# Learning to Reconstruct Signals From Binary Measurements

arXiv: https://arxiv.org/abs/2303.08691 · HTML: https://mlsanity.com/paper/2303.08691/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 15 Mar 2023.

## Builds on (most cited first, 10 of 10)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Unsupervised Learning From Incomplete Measurements for Inverse Problems](https://mlsanity.com/paper/2201.12151/) (2022)
- [Dictionary Learning for Blind One Bit Compressed Sensing](https://mlsanity.com/paper/1508.07648/) (2015)
- [Near-Optimal Bounds for Binary Embeddings of Arbitrary Sets](https://mlsanity.com/paper/1512.04433/) (2015)
- [Sparse Recovery and Dictionary Learning from Nonlinear Compressive Measurements](https://mlsanity.com/paper/1809.09639/) (2018)

## Built on by (most cited first, 5 of 5)

- [Equivariance-based self-supervised learning for audio signal recovery from clipped measurements](https://mlsanity.com/paper/2409.15283/) (2024)
- [Self-Supervised Learning from Noisy and Incomplete Data](https://mlsanity.com/paper/2601.03244/) (2026)
- [Self-supervised learning for phase retrieval](https://mlsanity.com/paper/2509.26203/) (2025)
- [Learning to reconstruct from saturated data: audio declipping and high-dynamic range imaging](https://mlsanity.com/paper/2602.22279/) (2026)
- [Random features for Grassmannian kernel approximation with bounded rank-one projections](https://mlsanity.com/paper/2608.04227/) (2026)

## Abstract (arXiv)

Recent advances in unsupervised learning have highlighted the possibility of learning to reconstruct signals from noisy and incomplete linear measurements alone. These methods play a key role in medical and scientific imaging and sensing, where ground truth data is often scarce or difficult to obtain. However, in practice, measurements are not only noisy and incomplete but also quantized. Here we explore the extreme case of learning from binary observations and provide necessary and sufficient conditions on the number of measurements required for identifying a set of signals from incomplete binary data. Our results are complementary to existing bounds on signal recovery from binary measurements. Furthermore, we introduce a novel self-supervised learning approach, which we name SSBM, that only requires binary data for training. We demonstrate in a series of experiments with real datasets that SSBM performs on par with supervised learning and outperforms sparse reconstruction methods with a fixed wavelet basis by a large margin.