PSA via Singular Value Decomposition

Gamma ray tracking is a substantial feature of upcoming gamma ray detector arrays (e.g. AGATA, GRETA). The precision and efficiency of tracking algorithms heavily depends on the knowledge of the exact interaction position inside the detector volume. To determine the position inside a segment of the detector pulse shape analysis (PSA) is applied. Due to a complicated electric field in parts of the detector there is no simple method to determine the position for a given pulse. Instead a database of pulse shapes with corresponding positions is created either by scanning the detector or from electric field simulations. The problem of finding the exact position for a given pulse is reduced to finding the best fit to this signal from the database. Finding the best fit from the database can be substantially accelerated by applying a transformation to the signals in the database and to the recorded pulse shape of the event before comparing them. An optimal linear transformation is obtained by calculating a Singular Value Decomposition of all the signals in the database.