  For experiments with high arrival rates, reliable identification of
nearly-coincident events can be crucial. For calorimetric measurements to
directly measure the neutrino mass such as HOLMES, unidentified pulse pile-ups
are expected to be a leading source of experimental error. Although Wiener
filtering can be used to recognize pile-up, it suffers errors due to
pulse-shape variation from detector nonlinearity, readout dependence on
sub-sample arrival times, and stability issues from the ill-posed deconvolution
problem of recovering Dirac delta-functions from smooth data. Due to these
factors, we have developed a processing method that exploits singular value
decomposition to (1) separate single-pulse records from piled-up records in
training data and (2) construct a model of single-pulse records that accounts
for varying pulse shape with amplitude, arrival time, and baseline level,
suitable for detecting nearly-coincident events. We show that the resulting
processing advances can reduce the required performance specifications of the
detectors and readout system or, equivalently, enable larger sensor arrays and
better constraints on the neutrino mass.
