Abstract
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.