A Multi-Parameter Persistence Algorithm for the Automatic Energy Calibration of Scintillating Radiation Sensors

Peak detection is a fundamental task in spectral and time-series data analysis across diverse scientific and engineering disciplines, yet traditional approaches are highly sensitive to the choice of algorithm parameters, complicating reliable and consistent interpretation. Triggered by the requirement of the energy calibration for the 128 detectors of the PI3SO gamma ray scanner, we introduce a versatile methodology inspired by concepts from persistent homology, extending the traditional notion of persistence to a multi-parameter setting. Our approach systematically explores the space defined by multiple detection parameters and quantifies peak robustness through the hyper-volume in parameter space where each peak is consistently identified. This volumetric multi-parameter persistence (VM-PP) measure enables robust peak ranking and significantly reduces the sensitivity of detection outcomes to individual parameter selection, demonstrating utility across simulated and experimental spectral datasets. Extensive validation reveals that this method reliably differentiates genuine peaks from noise-induced fluctuations under diverse noise conditions, proving effective in practical spectroscopic calibration scenarios. This framework, general by design, can be readily adapted to diverse signal-processing applications, enhancing interpretability and reliability in complex feature-detection tasks.