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We recently unrolled the D-AMP compressive sensing recovery algorithm to form the Learned D-AMP neural network. This network is interpretable, is easy to train, isn't specific to a particular measurement matrix, and offers great run-times and accuracy. We thought it might be of interest to your readers.
The paper can be found here: https://arxiv.org/abs/1704.06625
Matlab and TensorFlow implementations can be found here: https://github.com/ricedsp/D-AMP_Toolbox
Learned D-AMP: Principled Neural Network based Compressive Image Recovery by Christopher A. Metzler, Ali Mousavi, Richard G. Baraniuk
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. Taking inspiration from this work, we develop a novel neural network architecture that mimics the behavior of the denoising-based approximate message passing (D-AMP) algorithm. We call this new network Learned D-AMP (LDAMP).
The LDAMP network is easy to train, can be applied to a variety of different measurement matrices, and comes with a state-evolution heuristic that accurately predicts its performance. Most importantly, it outperforms the state-of-the-art BM3D-AMP and NLR-CS algorithms in terms of both accuracy and run time. At high resolutions, and when used with sensing matrices that have fast implementations, LDAMP runs over 50\timesfaster than BM3D-AMP and hundreds of times faster than NLR-CS.
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