  The problem of estimating a complex measure made up by a linear combination
of Dirac distributions centered on points of the complex plane from a finite
number of its complex moments affected by additive i.i.d. Gaussian noise is
considered. A random measure is defined whose expectation approximates the
unknown measure under suitable conditions. An estimator of the approximating
measure is then proposed as well as a new discrete transform of the noisy
moments that allows to compute an estimate of the unknown measure. A small
simulation study is also performed to experimentally check the goodness of the
approximations.
