  We present a new algorithm for estimating the Point Spread Function (PSF) in
wide-field astronomical images with extreme source crowding. Robust and
accurate PSF estimation in crowded astronomical images dramatically improves
the fidelity of astrometric and photometric measurements extracted from
wide-field sky monitoring imagery. Our radically new approach utilizes
convolutional sparse representations to model the continuous functions involved
in the image formation. This approach avoids the need to detect and precisely
localize individual point sources that is shared by existing methods. In
experiments involving simulated astronomical imagery, it significantly
outperforms the recent alternative method with which it is compared.
