The ECG Feature Wave Detection And Data Compression Based On The Sparse Decomposition

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.