
Compressive sensing with untrained neural networks: Gradient descent finds the smoothest approximation
Untrained convolutional neural networks have emerged as highly successf...
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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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Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators
Convolutional Neural Networks (CNNs) have emerged as highly successful t...
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Deep Decoder: Concise Image Representations from Untrained Nonconvolutional Networks
Deep neural networks, in particular convolutional neural networks, have ...
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Convolutional Neural Networks Analyzed via Inverse Problem Theory and Sparse Representations
Inverse problems in imaging such as denoising, deblurring, superresoluti...
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Onedimensional Deep Image Prior for Time Series Inverse Problems
We extend the Deep Image Prior (DIP) framework to onedimensional signal...
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Inverse problems with secondorder Total Generalized Variation constraints
Total Generalized Variation (TGV) has recently been introduced as penalt...
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Regularizing linear inverse problems with convolutional neural networks
Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized that even without training, convolutional networks can function as concise image models, and thus regularize inverse problems. In this paper, we provide further evidence for this finding by studying variations of convolutional neural networks that map few weight parameters to an image. The networks we consider only consist of convolutional operations, with either fixed or parameterized filters followed by ReLU nonlinearities. We demonstrate that with both fixed and parameterized convolutional filters those networks enable representing images with few coefficients. What is more, the underparameterization enables regularization of inverse problems, in particular recovering an image from few observations. We show that, similar to standard compressive sensing guarantees, on the order of the number of model parameters many measurements suffice for recovering an image from compressive measurements. Finally, we demonstrate that signal recovery with a untrained convolutional network outperforms standard l1 and total variation minimization for magnetic resonance imaging (MRI).
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