基于稀疏分解的心电信号特征波检测及心电数据压缩
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摘要
心脏病一直是威胁人类健康的主要疾病之一,心电图(Electrocardiogram, ECG)是心脏病检查重要的无创性辅助工具,因而心电信号处理在医学信号处理中一直占据重要地位。每种新信号处理理论出现后,都会被应用于心电信号处理领域,给心电信号处理带来新研究方向和方法。随着信号处理理论的发展,心电信号处理也相应地出现时域处理算法、变换域处理算法(傅立叶变换(FT)、离散余弦变换(DCT)、小波变换等)、参数空间算法(句法、神经网络、支持矢量机、隐马尔科夫模型等)等多种处理算法。
心电信号处理主要包括心电信号去噪、心电信号特征波检测识别、心电信号数据压缩等内容。现有心电信号处理算法在以上的各个方面都取得了很多成就,但无论理论还是应用上,心电信号处理的这些方面都需进一步研究。稀疏分解理论的出现为心电信号处理提供了新切入点,论文的主要工作就是稀疏分解理论研究及其在心电信号特征波检测识别和心电数据压缩两方面的应用。
稀疏分解在心电信号的特征波检测识别中的应用:论文中提出三种超完备字典,并根据稀疏分解所用超完备字典的不同,提出三种基于稀疏分解的心电信号特征波检测识别算法:第一种算法所用超完备字典是先根据心电信号特征波确定生成函数,再通过离散化生成函数参数构造的超完备字典;第二种算法所用超完备字典是根据实际心电数据和先验知识产生的训练样本,通过K-SVD算法训练得到超完备字典;第三种算法所用超完备字典是改进的Gabor字典。第一种算法和第二种算法所使用字典,是根据心电信号特征波的特征得到,因此该字典对心电信号特征波具有良好的可分性(指根据原子自身特点区分其代表波形属那种特征波的能力),可分性对特征波检测识别至关重要。可分性使得稀疏分解的结果可以直接用来检测识别心电信号的各种特征波,保证了算法的检测识别正确率。第三种特征波检测识别算法所用的改进的Gabor字典是一个固定的字典,因为生成函数是Gabor函数而得名,Gabor字典不随待分解信号种类的改变而改变,其在对心电信号特征波的可分性方面不如根据心电信号特征波构造的超完备字典好,这导致在Gabor字典上得到心电信号的稀疏分解结果不能直接用于特征波检测识别,需要结合其它理论来完成特征波检测识别。论文提出两种算法完成特征波检测识别:其一、把基于Gabor字典的稀疏分解结果和模糊理论相结合,利用模糊理论的不确定信息处理能力检测识别特征波;其二、把基于Gabor字典的稀疏分解结果和神经网络结合,利用神经网络的非线性分类能力检测识别特征波。两个途径都实现了P波、QRS波群及T波的检测识别,从检测识别正确率来看,二者相当,和神经网络相结合的算法能同时得到P波、QRS波群、T波的位置、波宽等参数,而和模糊理论相结合的算法需要先检测识别QRS波群,再根据QRS波群和医学先验知识检测识别P波、T波。
稀疏分解在心电数据压缩中的应用:随着心电图的广泛应用,大量心电数据需要存储和传输,这使得心电数据压缩成为心电信号处理的重要内容。论文提出基于稀疏分解的心电数据压缩算法,该算法首先对心电数据进行稀疏分解,得到心电数据的稀疏表示,存储心电数据时,只需存储心电数据解向量非零元的位置、大小和稀疏分解所用的超完备字典。此处稀疏分解所用超完备字典是由K-SVD算法对心电样本数据进行训练得到的,该字典能从整体上充分体现心电信号的特征。因此,在压缩比相同的条件下,和其它心电数据压缩算法相比,该压缩算法的重构信号失真更小。该心电数据压缩算法能根据实际需要选择数据的压缩率。
稀疏分解最优匹配原子搜索算法的优化:信号的稀疏分解能得到信号的稀疏表示方法,有利于后续信号处理,但稀疏分解涉及到NP难题的求解,计算复杂。这个缺点是制约信号稀疏分解广泛应用的瓶颈。分析可知,造成稀疏分解计算量过大的原因有两个:一是稀疏分解中最优匹配原子搜索算法计算复杂;二是超完备字典中原子数目较大。论文提出用粒子群优化算法优化稀疏分解最优匹配原子搜索的粒子群匹配追踪算法(PSO-MP),使信号的稀疏分解速度和用匹配追踪算法搜索最优匹配原子的稀疏分解相比提高两个数量级。第二个问题关键在于如何保证超完备字典性能的前提下,尽量减少原子数目,目前此问题仍然是一个开放的问题。论文研究Gabor字典在心电信号检测识别中的应用时,把原来的Gabor字典用Gabor函数的参数空间代替,用粒子群匹配追踪算法在参数空间上搜索最优匹配原子,这样造成稀疏分解计算量过大的两个问题同时得到解决。
超完备字典的构造:稀疏分解超完备字典的构造方法可以分为无训练字典构造方法和有训练字典构造方法两种。论文在第三章中根据心电信号特征波先验知识构造超完备字典以及第四章提出的改进的Gabor字典都属于无训练的字典。第三章和第六章中通过K-SVD算法训练得到超完备字典的字典构造算法属有训练字典构造方法。第三章通过K-SVD算法训练得到超完备字典对心电信号特征波保持了良好的可分性;第六章通过K-SVD算法训练得到超完备字典则能充分体现心电信号整体特征的超完备字典,但该字典对特征波的可分性表现较差,这一特点使得通过有训练超完备字典方法构造的超完备字典在应用于心电数据压缩时表现出很好的性能,但无法应用于心电信号的特征波检测识别。
Cardiopathy is one of the major diseases which threaten human health. As an important non-invasive assistant tool for the diagnosis of cardiopathy, electrocardiogram (ECG) signal processing plays an important role in the medical signal processing. The new signal processing theory will alaways be soon applied to the field of ECG signal and bring new directions and methods for the study of ECG signal processing. Along with the development of signal processing theory, a great deal of different algorithms has been emerged in the ECG Signal processing e.g. time domain processing algorithms, transform domain processing algorithms (Fourier Transform (FT), discrete cosine transform (DCT), wavelet transform, etc.), the parameter space algorithm ( Syntax, neural network and support vector machines, HMM) and such.
ECG signal processing includes the ECG signal denoising, the detection and recognition of ECG signal feature waveform, the ECG data compression, etc. Though these existing ECG signal processing algorithms mentioned above have made a lot of success, theories and applications of them are required to investigate further. Recently, sparse decomposition theory provides a new developmental direction for ECG signal processing. This thesis foucses mainly on the theories of sparse decomposition and its applications in the detection and recognition of ECG signal feature waveform as well as in the ECG data compression.
Application of sparse decomposition in the detection and recognition of ECG signal feature waveform: In this thesis, three over-complete dictionary are created. According to the differences of over-complete dictionaries used in the sparse decomposition, the detection and recognition algorithms of ECG signal feature waveform can be divided into three kinds. In the first kind of algorithm, over-complete dictionary is created through discretization the parameter of generating function which is made according to the ECG signal feather waveform. In the second kind of algorithm, over-complete dictionary is trained by K-SVD algorithm whose sample data is brought form ECG data and the prior knowledge. In the third kind of algorithm, over-complete dictionary is the improved Gabor dictionary. As the over-complete dictionary used in the first algorithm and the second algorithm are obtained according to the ECG signal feature waveform, they have good separability towards the feature waveforms, which is especially important in the detection and recognition of ECG feature waveform. This separability makes the results of sparse decomposition be used directly in the detection and recognition of ECG signal feature waveform and, at the same time, it ensures the right ratio of the detection and recognition. The Gabor dictionary used in the third algorithm is a fixed dictionary. It is named as Gabor dictionary because of its generating function being Gabor function. It is unchangeable to the change of the signal decomposed and, its separability towards the feature waveforms is poorer than the dictionary constructed according to various characteristics of the feature waveforms, which leads the sparse representation of the ECG signal based on the Gabor dictionary not to be directly used for the detection and recognization ECG feature waveforms. Therefore, we need to combine other theories to fulfill the detection and recognition. There are two approaches used in this thesis to solve the above problem, one is to combine the result of sparse decomposition based on Gabor dictionary and the fuzzy theory and use its process capability of the uncertainty information to detect and recognize ECG feature waveforms. The other one is to combine the result of sparse decomposition based on Gabor dictionary and the neural network and use its non-linear classification capability to do this job. Both of above approaches can realized the detections and recognitions of P wave, QRS wave groups and T wave. The accuracy of the detections and recognitions shows the capabilities of two approaches are almost equivalent. The approach combining neural network can get simultaneously the waveform parameters, such as P wave, QRS complex, T wave’s position, span, etc. While the approach combining fuzzy theory needs to detect QRS complex first, then P wave and T wave are detected and recognized according to the position of QRS complex and the medical knowledge.
Application of sparse decomposition in the ECG data compression: With the extensive applications of ECG and the urgent requirement of storage and transmission of ECG data, the compression of ECG data has been an important domain of ECG processing. An ECG data compression algorithm based on sparse decomposition is presented in this thesis. First the sparse representation of ECG data is obtained on the bases of the sparse decomposition carried by this algorithm. When ECG data are compressed, we only need to store the position and non-zero value in the solution vector and over-complete dictionary used in the sparse decomposition of ECG data. The over-complete dictionary used here is acquired by the learning of the ECG sample data with K-SVD algorithm which makes it embody sufficiently the whole feature of ECG data. Compared with other algorithms of ECG data compression when the compression ratios are equal, the distortion of the ECG signal reconstructed with this algorithm is much smaller. Moreover, this ECG data compression algorithm can change the compression ratio to meet the practical needs.
Optimization of the best matching atom searching algorithm: Sparse decomposition of signal can get the sparse representation of signal which is of great advantage to signal processing. However, the complex calculation because of solving NP problem has become the bottleneck that restricts the application of the signal sparse decomposition. There are two causes result in the excessive calculation complexity of sparse decomposition, one is the algorithm searching the best matching atom is too complex, the other one is the number of the atoms is too large in the over-complete dictionary. This thesis brings forward an optimization algorithm namely PSO-MP for searching best matching atom. Using PSO-MP, the time expensivement of the sparse decomposition is 2 orders of magnitude less than the basic MP. The key to second problem is how to minimize the number of atoms on the premise of ensuring the quality of the over-complete dictionary, and now, it is an open question still. Two main steps are presented in this thesis for the studies of the Gabor dictionary’s application in the ECG signal processing. One is to replace the original Gabor dictionary by the Gabor function's parameter space, the other one is to search the best matching atom in parameter space by PSO method. Then, the two problems causing the excessive calculation complexity of sparse decomposition can be solved at the same time.
How to construct the over-complete dictionary: The methods of constructing the over-complete dictionary can be divided into the non-learning constructing method and the learning constructing method. In the third chapter of this thesis, the over-complete dictionary constructed according to the character of the feature waveforms belongs to non-learning dictionary. In the fourth chapter, the modified Gabor dictionary belongs to non-learning dictionary as well. In the third chapter and the sixth chapter, two over-complete dictionary are constructed by learning the ECG data with K-SVD algorithm, these over-complete dictionary are belonged to the learning constructing method. The over-complete dictionary constructed by K-SVD algorithm in third chapter keep the separability of waveforms, however, the dictionary in the sixth chapter gives a poor performance to the separability of waveforms. This characteristics makes the over-complete dictionary based on the learning constructing method do good in the ECG data compression learning. Yet it can not be applied in the detection and recognition of ECG feature waveform.
心电信号处理主要包括心电信号去噪、心电信号特征波检测识别、心电信号数据压缩等内容。现有心电信号处理算法在以上的各个方面都取得了很多成就,但无论理论还是应用上,心电信号处理的这些方面都需进一步研究。稀疏分解理论的出现为心电信号处理提供了新切入点,论文的主要工作就是稀疏分解理论研究及其在心电信号特征波检测识别和心电数据压缩两方面的应用。
稀疏分解在心电信号的特征波检测识别中的应用:论文中提出三种超完备字典,并根据稀疏分解所用超完备字典的不同,提出三种基于稀疏分解的心电信号特征波检测识别算法:第一种算法所用超完备字典是先根据心电信号特征波确定生成函数,再通过离散化生成函数参数构造的超完备字典;第二种算法所用超完备字典是根据实际心电数据和先验知识产生的训练样本,通过K-SVD算法训练得到超完备字典;第三种算法所用超完备字典是改进的Gabor字典。第一种算法和第二种算法所使用字典,是根据心电信号特征波的特征得到,因此该字典对心电信号特征波具有良好的可分性(指根据原子自身特点区分其代表波形属那种特征波的能力),可分性对特征波检测识别至关重要。可分性使得稀疏分解的结果可以直接用来检测识别心电信号的各种特征波,保证了算法的检测识别正确率。第三种特征波检测识别算法所用的改进的Gabor字典是一个固定的字典,因为生成函数是Gabor函数而得名,Gabor字典不随待分解信号种类的改变而改变,其在对心电信号特征波的可分性方面不如根据心电信号特征波构造的超完备字典好,这导致在Gabor字典上得到心电信号的稀疏分解结果不能直接用于特征波检测识别,需要结合其它理论来完成特征波检测识别。论文提出两种算法完成特征波检测识别:其一、把基于Gabor字典的稀疏分解结果和模糊理论相结合,利用模糊理论的不确定信息处理能力检测识别特征波;其二、把基于Gabor字典的稀疏分解结果和神经网络结合,利用神经网络的非线性分类能力检测识别特征波。两个途径都实现了P波、QRS波群及T波的检测识别,从检测识别正确率来看,二者相当,和神经网络相结合的算法能同时得到P波、QRS波群、T波的位置、波宽等参数,而和模糊理论相结合的算法需要先检测识别QRS波群,再根据QRS波群和医学先验知识检测识别P波、T波。
稀疏分解在心电数据压缩中的应用:随着心电图的广泛应用,大量心电数据需要存储和传输,这使得心电数据压缩成为心电信号处理的重要内容。论文提出基于稀疏分解的心电数据压缩算法,该算法首先对心电数据进行稀疏分解,得到心电数据的稀疏表示,存储心电数据时,只需存储心电数据解向量非零元的位置、大小和稀疏分解所用的超完备字典。此处稀疏分解所用超完备字典是由K-SVD算法对心电样本数据进行训练得到的,该字典能从整体上充分体现心电信号的特征。因此,在压缩比相同的条件下,和其它心电数据压缩算法相比,该压缩算法的重构信号失真更小。该心电数据压缩算法能根据实际需要选择数据的压缩率。
稀疏分解最优匹配原子搜索算法的优化:信号的稀疏分解能得到信号的稀疏表示方法,有利于后续信号处理,但稀疏分解涉及到NP难题的求解,计算复杂。这个缺点是制约信号稀疏分解广泛应用的瓶颈。分析可知,造成稀疏分解计算量过大的原因有两个:一是稀疏分解中最优匹配原子搜索算法计算复杂;二是超完备字典中原子数目较大。论文提出用粒子群优化算法优化稀疏分解最优匹配原子搜索的粒子群匹配追踪算法(PSO-MP),使信号的稀疏分解速度和用匹配追踪算法搜索最优匹配原子的稀疏分解相比提高两个数量级。第二个问题关键在于如何保证超完备字典性能的前提下,尽量减少原子数目,目前此问题仍然是一个开放的问题。论文研究Gabor字典在心电信号检测识别中的应用时,把原来的Gabor字典用Gabor函数的参数空间代替,用粒子群匹配追踪算法在参数空间上搜索最优匹配原子,这样造成稀疏分解计算量过大的两个问题同时得到解决。
超完备字典的构造:稀疏分解超完备字典的构造方法可以分为无训练字典构造方法和有训练字典构造方法两种。论文在第三章中根据心电信号特征波先验知识构造超完备字典以及第四章提出的改进的Gabor字典都属于无训练的字典。第三章和第六章中通过K-SVD算法训练得到超完备字典的字典构造算法属有训练字典构造方法。第三章通过K-SVD算法训练得到超完备字典对心电信号特征波保持了良好的可分性;第六章通过K-SVD算法训练得到超完备字典则能充分体现心电信号整体特征的超完备字典,但该字典对特征波的可分性表现较差,这一特点使得通过有训练超完备字典方法构造的超完备字典在应用于心电数据压缩时表现出很好的性能,但无法应用于心电信号的特征波检测识别。
Cardiopathy is one of the major diseases which threaten human health. As an important non-invasive assistant tool for the diagnosis of cardiopathy, electrocardiogram (ECG) signal processing plays an important role in the medical signal processing. The new signal processing theory will alaways be soon applied to the field of ECG signal and bring new directions and methods for the study of ECG signal processing. Along with the development of signal processing theory, a great deal of different algorithms has been emerged in the ECG Signal processing e.g. time domain processing algorithms, transform domain processing algorithms (Fourier Transform (FT), discrete cosine transform (DCT), wavelet transform, etc.), the parameter space algorithm ( Syntax, neural network and support vector machines, HMM) and such.
ECG signal processing includes the ECG signal denoising, the detection and recognition of ECG signal feature waveform, the ECG data compression, etc. Though these existing ECG signal processing algorithms mentioned above have made a lot of success, theories and applications of them are required to investigate further. Recently, sparse decomposition theory provides a new developmental direction for ECG signal processing. This thesis foucses mainly on the theories of sparse decomposition and its applications in the detection and recognition of ECG signal feature waveform as well as in the ECG data compression.
Application of sparse decomposition in the detection and recognition of ECG signal feature waveform: In this thesis, three over-complete dictionary are created. According to the differences of over-complete dictionaries used in the sparse decomposition, the detection and recognition algorithms of ECG signal feature waveform can be divided into three kinds. In the first kind of algorithm, over-complete dictionary is created through discretization the parameter of generating function which is made according to the ECG signal feather waveform. In the second kind of algorithm, over-complete dictionary is trained by K-SVD algorithm whose sample data is brought form ECG data and the prior knowledge. In the third kind of algorithm, over-complete dictionary is the improved Gabor dictionary. As the over-complete dictionary used in the first algorithm and the second algorithm are obtained according to the ECG signal feature waveform, they have good separability towards the feature waveforms, which is especially important in the detection and recognition of ECG feature waveform. This separability makes the results of sparse decomposition be used directly in the detection and recognition of ECG signal feature waveform and, at the same time, it ensures the right ratio of the detection and recognition. The Gabor dictionary used in the third algorithm is a fixed dictionary. It is named as Gabor dictionary because of its generating function being Gabor function. It is unchangeable to the change of the signal decomposed and, its separability towards the feature waveforms is poorer than the dictionary constructed according to various characteristics of the feature waveforms, which leads the sparse representation of the ECG signal based on the Gabor dictionary not to be directly used for the detection and recognization ECG feature waveforms. Therefore, we need to combine other theories to fulfill the detection and recognition. There are two approaches used in this thesis to solve the above problem, one is to combine the result of sparse decomposition based on Gabor dictionary and the fuzzy theory and use its process capability of the uncertainty information to detect and recognize ECG feature waveforms. The other one is to combine the result of sparse decomposition based on Gabor dictionary and the neural network and use its non-linear classification capability to do this job. Both of above approaches can realized the detections and recognitions of P wave, QRS wave groups and T wave. The accuracy of the detections and recognitions shows the capabilities of two approaches are almost equivalent. The approach combining neural network can get simultaneously the waveform parameters, such as P wave, QRS complex, T wave’s position, span, etc. While the approach combining fuzzy theory needs to detect QRS complex first, then P wave and T wave are detected and recognized according to the position of QRS complex and the medical knowledge.
Application of sparse decomposition in the ECG data compression: With the extensive applications of ECG and the urgent requirement of storage and transmission of ECG data, the compression of ECG data has been an important domain of ECG processing. An ECG data compression algorithm based on sparse decomposition is presented in this thesis. First the sparse representation of ECG data is obtained on the bases of the sparse decomposition carried by this algorithm. When ECG data are compressed, we only need to store the position and non-zero value in the solution vector and over-complete dictionary used in the sparse decomposition of ECG data. The over-complete dictionary used here is acquired by the learning of the ECG sample data with K-SVD algorithm which makes it embody sufficiently the whole feature of ECG data. Compared with other algorithms of ECG data compression when the compression ratios are equal, the distortion of the ECG signal reconstructed with this algorithm is much smaller. Moreover, this ECG data compression algorithm can change the compression ratio to meet the practical needs.
Optimization of the best matching atom searching algorithm: Sparse decomposition of signal can get the sparse representation of signal which is of great advantage to signal processing. However, the complex calculation because of solving NP problem has become the bottleneck that restricts the application of the signal sparse decomposition. There are two causes result in the excessive calculation complexity of sparse decomposition, one is the algorithm searching the best matching atom is too complex, the other one is the number of the atoms is too large in the over-complete dictionary. This thesis brings forward an optimization algorithm namely PSO-MP for searching best matching atom. Using PSO-MP, the time expensivement of the sparse decomposition is 2 orders of magnitude less than the basic MP. The key to second problem is how to minimize the number of atoms on the premise of ensuring the quality of the over-complete dictionary, and now, it is an open question still. Two main steps are presented in this thesis for the studies of the Gabor dictionary’s application in the ECG signal processing. One is to replace the original Gabor dictionary by the Gabor function's parameter space, the other one is to search the best matching atom in parameter space by PSO method. Then, the two problems causing the excessive calculation complexity of sparse decomposition can be solved at the same time.
How to construct the over-complete dictionary: The methods of constructing the over-complete dictionary can be divided into the non-learning constructing method and the learning constructing method. In the third chapter of this thesis, the over-complete dictionary constructed according to the character of the feature waveforms belongs to non-learning dictionary. In the fourth chapter, the modified Gabor dictionary belongs to non-learning dictionary as well. In the third chapter and the sixth chapter, two over-complete dictionary are constructed by learning the ECG data with K-SVD algorithm, these over-complete dictionary are belonged to the learning constructing method. The over-complete dictionary constructed by K-SVD algorithm in third chapter keep the separability of waveforms, however, the dictionary in the sixth chapter gives a poor performance to the separability of waveforms. This characteristics makes the over-complete dictionary based on the learning constructing method do good in the ECG data compression learning. Yet it can not be applied in the detection and recognition of ECG feature waveform.
引文
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