Learned convex regularizers for inverse problems
- URL: http://arxiv.org/abs/2008.02839v2
- Date: Mon, 1 Mar 2021 18:56:30 GMT
- Title: Learned convex regularizers for inverse problems
- Authors: Subhadip Mukherjee, S\"oren Dittmer, Zakhar Shumaylov, Sebastian Lunz,
Ozan \"Oktem, and Carola-Bibiane Sch\"onlieb
- Abstract summary: We propose to learn a data-adaptive input- neural network (ICNN) as a regularizer for inverse problems.
We prove the existence of a sub-gradient-based algorithm that leads to a monotonically decreasing error in the parameter space with iterations.
We 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.
- Score: 3.294199808987679
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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