Sparse regression algorithm for activity estimation in $γ$ spectrometry

Details Sparse regression algorithm for activity estimation in $γ$ spectrometry Sparse regression algorithm for activity estimation in $γ$ spectrometry

2012-02-27

arxiv.org/abs/1202.6011v1

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Scientific paper

We consider the counting rate estimation of an unknown radioactive source, which emits photons at times modeled by an homogeneous Poisson process. A spectrometer converts the energy of incoming photons into electrical pulses, whose number provides a rough estimate of the intensity of the Poisson process. When the activity of the source is high, a physical phenomenon known as pileup effect distorts the measurements and introduces a significant bias to the standard estimators of the source activities. We show in this paper that the problem of counting rate estimation can be interpreted as a sparse regression problem. We suggest a post-processed version of the Least Absolute Shrinkage and Selection Operator (LASSO) to estimate the photon arrival times, and derive necessary conditions which guarantee that the arrival times will be selected. The performances of the proposed approach are studied on simulations and real datasets.

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