Superresolution algorithms for data analysis of discrete detectors in nuclear physics

It is shown that the recovery of particle coordinates by detectors with intrinsic resolution determined by the point spread function and finite size of detector bins can be reduced to a solution of the standard convolution integral equation with a modified point spread function. Two approaches are proposed and investigated for this problem: parametric and non-parametric ones. Algorithms and their testing for both the approaches are given. It was shown that both the algorithms can resolve the coordinates of particles with a resolving power better than the bin size of the detector granulation unit and the point spread function characteristic scale. It is also demonstrated that the superresolution efficiency of the proposed parametric algorithm almost attains the Cramér–Rao limit and Shannonʹs limit for the non-parametric algorithm. Results of numerical experiments and of real data processing of the CERES silicon drift detector are given.