Terated sparse reconstruction for activity estimation in nuclear spectroscopy

The aim of nuclear spectroscopy is to provide as many information as possible regarding the activity and the content of an unknown radioactive source. Due to some random perturbations called pileup phenomenon, electrical pulses recorded by the spectrometric apparatus may overlap. Recent developments in compressive sensing and sparse signal reconstruction allow us to build efficient algorithms for the estimation of the activity. We suggest in this paper an iterative algorithm which improves this estimation. This algorithm is based on successive sparse approximations of the residual signal with a slowly decreasing sparsity parameter, so that at each step pulses with smaller amplitude are detected. The algorithm is detailed and its performances compared to other methods based on sparse reconstruction. Results show that the proposed approach perform better than the state-of-the-art methods, and emphasize the usefulness of the iterative scheme.