A deep learning approach to structured signal recovery

By Ali Mousavi, Ankit B. Patel, Richard Baraniuk. Allerton Conference on Communication, Control, and Computing, 2015

467 citations recorded by the source corpus.

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/08ca35366a4708ead695497c82edf1401d1bbf27

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In Computational Mechanics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Learning Optimal Nonlinearities for Iterative Thresholding Algorithms (2015, background): “A general application of deep learning to compressive sensing was presented in [26], while the idea of learning the activation functions was discussed in [27].”
ReconNet: Non-Iterative Reconstruction of Images from Compressively Sensed Measurements (2016, background): “org, but not yet peer-reviewed or published [25]) that presents stacked denoising auto-encoders (SDAs) based non-iterative approach for this problem.”
ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing (2017, methodology): “From Table 1, we observe that SDA and ReconNet work better at 1We use the source code made publicly available by the authors of TVAL3 [22], D-AMP [28], IRCNN [49], and ReconNet [21] and implement SDA [30] ourselves, since its source code is not available. extremely low CS ratios of 1% and 4%, while ”
Using Deep Neural Networks for Inverse Problems in Imaging: Beyond Analytical Methods (2018, background): “[39], who use stacked denoising autoencoders to sense and reconstruct signals, and Bora et al.”
AMP-Inspired Deep Networks for Sparse Linear Inverse Problems (2016, methodology): “For example, convolutional neural networks and stacked denoising autoencoders have been applied to speech enhancement [27], image denoising [28], image deblurring [29], [30], image super resolution [31], 3D imaging [32], compressive imaging [33]– [35], and video compressive sensing [36].”
ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing (2020, methodology): “[32] used a stacked auto-encoder to recover the signals from CS measurements.”
Deep Learning Techniques for Inverse Problems in Imaging (2020, background): “deep neural networks can leverage large collections of training data to directly compute regularized reconstructions across a host of computational imaging tasks [16]–[24].”
Learning to invert: Signal recovery via Deep Convolutional Networks (2017, background): “The ﬁrst paper to study the problem of structured signal recovery from a set of undersampled measurements using a deep learning approach was [11].”
Image Compressed Sensing Using Convolutional Neural Network (2020, methodology): “Recently, a few deep learning based methods have also been developed for image CS reconstruction [1], [27]–[29].”
Deep learning for wireless physical layer: Opportunities and challenges (2017, methodology): “For certain algorithms with iterations (e.g., data detection [6], decoding [25], and compressive sensing [41], [42], [43]), a straightforward method is to unfold the iterations as layer structures, and weights can be added to the original iterative formulas for training.”
One Network to Solve Them All — Solving Linear Inverse Problems Using Deep Projection Models (2017, methodology): “Such methods have achieved state-of-the-art performance in many challenging image inverse problems like super-resolution [17, 29], inpainting [38], compressive sensing [28, 35, 36], and image debluring [49].”
DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensing (2017, methodology): “In [26], Stacked Denoising Auto-encoders (SDAs) are employed to learn a mapping between CS measurements and image blocks.”
Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk (2017, background): “These more sophisticated priors are recently emerging in empirical applications of many fields of imaging, such as medical imaging [70, 30, 24, 55, 17, 1, 49, 68, 53, 43, 32, 42, 16, 69], microscopy [59], inpainting [45, 71], superresolution [60, 33, 28], compressed sensing [38, 37, 51, 50], image m”
Distributed Compressive Sensing: A Deep Learning Approach (2015, methodology): “In [14], it has been theoretically shown that using signal models that exploit these structures will result in a decrease in the number of measurements.”
AMP-Net: Denoising-Based Deep Unfolding for Compressive Image Sensing (2020, methodology): “Some methods [29], [30] use hand-crafted denoisers to deblock images.”
Solving Linear Inverse Problems Using Gan Priors: An Algorithm with Provable Guarantees (2018, methodology): “This approach is used in [28, 29, 30, 31, 32, 33] to solve different inverse problems, and has met with considerable success.”
Denoising genome-wide histone ChIP-seq with convolutional neural networks (2016, methodology): “Our approach is conceptually related to the existing literature on structured signal recovery, in particular supervised denoising in images (Jain and Seung, 2009; Xie et al. , 2012; Mousavi et al. , 2015) and speech (Maas and Le, 2012).”