A generative learned unrolling algorithm for Poisson source separation applied to gamma-ray spectrometry

Recovering radionuclide contributions from γ-ray spectra is a central task in nuclear signal processing, which goal is to estimate both the underlying source spectra and their proportions in a measured signal. This source separation problem relies on prior spectral knowledge to guide the estimation, but it remains challenging due to noise and spectral variabilities due to not well-known measurement conditions, caused by γ-photon interactions in the source surroundings or differing source geometries. The problem is semi-blind in nature: the radionuclide sources are known, but their exact spectral responses are unknown. Existing unmixing algorithms either rely on iterative solvers which are slow, or use “black-box” neural networks overlooking the underlying physical structure of the problem. In this work, we propose GLUPSS, a Generative Learned Unrolling algorithm for Poisson Source Separation. Our approach leverages the statistical nature of the data by incorporating a Poisson log-likelihood loss and models the spectral variability using a 1D manifold learned through a generative Interpolating AutoEncoder (IAE). Furthermore, building on algorithm unrolling, we propose a neural network which mimics a proximal optimization scheme but drastically reduces the number of iterations, making GLUPSS usable for real-life, time-sensitive applications. Experimental results on realistic synthetic data show that GLUPSS achieves an estimation accuracy within 1% (in terms of Absolute Relative Error) of the state-of-the-art SEMSUN iterative methods while offering a 60 ×  speedup compared to this method.11Our code is available at https://github.com/aleph-group/GLUPSS.