  Astronomical data often suffer from noise and incompleteness. We extend the
common mixtures-of-Gaussians density estimation approach to account for
situations with a known sample incompleteness by simultaneous imputation from
the current model. The method, called GMMis, generalizes existing
Expectation-Maximization techniques for truncated data to arbitrary truncation
geometries and probabilistic rejection processes, as long as they can be
specified and do not depend on the density itself. The method accounts for
independent multivariate normal measurement errors for each of the observed
samples and recovers an estimate of the error-free distribution from which both
observed and unobserved samples are drawn. It can perform a separation of a
mixtures-of-Gaussian signal from a specified background distribution whose
amplitude may be unknown. We compare GMMis to the standard Gaussian mixture
model for simple test cases with different types of incompleteness, and apply
it to observational data from the NASA Chandra X-ray telescope. The python code
is released as an open-source package at https://github.com/pmelchior/pyGMMis
