Blind End-Member and Abundance Extraction for Multispectral Fluorescence Lifetime Imaging Microscopy Data

Abstract

This paper proposes a new blind end-member and abundance extraction (BEAE) method for multispectral fluorescence lifetime imaging microscopy (m-FLIM) data. The chemometrical analysis relies on an iterative estimation of the fluorescence decay end-members and their abundances. The proposed method is based on a linear mixture model with positivity and sum-to-one restrictions on the abundances and end-members to compensate for signature variability. The synthesis procedure depends on a quadratic optimization problem, which is solved by an alternating least-squares structure over convex sets. The BEAE strategy only assumes that the number of components in the analyzed sample is known a spriori. The proposed method is first validated by using synthetic m-FLIM datasets at 15, 20, and 25dB signal-to-noise ratios. The samples simulate the mixed response of tissue containing multiple fluorescent intensity decays. Furthermore, the results were also validated with six m-FLIM datasets from fresh postmortem human coronary atherosclerotic plaques. A quantitative evaluation of the BEAE was made against two popular techniques: minimum volume constrained nonnegative matrix factorization (MVC-NMF) and multivariate curve resolution-alternating least-squares (MCR-ALS). Our proposed method (BEAE) was able to provide more accurate estimations of the end-members: 0.32% minimum relative error and 13.82% worst-case scenario, despite different initial conditions in the iterative optimization procedure and noise effect. Meanwhile, MVC-NMF and MCR-ALS presented more variability in estimating the end-members: 0.35% and 0.34% for minimum errors and 15.31% and 13.25% in the worst-case scenarios, respectively. This tendency was also maintained for the abundances, where BEAE obtained 0.05 as the minimum absolute error and 0.12 in the worst-case scenario; MCR-ALS and MVC-NMF achieved 0.04 and 0.06 for the minimum absolute errors, and 0.15 and 0.17 under the worst-case conditions, respectively. In addition, the average computation time was evaluated for the synthetic datasets, where MVC-NMF achieved the fastest time, followed by BEAE and finally MCR-ALS. Consequently, BEAE improved MVC-NMF in convergence to a local optimal solution and robustness against signal variability, and it is roughly 3.6 time faster than MCR-ALS.