基於平移不變性的螢光生命週期之全區分析

Shift Invariance Based Global Analysis of Fluorescence Lifetime

劉彥伶(Yen-Ling Liu)

指導教授 ： 祁忠勇

國立清華大學/電機資訊學院/通訊工程研究所/碩士(2009年)

摘要

螢光生命週期成像術(fluorescence lifetime imaging, FLIM)為利用螢光衰減常數(fluorescence decay constant)(或者稱為螢光生命週期(fluorescence lifetime))產生時間序列圖像的一種技術，也已經被當作觀察在活體細胞中分子交互作用的重要工具。螢光生命週期成像術與光學顯微鏡之整合，除了可以觀測細胞上各種組成成分的幾何分布資訊(geometric distribution information)外，還可以觀察到細胞與週遭環境的功能性資訊(functional information)。另外，因為螢光衰減常數隨欲檢測的區域(region of interest, ROI)生化環境的不同而變化，所以可作為ROI的特徵。而當ROI為同質性(homogeneous) (例如:在ROI內只存在單一個螢光衰減常數)時，因FLIM對生化環境的變化是高度敏感的，所以可以得到精確的螢光衰減常數；但是，當ROI為異質性(heterogeneous) (例如:在ROI內存在多個螢光衰減常數)時，準確估測ROI內的螢光衰減常數將成為FLIM的挑戰課題。除此之外，如何在低強度的激發光源且有雜訊影響的環境下，準確地估測到螢光衰減常數亦為重要的研究方向。在現存方法中，利用非線性擬合法(nonlinear fitting method)已被認為是估測螢光衰減常數效能最好的方法，但是此方法求解之精確度仍受限於雜訊的影響。
在本論文中，我們首先利用降階Hankel矩陣近似法降低雜訊的影響後，再提出三種演算法以全區分析的方法估測螢光衰減常數。第一種稱之為GA-EDCHA (global analysis based estimation of decay constant via Ho's algorithm)，此方法是利用Ho's演算法(Ho's algorithm)先估測螢光生命週期狀態空間模型(state space model)的系統矩陣，再求得螢光衰減常數。第二種和第三種皆為基於利用平移不變性的方法，分別稱為GA-HSVD (global analysis based Hankel singular value decomposition)和GA-EDCSIP (global analysis based estimation of decay constant via sift-invariance properties)，前者利用線性最小平方估計(linear least squares estimation)求得螢光衰減常數，而後者則增加考慮螢光衰減常數為正的性質，再藉由解凸規劃問題(convex optimization problem)求得螢光衰減常數。由模擬結果顯示此三種方法之效能和運算複雜度皆較非線性擬合法佳。以效能做比較時，為GA-EDCSIP之效能為最好，其次是GA-HSVD，再者為GA-EDCHA；但是若比較運算複雜度，GA-HSVD則為最優，再來為GA-EDCSIP和GA-EDCHA。

關鍵字

螢光生命週期成像術 ； 螢光衰減常數 ； 螢光生命週期

並列摘要

Fluorescence lifetime imaging (FLIM) exploits the fluorescence decay constant (or fluorescence lifetime) to generate image time series, and has been an important tool for imaging interactions between molecules in living cells. The integration of FLIM and optical microscopy called FLIM microscopy not only can observe the geometric distribution of molecules in a living cell, but also observe the functional interactions between cells and the surrounding environment. Since the fluorescence decay constant changes with the biochemical variation within the region of interest (ROI), it can be regarded as a feature of that ROI. FLIM is highly sensitive to the biochemical changes and thus can provide an accurate estimation of the fluorescence decay constant when the ROI is homogeneous (i.e., there exists only a single fluorescence decay constant within the ROI). However, when the ROI is heterogeneous (i.e., there exist multiple fluorescence decay constants within the ROI), accurate estimation of the fluorescence decay constants within the ROI will be a challenging issue in FLIM. Moreover, how to accurately estimate the fluorescence decay constants under the scenario of low-intensity source excitation and noise effect is also an important research direction. Among the existing fluorescence decay constant estimation methods, non-linear fitting method has been widely acknowledged as the one with the best performance, but its performance is still limited due to the noise condition.
In this thesis, we first propose a low rank approximation of Hankel matrix for noise reduction, and then develop three global analysis based fluorescence decay constant estimation algorithms. The first one, called global analysis based estimation of fluorescence decay constant via Ho's algorithm (GA-EDCHA), estimates fluorescence decay constants via obtaining fluorescence lifetime state space model by Ho's algorithm. The second and the third algorithms use shift invariance property, called global analysis based Hankel singular value decomposition (GA-HSVD) and global analysis based estimation of fluorescence decay constant via sift-invariance properties (GA-EDCSIP), respectively. The former obtains fluorescence decay constants by linear leas t squares estimation. The latter considers the non-negative nature of the fluorescence decay constants, and obtains fluorescence decay constants by solving a convex optimization problem. Some simulation results are presented to demonstrate that the proposed three algorithms are superior over the conventional non-linear fitting method, in terms of performance and computational complexity. In term of performance, GA-EDCSIP is the best, followed by GA-HSVD and GA-EDCHA, but in term of computational complexity, GA-HSVD shows to be the best, which is followed by GA-EDCSIP and GA-EDCHA.

並列關鍵字

fluorescence lifetime imaging ； FLIM ； fluorescence decay constant ； fluorescence lifetime

參考文獻

楊登凱,利用DNA序列方位性進行預雜合以增強微陣列探針-標的物之雜合效率,中原化工碩士論文, July, 2008.

D. Stephens, Cell Imaging: Methods Express. UK: Scion Publishing, 2006.

王興雯,生醫光學在臨床之診斷及治療監測:自體螢光和生理參數,物理雙月刊,二十九卷,六期, pp. 1048-1055, 2007.

D. J. Stephens and V. J. Allan, “Light microscopy techniques for living cell imaging,” Science, vol. 300, pp. 82-86, Apr. 2003.

J. A. Jo, Q. Fang, and L. Marcu, “Ultrafast method for the analysis of fluorescence lifetime imaging microscopy data based on the Laguerre expansion technique,” IEEE J. Sel. Topics Quantum Electron., vol. 11, no. 4, pp. 835-845, Jul./Aug. 2005.