Solving a Deconvolution Problem in Photon Spectrometry

We solve numerically a deconvolution problem to extract the undisturbed spectrum from the measured distribution contaminated by the finite resolution of the measuring device. A problem of this kind emerges when one wants to infer the momentum distribution of the neutral pions by detecting the π 0 decay photons using the photon spectrometer of the ALICE LHC experiment at CERN [1]. The underlying integral equation connecting the sought for pion spectrum and the measured gamma spectrum has been discretized and subsequently reduced to a system of linear algebraic equations. The latter system, however, is known to be ill-posed and must be regularized to obtain a stable solution. This task has been accomplished here by means of the Tikhonov regularization scheme combined with the L-curve method. The resulting pion spectrum is in an excellent quantitative agreement with the pion spectrum obtained from a Monte Carlo simulation.