Sparse reconstruction algorithm for nonhomogeneous counting rate estimation

One of the main objectives of nuclear spectroscopy is the estimation of the counting rate of unknown radioactive sources. Recently, we proposed an algorithm based on a sparse reconstruction of the time signal in order to estimate precisely this counting rate, under the assumption that it remained constant over time. Computable bounds were obtained to quantify the performances. This approach, based on a postprocessed approach of a non-negative sparse regression of the time signal, performed well even when the activity of the source was high. The purpose of this paper is to present an extension of the previous method for an activity varying over time. It relies on the same preliminary sparse reconstruction. However, the postprocessed and plug-in steps are made differently to fit the nonhomogeneous framework. The adapted bounds are presented, and results on simulations illustrate the advantages and limitations of this method.