# Robust one-bit compressed sensing with partial circulant matrices

arXiv: https://arxiv.org/abs/1812.06719 · HTML: https://mlsanity.com/paper/1812.06719/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2018.

## Built on by (most cited first, 4 of 4)

- [The Separation Capacity of Random Neural Networks](https://mlsanity.com/paper/2108.00207/) (2021)
- [High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization](https://mlsanity.com/paper/2202.13157/) (2022)
- [Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors](https://mlsanity.com/paper/2108.03570/) (2021)
- [Plug-in Channel Estimation with Dithered Quantized Signals in Spatially Non-Stationary Massive MIMO Systems](https://mlsanity.com/paper/2301.04641/) (2023)

## Abstract (arXiv)

We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly sub-sampled circulant matrix) and is robust to analog pre-quantization noise as well as to adversarial bit corruptions in the quantization process. Our results imply that quantization is not a statistically expensive procedure in the presence of nontrivial analog noise: recovery requires the same sample size one would have needed had the measurement matrix been Gaussian and the noisy analog measurements been given as data.