Learned D-AMP: Principled Neural Network based Compressive Image Recovery

Compressive image recovery is a challenging problem that requires fast and algorithms. Recently, neural networks have been applied to this with promising results. By exploiting massively parallel GPU processing and oodles of training data, they can run orders of magnitude than existing techniques. However, these methods are largely black boxes that are difficult to train and often-times specific a single measurement matrix. It was recently demonstrated that iterative sparse-signal-recovery algorithms be "unrolled" to form interpretable deep networks. Taking inspiration from work, we develop a novel neural network architecture that mimics the of the denoising-based approximate message passing (D-AMP) algorithm. call this new network Learned D-AMP (LDAMP). The LDAMP network is easy to train, can be applied to a variety of different matrices, and comes with a state-evolution heuristic that predicts its performance. Most importantly, it outperforms the-of-the-art BM3D-AMP and NLR-CS algorithms in terms of both accuracy and time. At high resolutions, and when used with sensing matrices that have implementations, LDAMP runs over 50\ faster than BM3D-AMP and of times faster than NLR-CS.