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A Review of Convolutional Neural Networks for Inverse Problems in Imaging

In this survey paper, we review recent uses of convolution neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding performance on object classification and segmentation tasks. Motivated by these successes, researchers have begun to apply CNNs to the resolution of inverse problems such as denoising, deconvolution, super-resolution, and medical image reconstruction, and they have started to report improvements over state-of-the-art methods, including sparsity-based techniques such as compressed sensing. Here, we review the recent experimental work in these areas, with a focus on the critical design decisions: Where does the training data come from? What is the architecture of the CNN? and How is the learning problem formulated and solved? We also bring together a few key theoretical papers that offer perspective on why CNNs are appropriate for inverse problems and point to some next steps in the field.

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