Title: Restoring a smooth function from its noisy integrals,
Abstract: Numerical (and experimental) data analysis often requires the restoration of
a smooth function from a set of sampled integrals over finite bins. We present
the bin hierarchy method that efficiently computes the maximally smooth
function from the sampled integrals using essentially all the information
contained in the data. We perform extensive tests with different classes of
functions and levels of data quality, including Monte Carlo data suffering from
a severe sign problem and physical data for the Green's function of the
Fröhlich polaron.