{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T19:12:52Z","timestamp":1782155572744,"version":"3.54.5"},"reference-count":28,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2021,11,28]],"date-time":"2021-11-28T00:00:00Z","timestamp":1638057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology on Near-Surface Detection Laboratory","award":["TCGZ2017A005"],"award-info":[{"award-number":["TCGZ2017A005"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The single-pixel imaging (SPI) technique enables the tracking of moving targets at a high frame rate. However, when extended to the problem of multi-target tracking, there is no effective solution using SPI yet. Thus, a multi-target tracking method using windowed Fourier single-pixel imaging (WFSI) is proposed in this paper. The WFSI technique uses a series of windowed Fourier basis patterns to illuminate the target. This method can estimate the displacements of K independently moving targets by implementing 6K measurements and calculating 2K windowed Fourier coefficients, which is a measurement method with low redundancy. To enhance the capability of the proposed method, we propose a joint estimation approach for multi-target displacement, which solves the problem where different targets in close proximity cannot be distinguished. Using the independent and joint estimation approaches, multi-target tracking can be implemented with WFSI. The accuracy of the proposed multi-target tracking method is verified by numerical simulation to be less than 2 pixels. The tracking effectiveness is analyzed by a video experiment. This method provides, for the first time, an effective idea of multi-target tracking using SPI.<\/jats:p>","DOI":"10.3390\/s21237934","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T01:45:02Z","timestamp":1638323102000},"page":"7934","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Multi-Target Tracking Using Windowed Fourier Single-Pixel Imaging"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8321-4519","authenticated-orcid":false,"given":"Jinyu","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Electronic Engineering and Optical Technology, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1815-7551","authenticated-orcid":false,"given":"Taiyang","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering and Optical Technology, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaolang","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering and Optical Technology, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5841-114X","authenticated-orcid":false,"given":"Mengxuan","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering and Optical Technology, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingjiao","family":"Rong","sequence":"additional","affiliation":[{"name":"Science and Technology on Near-Surface Detection Laboratory, Wuxi 214035, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zelong","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering and Optical Technology, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2682","DOI":"10.1109\/TGRS.2019.2953355","article-title":"Ship Detection by an Airborne Passive Interferometric Microwave Sensor (PIMS)","volume":"58","author":"Lu","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, J., Hu, T., Li, W., Li, L., and Yang, J. (2020, January 29\u201331). Research on Millimeter-wave Radiation Characteristics of Stereo Air Target. Proceedings of the 2020 IEEE MTT-S International Microwave Workshop Series on Advanced Materials and Processes for RF and THz Applications (IMWS-AMP), Suzhou, China.","DOI":"10.1109\/IMWS-AMP49156.2020.9199665"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2560","DOI":"10.1364\/BOE.382391","article-title":"Development of a low-cost imaging system for remote mosquito surveillance","volume":"11","author":"Goodwin","year":"2020","journal-title":"Biomed. Opt. Express"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/JPROC.1997.554211","article-title":"Distributed fusion architectures and algorithms for target tracking","volume":"85","author":"Liggins","year":"1997","journal-title":"Proc. IEEE"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Case, E.E., Zelnio, A.M., and Rigling, B.D. (2008, January 16\u201318). Low-Cost Acoustic Array for Small UAV Detection and Tracking. Proceedings of the 2008 IEEE National Aerospace and Electronics Conference, Dayton, OH, USA.","DOI":"10.1109\/NAECON.2008.4806528"},{"key":"ref_6","first-page":"99880B","article-title":"Optical and acoustical UAV detection","volume":"Volume 9988","author":"Christnacher","year":"2016","journal-title":"Proceedings of the Electro-Optical Remote Sensing X"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"231104","DOI":"10.1063\/1.4809836","article-title":"Compressive object tracking using entangled photons","volume":"102","author":"Howland","year":"2013","journal-title":"Appl. Phys. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27851","DOI":"10.1364\/OE.27.027851","article-title":"Tracking and imaging of moving objects with temporal intensity difference correlation","volume":"27","author":"Sun","year":"2019","journal-title":"Opt. Express"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1109\/TIP.2000.826791","article-title":"A new diamond search algorithm for fast block-matching motion estimation","volume":"9","author":"Zhu","year":"2000","journal-title":"IEEE Trans. Image Process."},{"key":"ref_10","first-page":"225","article-title":"Block matching algorithms for motion estimation","volume":"8","author":"Barjatya","year":"2004","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhou, D., Cao, J., Cui, H., Hao, Q., Chen, B.k., and Lin, K. (2021). Complementary Fourier single-pixel imaging. Sensors, 21.","DOI":"10.3390\/s21196544"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1038\/s41566-018-0300-7","article-title":"Principles and prospects for single-pixel imaging","volume":"13","author":"Edgar","year":"2019","journal-title":"Nat. Photonics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"091614","DOI":"10.1117\/1.OE.51.9.091614","article-title":"Passive millimeter-wave imaging with compressive sensing","volume":"51","author":"Gopalsami","year":"2012","journal-title":"Opt. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7889","DOI":"10.1364\/OE.387024","article-title":"Imaging high-speed moving targets with a single-pixel detector","volume":"28","author":"Jiang","year":"2020","journal-title":"Opt. Express"},{"key":"ref_15","unstructured":"Zhou, F., Shi, X., Chen, J., Tang, T., and Liu, Y. (2021). Non-imaging real-time detection and tracking of fast-moving objects. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4095","DOI":"10.1364\/AO.421033","article-title":"Single-pixel imaging of high-temperature objects","volume":"60","author":"Xu","year":"2021","journal-title":"Appl. Opt."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3379","DOI":"10.1021\/acsphotonics.8b00653","article-title":"Time-resolved nonlinear ghost imaging","volume":"5","author":"Olivieri","year":"2018","journal-title":"ACS Photonics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1364\/OPTICA.381035","article-title":"Hyperspectral terahertz microscopy via nonlinear ghost imaging","volume":"7","author":"Olivieri","year":"2020","journal-title":"Optica"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41377-020-0338-4","article-title":"Ghost spintronic THz-emitter-array microscope","volume":"9","author":"Chen","year":"2020","journal-title":"Light. Sci. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3795","DOI":"10.1364\/OE.384134","article-title":"Time-domain terahertz compressive imaging","volume":"28","author":"Zanotto","year":"2020","journal-title":"Opt. Express"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12841","DOI":"10.1364\/OE.27.012841","article-title":"Motion estimation and quality enhancement for a single image in dynamic single-pixel imaging","volume":"27","author":"Jiao","year":"2019","journal-title":"Opt. Express"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7712","DOI":"10.1038\/s41598-021-83810-z","article-title":"Single-pixel imaging of dynamic objects using multi-frame motion estimation","volume":"11","author":"Monin","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.optcom.2019.02.006","article-title":"Fast tracking of moving objects using single-pixel imaging","volume":"440","author":"Shi","year":"2019","journal-title":"Opt. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"35394","DOI":"10.1364\/OE.27.035394","article-title":"Image-free real-time detection and tracking of fast moving object using a single-pixel detector","volume":"27","author":"Zhang","year":"2019","journal-title":"Opt. Express"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4734","DOI":"10.1364\/OL.399204","article-title":"Image-free real-time 3-D tracking of a fast-moving object using dual-pixel detection","volume":"45","author":"Deng","year":"2020","journal-title":"Opt. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"30327","DOI":"10.1364\/OE.436348","article-title":"Single-pixel tracking of fast-moving object using geometric moment detection","volume":"29","author":"Zha","year":"2021","journal-title":"Opt. Express"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6225","DOI":"10.1038\/ncomms7225","article-title":"Single-pixel imaging by means of Fourier spectrum acquisition","volume":"6","author":"Zhang","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"12029","DOI":"10.1038\/s41598-017-12228-3","article-title":"Fast Fourier single-pixel imaging via binary illumination","volume":"7","author":"Zhang","year":"2017","journal-title":"Sci. Rep."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/23\/7934\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:36:53Z","timestamp":1760168213000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/23\/7934"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,28]]},"references-count":28,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["s21237934"],"URL":"https:\/\/doi.org\/10.3390\/s21237934","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,28]]}}}