Learning to invert: Signal recovery via Deep Convolutional Networks

By Ali Mousavi, Richard Baraniuk. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2017

296 citations recorded by the source corpus.

The promise of compressive sensing (CS) has been offset by two significant challenges. First, real-world data is not exactly sparse in a fixed basis. Second, current high-performance recovery algorithms are slow to converge, which limits CS to either non-real-time applications or scenarios where massive back-end computing is available. In this paper, we attack both of these challenges head-on by developing a new signal recovery framework we call DeepInverse that learns the inverse transformation from measurement vectors to signals using a deep convolutional network. When trained on a set of representative images, the network learns both a representation for the signals (addressing challenge one) and an inverse map approximating a greedy or convex recovery algorithm (addressing challenge two). Our experiments indicate that the DeepInverse network closely approximates the solution produced by state-of-the-art CS recovery algorithms yet is hundreds of times faster in run time. The tradeoff for the ultrafast run time is a computationally intensive, off-line training procedure typical to deep networks. However, the training needs to be completed only once, which makes the approach attractive for a host of sparse recovery problems.

Subfields: Biomedical Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/48a79bdc5576bd81572210cb253671a25494f548

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Citations in the corpus

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.”
Exploiting the Potential of Standard Convolutional Autoencoders for Image Restoration by Evolutionary Search (2018, background): “…tasks, such as image denoising (Xie et al., 2012; Zhang. et al., 2017), single image super-resolution (SISR) (Dong et al., 2014; Ledig et al., 2017), deblurring and compressive sensing (Xu et al., 2014; Kulkarni et al., 2016; Mousavi & Baraniuk, 2017), in addition to those mentioned in Sec.1.”
Learning to Detect (2018, background): “Recently, there were works on learning to invert linear channels and reconstruct signals [15], [16], [31].”
ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing (2017, background): “Mousavi and Baraniuk recently propose an all-convolutional network for image CS reconstruction [29].”
Learned D-AMP: Principled Neural Network based Compressive Image Recovery (2017, methodology): “Other papers in this line of work used either pure convolutional layers (DeepInverse [6]) or a combination of convolutional and fully-connected layers (DR 2 -Net [7] and ReconNet [5]) to build deep learning frameworks capable of solving the CS recovery problem.”
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 [19]–[32], microscopy [33], inpainting [34], [35], superresolution [36]–[38], compressed sensing [39]–[42], image manipulation [43], and many more.”
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].”
MoDL: Model-Based Deep Learning Architecture for Inverse Problems (2017, background): “Improved results may be possibly obtained by fixing the sampling pattern during training, as pursued by most of the deep learning image recovery strategies [16], [18], [33], [34], [43], albeit with increased sensitivity to acquisition settings.”
AMP-Inspired Deep Networks for Sparse Linear Inverse Problems (2016, methodology): “In particular, we tried an implementation of the DeepInverse approach from [35].”
Deep MIMO detection (2017, background): “Recently, there were many works on learning to invert linear channels and reconstruct signals [11], [12], [15].”
Deep Learning in Physical Layer Communications (2018, methodology): “However, traditional CS algorithms face challenges as real-world data is not exactly sparse and the convergence speed of the existing signal recovery algorithms is relatively slow, which has limited the practical applications of CS [7].”
Deep Learning Based Communication Over the Air (2017, background): “Among them are belief propagation for channel decoding [16], [17], one-shot channel decoding [18], compressed sensing [19], [20], coherent [21] and blind [22]”
ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing (2020, background): “In [33], [43], [44], fullyconnected deep networks or deep convolutional nets were”