# One-bit Compressed Sensing using Generative Models

arXiv: https://arxiv.org/abs/2502.12762 · HTML: https://mlsanity.com/paper/2502.12762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priors](https://mlsanity.com/paper/2002.01697/) (2020)
- [One-bit compressive sensing with norm estimation](https://mlsanity.com/paper/1404.6853/) (2014)
- [Deep Signal Recovery with One-Bit Quantization](https://mlsanity.com/paper/1812.00797/) (2018)
- [One-Bit Radar Processing with Time-Varying Sampling Thresholds](https://mlsanity.com/paper/1911.10170/) (2019)
- [Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors](https://mlsanity.com/paper/2108.03570/) (2021)
- [Binary Linear Classification and Feature Selection via Generalized Approximate Message Passing](https://mlsanity.com/paper/1401.0872/) (2014)

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

- [Deep Probabilistic Unfolding for Quantized Compressive Sensing](https://mlsanity.com/paper/2605.11475/) (2026)

## Abstract (arXiv)

This paper addresses the classical problem of one-bit compressed sensing using a deep learning-based reconstruction algorithm that leverages a trained generative model to enhance the signal reconstruction performance. The generator, a pre-trained neural network, learns to map from a low-dimensional latent space to a higher-dimensional set of sparse vectors. This generator is then used to reconstruct sparse vectors from their one-bit measurements by searching over its range. The presented algorithm provides an excellent reconstruction performance because the generative model can learn additional structural information about the signal beyond sparsity. Furthermore, we provide theoretical guarantees on the reconstruction accuracy and sample complexity of the algorithm. Through numerical experiments using three publicly available image datasets, MNIST, Fashion-MNIST, and Omniglot, we demonstrate the superior performance of the algorithm compared to other existing algorithms and show that our algorithm can recover both the amplitude and the direction of the signal from one-bit measurements.