  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.
