Chin. Phys. B, 2022, Vol. 31(8): 084202    DOI: 10.1088/1674-1056/ac5e99
 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next

# Orthogonal-triangular decomposition ghost imaging

Jin-Fen Liu(刘进芬)1,2, Le Wang(王乐)1, and Sheng-Mei Zhao(赵生妹)1,3,†
1 Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
2 Nanjing Tech University Pujiang Institute, Nanjing 211222, China;
3 Key Laboratory of Broadband Wireless Communication and Sensor Network Technology, Ministry of Education, Nanjing 210003, China
Abstract  Ghost imaging (GI) offers great potential with respect to conventional imaging techniques. However, there are still some obstacles for reconstructing images with high quality, especially in the case that the orthogonal measurement matrix is impossible to construct. In this paper, we propose a new scheme based on the orthogonal-triangular (QR) decomposition, named QR decomposition ghost imaging (QRGI) to reconstruct a better image with good quality. In the scheme, we can change the randomly non-orthogonal measurement matrix into orthonormal matrix by performing QR decomposition in two cases. (1) When the random measurement matrix is square, it can be firstly decomposed into an orthogonal matrix $\bm Q$ and an upper triangular matrix $\bm R$. Then let the off-diagonal values of $\bm R$ equal to 0.0, the diagonal elements of $\bm R$ equal to a constant $k$, where $k$ is the average of all values of the main diagonal, so the resulting measurement matrix can be obtained. (2) When the random measurement matrix is with full rank, we firstly compute its transpose, and followed with above QR operation. Finally, the image of the object can be reconstructed by correlating the new measurement matrix and corresponding bucket values. Both experimental and simulation results verify the feasibility of the proposed QRGI scheme. Moreover, the results also show that the proposed QRGI scheme could improve the imaging quality comparing to traditional GI (TGI) and differential GI (DGI). Besides, in comparison with the singular value decomposition ghost imaging (SVDGI), the imaging quality and the reconstruction time by using QRGI are similar to those by using SVDGI, while the computing time (the time consuming on the light patterns computation) is substantially shortened.
Keywords:  orthogonal-triangular (QR) decomposition      ghost imaging      correlated imaging
Received:  25 November 2021      Revised:  11 March 2022      Accepted manuscript online:  17 March 2022
 PACS: 42.30.Va (Image forming and processing) 42.30.Wb (Image reconstruction; tomography)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61871234 and 62001249), the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX20 0729), Natural Science Research Project of Higher Education of Jiangsu Province, China (Grant No. 20KJB510030), and Research project of NanJing Tech University Pujiang Institute (Grant No. njpj2020-1-02).
Corresponding Authors:  Sheng-Mei Zhao     E-mail:  zhaosm@njupt.edu.cn