独立分量分析算法及其在生物医学中的应用研究
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摘要
独立分量分析(Independent Component Analysis，ICA)是近期发展起来的一种新的数据处理方法。其目的是从观测到的混合信号中分离(或提取)出分布未知但相互统计独立的源信号。基于ICA的盲源分离(Blind Source Separation，BSS)或盲源提取(Blind Source Extraction，BSE)已经引起了广泛的关注，并已经成功地应用于生物医学信号处理、无线通信、图象处理和语音信号处理等众多领域。目前，ICA已经成为国内外人工神经网络和信号处理等领域的研究热点。最近几年来，有关的理论和算法研究都得到了较快的发展。但仍然还存在一些尚未解决的问题，这使得进一步应用ICA受到了较大限制。目前有许多科研机构都在积极探索ICA与具体应用相结合的新方法，取得了许多有价值的研究成果，这些成果使得它在各个领域的应用前景更加广阔。
本文主要对标准ICA算法、约束ICA算法、噪声模型下的算法及其在生物医学中的应用进行了研究，主要研究内容和取得的创新性成果如下：
1．对目前标准ICA中某些算法存在收敛速度慢和某些算法存在不能分离多种分布的混合信号(特别是有偏信号)等问题进行研究，提出了一种基于全乘正交群的快速自适应算法。该算法采用一种包含三种分布的概率密度模型，不仅实现了对超高斯信号和亚高斯分布信号的分离，还成功实现了对有偏信号和分布接近高斯信号的同步分离，具有收敛速度快、分离精度高和不需要选择步长参数等优点，并将其应用到生物医学信号处理中成功获得了清晰的胎儿心电图。
2．研究了目前约束ICA中某些算法存在对野点鲁棒性差、某些算法存在对时延估计的鲁棒性差和某些算法存在需要更多的先验信息才能实现成功提取等问题，提出了一种基于近似负熵的鲁棒提取算法。该算法采用近似负熵作为代价函数，对野点具有很好的鲁棒性，且仅需要知道想要提取的源信号的峭度值范围，而不需要其它更多的先验信息便可实现对“感兴趣”源信号的成功提取。特别是，当有多个源信号的峭度值接近时，也能提取出清晰的源信号，并将其成功应用到直接提取胎儿心电图中，取得了不错的效果。
3．针对目前采用标准ICA或BSS算法获取房颤信号中存在操作和判断复杂(需要分离所有信号后再对每个信号分别进行频谱分析才能确定房颤信号)等问题，提出了一种基于两阶段的直接提取算法。该算法结合了约束ICA和基于时序结构这两种直接提取BSE的方法，成功实现了对单个房颤信号的直接提取。真实房颤病人数据的实验表明，该算法简化了判断过程，节省了大量的时间和存储空间，更适合应用到临床监护中。
4．对目前大多数ICA算法和直接提取BSE算法存在对噪声环境适用性差的问题进行研究，提出了一个适合于噪声模型的代价函数，并通过特征值分解后推导出一个噪声模型下的提取算法。该算法对时延估计具有鲁棒性(只要时延估计误差不太大)，而且能够在存在传感器噪声环境下成功提取出清晰的“感兴趣”源信号。该算法的有效性通过模拟数据集的仿真和真实世界数据集的实验得到了验证。
Independent component analysis (ICA) is a recently developed signal processing technique. Its basic task is separating or extracting independent source signals that are linearly combined in observations. Recently, there is a trend to develop blind source separation (BSS) or blind source extraction (BSE) algorithms based on ICA, due to its potential applications in a lot of fields, such as biomedical signal processing, telecommunication system, image processing and speech processing. In recent years, there are some progress in ICA theories and algorithms. However, there are still many unsolved problems exist, which could restrict the development of many ICA applications. Many organizations have done lots of work to promote the applications of ICA in many fields. As a result, ICA has become one of the most exciting hot topics both in the fields of neural networks and signal processing.
This dissertation mainly focuses on basic ICA algorithms, constrained ICA algorithms, extraction algorithms with noise model, and their applications to biomedical signals extraction. Especially, the main contents arc as follows:
1. This dissertation proposes a fast and adaptive algorithm based on fully-multiplicative orthogonal-group, which solves some problems of current basic ICA algorithms, such as slow convergence speed. The algorithm adopts a density model that combines the t-distribution density model, the light-tailed distribution density model, and the Pearson system model so that it not only can separate mixtures of sub-Gaussian and super-Gaussian source signals, but also can separate skewed and near Gaussian signals. Therefore the algorithm was successfully applied to obtain a clear Fetal Electrocardiogram (FECG) signal with better separation performance and faster convergence speed, compared with some famous basic ICA algorithms.
2. The dissertation develops a robust extraction algorithm based on approximate negentropy to overcome some drawbacks of current constrained ICA algorithms, such as bad robustness to outliers. The algorithm is very robust to outliers because of using an approximate negentropy. And it only needs to estimate the coarse kurtosis value range of a desired signal, not need the additional priori information. Moreover, the algorithm can work well in some adverse situations when the kurtosis values of some source signals are very close to each other. All these make that the algorithm is an appealing method which directly extracts an accurate and reliable FECG.
3. To solve the current problem about obtaining Atrial Fibrillation (AF) signal, the dissertation presents a two-stage based algorithm, which can successfully and directly extract a desired AF signal by two BSE methods. Compare with current BSS or basic ICA methods of separating all source signals, the algorithm based BSE is simple on operation, and can save a lots of times and resources. Extensive experiments on real-world data of patients suffering from AF have showed that it can rapidly and efficiently extract a clear AF signal and greatly reduce lots of noise. Therefore, the algorithm is expected to have great potential in clinical diagnosis.
4. Many existing ICA or BSE methods are limited to noise-free mixtures, which are not realistic. So the dissertation proposes a novel cost function from that the effect of noise is removed. Maximizing the cost function, it can obtain a BSE algorithm, which caters for the effects of noise. The algorithm is robust to the estimation errors of the time delay as long as the errors are not too large. Compared with some classical algorithms, the proposed algorithm has better extraction performance in the presence of noise, as confirmed by simulations and experiments on real-world data.
本文主要对标准ICA算法、约束ICA算法、噪声模型下的算法及其在生物医学中的应用进行了研究，主要研究内容和取得的创新性成果如下：
1．对目前标准ICA中某些算法存在收敛速度慢和某些算法存在不能分离多种分布的混合信号(特别是有偏信号)等问题进行研究，提出了一种基于全乘正交群的快速自适应算法。该算法采用一种包含三种分布的概率密度模型，不仅实现了对超高斯信号和亚高斯分布信号的分离，还成功实现了对有偏信号和分布接近高斯信号的同步分离，具有收敛速度快、分离精度高和不需要选择步长参数等优点，并将其应用到生物医学信号处理中成功获得了清晰的胎儿心电图。
2．研究了目前约束ICA中某些算法存在对野点鲁棒性差、某些算法存在对时延估计的鲁棒性差和某些算法存在需要更多的先验信息才能实现成功提取等问题，提出了一种基于近似负熵的鲁棒提取算法。该算法采用近似负熵作为代价函数，对野点具有很好的鲁棒性，且仅需要知道想要提取的源信号的峭度值范围，而不需要其它更多的先验信息便可实现对“感兴趣”源信号的成功提取。特别是，当有多个源信号的峭度值接近时，也能提取出清晰的源信号，并将其成功应用到直接提取胎儿心电图中，取得了不错的效果。
3．针对目前采用标准ICA或BSS算法获取房颤信号中存在操作和判断复杂(需要分离所有信号后再对每个信号分别进行频谱分析才能确定房颤信号)等问题，提出了一种基于两阶段的直接提取算法。该算法结合了约束ICA和基于时序结构这两种直接提取BSE的方法，成功实现了对单个房颤信号的直接提取。真实房颤病人数据的实验表明，该算法简化了判断过程，节省了大量的时间和存储空间，更适合应用到临床监护中。
4．对目前大多数ICA算法和直接提取BSE算法存在对噪声环境适用性差的问题进行研究，提出了一个适合于噪声模型的代价函数，并通过特征值分解后推导出一个噪声模型下的提取算法。该算法对时延估计具有鲁棒性(只要时延估计误差不太大)，而且能够在存在传感器噪声环境下成功提取出清晰的“感兴趣”源信号。该算法的有效性通过模拟数据集的仿真和真实世界数据集的实验得到了验证。
Independent component analysis (ICA) is a recently developed signal processing technique. Its basic task is separating or extracting independent source signals that are linearly combined in observations. Recently, there is a trend to develop blind source separation (BSS) or blind source extraction (BSE) algorithms based on ICA, due to its potential applications in a lot of fields, such as biomedical signal processing, telecommunication system, image processing and speech processing. In recent years, there are some progress in ICA theories and algorithms. However, there are still many unsolved problems exist, which could restrict the development of many ICA applications. Many organizations have done lots of work to promote the applications of ICA in many fields. As a result, ICA has become one of the most exciting hot topics both in the fields of neural networks and signal processing.
This dissertation mainly focuses on basic ICA algorithms, constrained ICA algorithms, extraction algorithms with noise model, and their applications to biomedical signals extraction. Especially, the main contents arc as follows:
1. This dissertation proposes a fast and adaptive algorithm based on fully-multiplicative orthogonal-group, which solves some problems of current basic ICA algorithms, such as slow convergence speed. The algorithm adopts a density model that combines the t-distribution density model, the light-tailed distribution density model, and the Pearson system model so that it not only can separate mixtures of sub-Gaussian and super-Gaussian source signals, but also can separate skewed and near Gaussian signals. Therefore the algorithm was successfully applied to obtain a clear Fetal Electrocardiogram (FECG) signal with better separation performance and faster convergence speed, compared with some famous basic ICA algorithms.
2. The dissertation develops a robust extraction algorithm based on approximate negentropy to overcome some drawbacks of current constrained ICA algorithms, such as bad robustness to outliers. The algorithm is very robust to outliers because of using an approximate negentropy. And it only needs to estimate the coarse kurtosis value range of a desired signal, not need the additional priori information. Moreover, the algorithm can work well in some adverse situations when the kurtosis values of some source signals are very close to each other. All these make that the algorithm is an appealing method which directly extracts an accurate and reliable FECG.
3. To solve the current problem about obtaining Atrial Fibrillation (AF) signal, the dissertation presents a two-stage based algorithm, which can successfully and directly extract a desired AF signal by two BSE methods. Compare with current BSS or basic ICA methods of separating all source signals, the algorithm based BSE is simple on operation, and can save a lots of times and resources. Extensive experiments on real-world data of patients suffering from AF have showed that it can rapidly and efficiently extract a clear AF signal and greatly reduce lots of noise. Therefore, the algorithm is expected to have great potential in clinical diagnosis.
4. Many existing ICA or BSE methods are limited to noise-free mixtures, which are not realistic. So the dissertation proposes a novel cost function from that the effect of noise is removed. Maximizing the cost function, it can obtain a BSE algorithm, which caters for the effects of noise. The algorithm is robust to the estimation errors of the time delay as long as the errors are not too large. Compared with some classical algorithms, the proposed algorithm has better extraction performance in the presence of noise, as confirmed by simulations and experiments on real-world data.
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