# One-Bit Quadratic Compressed Sensing: From Sample Abundance to Linear Feasibility

arXiv: https://arxiv.org/abs/2303.09594 · HTML: https://mlsanity.com/paper/2303.09594/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 16 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow](https://mlsanity.com/paper/1605.08285/) (2016)
- [On Unlimited Sampling and Reconstruction](https://mlsanity.com/paper/1905.03901/) (2019)
- [Sharp Analysis of Sketch-and-Project Methods via a Connection to Randomized Singular Value Decomposition](https://mlsanity.com/paper/2208.09585/) (2022)
- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [A Sampling Kaczmarz-Motzkin Algorithm for Linear Feasibility](https://mlsanity.com/paper/1605.01418/) (2016)
- [Sparse Phase Retrieval: Convex Algorithms and Limitations](https://mlsanity.com/paper/1303.4128/) (2013)
- [Sampling Kaczmarz Motzkin Method for Linear Feasibility Problems: Generalization & Acceleration](https://mlsanity.com/paper/2002.07321/) (2020)
- [One-Bit Phase Retrieval: More Samples Means Less Complexity?](https://mlsanity.com/paper/2203.08982/) (2022)
- [On the Randomized Kaczmarz Algorithm](https://mlsanity.com/paper/1402.2863/) (2014)
- [Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding](https://mlsanity.com/paper/1812.03977/) (2018)
- [Gridless Parameter Estimation for One-Bit MIMO Radar with Time-Varying Thresholds](https://mlsanity.com/paper/1908.10487/) (2019)
- [Phase retrieval for wavelet transforms](https://mlsanity.com/paper/1512.07024/) (2015)
- [ORKA: Accelerated Kaczmarz Algorithms for Signal Recovery from One-Bit Samples](https://mlsanity.com/paper/2301.03467/) (2022)

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

- [Matrix Completion from One-Bit Dither Samples](https://mlsanity.com/paper/2310.03224/) (2023)

## Abstract (arXiv)

One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In addition to such advantages, an attractive feature of one-bit analog-to-digital converters (ADCs) is their superior sampling rates as compared to their conventional multi-bit counterparts. This characteristic endows one-bit signal processing frameworks with what we refer to as sample abundance. On the other hand, many signal recovery and optimization problems are formulated as (possibly non-convex) quadratic programs with linear feasibility constraints in the one-bit sampling regime. We demonstrate, with a particular focus on quadratic compressed sensing, that the sample abundance paradigm allows for the transformation of such quadratic problems to merely a linear feasibility problem by forming a large-scale overdetermined linear system; thus removing the need for costly optimization constraints and objectives. To efficiently tackle the emerging overdetermined linear feasibility problem, we further propose an enhanced randomized Kaczmarz algorithm, called Block SKM. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.