# Robust 1-bit Compressive Sensing via Gradient Support Pursuit

arXiv: https://arxiv.org/abs/1304.6627 · HTML: https://mlsanity.com/paper/1304.6627/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2013.

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

- [Signal Reconstruction from Quantized Noisy Samples of the Discrete Fourier Transform](https://mlsanity.com/paper/2201.03114/) (2022)

## Abstract (arXiv)

This paper studies a formulation of 1-bit Compressed Sensing (CS) problem based on the maximum likelihood estimation framework. In order to solve the problem we apply the recently proposed Gradient Support Pursuit algorithm, with a minor modification. Assuming the proposed objective function has a Stable Restricted Hessian, the algorithm is shown to accurately solve the 1-bit CS problem. Furthermore, the algorithm is compared to the state-of-the-art 1-bit CS algorithms through numerical simulations. The results suggest that the proposed method is robust to noise and at mid to low input SNR regime it achieves the best reconstruction SNR vs. execution time trade-off.