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

TL;DR

Learned D-AMP (LDAMP) is a neural network architecture inspired by the D-AMP algorithm, offering fast, accurate, and versatile compressive image recovery with principled design and strong empirical performance.

Contribution

This paper introduces LDAMP, a neural network that unrolls the D-AMP algorithm, providing a principled, trainable, and measurement matrix-agnostic approach with predictable performance.

Findings

Outperforms BM3D-AMP and NLR-CS in accuracy and speed

Runs over 50 times faster than BM3D-AMP at high resolutions

Accurately predicts performance using state-evolution heuristic

Abstract

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 $50\times$ faster than BM3D-AMP and hundreds of times faster than NLR-CS.