心電信號壓縮感知采樣與恢復(fù)

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摘要 近年來，由心血管疾病導(dǎo)致的死亡人數(shù)在不斷增加，而心電圖是反映心臟生理活動的一種直觀的圖形表現(xiàn)形式，它對判斷心臟的功能和診斷心臟疾病有著重要的參考依據(jù)。因此如何通過壓縮來減少需要傳輸?shù)男碾姅?shù)據(jù)數(shù)量并利用壓縮后數(shù)據(jù)準(zhǔn)確恢復(fù)圖像在臨床上具有十分重要的意義。
為了便于對大量心電數(shù)據(jù)進(jìn)行存儲﹑分析﹑傳輸，則必須對其進(jìn)行有效地壓縮。傳統(tǒng)的壓縮技術(shù)一直遵循奈奎斯特采樣定理，由于該定理在采樣頻率上的限制，越來越滿足不了當(dāng)代的需求。壓縮感知理論是一種新型的信號壓縮理論，它能對信號進(jìn)行十分有效地壓縮且能準(zhǔn)確的恢復(fù)原信號，同時(shí)它在采樣頻率上不受奈奎斯特采樣定理的限制，大大提高了采樣的速率與效率。
本文介紹了壓縮感知理論的研究與發(fā)展，并將壓縮感知理論用于心電信號的壓縮與恢復(fù)，大大減少了心電信號的觀測數(shù)據(jù)，減少了信號的數(shù)據(jù)傳輸﹑分析以及處理等等。同時(shí)利用當(dāng)前壓縮感知領(lǐng)域的一種快速算法—正交匹配追蹤算法對壓縮后信號進(jìn)行仿真恢復(fù)并與原信號進(jìn)行對比并分析其誤差。
本文將壓縮感知理論運(yùn)用到心電信號的壓縮處理中，壓縮感知理論的壓縮能力強(qiáng)，它能夠?qū)崿F(xiàn)在不丟失心電信號重要信息的前提下進(jìn)行高效壓縮，并節(jié)省了重構(gòu)時(shí)間，從而給心電信號的壓縮提供了新的思路。

關(guān)鍵詞：心電信號，壓縮感知理論，正交匹配追蹤算法


Sampling and Recovery of ECG Signal Based on Compressed Sensing
Abstract In recent years,the number of deaths caused by cardiovascular disease is increasing, The ECG is an intuitive graphical representation reflects the physiological activities of the heart, it has an important reference to the function of the heart and the judgment of heart disease . So how to use compression to reduce the number of ECG data transmission and use compressed data to accurately recover the image has a very important significance in clinic.
In order to storage,analysis and transport the large number of ECG data, it must carry on the compression effectively. The traditional compression techniques have been guided by the Nyquist sampling theorem, since the theorem restrictions on the sampling frequency, can not meet contemporary needs.Compressed sensing theory is a new signal compression theory, it is very effective tor signal compression and it also can restore the original signal accurately,At the same time it is not on the sampling frequency Nyquist sampling theorem restrictions,improving the speed and efficiency of sampling greatly .
This paper introduces the research and development of the theory of compressed sensing, and used the compressed sensing theory for ECG signal, it reducing the observation data of ECG signal greatly,and reduces data transmission signal analysis and processing, etc.At the same time, using a fast algorithm of the compressed sensing domain -- orthogonal matching pursuit algorithm for the compressed signal and analyzed the error of the recovery and the original signal.
In this paper, the theory of compressed sensing applied to ECG compression, the compressed sensing theory compression capability is strong, it can realize high efficient compression without loss important information of ECG signal, and save the reconstruction time, which provides a new way for the compression of ECG signal.
Keywords: ECG signal, compressed sensing, orthogonal matching pursuit
algorithm

目 錄
第一章 緒論 1
1.1研究的背景 1
1.2心電信號（ECG）的特點(diǎn) 2
1.3心電信號壓縮的必要性 5
1.4 仿真平臺 5
1.5本文的主要工作與目標(biāo) 6
第二章 傳統(tǒng)心電數(shù)據(jù)壓縮方法 8
2.1概述 8
2.2壓縮方法的性能評價(jià) 9
2.3常見的心電信號壓縮方法 10
2.4小結(jié) 14
第三章 壓縮感知理論 15
3.1壓縮感知理論的概述 15
3.2傳統(tǒng)采樣與壓縮感知的比較 16
3.3壓縮感知理論的主要步驟 17
3.3.1信號的稀疏表示 18
3.3.2測量矩陣 20
3.3.3重構(gòu)算法 22
3.4壓縮感知理論的應(yīng)用和應(yīng)用瓶頸 25
第四章 基于壓縮感知的心電信號的壓縮采樣 27
4.1心電信號的獲取 27
4.2心電信號壓縮采樣﹑重構(gòu)的仿真實(shí)驗(yàn) 27
4.3仿真結(jié)果與分析 29
第五章 總結(jié)與展望 32
致 謝 34
參考文獻(xiàn) 35
附錄 37