An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration
This addresses the trade-off between optimization and modeling errors in image processing, offering an incremental improvement for practitioners in computer vision.
The paper tackles the problem of early stopping in variational image restoration methods by introducing an optimal stopping time learned via optimal control, achieving competitive results in image denoising and deblurring.
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.