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We present a novel, three-stage method to solve the fluorescence lifetime imaging problem under low-photon conditions. In particular, we reconstruct the fluorophore concentration along with its support and fluorescence lifetime from the time-dependent measurements of scattered light exiting the domain. Because detectors used for these problems are photon counting devices, measurements are corrupted by Poisson noise. Consequently, we explicitly consider Poisson noise in conjunction with SPIRAL-$\ell_p$ -- a sparsity-promoting nonconvex optimization method -- to solve this problem.

Parametric Bayesian spectral estimation methods have been previously utilized to improve frequency resolution. Ultrasound signals have been tested in such methods resulting in higher precision frequency detection compared to common non-parametric spectral estimation methods based on the Fourier transform. Such a technique using a reversible jump Markov Chain Monte Carlo algorithm has been developed to fully characterize signals and in addition to frequency, to provide amplitude and noise estimation.