小鼠心血管磁振造影(Cardiovascular Magnetic Resonance Imaging, CMR)得到的心臟影像會因為小鼠的心臟體積較小、心跳的快速跳動以及呼吸干擾，而有著相當嚴重的運動假影(motion artifacts)。心臟運動假影可以透過回溯式(retrospective)心電訊號監控(ECG navigation)降低運動假影帶來的影響。本論文的目的，是利用表面線圈收到的心跳訊號，找出心跳週期之時間點，藉此將磁振造影訊號以回溯式心電訊號監控方式重建，得到不同心跳相位時的動態影像。

本論文針對此一問題提出了三種解決方法，並進行比較與討論。第一種方法：使用移動平均濾波器(moving average)過濾高頻雜訊後再使用帶通濾波器 (bandpass filter)留下心跳訊號的頻率範圍。第二種方法主要以小波轉換(wavelet transform) 移除呼吸雜訊的基準線，接著使用權重移動平均濾波器(weighted moving average)平滑訊號。第三種方法主要使用Savitzky-Golay filter，使得訊號更加平滑之外，同時加上曲線擬合(curve fitting)的處理，讓訊號更貼近原始訊號，以利標示正確峰值。這三種方法最後都與半手動標示(gold standard)之結果進行比較。比較結果顯示，使用Savitzky-Golay filter的方法進行心臟影像回溯式訊號對位會有較準確的結果。

Mouse cardiovascular magnetic resonance imaging (CMR) often encounter severe motion artifacts because of the small size of heart, rapid heartbeats and breathing interference. Cardiac motion artifacts can be minimized using retrospective ECG navigation. The purpose of the work is to find out accurate time points of cardiac cycle with the signal acquired by surface coils so as to reconstruct MR signals to corresponding cardiac phases, and thus the CMR cine.
In this thesis we proposed three methods for comparison and discussion. The first one was using moving average filter to remove high frequency noise and then bandpass filter to extract heartbeat signals. Second one was to remove the baseline of breathing based on wavelet transform and then smoothed signals by weighted moving average. The third one was using Savitzky-Golay filter to achieve smoothing as well as curve fitting of original signals. These three methods were compared with gold standard, which was performed manually to label the R-peak. Our results showed that using Savitzky-Golay Filter to carry out R-wave detection achieved higher accuracy and thus better image reconstruction.

論文審定書 i
致謝 ii
中文摘要 iii
Abstract iv
目錄 v
圖目錄 viii
表目錄 x
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 1
1.3 動機與目的 4
1.4 圖表 5
第二章 研究方法與原理 7
2.1 研究方法 7
2.2 資料擷取 8
2.2.1 資料來源 8
2.2.2 表面線圈 8
2.2.3 FLASH (Fast Low-Angle Shot) 9
2.2.4 回溯式擷取(Retrospective Acquisition) 9
2.3 方法一：移動平均濾波器、帶通濾波器 10
2.3.1 移動平均濾波器 (Moving Average Filter) 10
2.3.2 帶通濾波器 (Bandpass Filter) 10
2.3.3 尋找心跳峰值 10
2.4 方法二：小波轉換、權重移動平均濾波器 12
2.4.1 小波轉換 12
2.4.2 移除呼吸基準線 12
2.4.3 權重移動平均濾波器 12
2.5 方法三：Savitzky-Golay Filter 14
2.6 比較方法與統計 15
2.7 圖表 16
3.1 方法一：移動平均濾波器、帶通濾波器 20
3.1.1 移動平均濾波器 (window size = 15 pt) 20
3.1.2 帶通濾波器(範圍：8 ~ 10 Hz) 20
3.1.3 頻域結果對回時域 20
3.1.4 方法一標示心跳峰值 20
3.1.5 方法一問題與討論 20
3.1.6 圖表 22
3.2 方法二：小波轉換、權重移動平均濾波器 26
3.2.1 小波轉換 26
3.2.2 移除呼吸基線 26
3.2.3 權重移動平均濾波器 (window size = 15 pt) 26
3.2.4 方法二標示心跳峰值及結果 26
3.2.5 方法二問題與討論 26
3.2.6 圖表 27
3.3 方法三：Savitzky - Golay濾波器 30
3.3.1 Savitzky - Golay濾波器 (window size = 15 pt) 30
3.3.2 方法三標示心跳峰值 30
3.3.3 方法三問題與討論 30
3.3.4 圖表 31
3.4 實驗數據及討論 33
3.4.1 實驗數據 33
3.4.2 結果與討論 41
3.5 對回影像結果 45
第四章 結論 46
第五章 參考文獻 47

[1] Paul C. Lauterbur, "Image formation by induced local interactions: Examples employing nuclear magnetic resonance", Nature, 242:190-191, 1973.
[2] R.Y. Kwong, "Cardiovascular Magnetic Resonance Imaging. Humana Press", Totowa, New Jersey, 2001.
[3] A Wessels and D Sedmera, "Developmental anatomy of the heart: a tale of mice and man. Physiol Genomics", 15(3):165–176, November 2003.
[4] Edwin Heijman, "Mouse Cardiac MRI", Eindhoven : Eindhoven University of Technology, 2008.
[5] Y Liu, et al., "Magnetization-prepared cardiac imaging using gradient echo acquisition", Magn Reson Med, 30(2):271–275, August 1993.
[6] Kellman P , et al., "High spatial and temporal resolution cardiac cine MRI from retrospective reconstruction of data acquired in real time using motion correction and resorting", Magn Res Med, 62: 1557–1564, 2009.
[7] CB Higgins, et al., "Magnetic resonance imaging in patients with congenital heart disease", Circulation, 70(5):851–860, November 1984.
[8] Fries P, et al., " Comparison of retrospectively self-gated and prospectively triggered FLASH sequences for cine imaging of the aorta in mice at 9.4 Tesla", Invest Radiol, 47:259–66, 2012.
[9] Larson AC, White RD, Laub G, McVeigh ER, Li D, Simonetti, "Self-gated cardiac cine MRI",Magn Reson Med, 51(1):93-102, 2004.
[10] A.Haase, et al., "FLASH imaging: rapid NMR imaging using low flip angle pulses",Journal of Magnetic Resonance, 67 258-266, 1986.
[11] Ridgway JP, "Cardiovascular magnetic resonance physics for clinicians: part I", Journal of Cardiovascular Magnetic Resonance, 2010.
[12] Spyros Makridakis, et al. "Adaptive Filtering: An Integrated Autoregressive /Moving Average Filter for Time Deries Forecasting", Operational Reaearch Quarterly, 28, 2, 425-437, 1977.
[13] Rolf Schaumann, et al., "Design of Analog Filter", Oxford University Press, 2nd Indian Edition, 2013.
[14] http://docs.scipy.org/doc/scipy-0.14.0/reference/index.html
[15] Mladen Victor Wickerhauser, "Adapted Wavelet Analysis From Theory to Software", A K Peters Ltd, ISBN 1-56881-041-5, 1994.
[16] http://www.mathworks.com/help/wavelet/ref/wavedec.html
[17] Liping Li, et al., "Comparison of Detrending Methods in Spectral Analysis of Heart Rate Variability", Journal ofApplied Science, Engineering and Technology 3(9): 1014-1021, 2011.
[18] Savitzky A, Golay MJE, " Smoothing and differentiation of data by simplified least squares procedures", Analytical Chemistry ,36, 1627–1639, 1964.