An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

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.
Originalspracheenglisch
Seitenumfang32
FachzeitschriftJournal of Mathematical Imaging and Vision
PublikationsstatusEingereicht - 2019

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Early Stopping
Image denoising
Gradient Flow
Image Restoration
optimal control
Paradox
Image reconstruction
stopping
Variational Methods
restoration
Spectrum analysis
Image quality
Optimal Control
Image processing
paradoxes
Optimal Stopping Time
Image Deblurring
Variational Model
gradients
Modeling Error

Dies zitieren

An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration. / Effland, Alexander; Kobler, Erich; Kunisch, Karl; Pock, Thomas.

in: Journal of Mathematical Imaging and Vision, 2019.

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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