  When images are statistically described by a generative model we can use this
information to develop optimum techniques for various image restoration
problems as inpainting, super-resolution, image coloring, generative model
inversion, etc. With the help of the generative model it is possible to
formulate, in a natural way, these restoration problems as Statistical
estimation problems. Our approach, by combining maximum a-posteriori
probability with maximum likelihood estimation, is capable of restoring images
that are distorted by transformations even when the latter contain unknown
parameters. The resulting optimization is completely defined with no parameters
requiring tuning. This must be compared with the current state of the art which
requires exact knowledge of the transformations and contains regularizer terms
with weights that must be properly defined. Finally, we must mention that we
extend our method to accommodate mixtures of multiple images where each image
is described by its own generative model and we are able of successfully
separating each participating image from a single mixture.
