{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:49:04Z","timestamp":1760240944770,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T00:00:00Z","timestamp":1571788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61871386;No. 61571011;No. 61701513"],"award-info":[{"award-number":["No. 61871386;No. 61571011;No. 61701513"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["No. 2018M633666"],"award-info":[{"award-number":["No. 2018M633666"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Phaseless terahertz coded-aperture imaging (PL-TCAI) is a novel radar computational imaging method that utilizes the coded aperture and the incoherent detector array to achieve forward-looking and high-resolution imaging without relying on relative motion. In this paper, we propose a more reasonable and compact architecture for the PL-TCAI system and derive the imaging model of PL-TCAI based on the random frequency-hopping signal. Since most phase retrieval algorithms for PL-TCAI utilize only the intensity of echo signals to accurately reconstruct the target, excessive measurement samples are usually required. In order to reduce the number of measurement samples required for imaging, this paper proposes a sparse Wirtinger flow algorithm with optimal stepsize (SWFOS) by using the sparse prior of the target. The specific procedures of the SWFOS algorithm include the support recovery, initialization by truncated spectral method, iteration via gradient descent scheme, hard threshold operation, and stepsize optimization of iteration. Numerical simulations are performed, and the results show that the SWFOS algorithm not only has good performance for the PR problem, but can also sharply reduce the number of measurement samples required for imaging in the PL-TCAI system.<\/jats:p>","DOI":"10.3390\/s19214617","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T03:20:36Z","timestamp":1571973636000},"page":"4617","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Phaseless Terahertz Coded-Aperture Imaging for Sparse Target Based on Phase Retrieval Algorithm"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4589-8064","authenticated-orcid":false,"given":"Long","family":"Peng","sequence":"first","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenggao","family":"Luo","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Deng","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongqiang","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9398-0009","authenticated-orcid":false,"given":"Shuo","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Electronic Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Dong","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Hunan Normal University, Changsha 410081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, S., Hua, X., Wang, H., Luo, C., Cheng, Y., and Deng, B. (2018). Three-Dimensional Terahertz Coded-Aperture Imaging Based on Geometric Measures. Sensors, 18.","DOI":"10.3390\/s18051582"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"42650","DOI":"10.1038\/srep42650","article-title":"Large Metasurface Aperture for Millimeter Wave Computational Imaging at the Human-Scale","volume":"7","author":"Gollub","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"23731","DOI":"10.1038\/srep23731","article-title":"Transmission-Type 2-Bit Programmable Metasurface for Single-Sensor and Single-Frequency Microwave Imaging","volume":"6","author":"Li","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chen, S., Luo, C., Wang, H., Wang, W., Peng, L., and Zhuang, Z. (2018). Three-Dimensional Terahertz Coded-Aperture Imaging Based on Back Projection. Sensors, 18.","DOI":"10.3390\/s18082510"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1109\/TMTT.2018.2885969","article-title":"Microwave Imaging Customized on Demand Under Random Field Illumination","volume":"67","author":"Zhou","year":"2018","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1038\/nphoton.2014.139","article-title":"Terahertz compressive imaging with metamaterial spatial light modulators","volume":"8","author":"Watts","year":"2014","journal-title":"Nat. Photonics"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Perez-Palomino, G., Encinar, J.A., Dickie, R., and Cahill, R. (2013, January 7\u201313). Preliminary design of a liquid crystal-based reflectarray antenna for beam-scanning in THz. Proceedings of the 2013 IEEE Antennas and Propagation Society International Symposium, Orlando, FL, USA.","DOI":"10.1109\/APS.2013.6711797"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3722","DOI":"10.1109\/TAP.2015.2434421","article-title":"Design and Demonstration of an Electronically Scanned Reflectarray Antenna at 100 GHz Using Multiresonant Cells Based on Liquid Crystals","volume":"63","author":"Barba","year":"2015","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1117\/1.JEI.26.5.053022","article-title":"Study on coding strategies for radar coded-aperture imaging in terahertz band","volume":"26","author":"Chen","year":"2017","journal-title":"J. Electron. Imaging"},{"key":"ref_10","first-page":"2261","article-title":"Radar Coincidence Imaging: An Instantaneous Imaging Technique with Stochastic Signals","volume":"52","author":"Li","year":"2013","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1088\/2058-7058\/13\/4\/24","article-title":"Terahertz imaging comes into view","volume":"13","author":"Arnone","year":"2000","journal-title":"Phys. World"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3293","DOI":"10.1364\/AO.58.003293","article-title":"High-resolution terahertz coded-aperture imaging for near-field three-dimensional target","volume":"58","author":"Luo","year":"2019","journal-title":"Appl. Opt."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Chen, S., Luo, C., Deng, B., Wang, H., Cheng, Y., and Zhuang, Z. (2018). Three-Dimensional Terahertz Coded-Aperture Imaging Based on Single Input Multiple Output Technology. Sensors, 18.","DOI":"10.3390\/s18010303"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1109\/TTHZ.2011.2159556","article-title":"THz Imaging Radar for Standoff Personnel Screening","volume":"1","author":"Cooper","year":"2011","journal-title":"IEEE Trans. Terahertz Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Dickmann, J., Klappstein, J., Hahn, M., Appenrodt, N., Bloecher, H., Werber, K., and Sailer, A. (2016, January 2\u20136). Automotive radar the key technology for autonomous driving: From detection and ranging to environmental understanding. Proceedings of the 2016 IEEE Radar Conference, Philadelphia, PA, USA.","DOI":"10.1109\/RADAR.2016.7485214"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"346","DOI":"10.2478\/s11772-011-0033-3","article-title":"Terahertz detectors and focal plane arrays","volume":"19","author":"Rogalski","year":"2011","journal-title":"Opto-Electron. Rev."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1109\/TTHZ.2012.2213818","article-title":"Development of Superconducting Spectroscopic Array Receiver: A Multibeam 2SB SIS Receiver for Millimeter-Wave Radio Astronomy","volume":"2","author":"Shan","year":"2012","journal-title":"IEEE Trans. Terahertz Sci. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1109\/77.919505","article-title":"Terahertz-frequency waveguide NbN hot-electron bolometer mixer","volume":"11","author":"Kawamura","year":"2001","journal-title":"IEEE Trans. Appl. Supercond."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"14884","DOI":"10.1109\/ACCESS.2018.2816341","article-title":"Relaxation of Alignment Errors and Phase Calibration in Computational Frequency-Diverse Imaging using Phase Retrieval","volume":"6","author":"Yurduseven","year":"2018","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Peng, L., Luo, C., Deng, B., Wang, H., Qin, Y., and Chen, S. (2019). Phaseless Terahertz Coded-Aperture Imaging Based on Incoherent Detection. Sensors, 19.","DOI":"10.3390\/s19020226"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1038\/22498","article-title":"Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens","volume":"400","author":"Miao","year":"1999","journal-title":"Nature"},{"key":"ref_22","first-page":"275","article-title":"Phase retrieval and image reconstruction for astronomy","volume":"231","author":"Fienup","year":"1987","journal-title":"Image Recovery Theory Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"015005","DOI":"10.1088\/0266-5611\/27\/1\/015005","article-title":"Array imaging using intensity-only measurements","volume":"27","author":"Chai","year":"2010","journal-title":"Inverse Probl."},{"key":"ref_24","first-page":"237","article-title":"A practical algorithm for the determination of phase from image and diffraction plane pictures","volume":"35","author":"Gerchberg","year":"1972","journal-title":"Optik"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.1002\/cpa.21432","article-title":"Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming","volume":"66","author":"Candes","year":"2013","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1109\/TIT.2015.2399924","article-title":"Phase Retrieval via Wirtinger Flow: Theory and Algorithms","volume":"61","author":"Li","year":"2015","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1002\/cpa.21638","article-title":"Solving random quadratic systems of equations is nearly as easy as solving linear systems","volume":"70","author":"Chen","year":"2017","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_28","unstructured":"Kolte, R., and \u00d6zg\u00fcr, A. (2016). Phase retrieval via incremental truncated Wirtinger flow. arXiv."},{"key":"ref_29","first-page":"5164","article-title":"A nonconvex approach for phase retrieval: Reshaped wirtinger flow and incremental algorithms","volume":"18","author":"Zhang","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1109\/TIT.2017.2756858","article-title":"Solving systems of random quadratic equations via truncated amplitude flow","volume":"64","author":"Wang","year":"2017","journal-title":"IEEE T. Inform. Theory"},{"key":"ref_31","first-page":"1","article-title":"Phase Retrieval via Reweighted Amplitude Flow","volume":"66","author":"Wang","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2221","DOI":"10.1214\/16-AOS1443","article-title":"Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow","volume":"44","author":"Cai","year":"2016","journal-title":"Ann. Stat."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wang, G., Giannakis, G.B., Chen, J., and Ak\u00e7akaya, M. (2017, January 5\u20139). SPARTA: Sparse phase retrieval via truncated amplitude flow. Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing, New Orleans, LA, USA.","DOI":"10.1109\/ICASSP.2017.7952902"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.cam.2019.01.009","article-title":"Phase retrieval via Sparse Wirtinger Flow","volume":"355","author":"Yuan","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1109\/LSP.2016.2611940","article-title":"Wirtinger Flow Method with Optimal Stepsize for Phase Retrieval","volume":"23","author":"Rajan","year":"2016","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JSTQE.2016.2640452","article-title":"Terahertz reflectarrays and nonuniform metasurfaces","volume":"23","author":"Headland","year":"2016","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"e218","DOI":"10.1038\/lsa.2014.99","article-title":"Coding metamaterials, digital metamaterials and programmable metamaterials","volume":"3","author":"Cui","year":"2014","journal-title":"Light. Sci. Appl."},{"key":"ref_38","first-page":"127","article-title":"Research on Resolution of Terahertz Coded-aperture Imaging","volume":"7","author":"Chen","year":"2018","journal-title":"J. Radars"},{"key":"ref_39","unstructured":"Huang, J. (1995, January 18\u201323). Bandwidth study of microstrip reflectarray and a novel phased reflectarray concept. Proceedings of the IEEE Antennas and Propagation Society International Symposium, Newport Beach, CA, USA."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1215\/S0012-7094-48-01568-3","article-title":"The central limit theorem for dependent random variables","volume":"15","author":"Hoeffding","year":"1948","journal-title":"Duke Math. J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/21\/4617\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:28:49Z","timestamp":1760189329000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/21\/4617"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,23]]},"references-count":40,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["s19214617"],"URL":"https:\/\/doi.org\/10.3390\/s19214617","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,10,23]]}}}