Jolideco: Joint Likelihood Deconvolution in the Presence of Poisson Noise

We present a new method for jointly deconvolving a set of astronomical observations of the same sky region in the presence of Poisson noise. The method reconstructs a flux image from a set of observations by finding a maximum a-posteriori estimate of the joint Poisson likelihood of all observations under a patch based image prior. The patch prior is parametrized by a standard Gaussian Mixture Model (GMM) learned from astronomical images at other wavelenghts. The flexibility of the GMM allows the prior to adapt to the structures in the image and reconstruct point-like as well as diffuse features equally well. By applying the method to simulated data we show that the combination of multiple observations leads to an improved reconstruction quality especially in the low S/N regime. We also show that the method yields superior reconstruction quality to alternative standard methods such as the Richardson-Lucy or the LIRA method. Finally we present results of the method applied to extragalactic and Galactic Chandra and XMM observations. The work is supported by NASA APRA grant 80NSSC21K0285 and NASA CXC NAS8-03060.