# One-Bit Phase Retrieval: More Samples Means Less Complexity?

arXiv: https://arxiv.org/abs/2203.08982 · HTML: https://mlsanity.com/paper/2203.08982/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2022.

## Built on by (most cited first, 6 of 6)

- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [ORKA: Accelerated Kaczmarz Algorithms for Signal Recovery from One-Bit Samples](https://mlsanity.com/paper/2301.03467/) (2022)
- [One-Bit Quadratic Compressed Sensing: From Sample Abundance to Linear Feasibility](https://mlsanity.com/paper/2303.09594/) (2023)
- [HDR Imaging With One-Bit Quantization](https://mlsanity.com/paper/2309.03982/) (2023)
- [Matrix Completion from One-Bit Dither Samples](https://mlsanity.com/paper/2310.03224/) (2023)
- [DOA Estimation from One-Bit Magnitude-Only Measurements via Sign-Consistency Optimization](https://mlsanity.com/paper/2607.12491/) (2026)

## Abstract (arXiv)

The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using one-bit analog-to-digital converters (ADCs). A significant advantage of deploying one-bit ADCs in signal processing systems is their superior sampling rates as compared to their high-resolution counterparts. This leads to an enormous amount of one-bit samples gathered at the output of the ADC in a short period of time. We demonstrate that this advantage pays extraordinary dividends when it comes to convex phase retrieval formulations, namely that the often encountered matrix semi-definiteness constraints as well as rank constraints (that are computationally prohibitive to enforce), become redundant for phase retrieval in the face of a growing sample size. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.