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 on the atmospheric conditions during observation. A typical astronomical image will likely have a unique PSF, that is non-circular and different in different bands. At the same time, observations of known stars also give us an accurate 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). This algorithm belongs to a class of non-blind deconvolution algorithms, since it assumes the PSF shape is known. We study the performance of different versions of this algorithm under realistic observational conditions in terms of the recovery of the most relevant astronomical quantities such as colors, ellipticities and orientations. We investigate custom loss functions that optimize the recovery of astronomical quantities with mixed results.