  Recent interferometers (e.g. ALMA and NOEMA) allow us to obtain the detailed
brightness distribution of the astronomical sources in 3 dimension (R.A., Dec.,
frequency). However, the interpixel correlation of the noise due to the limited
uv coverage makes it difficult to evaluate the statistical uncertainty of the
measured quantities and the statistical significance of the obtained results.
The noise correlation properties are characterized by the noise autocorrelation
function (ACF). We will present the method for (1) estimating the statistical
uncertainty due to the correlated noise in the spatially integrated flux and
spectra directly from the noise ACF and (2) simulating the correlated noise to
perform a Monte Carlo simulation in image analyses. Our method has potential
applications to a range of astronomical images of not only interferometers but
also single dish mapping observation and interpolated and resampled optical
images.

Instrumentation and Methods for Astrophysics;Astrophysics of Galaxies