# Learning to Invert: Signal Recovery via Deep Convolutional Networks

arXiv: https://arxiv.org/abs/1701.03891 · HTML: https://mlsanity.com/paper/1701.03891/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2017.

## Built on by (most cited first, 22 of 22)

- [Plug-and-Play Algorithms for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2101.04822/) (2021)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [Provable Compressed Sensing with Generative Priors via Langevin Dynamics](https://mlsanity.com/paper/2102.12643/) (2021)
- [PnP-ReG: Learned Regularizing Gradient for Plug-and-Play Gradient Descent](https://mlsanity.com/paper/2204.13940/) (2022)
- [Global Sensing and Measurements Reuse for Image Compressed Sensing](https://mlsanity.com/paper/2206.11629/) (2022)
- [Deep Physics-Guided Unrolling Generalization for Compressed Sensing](https://mlsanity.com/paper/2307.08950/) (2023)
- [JR2net: A Joint Non-Linear Representation and Recovery Network for Compressive Spectral Imaging](https://mlsanity.com/paper/2205.07770/) (2022)
- [Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction](https://mlsanity.com/paper/2308.03807/) (2023)
- [Dynamic Proximal Unrolling Network for Compressive Imaging](https://mlsanity.com/paper/2107.11007/) (2021)
- [Unrolled Compressed Blind-Deconvolution](https://mlsanity.com/paper/2209.14165/) (2022)
- [Deep Learning-based Compressive Beam Alignment in mmWave Vehicular Systems](https://mlsanity.com/paper/2103.00125/) (2021)
- [Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models](https://mlsanity.com/paper/2105.06371/) (2021)
- [Survey of Deep Learning Methods for Inverse Problems](https://mlsanity.com/paper/2111.04731/) (2021)
- [Deep Coding Patterns Design for Compressive Near-Infrared Spectral Classification](https://mlsanity.com/paper/2205.14069/) (2022)
- [PETAL: Physics Emulation Through Averaged Linearizations for Solving Inverse Problems](https://mlsanity.com/paper/2305.11056/) (2023)
- [On the Fine-Grained Hardness of Inverting Generative Models](https://mlsanity.com/paper/2309.05795/) (2023)
- [Comprehensive Examination of Unrolled Networks for Solving Linear Inverse Problems](https://mlsanity.com/paper/2501.04608/) (2025)
- [DAEs for Linear Inverse Problems: Improved Recovery with Provable Guarantees](https://mlsanity.com/paper/2101.05130/) (2021)
- [Learning DNN networks using un-rectifying ReLU with compressed sensing application](https://mlsanity.com/paper/2101.06940/) (2021)
- [Deep Learning Techniques for Compressive Sensing-Based Reconstruction and Inference -- A Ubiquitous Systems Perspective](https://mlsanity.com/paper/2105.13191/) (2021)
- [JSRNN: Joint Sampling and Reconstruction Neural Networks for High Quality Image Compressed Sensing](https://mlsanity.com/paper/2211.05963/) (2022)
- [Dual-Path Hyperprior Informed Deep Unfolding Network for Image Compressive Sensing](https://mlsanity.com/paper/2605.09566/) (2026)

## Abstract (arXiv)

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 em DeepInverse that learns the inverse transformation from measurement vectors to signals using a em 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.