Compressive image recovery is a challenging problem that requires fast and accurate algorithms. Recently, neural networks have been applied to this problem with promising results. By exploiting massively parallel GPU processing architectures and oodles of training data, they can run orders of magnitude faster than existing techniques. However, these methods are largely unprincipled black boxes that are difficult to train and often-times specific to a single measurement matrix. It was recently demonstrated that iterative sparse-signal-recovery algorithms can be ``unrolled'' to form interpretable deep networks.

Summary of the work: The authors present a theoretically motivated NN architecture for solving inverse problems arising in compressed sensing. The network architecture arises from'unrolling' the denoiser-based approximate message passing (D-AMP) algorithm with convolutional denoiser networks inside. The work is nicely presented, and to my knowledge, original. The authors present competitive results on known benchmark data. Overall evaluation: I enjoyed reading this paper, well presented, theoretically motivated work. I was pleased to see that the method achieves very competitive performance in the end both in terms of accuracy and in terms of speed.

Compressive image recovery is a challenging problem that requires fast and accurate algorithms. Recently, neural networks have been applied to this problem with promising results. By exploiting massively parallel GPU processing architectures and oodles of training data, they can run orders of magnitude faster than existing techniques. However, these methods are largely unprincipled black boxes that are difficult to train and often-times specific to a single measurement matrix. It was recently demonstrated that iterative sparse-signal-recovery algorithms can be unrolled'' to form interpretable deep networks.