基于壓縮感知理論的腦電信號壓縮方法研究

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摘要 本文對課題“基于壓縮感知理論的腦電信號壓縮采樣”進行了研究，首先簡述了傳統(tǒng)概念上的信號采樣，同時也介紹了一種新的信號采樣方法，即壓縮感知理論，并對二者進行了對比。本文采用的方法為正交匹配追蹤算法，并通過Matlab編程對EEG采樣信號的兩組信號進行了仿真，并將最終復(fù)原的信號與原始信號進行了比對，效果較為理想。
在醫(yī)學(xué)實踐中，腦電信號的提取和采集復(fù)原是很重要的，但又因為腦電信號的信號數(shù)量繁多，因此會產(chǎn)生大量數(shù)據(jù)，給信號的采集與分析帶來了很多不便。怎樣高效采集分析這些數(shù)據(jù)是一個有待解決的問題。而有別于傳統(tǒng)采樣理論的壓縮感知理論，為有效解決這個問題提出了全新的解決思路?；谶@項全新的理論，本文首先介紹了EEG信號的基礎(chǔ)知識以及傳統(tǒng)的EEG的采樣方法，然后介紹了壓縮感知的理論框架，并用框圖簡單說明了這兩種方法。
接下來，本文研究了基于壓縮感知理論對單EEG信號的壓縮采樣，內(nèi)容包括腦電信號最佳稀疏分解，通過實驗對比，展示了EEG信號經(jīng)過壓縮感知理論采樣還原后的效果。本文中主要采取的方法為正交匹配追蹤法。通過實驗我們可以實現(xiàn)EEG信號的較好的稀疏分解，在實驗中，我們對測量矩陣進行了選擇，比較了常用測量矩陣對重構(gòu)誤差的影響，接下來使用測量矩陣對稀疏分解系數(shù)向量進行觀測得到測量值并完成壓縮采樣，最后由這些測量值運用正交匹配追蹤算法恢復(fù)出系數(shù)向量，繼而完成原EEG信號的重構(gòu)。
關(guān)鍵詞：壓縮感知 壓縮采樣 EEG 正交匹配追蹤法


Research on the Compression of EEG Based on Compressive Sensing
Abstract: This paper mainly does a research on the topic “The data acquisition of EEG based on compressive sampling”. Firstly， this paper introduces the traditional way of data acquisition，then a brand new theory which called “compressive sampling” is given. There are a few words used to compare the two ways of collecting signals and their pros and cons are shown as well.
In the medial practice，it is essential and complicated to collect enough and effective EEG signals. The huge number of the signals makes the collection process even harder and time-wasting. How to collect and analyze those signals with high efficiency has been a problem for a long time. Differed from the traditional ways，compressive sampling provides a new approach to that problem.
Based on that theory，this paper at first introduces the basic knowledge of EEG and old ways of collecting signals and then briefly introduces the outline of the compressive sampling with some flow diagrams for both methods. Next，there are some researches which were done to the EEG signals including its sparsity. Finally，the results of two methods are compared with each other.
This paper uses Orthogonal Matching Pursuit to reconstruct the original signal and through the experiment it can be seen that signal witch is collected and processed with that method turned to be recovered well. The matrix used in this article is common matrix and the testing matrix is made especially for the signals.
Through the compressive sampling we can collect the signals much smaller in the quantity and recover the signals with higher quality.
Key words: Compressive sensing EEG Orthogonal Matching Pursuit


目錄
第一章 緒論 1
1.1研究背景、目的、意義 1
1.2 國內(nèi)外相關(guān)領(lǐng)域的研究現(xiàn)狀 4
1.3 EEG的基礎(chǔ)知識 5
1.4 腦電壓縮技術(shù)簡介 9
1.5 壓縮與重建測評指標(biāo) 11
第二章 壓縮感知理論 12
2.1傳統(tǒng)采樣與壓縮感知的比較 12
2.2 壓縮感知的模型架構(gòu)簡介 13
2.3 信號的稀疏表示 15
2.4 測量矩陣的設(shè)計 16
2.5 重構(gòu)算法的簡介 18
第三章 基于壓縮感知理論的EEG采樣 20
3.1 Matlab技術(shù)簡介 20
3.2 稀疏基和冗余字典 21
3.3 正交匹配追蹤算法 21
3.4 其他重構(gòu)算法 22
3.5 正交匹配追蹤算法流程圖 23
第四章 總結(jié)與展望 26
致謝 27
參考文獻 28
附錄A 30