Astronomical image reconstruction with convolutional neural networks

Astronomical image observation is plagued by the fact the the observed image is the result of a convolution between the observed object and what the astronomers call a Point Spread Function (PSF) [1] [2]. In addition to the convolution the image is also polluted by noise that is due to the low energy of the observed objects (photon noise) or to the sensor. The PSF is usually known a priori, thanks to a physical model for the telescope of estimation from known objects. State of the art approaches in astronomical image reconstruction aim at solving an optimization problem that encodes both a data fitting (with observation and PSF) and a regularization term that promote wanted properties in the images [1], [3], [4]. Still, solving a large optimization problem for each new image can be costly and might not be practical in the future. Indeed in the coming years several new generations of instruments such as the Square kilometer Array [5] will provide very large images (both in spatial and spectral dimensions) that will need to be processed efficiently. The most successful image reconstruction approaches rely on convex optimization [3], [4], [6] and are all based on gradient [7] or proximal splitting gradient descent [8]. Interestingly those methods have typically a linear convergence, meaning that the number of iterations necessary to reach a given precision is proportional to the dimension n of the problem [9], where n is the number of pixels.