斯和亚高斯信号时的分离性能。鉴于共轭梯度算法在神经网络学习中所表现出的卓越性能，提出了一种基于共轭梯度的自适应盲信号分离算法。该算法在传统的随机梯度和自然梯度算法的基础上，结合互信息准则，将共轭梯度搜索原理引入到了最优分离矩阵的求解中。即分离矩阵总是沿着与当前搜索方向共轭的方向进行更新。作为算法成功与否的关键点，采用核概率密度估计方法来估计分离信号的概率密度，进而直接估计出对应的评价函数，而不是依据经验来选取单一的非线性函数。仿真结果验证了基于共轭梯度的BSS算法的有效性。对于传感器接收的观测信号数目多于源信号，且混合矩阵为列满秩矩阵的情形，提出了一种快速收敛的超定盲信号分离方法。该方法从对分离矩阵进行奇异值分解入手，引入了超定BSS的代价函数。然后依据该代价函数，利用共轭梯度搜索原理推导了迭代计算分离矩阵的学习算法。并在算法的每一步计算中，利用随机变量概率密度函数的核密度估计法估计分离信号的评价函数。在计算机仿真中，通过与随机梯度算法和自然梯度算法相比较，验证了所提超定BSS算法的性能。针对欠定混合模型中观测信号数量不足的问题，研究了在欠定混合条件下的非稀疏信号的BSS问题，提出了一种基于局部平均分解的欠定混合BSS方法。该方法的基本思想是首先通过对混合信号进行局部平均分解处理，生成若干乘积函数。按照一定的标准挑选出足够数目的乘积函数，进而构造出一组额外的混合信号。将该组信号加入到原来的混合信号中，使得欠定盲分离模型转变为适定或超定盲分离模型以便于处理。对于新的混合信号和新的混合模型，使用两种高效的盲分离算法分离出源信号。理论上，局部平均分解算法的应用对于信号的类别是没有限制的。因此，所提的欠定盲分离算法可以打破大多数方法中存在的稀疏性约束，适用范围更广。另一方面，所提算法直接计算源信号，而不用预先估计出欠定混合矩阵，免去了不必要的计算。仿真结果验证了算法的性能。除了上述线性混合模型以外，对于非线性混合模型，提出了一种基于感知器网络的非线性盲信号分离方法。该方法采用感知器网络构建非线性分离系统来分离源信号，以最大输出信息熵原理作为分离准则调整非线性分离系统的参数，利用共轭梯度优化算法计算分离感知器的隐层和输出层连接权矩阵。算法中的Sigmoid函数选为分离信号的概率分布函数，并采用一种自适应参数化概率密度估计方法对其进行估计。仿真结果验证了所提算法的有效性。最后，提出了一种用于线性卷积混合信号盲分离的联合对角化方法。当信号的混合过程并不是瞬时完成，也就是在将源信号到传感器的传输过程中的延时也考虑进去的时候，盲信号分离问题的混合模型就变成了一个多维信号的卷积混合模型。所提的BSS方法首先将卷积混合模型变换为瞬时混合模型，得到新的瞬时混合信号，然后对变换后的模型应用联合对角化技术求取分离矩阵。同时，仿真结果表明该方法可成功实现线性卷积混合信号的盲分离。更多还原

【Abstract】 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.更多还原