[Paper Review] Signal Processing Based Pile-up Compensation for Gated Single-Photon Avalanche Diodes

Adithya Pediredla, Aswin C. Sankaranarayanan+3 more|arXiv (Cornell University)|Jun 14, 2018

Advanced Optical Sensing Technologies40 citations

TL;DR

The paper develops an estimation-theoretic framework (ML and MAP) to compensate pile-up in gated SPAD-based TCSPC transients, enabling high-illumination operation and validating with experiments.

ABSTRACT

Single-photon avalanche diode (SPAD) based transient imaging suffers from an aberration called pile-up. When multiple photons arrive within a single repetition period of the illuminating laser, the SPAD records only the arrival of the first photon; this leads to a bias in the recorded light transient wherein the transient response at later time-instants are under-estimated. An unfortunate consequence of this is the need to operate the illumination at low-power levels to reduce the probability of multiple photons returning in a single period. Operating the laser at low power results in either low signal-to-noise ratio (SNR) in the measured transients or reduced frame rate due to longer exposure durations to achieve a high SNR. In this paper, we propose a signal processing-based approach to compensate pile-up in post-processing, thereby enabling high power operation of the illuminating laser. While increasing illumination does cause a fundamental information loss in the data captured by SPAD, we quantify this information loss using Cramer-Rao bound and show that the errors in our framework are only limited to this information loss. We experimentally validate our hypotheses using real data from a lab prototype.

Motivation & Objective

• Motivate and model pile-up distortion in gated SPAD TCSPC systems.
• Develop ML and MAP estimators to recover true transients from piled-up histograms.
• Derive Cramer-Rao bound to quantify estimation limits.
• Demonstrate improved SNR and recovery of signals under strong ambient/light conditions via post-processing.

Proposed method

• Model SPAD TCSPC transients with a probabilistic forward model linking observed histograms to true photon arrivals.
• Show that the per-bin photon counts follow a Poisson process and derive a multinomial-based forward model for the gated SPAD histogram (Equation 3).
• Derive an ML estimator for the transient by maximizing the likelihood of observed histogram (resulting in rom the paper).
• Provide a MAP estimator using a conjugate prior to regularize transient recovery.
• Quantify estimation limits with the Cramer-Rao bound and discuss information loss relative to fundamental data limits.
• Implement GPU-accelerated simulation to validate pile-up behavior and estimator performance.

Experimental results

Research questions

• RQ1 How does pile-up bias spoil SPAD-based TCSPC transients at higher illumination powers?
• RQ2 Can ML and MAP estimators recover the underlying transient from piled-up histograms?
• RQ3 What are the theoretical limits (CRB) on pile-up compensated transient estimation?
• RQ4 How does the proposed processing enable higher illumination rates without sacrificing reconstruction quality?
• RQ5 What is the practical demonstration of the method on real SPAD/TCSPC hardware?

Key findings

• An ML estimator recovers the ideal transient from piled-up TCSPC histograms.
• A conjugate-prior MAP estimator is developed to regularize transient recovery.
• A Cramer-Rao bound is derived to characterize the estimation accuracy limits under pile-up.
• Experiments show improved SNR in recovered transients and recovery of signals under strong ambient illumination.
• Hardware validation demonstrates the method enabling higher illumination power and effective pile-up compensation.
• The work suggests SPAD detection efficiency (up to about 90%) can be achieved from a typical 5% baseline through the processing framework.