Fast and robust single-exponential decay recovery from noisy fluorescence lifetime imaging

Fluorescence lifetime imaging is a valuable technique for probing characteristics of wide ranging samples and sensing of the molecular environment. However, the desire to measure faster and reduce effects such as photo bleaching in optical photon-count measurements for lifetime estimation lead to inevitable effects of convolution with the instrument response functions and noise, causing a degradation of the lifetime accuracy and precision. To tackle the problem, this paper presents a robust and computationally efficient framework for recovering fluorophore sample decay from the histogram of photon-count arrivals modelled as a decaying single-exponential function. In the proposed approach, the temporal histogram data is first decomposed into multiple bins via an adaptive multi-bin signal representation. Then, at each level of the multi-resolution temporal space, decay information including both the amplitude and the lifetime of a single-exponential function is rapidly decoded based on a novel statistical estimator. Ultimately, a game-theoretic model consisting of two players in an "amplitude-lifetime" game is constructed to be able to robustly recover optimal fluorescence decay signal from a set of fused multi-bin estimates. In addition to theoretical demonstrations, the efficiency of the proposed framework is experimentally shown on both synthesised and real data in different imaging circumstances. On a challenging low photon-count regime, our approach achieves about 28% improvement in bias than the best competing method. On real images, the proposed method processes data on average around 63 times faster than the gold standard least squares fit. Implementation codes are available to researchers.