Related papers: Total Deep Variation for Linear Inverse Problems

Total Deep Variation for Linear Inverse Problems

URL: http://arxiv.org/abs/2001.05005v2
Date: Mon, 17 Feb 2020 19:39:23 GMT
Title: Total Deep Variation for Linear Inverse Problems
Authors: Erich Kobler and Alexander Effland and Karl Kunisch and Thomas Pock
Abstract summary: We propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems.
Score: 71.90933869570914
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning. We cast the learning problem as a discrete sampled optimal control problem, for which we derive the adjoint state equations and an optimality condition. By exploiting the variational structure of our approach, we perform a sensitivity analysis with respect to the learned parameters obtained from different training datasets. Moreover, we carry out a nonlinear eigenfunction analysis, which reveals interesting properties of the learned regularizer. We show state-of-the-art performance for classical image restoration and medical image reconstruction problems.

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