Breaking the Limits of Gamma-Ray Spectrometry by Exploiting Sparsity of Photon Arrivals

State-of-the-art gamma-ray spectrometry suffers from physical limitations of the sensing system. Pulse pile-up and dead time losses lead to wrong measurements of both the number of pulses and their amplitude. Current techniques based on maxima detection, be in analog domain or after fine digitalization, offer limited resolution, bounded by the instrument response function (IRF). In this work we show how spectral sampling can help breaking the current limits of gamma-ray spectrometry. By means of a sparsity-based sensing model and using a fast and robust parametric spectral estimation method, we show that the unknown parameters, namely time of arrival and energy of the γ-photons, can be accurately estimated from few m ≥ 2K + 1 frequency samples. In the noiseless case parameter estimation is exact to machine precision and the method has virtually no resolution limit. A thorough experimental evaluation using an empirical IRF unveiled excellent performance, even in overpessimistic conditions.