  We investigate a well-known phenomenon of variational approaches in image
processing, where typically the best image quality is achieved when the
gradient flow process is stopped before converging to a stationary point. This
paradox originates from a tradeoff between optimization and modelling errors of
the underlying variational model and holds true even if deep learning methods
are used to learn highly expressive regularizers from data. In this paper, we
take advantage of this paradox and introduce an optimal stopping time into the
gradient flow process, which in turn is learned from data by means of an
optimal control approach. As a result, we obtain highly efficient numerical
schemes that achieve competitive results for image denoising and image
deblurring. A nonlinear spectral analysis of the gradient of the learned
regularizer gives enlightening insights about the different regularization
properties.
