arXiv subjects

Ao Qiu

Publications and source records attributed to Ao Qiu.

4 recordsLinked to original sources

arXiv2026

Multi-Threshold Sampling: Signal Space, Sampling Operators, and Crossing-Time Distributions

Multi-threshold (MT) sampling records crossing times at selected thresholds for parameter estimation and waveform reconstruction. For suitable high-speed signals, it can reduce data volume, hardware cost, and power consumption compared with high-rate uniform time-domain sampling. Applications in nuclear science include positron emission tomography, oil well logging, and photon-counting X-ray imaging. However, its theoretical foundations require further development to support performance evaluation and system design. A necessary first step is to rigorously define the signal space and sampling operators, but a general mathematical framework for this purpose is still needed. We propose a unified mathematical framework that maps the signal distribution to the distribution of recorded crossings through the sampling operators. It provides a common description of how mismatch and noise in signals and thresholds, time quantization, and selection shape the recorded data, enabling their individual and combined effects to be analyzed. For nonhomogeneous Poisson photon arrivals and deterministic MT sampling, the framework yields the exact distribution of the first recorded crossing time at a specified threshold within a given recorded-time interval. Predictions for a scintillation pulse model agree with independent Monte Carlo simulations, demonstrating the framework's predictive capability. The framework lays the groundwork for determining the fundamental performance limits of MT sampling and designing systems that approach those limits.

eess.SP↗

arXiv2026

A Unified Analytical Framework for LYSO-SiPM Scintillation Pulse Dynamics

Existing scintillation-detector models typically treat scintillation kinetics, optical transport, silicon photomultiplier (SiPM) response, and timing statistics separately, limiting end-to-end prediction of waveform formation and detector performance. We present a unified analytical framework for lutetium-yttrium oxyorthosilicate (LYSO)-SiPM scintillation detectors that links these processes within a single forward model. The framework incorporates finite thermalization, depth-dependent optical transit-time spread, and microcell occupancy dynamics to provide a physics-based description of macroscopic pulse formation. It yields closed-form exponentially modified Gaussian pulses in the linear regime, state-dependent integral solutions in saturation, and recovers the conventional bi-exponential pulse model---ubiquitously used yet hitherto only empirically justified in scintillation pulse fitting and sparse-sampling reconstruction---as a controlled reduction of the full optoelectronic cascade. Experimental validation on 10,000 directly digitized Na-22 pulses shows that the dynamic saturation model captures amplitude-dependent waveform distortion and is favored by the Akaike information criterion (AIC) over a matched bi-exponential baseline in 100/100 high-amplitude pulses and 98/100 medium-amplitude pulses. By coupling the dynamic triggering rate to compound Poisson statistics, the framework also predicts current-variance envelopes and Fisher-information-based timing limits, including an intrinsic coincidence timing resolution lower bound of about 100 ps full width at half maximum (FWHM) for a reference 511-keV LYSO-SiPM configuration. These results deepen the physical understanding of scintillation-detector waveform formation and timing limits by clarifying how scintillation kinetics, optical transport, and SiPM microcell dynamics jointly shape the observed response.

physics.med-ph↗

arXiv2026

Prior-Based Multi-Voltage Threshold Sampling as a Structured Inverse Problem

Prior-based Multi-Voltage Threshold (MVT) sampling reconstructs pulse parameters from sparse threshold-crossing times rather than full waveforms, making parameter recovery inherently a model-dependent inverse problem. However, prior-based MVT has lacked a formal mathematical statement, leaving identifiability, stochastic error propagation, and threshold design without a unified theoretical foundation. We formalize prior-based MVT for strictly unimodal pulse families as a structured inverse problem. On that foundation, we develop the first unified theory of prior-based MVT, comprising deterministic identifiability conditions, a stochastic timing-error model with leading-order mismatch bias, and a nuisance-profiled threshold-design theory centered on an effective-information equation for robust single-event and partial-trigger multi-event operation. We instantiate the framework for the bi-exponential pulse model, derive executable design recipes, and validate the resulting predictions on a 10,000-pulse $^{22}$Na/LYSO/SiPM dataset. The experiments confirm that the framework yields useful threshold designs in the photopeak regime while also revealing the regime boundary at which partial triggering and model mismatch limit the predictive power of Fisher-guided optimization. These results provide the first unified mathematical foundation for prior-based MVT and recast it from an empirical threshold heuristic as a principled inferential framework.

physics.med-ph↗

arXiv2025

Analytic Model of Trans-axial Sensitivity in Cylindrical PET Systems Based on Solid Angle

In positron emission tomography (PET), a clear theoretical model describing how system sensitivity varies as a source is moved trans-axially within the field of view (FOV) is lacking. The current understanding and practical intuition often suggest that sensitivity is maximum at the center of the FOV, an assumption reflected in standardized protocols. In this work, we derive an analytic model for the trans-axial-plane sensitivity distribution in a cylindrical PET scanner based on solid angle. The model, formulated as a function of trans-axial offset from the center, is validated through both Monte Carlo simulations and physical experiments on a representative system. We find that the derived theoretical distribution is essentially consistent with simulation and experimental results, revealing a non-intuitive feature: sensitivity increases with trans-axial offset, peaks at the edge of the FOV, and drops off sharply beyond it. This study provides the first closed-form model of trans-axial geometric sensitivity in cylindrical PET scanners, offering a vital benchmark for isolating detector technology improvements and revealing a non-intuitive, offset-dependent sensitivity profile that enables new protocol optimization strategies.

physics.med-ph↗