Sub-Nyquist single-pixel imaging by optimizing sampling basis

ZHAO Zi-dong; YANG Zhao-hua; LI Gao-liang

doi:10.37188/OPE.20212905.1008

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Sub-Nyquist single-pixel imaging by optimizing sampling basis

Modern Applied Optics | 更新时间：2026-09-11

- Sub-Nyquist single-pixel imaging by optimizing sampling basis
- Optics and Precision Engineering Vol. 29, Issue 5, Pages: 1008-1013(2021)
- 作者机构：
  
  1.北京航空航天大学仪器科学与光电工程学院，北京 100191
  2.北京华航无线电测量研究所，北京 100010
- 作者简介：
  
  E-mail： yangzh@buaa.edu.cn
- 基金信息：
- DOI：10.37188/OPE.20212905.1008
  CLC： O431.2
- Received：14 October 2020，
  
  Revised：2020-10-29，
  
  Published：15 May 2021
- 稿件说明：
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赵梓栋,杨照华,李高亮.基于测量基优化的低采样率单像素成像[J].光学精密工程,2021,29(05):1008-1013.

ZHAO Zi-dong,YANG Zhao-hua,LI Gao-liang.Sub-Nyquist single-pixel imaging by optimizing sampling basis[J].Optics and Precision Engineering,2021,29(05):1008-1013.
赵梓栋,杨照华,李高亮.基于测量基优化的低采样率单像素成像[J].光学精密工程,2021,29(05):1008-1013. DOI： 10.37188/OPE.20212905.1008.

ZHAO Zi-dong,YANG Zhao-hua,LI Gao-liang.Sub-Nyquist single-pixel imaging by optimizing sampling basis[J].Optics and Precision Engineering,2021,29(05):1008-1013. DOI： 10.37188/OPE.20212905.1008.

摘要

单像素成像结合压缩感知相关算法利用很少一部分无空间分辨的桶探测器采样值就能重构出成像物体的高质量图像。然而，随机地选取投射的散斑序列无法在更低的采样率下成像。为进一步实现单像素成像在极低采样率下的成像效果，本文提出了基于数据驱动的哈达玛矩阵排序方案，利用对整个数据集的训练效果来自适应地选择透射的散斑信号序列，在重构图像过程中使用两种不同的压缩感知相关算法在数值仿真和实验条件下实现了5%超低采样率下对成像物体的图像重构，并和目前最优的哈达玛矩阵排序方案进行了比较，发现在1%~5%的采样率下本文方法的重构效果更优。本文研究成果可用于提升单像素成像的成像速度，在成像制导和医学成像中有着极大的应用前景。

Abstract

Single-pixel imaging combined with compressed sensing can reconstruct high-quality images of an imaged object from a small part of the measurement results of a bucket detector without a spatial resolution. However， at low sampling rates， randomly selected projected speckle sequences limit the quality of reconstructed images. To achieve improved imaging at very low sampling rates， this paper proposes a data-driven Hadamard matrix sorting scheme， which uses the training effect of an entire dataset to adaptively select transmitted speckle signal sequences. In the process of reconstructing an image， two different compressed-sensing-related algorithms are employed to realize the image reconstruction of an imaged object at an ultra-low sampling rate of 5% in a numerical simulation and physical experiment， and it is sorted with the current optimal correlation Hadamard matrix. The schemes are compared， and it is found that the reconstruction effect of the method proposed in this paper is better at sampling rates of 1% to 5%. The research results presented in this paper can be used to increase the imaging speed of single-pixel imaging， and can be applied to fields such as imaging guidance and medical imaging.

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references

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