Learned convex regularizers for inverse problems

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially to discern ground-truth images from unregularized reconstruct...

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Bibliographic Details
Published inarXiv.org
Main Authors Mukherjee, Subhadip, Dittmer, Sören, Shumaylov, Zakhar, Lunz, Sebastian, Öktem, Ozan, Schönlieb, Carola-Bibiane
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 01.03.2021
Subjects
Algorithms
Computed tomography
Convergence
Convexity
Image reconstruction
Inverse problems
Mathematical analysis
Medical imaging
Neural networks
Parameters
Regularization
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Summary:We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially to discern ground-truth images from unregularized reconstructions. Convexity of the regularizer is desirable since (i) one can establish analytical convergence guarantees for the corresponding variational reconstruction problem and (ii) devise efficient and provable algorithms for reconstruction. In particular, we show that the optimal solution to the variational problem converges to the ground-truth if the penalty parameter decays sub-linearly with respect to the norm of the noise. Further, we prove the existence of a sub-gradient-based algorithm that leads to a monotonically decreasing error in the parameter space with iterations. To demonstrate the performance of our approach for solving inverse problems, we consider the tasks of deblurring natural images and reconstructing images in computed tomography (CT), and show that the proposed convex regularizer is at least competitive with and sometimes superior to state-of-the-art data-driven techniques for inverse problems.
ISSN:2331-8422