# Computing One-bit Compressive Sensing via Double-Sparsity Constrained Optimization

arXiv: https://arxiv.org/abs/2101.03599 · HTML: https://mlsanity.com/paper/2101.03599/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2021.

## Built on by (most cited first, 3 of 3)

- [0/1 Deep Neural Networks via Block Coordinate Descent](https://mlsanity.com/paper/2206.09379/) (2022)
- [Sparse Decentralized Federated Learning](https://mlsanity.com/paper/2308.16671/) (2023)
- [Enhancing Unsupervised Feature Selection via Double Sparsity Constrained Optimization](https://mlsanity.com/paper/2501.00726/) (2025)

## Abstract (arXiv)

One-bit compressive sensing gains its popularity in signal processing and communications due to its low storage costs and low hardware complexity. However, it has been a challenging task to recover the signal only by exploiting the one-bit (the sign) information. In this paper, we appropriately formulate the one-bit compressive sensing into a double-sparsity constrained optimization problem. The first-order optimality conditions for this nonconvex and discontinuous problem are established via the newly introduced τ-stationarity, based on which, a gradient projection subspace pursuit (textttGPSP) algorithm is developed. It is proven that textttGPSP can converge globally and terminate within finite steps. Numerical experiments have demonstrated its excellent performance in terms of a high order of accuracy with a fast computational speed.