# Superset Technique for Approximate Recovery in One-Bit Compressed Sensing

arXiv: https://arxiv.org/abs/1910.13971 · HTML: https://mlsanity.com/paper/1910.13971/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2019.

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

- [Binary Iterative Hard Thresholding Converges with Optimal Number of Measurements for 1-Bit Compressed Sensing](https://mlsanity.com/paper/2207.03427/) (2022)
- [Support Recovery of Sparse Signals from a Mixture of Linear Measurements](https://mlsanity.com/paper/2106.05951/) (2021)
- [Support Recovery in Universal One-bit Compressed Sensing](https://mlsanity.com/paper/2107.09091/) (2021)
- [Improved Support Recovery in Universal One-bit Compressed Sensing](https://mlsanity.com/paper/2210.16657/) (2022)
- [On the Role of Normalization in Binary Iterative Hard Thresholding for 1-bit Compressed Sensing](https://mlsanity.com/paper/2607.15530/) (2026)

## Abstract (arXiv)

One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to the problem of learning a sparse hyperplane-classifier. In this paper, we propose a novel approach for signal recovery in nonadaptive 1bCS that matches the sample complexity of the current best methods. We construct 1bCS matrices that are universal - i.e. work for all signals under a model - and at the same time recover very general random sparse signals with high probability. In our approach, we divide the set of samples (measurements) into two parts, and use the first part to recover the superset of the support of a sparse vector. The second set of measurements is then used to approximate the signal within the superset. While support recovery in 1bCS is well-studied, recovery of superset of the support requires fewer samples, and to our knowledge has not been previously considered for the purpose of approximate recovery of signals.