Optical astronomical images are strongly affected by the point spread
function (PSF) of the optical system and the atmosphere (seeing) which blurs
the observed image. The amount of blurring depends both on the observed band,
and more crucially, on the atmospheric conditions during observation. A typical
astronomical image will therefore have a unique PSF that is non-circular and
different in different bands. Observations of known stars give us a
determination of this PSF. Therefore, any serious candidate for production
analysis of astronomical images must take the known PSF into account during the
image analysis. So far the majority of applications of neural networks (NN) to
astronomical image analysis have ignored this problem by assuming a fixed PSF
in training and validation. We present a neural network based deconvolution
algorithm based on Deep Wiener Deconvolution Network (DWDN) that takes the PSF
shape into account when performing deconvolution as an example of one possible
approach to enabling neural network to use the PSF information. We study the
performance of several versions of this algorithm under realistic observational
conditions in terms of recovery of most relevant astronomical quantities such
as colors, ellipticities and orientations. We also investigate the performance
of custom loss functions and find that they cause modest improvements in the
recovery of astronomical quantities.Comment: 12 pages, 6 figure