
Deep Learning for Inverse Problems: Bounds and Regularizers
Inverse problems arise in a number of domains such as medical imaging, r...
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Deep Decomposition Learning for Inverse Imaging Problems
Deep learning is emerging as a new paradigm for solving inverse imaging ...
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Deep learning for inverse problems with unknown operator
We consider illposed inverse problems where the forward operator T is u...
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Model Adaptation for Inverse Problems in Imaging
Deep neural networks have been applied successfully to a wide variety of...
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Solving Inverse Problems With Deep Neural Networks – Robustness Included?
In the past five years, deep learning methods have become stateofthea...
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Unrolled Optimization with Deep Priors
A broad class of problems at the core of computational imaging, sensing,...
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Pocket Guide to Solve Inverse Problems with GlobalBioIm
GlobalBioIm is an opensource MATLAB library for solving inverse problem...
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ModelAware Regularization For Learning Approaches To Inverse Problems
There are various inverse problems – including reconstruction problems arising in medical imaging – where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask whether such knowledge of the forward operator can be exploited in deep learning approaches increasingly used to solve inverse problems. In this paper, we provide one such way via an analysis of the generalisation error of deep learning methods applicable to inverse problems. In particular, by building on the algorithmic robustness framework, we offer a generalisation error bound that encapsulates key ingredients associated with the learning problem such as the complexity of the data space, the size of the training set, the Jacobian of the deep neural network and the Jacobian of the composition of the forward operator with the neural network. We then propose a 'plugandplay' regulariser that leverages the knowledge of the forward map to improve the generalization of the network. We likewise also propose a new method allowing us to tightly upper bound the Lipschitz constants of the relevant functions that is much more computational efficient than existing ones. We demonstrate the efficacy of our modelaware regularised deep learning algorithms against other stateoftheart approaches on inverse problems involving various subsampling operators such as those used in classical compressed sensing setup and accelerated Magnetic Resonance Imaging (MRI).
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