  This paper proposes a new way of regularizing an inverse problem in imaging
(e.g., deblurring or inpainting) by means of a deep generative neural network.
Compared to end-to-end models, such approaches seem particularly interesting
since the same network can be used for many different problems and experimental
conditions, as soon as the generative model is suited to the data. Previous
works proposed to use a synthesis framework, where the estimation is performed
on the latent vector, the solution being obtained afterwards via the decoder.
Instead, we propose an analysis formulation where we directly optimize the
image itself and penalize the latent vector. We illustrate the interest of such
a formulation by running experiments of inpainting, deblurring and
super-resolution. In many cases our technique achieves a clear improvement of
the performance and seems to be more robust, in particular with respect to
initialization.
