TCSPC histogram data modeling

authors

• Poisson Valentin
• Guicquero William
• Sicard Gilles

abstract

In active 3D imaging based on a Time Correlated Single Photon Counting (TCSPC) system, photons "of interest" measured with Single Photon Avalanche Diodes (SPADs) are often mixed with high background photon noise. This low Signal-to-Background ratio (SBR) makes the reconstruction of luminance and depth maps difficult. State-of-the-art (SoA) works relying on Bayesian approaches [1], [2] or Deep Learning (DL) [3], [4] usually study the restrictive case of low-photon counts mode of operation. On the contrary, this paper aims to consider the high photon counts, synchronous operating mode, where the SPAD "Dead Time" is spread over a large number of bins of the Time-of-Flight (ToF) histogram (i.e., pileup effect). A new method is then proposed to estimate pixel parameters from such a ToF histogram in which the photon arrival times is assumed to follow a truncated-Shifted Erlang ($E$) distribution. The underlying algorithmic task consists in estimating 4 latent parameters of each $E$ distribution of a mixture model, only from an observed draw of the process distribution in the shape of a ToF histogram. To solve the highly non-convex nature of this problem, a customized nested Expectation-Maximization algorithm (c-GEM) has been designed based on a proper combination of Maximum Likelihood Estimation, Moments Matching, Parametric Imputation and support estimation via Variable Neighborhood Search. The proposed framework was successfully evaluated with synthetically generated data leading to accurate depth-luminance reconstructions.

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