A MAXIMUM LIKELIHOOD METHOD FOR LIFETIME ESTIMATION IN PHOTON COUNTING-BASED FLUORESCENCE LIFETIME IMAGING MICROSCOPY A. Chessel, F. Waharte, J. Salamero UMR 144 CNRS - PICT IBiSA 26 rue d’Ulm 75 248 Paris cedex 05, France C. Kervrann Inria, Centre de Rennes - Bretagne Atlantique Campus Universitaire de Beaulieu 35 042 Rennes Cedex, France ABSTRACT In this paper we derive a Maximum Likelihood (ML) frame- work for photon counting-based fluorescence lifetime estima- tion in Fluorescence Lifetime Imaging Microscopy (FLIM) from the biophysical phenomenon and instrument models. Data collected at a given pixel consist of photon counts exponentially decreasing along time and are assumed to fol- low Poisson statistics. Both pointwise approaches and a neighborhood-wise approach are proposed to take explic- itly into account the spatial correlation of data. Evaluations and comparisons are presented on simulated as well as on experimental biological image data. Index Terms— Photon counting, Poisson statistics, lifte- time estimation, fluorescence microscopy 1. INTRODUCTION Fluorescence microscopy and Green Fluorescent Protein (GFP) tagging have become widely used tools of modern cellular biology. Unlike traditional fluorescence imaging techniques, FLIM imaging aims at estimating fluorescence lifetime [3], that is the average time during which the fluo- rescent molecule stays in the excited state before returning to the ground state by emitting a photon [7]. Typical biologi- cal applications include imaging spectrally indistinguishable fluorescing species or measuring molecular proximity be- tween two fluorophores by F¨ orster Resonance Energy Trans- fer (FRET). Fluorescence lifetime measurements were first exploited in spectroscopy on homogeneous samples with a high precision to characterize the photophysical properties of a specific compound. It is now routinely used in biology, but mainly to analyse images from dimmer and heterogeneous fluorescent samples. In FLIM imaging, at each pixel the response of the fluo- rescent sample to a periodic excitation light is measured (rep- etition of pulses for time-domain approaches or modulated light for frequency domain techniques). In the time-domain method, this response is the number of detected photons de- creasing in time (see Fig. 1). This decay in fluorescence can be described by a first-order reaction and thus can be modeled by an exponential with a fixed rate, called the fluorescence lifetime of the fluorophore. In our study, we focus on the Time-Correlated Single Photon Counting (TCSPC) technique [6] so the measurement corresponds at each time point to the number of photons reaching the detector and obeys Poisson statistics. The most standard approach to estimate lifetime is based on a least-square fitting of a mono-exponential (or multi- exponential) function to the real data [8] and the Poisson dis- tribution is generally assumed to be approximately Gaussian. Nevertheless, the Maximum Likelihood approach is probably more recommended as for many image reconstruction prob- lems. In photon counting-based image reconstruction, ML is known to be equivalent to minimizing the Kullback-Leibler (KL) divergence of the computed data from the acquired data. Nevertheless, taking into account the spatial coherence the data and image smoothness as considered in our approach, is especially relevant in the case of very low photon counts for applications in cell biology. The remainder of the paper is organized as follows. In Section 2, we present the theory and models in TCSPC-FLIM imaging. In Section 3, we formulate the lifetime estimation problem as a pointwise and neighborhood-wise ML problem. In Section 4 the performance of the algorithm is evaluated on synthetic and experimental data. The proposed method allows for recovering the spatial lifetime information and en- ables to demonstrate experimentally localized spatial interac- tion of the two proteins of interest on endosomes. 2. TCSPC-FLIM IMAGING In this section, we present the theory in TCSPC FLIM imag- ing, now routinely used in biology for lifetime estimation and spatially-resolved estimation of nanometer-scale molecu- lar proximity between proteins. Biophysical models of fluorescence A fluorescence sub- stance can absorb a photon of a given wavelength and remit a very short time later (with a picosecond (ps) to a nanosecond (ns) delay) a photon at another wavelength (corresponding to EUSIPCO 2013 1569746181 1