# Learning to invert: Signal recovery via Deep Convolutional Networks

@article{Mousavi2017LearningTI, title={Learning to invert: Signal recovery via Deep Convolutional Networks}, author={Ali Mousavi and Richard Baraniuk}, journal={2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, year={2017}, pages={2272-2276} }

The promise of compressive sensing (CS) has been offset by two significant challenges. [] Key Method 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…

## 244 Citations

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

- Computer ScienceNIPS
- 2017

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, which outperforms the state-of-the-art BM3D-AMP and NLR-CS algorithms in terms of both accuracy and run time.

### Deep Learning Approach Based on Tensor-Train for Sparse Signal Recovery

- Computer ScienceIEEE Access
- 2019

The proposed TT-SDA network can preserve the reconstruction performance of the conventional SDA network and outperform the traditional methods, especially with low measurement rates, and it can also significantly reduce the computational complexity and occupied memory space, which becomes a time and memory efficient method in compressive sensing problem.

### JR2net: A Joint Non-Linear Representation and Recovery Network for Compressive Spectral Imaging

- Computer ScienceApplied optics
- 2022

This work proposes a joint non-linear representation and recovery network (JR2net), linking the representation and Recovery task into a single optimization problem, showing superiority over state-of-the-art methods.

### Learning to Sense and Reconstruct A Class of Signals

- Computer Science2019 IEEE Radar Conference (RadarConf)
- 2019

Initial results show that the measurement matrix learned through the proposed technique provides higher peak signal to noise ratio (PSNR) levels compared to both randomly selected matrices or designed measurement matrices for an assumed sparsity basis for the dataset.

### Learned D-AMP: A Principled CNN-based Compressive Image Recovery Algorithm

- Computer ScienceArXiv
- 2017

Novel neural network architectures that mimic the behavior of the denoising-based approximate message passing (D-AMP) and denoised-based vector approximate messagePassing algorithms are developed and outperform the state-of-the-art BM3d-AMP and NLR-CS algorithms in terms of both accuracy and runtime.

### Convolutional Neural Networks for Noniterative Reconstruction of Compressively Sensed Images

- Computer ScienceIEEE Transactions on Computational Imaging
- 2018

This paper proposes a data-driven noniterative algorithm, ReconNet, which is a deep neural network learned end-to-end to map block-wise compressive measurements of the scene to the desired image blocks, and discusses how adding a fully connected layer to the existing ReconNet architecture allows for jointly learning the measurement matrix and the reconstruction algorithm in a single network.

### Deep Coupled-Representation Learning for Sparse Linear Inverse Problems With Side Information

- Computer ScienceIEEE Signal Processing Letters
- 2019

The first deep unfolding method with SI is introduced, which actually comes from a different modality, and is used to learn coupled representations of correlated signals from different modalities, enabling the recovery of multi-modal data at a low computational cost.

### AMP-Inspired Deep Networks for Sparse Linear Inverse Problems

- Computer ScienceIEEE Transactions on Signal Processing
- 2017

This paper proposes two novel neural-network architectures that decouple prediction errors across layers in the same way that the approximate message passing (AMP) algorithms decouple them across iterations: through Onsager correction.

### FompNet: Compressive sensing reconstruction with deep learning over wireless fading channels

- Computer Science2017 9th International Conference on Wireless Communications and Signal Processing (WCSP)
- 2017

Experimental results show that FompNet outperforms existing reconstruction approaches in terms of distortion and computational complexity under various channel conditions.

### Data Driven Measurement Matrix Learning for Sparse Reconstruction

- Computer Science2019 IEEE Data Science Workshop (DSW)
- 2019

Results show that the proposed technique provides higher peak signal to noise ratio (PSNR) levels and hence learns better measurement matrices than that of the randomly selected or specifically designed for a known sparsity basis to reduce average coherence.

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