# One-Bit Compressive Sensing: Can We Go Deep and Blind?

arXiv: https://arxiv.org/abs/2203.11278 · HTML: https://mlsanity.com/paper/2203.11278/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 13 Mar 2022.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [On weight initialization in deep neural networks](https://mlsanity.com/paper/1704.08863/) (2017)
- [Deep Compressed Sensing](https://mlsanity.com/paper/1905.06723/) (2019)
- [Deep Fully-Connected Networks for Video Compressive Sensing](https://mlsanity.com/paper/1603.04930/) (2016)
- [One-bit compressive sensing with norm estimation](https://mlsanity.com/paper/1404.6853/) (2014)
- [LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receivers](https://mlsanity.com/paper/2102.02993/) (2021)
- [Support Recovery in Universal One-bit Compressed Sensing](https://mlsanity.com/paper/2107.09091/) (2021)
- [Dictionary Learning for Blind One Bit Compressed Sensing](https://mlsanity.com/paper/1508.07648/) (2015)
- [Theoretical Interpretation of Learned Step Size in Deep-Unfolded Gradient Descent](https://mlsanity.com/paper/2001.05142/) (2020)
- [Sparse linear regression from perturbed data](https://mlsanity.com/paper/2003.14389/) (2020)
- [ConvCSNet: A Convolutional Compressive Sensing Framework Based on Deep Learning](https://mlsanity.com/paper/1801.10342/) (2018)

## Built on by (most cited first, 1 of 1)

- [Deep Learning Meets Adaptive Filtering: A Stein's Unbiased Risk Estimator Approach](https://mlsanity.com/paper/2307.16708/) (2023)

## Abstract (arXiv)

One-bit compressive sensing is concerned with the accurate recovery of an underlying sparse signal of interest from its one-bit noisy measurements. The conventional signal recovery approaches for this problem are mainly developed based on the assumption that an exact knowledge of the sensing matrix is available. In this work, however, we present a novel data-driven and model-based methodology that achieves blind recovery; i.e., signal recovery without requiring the knowledge of the sensing matrix. To this end, we make use of the deep unfolding technique and develop a model-driven deep neural architecture which is designed for this specific task. The proposed deep architecture is able to learn an alternative sensing matrix by taking advantage of the underlying unfolded algorithm such that the resulting learned recovery algorithm can accurately and quickly (in terms of the number of iterations) recover the underlying compressed signal of interest from its one-bit noisy measurements. In addition, due to the incorporation of the domain knowledge and the mathematical model of the system into the proposed deep architecture, the resulting network benefits from enhanced interpretability, has a very small number of trainable parameters, and requires very small number of training samples, as compared to the commonly used black-box deep neural network alternatives for the problem at hand.