非线性盲信号抽取及应用研究
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摘要
在源信号和传输信道均未知情况下，从若干观测到的多个信号的混合信号中恢复出源信号的信号处理方法，称为盲信号分离（Blind Source Separation, BSS）。由于其在物医学工程、声呐、雷达、语音增强、无线通讯和图像处理等领域的广泛应用，盲信号分离成为信号处理领域的重要研究课题之一。目前提出的大多数的盲信号分离算法是基于线性瞬时混合模型，并且同时恢复出所有的未知源信号。在许多实际应用场景下，由于传感器非线性传输特性的影响，实际问题被建模为非线性混合方式将更加准确和符合实际情况，而且感兴趣的源信号往往只是少数几个甚至一个。此时，采用盲信号分离技术同时恢复出所有的未知源信号将带来很多不必要的计算，消耗大量的时间。针对上述问题，本学位论文重点研究了非线性盲信号抽取（Blind Source Extraction，BSE）及其在生物医学工程中的应用，取得了以下创新性成果：
1.提出一种基于峭度的非线性盲抽取算法：该算法是将感兴趣源信号的归一化峭度范围这一先验知识当做约束条件加入到盲信号分离的对照函数中，从而构造成一个带有约束条件的优化问题。该优化问题通过增广拉格朗日函数法被转化为无约束的优化问题，然后利用标准的梯度下降学习法求解，从而抽取出感兴趣的源信号。由于先验知识的运用，该算法可以从后非线性混合信号中一次性地抽取感兴趣的源信号，从而有效地避免很多不必要的计算，节省了大量的时间。
2.提出一种基于参考信号的非线性盲抽取算法：首先传统的限制独立成分分析框架被扩展到后非线性混合模型中，然后基于该框架，一种基于参考信号的非线性盲抽取算法被提出。该算法是将参考信号和抽取信号之间的相似性函数当作新的目标函数，采用标准梯度上升学习法交替更新该目标函数和盲信号分离的负熵对照函数，从而可以从后非线性混合信号中一次性地抽取出感兴趣源信号的准确波形。由于利用了参考信号这一先验知识，并避免了阈值设置问题，该算法可以大大地减少计算量，并有效地提高信号盲抽取的精度和准确性。
3.提出了一种基于高斯化的非线性盲抽取算法：该算法分为两个阶段，第一个阶段根据中心极限定理，利用高斯化变换技术补偿掉后非线性混合模型中的未知非线性畸变，得到近似的线性混合信号；第二个阶段利用已知的感兴趣源信号的归一化峭度范围这一先验知识，从非线性畸变补偿之后得到的近似线性混合信号中抽取出我们感兴趣的源信号。因为规避了未知非线性函数的逼近和拟合问题，并分两个阶段实现后非线性混合信号的盲抽取，所以，该算法不仅简单灵活，而且还可以有效地提高信号盲抽取的效率。
4.提出两种非线性胎儿心电信号抽取算法：胎儿心电信号抽取是生物医学工程领域的重要研究课题之一，它具有非常重要的临床意义。基于信息最小化原则，本学位论文提出了一种新的目标函数，并基于该目标函数提出了两种新颖的非线性胎儿心电信号抽取算法。第一种算法是采用直接估计和计算概率密度函数实现的，其推导过程简单明了。第二种算法规避了未知概率密度函数的估计问题，利用可逆变换不影响互信息大小这个良好性质推导实现的。计算机仿真实验结果证实了这两种算法的正确性和有效性。
Blind source separation (BSS) is a signal processing method which aims atrecovering the original sources simultaneously from all kinds of their observed mixtures,without the need for prior knowledge of the mixing process and the sources themselves.It has become an important research topic in the signal processing area due to its wideapplications in many fields, such as biomedical engineering, sonar, radar, speechenhancement, telecommunications, and image processing, and so on. Most existing BSSalgorithms have been specially designed for the linear instantaneous mixture model andrecovered all the unknown sources simultaneously. In many practical situations, it ismore appropriate to model many practical problems to the nonlinear mixtures due to thenonlinear distortions that sensors introduce. Besides, only a single source or a subset ofsources is subject of interest and separating all the sources at a time could take a largetime and have mach unnecessary computation. For the above problems, in this thesis thenonlinear blind source extraction (BSE) and its applications in the biomedicalengineering are focused on and the innovative results are obtained as follows:
1. A kurtosis-based nonlinear blind source extraction algorithm is proposed. Inthis algorithm, the prior knowledge of the normalized kurtosis range about the desiredsource is treated as a constraint and incorporated into the contrast function of blindsource separation. Therefore, a constrained optimization problem is formulated. By theaugmented Lagrange function method, this constrained optimization problem istransformed into an unconstrained optimization problem, which is solved by thestandard gradient descent learning. Due to the use of the prior knowledge, the source ofinterest can be extracted at a time from the post-nonlinear (PNL) mixtures by thisalgorithm, which effectively avoids much unnecessary calculations and saves a lot oftime.
2. A reference-based nonlinear blind source extraction algorithm is proposed.First, the traditional constrained independent component analysis (cICA) framework isextended to the PNL mixture model. Then, a reference-based nonlinear blind sourceextraction algorithm is proposed based on this new framework. In this algorithm, thecloseness measure between the estimated output and the reference signal is treated as a new objective function. By alternately optimizing the contrast function and this newobjective function with standard gradient ascent learning, the desired source can beextracted from the PNL mixtures. Due to the prior knowledge of the reference signaland circumventing the threshold per-determined problem, the computation time isreduced greatly and the accuracy of the desired source is improved.
3. A Gaussianization-based nonlinear blind source extraction algorithm isproposed. The proposed algorithm is a two-stage process that consists of aGaussianizing transformation and extracting the desired source with specific kurtosisrange. First, according to the central limit theorem, the nonlinear distortions in the PNLmixture are compensated by the Gaussianizing transformation and the approximatelylinear-mixed signals are obtained. Then, with the augmented Lagrange function method,the source of interest is extracted from these signals by using the prior knowledge of thenormalized kurtosis range about the desired source. Due to two stages and avoiding theapproximation problem of the unknown functions, this algorithm is simple and flexible.Besides, the efficiency of blind source extraction is improved greatly.
4. Two nonlinear fetal electrocardiogram (FECG) extraction algorithms areproposed. The extraction of FECG is an important research topic in the field of thebiomedical engineering and it has clinical significance. Based on the informationminimization principle, a new objective function is proposed. Then, based on this newobjective function, two novel algorithms to extract FECG from the nonlinear mixturesare proposed. The first one is relatively simple, in which the probability density function(PDF) is directly estimated and calculated. By the good nature of mutual informationthat it can’t be affected by the invertible transformation, the PDF estimation problem iscircumvented in the second algorithm. The correctness and validity of these twoalgorithms are confirmed by the computer simulations and experiments.
1.提出一种基于峭度的非线性盲抽取算法：该算法是将感兴趣源信号的归一化峭度范围这一先验知识当做约束条件加入到盲信号分离的对照函数中，从而构造成一个带有约束条件的优化问题。该优化问题通过增广拉格朗日函数法被转化为无约束的优化问题，然后利用标准的梯度下降学习法求解，从而抽取出感兴趣的源信号。由于先验知识的运用，该算法可以从后非线性混合信号中一次性地抽取感兴趣的源信号，从而有效地避免很多不必要的计算，节省了大量的时间。
2.提出一种基于参考信号的非线性盲抽取算法：首先传统的限制独立成分分析框架被扩展到后非线性混合模型中，然后基于该框架，一种基于参考信号的非线性盲抽取算法被提出。该算法是将参考信号和抽取信号之间的相似性函数当作新的目标函数，采用标准梯度上升学习法交替更新该目标函数和盲信号分离的负熵对照函数，从而可以从后非线性混合信号中一次性地抽取出感兴趣源信号的准确波形。由于利用了参考信号这一先验知识，并避免了阈值设置问题，该算法可以大大地减少计算量，并有效地提高信号盲抽取的精度和准确性。
3.提出了一种基于高斯化的非线性盲抽取算法：该算法分为两个阶段，第一个阶段根据中心极限定理，利用高斯化变换技术补偿掉后非线性混合模型中的未知非线性畸变，得到近似的线性混合信号；第二个阶段利用已知的感兴趣源信号的归一化峭度范围这一先验知识，从非线性畸变补偿之后得到的近似线性混合信号中抽取出我们感兴趣的源信号。因为规避了未知非线性函数的逼近和拟合问题，并分两个阶段实现后非线性混合信号的盲抽取，所以，该算法不仅简单灵活，而且还可以有效地提高信号盲抽取的效率。
4.提出两种非线性胎儿心电信号抽取算法：胎儿心电信号抽取是生物医学工程领域的重要研究课题之一，它具有非常重要的临床意义。基于信息最小化原则，本学位论文提出了一种新的目标函数，并基于该目标函数提出了两种新颖的非线性胎儿心电信号抽取算法。第一种算法是采用直接估计和计算概率密度函数实现的，其推导过程简单明了。第二种算法规避了未知概率密度函数的估计问题，利用可逆变换不影响互信息大小这个良好性质推导实现的。计算机仿真实验结果证实了这两种算法的正确性和有效性。
Blind source separation (BSS) is a signal processing method which aims atrecovering the original sources simultaneously from all kinds of their observed mixtures,without the need for prior knowledge of the mixing process and the sources themselves.It has become an important research topic in the signal processing area due to its wideapplications in many fields, such as biomedical engineering, sonar, radar, speechenhancement, telecommunications, and image processing, and so on. Most existing BSSalgorithms have been specially designed for the linear instantaneous mixture model andrecovered all the unknown sources simultaneously. In many practical situations, it ismore appropriate to model many practical problems to the nonlinear mixtures due to thenonlinear distortions that sensors introduce. Besides, only a single source or a subset ofsources is subject of interest and separating all the sources at a time could take a largetime and have mach unnecessary computation. For the above problems, in this thesis thenonlinear blind source extraction (BSE) and its applications in the biomedicalengineering are focused on and the innovative results are obtained as follows:
1. A kurtosis-based nonlinear blind source extraction algorithm is proposed. Inthis algorithm, the prior knowledge of the normalized kurtosis range about the desiredsource is treated as a constraint and incorporated into the contrast function of blindsource separation. Therefore, a constrained optimization problem is formulated. By theaugmented Lagrange function method, this constrained optimization problem istransformed into an unconstrained optimization problem, which is solved by thestandard gradient descent learning. Due to the use of the prior knowledge, the source ofinterest can be extracted at a time from the post-nonlinear (PNL) mixtures by thisalgorithm, which effectively avoids much unnecessary calculations and saves a lot oftime.
2. A reference-based nonlinear blind source extraction algorithm is proposed.First, the traditional constrained independent component analysis (cICA) framework isextended to the PNL mixture model. Then, a reference-based nonlinear blind sourceextraction algorithm is proposed based on this new framework. In this algorithm, thecloseness measure between the estimated output and the reference signal is treated as a new objective function. By alternately optimizing the contrast function and this newobjective function with standard gradient ascent learning, the desired source can beextracted from the PNL mixtures. Due to the prior knowledge of the reference signaland circumventing the threshold per-determined problem, the computation time isreduced greatly and the accuracy of the desired source is improved.
3. A Gaussianization-based nonlinear blind source extraction algorithm isproposed. The proposed algorithm is a two-stage process that consists of aGaussianizing transformation and extracting the desired source with specific kurtosisrange. First, according to the central limit theorem, the nonlinear distortions in the PNLmixture are compensated by the Gaussianizing transformation and the approximatelylinear-mixed signals are obtained. Then, with the augmented Lagrange function method,the source of interest is extracted from these signals by using the prior knowledge of thenormalized kurtosis range about the desired source. Due to two stages and avoiding theapproximation problem of the unknown functions, this algorithm is simple and flexible.Besides, the efficiency of blind source extraction is improved greatly.
4. Two nonlinear fetal electrocardiogram (FECG) extraction algorithms areproposed. The extraction of FECG is an important research topic in the field of thebiomedical engineering and it has clinical significance. Based on the informationminimization principle, a new objective function is proposed. Then, based on this newobjective function, two novel algorithms to extract FECG from the nonlinear mixturesare proposed. The first one is relatively simple, in which the probability density function(PDF) is directly estimated and calculated. By the good nature of mutual informationthat it can’t be affected by the invertible transformation, the PDF estimation problem iscircumvented in the second algorithm. The correctness and validity of these twoalgorithms are confirmed by the computer simulations and experiments.
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