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

By Christopher A. Metzler, Ali Mousavi, Richard Baraniuk. Neural Information Processing Systems, 2017

321 citations recorded by the source corpus.

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 {\em 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.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/5aaef8fa91997674725979df2ca3210dac599632

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Model-Based Deep Learning (2020, background): “Deep unfolded networks have since been applied in various applications in image denoising [7], [39], [40], sparse recovery [9], [25], [41], dictionary learning [42], [43], communications [19], [44]–[47], ultrasound [48], [49], and super resolution [50]–[52].”
GAN-Based Projector for Faster Recovery With Convergence Guarantees in Linear Inverse Problems (2019, background): “Neural networkbased inverse problem solvers have been explored recently [14, 35, 31, 1, 12, 15, 25, 32, 22, 37, 26].”
Denoising Diffusion Restoration Models (2022, methodology): “A similar use of denoisers in different iterative algorithms is proposed in [34, 16, 30].”
Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing (2019, unknown): “[64] Kulkarni et al.”
Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise (2022, methodology): “Iterative neural models have been used for various inverse problems [Romano et al., 2016, Metzler et al., 2017].”
Deep Learning Techniques for Inverse Problems in Imaging (2020, methodology): “In [85], [86], [114], the authors apply SURE to train the DnCNN [21] and Learned Denoising-Based Approximate Message Passing (LDAMP) networks [88] for denoising and compressive sensing tasks.”
ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing (2020, methodology): “measurements by randomly permuted coded diffraction operators and randomly permuted Walsh-Hadamard operators [9], [10], [64].”
Neural Proximal Gradient Descent for Compressive Imaging (2018, background): “The second category is inspired by unrolling the iterations of classical optimization algorithms, and learns the filters and nonlinearities by training deep CNNs [25, 16, 26, 27].”
Deep Learning in Physical Layer Communications (2018, unknown): “Learned denoising-based AMP (LDAMP) [9] is one of the excellent signal recovery algorithms in terms of both accuracy and speed, which has been applied to channel estimation in millimeter-wave (mmWave) communications [2].”
Deep Learning-Based Channel Estimation for Beamspace mmWave Massive MIMO Systems (2018, methodology): “Deep learning has been recently applied to solve compressive image recovery [5] and wireless communications [7], [8].”
Small Sample Learning in Big Data Era (2018, methodology): “, 2017; Adler and Öktem, 2018), compressive image reconstruction (Metzler et al., 2017; Zhang and Ghanem, 2018).”
Plug-and-Play Methods Provably Converge with Properly Trained Denoisers (2019, methodology): “(4)Some recent deep-learning based methods (Yang et al., 2016; Kulkarni et al., 2016; Metzler et al., 2017; Zhang & Ghanem, 2018) are not compared here because we assume we do not have enough medical images for training.”
Learning to Optimize: A Primer and A Benchmark (2021, background): “Th works [175; 153; 76; 256]use data-driven training to learn a proximal or a projection operator and apply it in the unrolled algorithm.”