{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T15:22:51Z","timestamp":1761060171638,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2016,7,22]],"date-time":"2016-07-22T00:00:00Z","timestamp":1469145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Technology of China","award":["2012BAK04B03"],"award-info":[{"award-number":["2012BAK04B03"]}]},{"name":"International S&amp;T Cooperation: Core Technology Import of THz Nondestructive Testing and Imaging","award":["2015DFA11200"],"award-info":[{"award-number":["2015DFA11200"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With the development of terahertz (THz) technology, the applications of this spectrum have become increasingly wide-ranging, in areas such as non-destructive testing, security applications and medical scanning, in which one of the most important methods is imaging. Unlike remote sensing applications, THz imaging features sources of array elements that are almost always supposed to be spherical wave radiators, including single antennae. As such, well-developed methodologies such as Range-Doppler Algorithm (RDA) are not directly applicable in such near-range situations. The Back Projection Algorithm (BPA) can provide products of high precision at the the cost of a high computational burden, while the Range Migration Algorithm (RMA) sacrifices the quality of images for efficiency. The Phase-shift Migration Algorithm (PMA) is a good alternative, the features of which combine both of the classical algorithms mentioned above. In this research, it is used for mechanical scanning, and is extended to array imaging for the first time. In addition, the performances of PMA are studied in detail in contrast to BPA and RMA. It is demonstrated in our simulations and experiments described herein that the algorithm can reconstruct images with high precision.<\/jats:p>","DOI":"10.3390\/s16071139","type":"journal-article","created":{"date-parts":[[2016,7,22]],"date-time":"2016-07-22T09:54:45Z","timestamp":1469181285000},"page":"1139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A High Precision Terahertz Wave Image Reconstruction Algorithm"],"prefix":"10.3390","volume":"16","author":[{"given":"Qijia","family":"Guo","sequence":"first","affiliation":[{"name":"School of Instrumentation Science and Electrical Engineering, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0161-308X","authenticated-orcid":false,"given":"Tianying","family":"Chang","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Electrical Engineering, Jilin University, Changchun 130012, China"},{"name":"Institute of Automation, Shandong Academy of Sciences, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoshuai","family":"Geng","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Electrical Engineering, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengyan","family":"Jia","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Electrical Engineering, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2443-5167","authenticated-orcid":false,"given":"Hong-Liang","family":"Cui","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Electrical Engineering, Jilin University, Changchun 130012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,7,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11774","DOI":"10.3390\/s111211774","article-title":"Electromagnetic imaging methods for nondestructive evaluation applications","volume":"11","author":"Deng","year":"2011","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1007\/s10762-012-9949-z","article-title":"In introductory review to THZ non-destructive testing of composite mater","volume":"34","author":"Amenabar","year":"2012","journal-title":"J. Infrared Millim. Terahertz Waves"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1109\/JSEN.2004.841341","article-title":"Nondestructive defect identification with terahertz time-of-flight tomography","volume":"5","author":"Zhong","year":"2005","journal-title":"IEEE Sens. J."},{"key":"ref_4","unstructured":"Ahmed, S.S., Schiessl, A., and Schmidt, L.P. (2012, January 23\u201326). A Novel Active Real-Time Digital-Beamforming Imager for Personnel Screening. Proceedings of the 9th European Conference on Synthetic Aperture Radar (EUSAR), Nuremberg, Germany."},{"key":"ref_5","unstructured":"Schiessl, A., Ahmed, S.S., Genghammer, A., and Schmidt, L. (2011, January 11\u201315). A technology demonstrator for a 0.5 m \u00d7 0.5 m fully electronic digital beamforming mm-wave imaging system. Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP), Rome, Italy."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1581","DOI":"10.1109\/22.942570","article-title":"Three-dimensional millimeter-wave imaging for concealed weapon detection","volume":"49","author":"Sheen","year":"2001","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_7","unstructured":"Moll, J., Boswirth, M., Krozer, V., and Bosse, J. (2013, January 8\u201312). Real-Time Data Acquisition and Signal Processing of a Multistatic mm-Wave Radar System. Proceedings of the 7th European Conference on Antennas and Propagation (EuCAP), Gothenburg, Sweden."},{"key":"ref_8","unstructured":"Gumbmann, F., and Schmidt, L. (2010, January 7\u201310). Design of sparse mimo arrays for short range imaging applications. Proceedings of the Microwave Conference Proceedings (APMC), Yokohama, Japan."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Tran, H.P., Gumbmann, F., Weinzierl, J., and Schmidt, L. (2006, January 13\u201315). A fast scanning w-band system for advanced millimetre-wave short range imaging applications. Proceedings of the Radar Conference, Manchester, UK.","DOI":"10.1109\/EURAD.2006.280295"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2027","DOI":"10.1109\/TMTT.2010.2050246","article-title":"Terahertz imaging systems with aperture synthesis techniques","volume":"58","author":"Krozer","year":"2010","journal-title":"Microw. Theory Tech. IEEE Trans."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"291494","DOI":"10.1155\/2012\/291494","article-title":"Three-dimensional near-field microwave holography for tissue imaging","volume":"2012","author":"Amineh","year":"2012","journal-title":"Int. J. Biomed. Imaging"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"055011","DOI":"10.1088\/0266-5611\/26\/5\/055011","article-title":"Two-dimensional near-field microwave holography","volume":"26","author":"Ravan","year":"2010","journal-title":"Inverse Probl."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Se\u0161ek, A., \u0160vigelj, A., and Trontelj, J. (2015, January 23\u201328). A thz tomography imaging system. Proceedings of the 40th International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz), Hong Kong, China.","DOI":"10.1109\/IRMMW-THz.2015.7327868"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Shashidharan, S., and Johny, J. (2015, January 24\u201325). Nanotechnology based terahertz imaging for cancer diaganosis. Proceedings of the International Conference on Electrical, Electronics, Signals, Communication and Optimization, Andhra Pradesh, India.","DOI":"10.1109\/EESCO.2015.7253715"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1007\/s10762-011-9809-2","article-title":"Review of near-field terahertz measurement methods and their applications","volume":"32","author":"Adam","year":"2011","journal-title":"J. Infrared Millim. Terahertz Waves"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Moon, K., Lee, I.M., Shin, J.H., Lee, E.S., Kim, N., Lee, W.H., Ko, H., Han, S.P., and Park, K.H. (2015). Bias field tailored plasmonic nano-electrode for high-power terahertz photonic devices. Sci. Rep., 5.","DOI":"10.1038\/srep13817"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"23107","DOI":"10.1038\/srep23107","article-title":"Ultra-high dynamic range electro-optic sampling for detecting millimeter and sub-millimeter radiation","volume":"6","author":"Ibrahim","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TTHZ.2016.2549367","article-title":"Near-field spectroscopy and imaging of subwavelength plasmonic terahertz resonators","volume":"6","author":"Mitrofanov","year":"2016","journal-title":"IEEE Trans. Terahertz Sci. Technol."},{"key":"ref_19","first-page":"3880","article-title":"Terahertz imaging with sub-wavelength resolution by femtosecond laser filament in air","volume":"4","author":"Zhao","year":"2013","journal-title":"Physics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"8439","DOI":"10.1038\/ncomms9439","article-title":"High-performing nonlinear visualization of terahertz radiation on a silicon charge-coupled device","volume":"6","author":"Shalaby","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1038\/nnano.2015.303","article-title":"Epitaxial graphene quantum dots for high-performance terahertz bolometers","volume":"11","author":"Fatimy","year":"2016","journal-title":"Nat. Nanotechnol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1007\/s10762-014-0057-0","article-title":"Review of terahertz tomography techniques","volume":"35","author":"Guillet","year":"2014","journal-title":"J. Infrared Millim. Terahertz Waves"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Li, J., and Stoica, P. (2009). Mimo Radar Signal Processing, Wiley-IEEE Press.","DOI":"10.1002\/9780470391488"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1109\/LAWP.2015.2469759","article-title":"A novel two-dimensional sparse mimo array topology for uwb short-range imaging","volume":"15","author":"Tan","year":"2015","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1049\/el.2015.0098","article-title":"Synthesis of extreme sparse array for real-time 3D acoustic imaging","volume":"51","author":"Liu","year":"2015","journal-title":"Electron. Lett."},{"key":"ref_26","first-page":"1","article-title":"Fast broadband beamforming using nonuniform fast fourier transform for underwater real-time 3-d acoustical imaging","volume":"41","author":"Chi","year":"2015","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1109\/LAWP.2015.2440432","article-title":"Modified real ga for the synthesis of sparse planar circular arrays","volume":"15","author":"Chen","year":"2016","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_28","unstructured":"Soumekh, M. (1999). Synthetic Aperture Radar Signal Processing, Wiley."},{"key":"ref_29","unstructured":"Zhang, S. (2009). Engineering Electromagnetic Theory, Science Press."},{"key":"ref_30","unstructured":"Chew, W.C. (1990). Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Kirsch, A. (2011). An Introduction to the Mathematical Theory of Inverse Problems, Springer Science & Business Media.","DOI":"10.1007\/978-1-4419-8474-6"},{"key":"ref_32","unstructured":"Groetsch, C.W. (1984). The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman Advanced Publishing Program."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1109\/MSP.2007.4286571","article-title":"Compressive sensing [lecture notes]","volume":"24","author":"Baraniuk","year":"2007","journal-title":"IEEE Signal. Process. Mag."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MSP.2007.914731","article-title":"An introduction to compressive sampling","volume":"25","author":"Candes","year":"2008","journal-title":"IEEE Signal. Proc. Mag."},{"key":"ref_35","unstructured":"Ozdemir, C., Demirci, S., Yigit, E., and Yilmaz, B. (2013, January 12\u201315). Compressed sensing based near-field inverse synthetic aperture radar imaging. Proceedings of the PIERS Proceedings, Stockholm, Sweden."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Yang, Z.L., and Zheng, Y.R. (2012, January 25\u201330). Near-field 3-D synthetic aperture radar imaging via compressed sensing. Proceedings of the 2012 IEEE International Conference on Acoustics, Speech and Signal, Kyoto, Japan.","DOI":"10.1109\/ICASSP.2012.6288427"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2723","DOI":"10.3390\/s150202723","article-title":"Fourier-sparsity integrated method for complex target ISAR imagery","volume":"15","author":"Gao","year":"2015","journal-title":"Sensors"},{"key":"ref_38","first-page":"864","article-title":"Back-projection algorithm to stepped-frequency through-the-wall radar imaging","volume":"6","author":"Cui","year":"2008","journal-title":"J. Univ. Electron. Sci. Technol. China"},{"key":"ref_39","unstructured":"Duersch, M. (2013). Backprojection for Synthetic Aperture Radar. [Ph.D. Thesis, Brigham Young University]."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1109\/8.855491","article-title":"3-D radar imaging using range migration techniques","volume":"48","year":"2000","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1111\/j.1365-2478.1976.tb00934.x","article-title":"The wave equation applied to migration*","volume":"24","author":"Loewenthal","year":"1976","journal-title":"Geophys. Prospect."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2522","DOI":"10.1109\/TUFFC.2010.1718","article-title":"Phase shift migration for imaging layered materials and objects immersed in water","volume":"57","author":"Olofsson","year":"2010","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1109\/TGRS.2012.2209892","article-title":"Three-dimensional image reconstruction of targets under the illumination of terahertz gaussian beam-theory and experiment","volume":"51","author":"Gu","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1109\/TTHZ.2014.2326004","article-title":"Fast three-dimensional image reconstruction of targets under the illumination of terahertz gaussian beams with enhanced phase-shift migration to improve computation efficiency","volume":"4","author":"Sun","year":"2014","journal-title":"IEEE Trans. Terahertz Sci. Technol."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Goldsmith, P.F. (1998). Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications, IEEE Press.","DOI":"10.1109\/9780470546291"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Ahmed, S.S., Schiessl, A., and Schmidt, L. (2009, January 16\u201318). Multistatic mm-wave imaging with planar 2D-arrays. Proceedings of the Microwave Conference, Munich, Germany.","DOI":"10.1109\/GEMIC.2009.4815908"},{"key":"ref_47","unstructured":"Fortuny, J. (2001). Efficient Algorithms for Three-Dimensional Near-Field Synthetic Aperture Radar Imaging. [Ph.D. Thesis, University of Karslruhe]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/7\/1139\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:26:47Z","timestamp":1760210807000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/7\/1139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,22]]},"references-count":47,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2016,7]]}},"alternative-id":["s16071139"],"URL":"https:\/\/doi.org\/10.3390\/s16071139","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,7,22]]}}}