{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T08:50:11Z","timestamp":1767084611000,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T00:00:00Z","timestamp":1709769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Hankyong National University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we propose a method for the three-dimensional (3D) image visualization of objects under photon-starved conditions using multiple observations and statistical estimation. To visualize 3D objects under these conditions, photon counting integral imaging was used, which can extract photons from 3D objects using the Poisson random process. However, this process may not reconstruct 3D images under severely photon-starved conditions due to a lack of photons. Therefore, to solve this problem, in this paper, we propose N-observation photon-counting integral imaging with statistical estimation. Since photons are extracted randomly using the Poisson distribution, increasing the samples of photons can improve the accuracy of photon extraction. In addition, by using a statistical estimation method, such as maximum likelihood estimation, 3D images can be reconstructed. To prove our proposed method, we implemented the optical experiment and calculated its performance metrics, which included the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), peak-to-correlation energy (PCE), and the peak sidelobe ratio (PSR).<\/jats:p>","DOI":"10.3390\/s24061731","type":"journal-article","created":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T08:59:37Z","timestamp":1709801977000},"page":"1731","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Three-Dimensional Image Visualization under Photon-Starved Conditions Using N Observations and Statistical Estimation"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1381-6116","authenticated-orcid":false,"given":"Hyun-Woo","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Computer Science and Networks, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka-shi 820-8502, Fukuoka, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8469-0288","authenticated-orcid":false,"given":"Min-Chul","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Networks, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka-shi 820-8502, Fukuoka, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2896-770X","authenticated-orcid":false,"given":"Myungjin","family":"Cho","sequence":"additional","affiliation":[{"name":"School of ICT, Robotics, and Mechanical Engineering, Hankyong National University, IITC, 327 Chungang-ro, Anseong 17579, Kyonggi-do, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,7]]},"reference":[{"key":"ref_1","first-page":"51","article-title":"Optical ranging system uses laser transmitter","volume":"34","author":"Stitch","year":"1961","journal-title":"Electronics"},{"key":"ref_2","first-page":"371","article-title":"Contributions to the physiology of vision\u2014Part the first. On some remarkable, and hitherto unobserved, phenomena of binocular vision","volume":"128","author":"Wheatstone","year":"1838","journal-title":"Philos. Trans. R. Soc. Lond."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1109\/MC.2005.252","article-title":"Autostereoscopic 3D displays","volume":"38","author":"Dodgson","year":"2005","journal-title":"Computer"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3446","DOI":"10.1364\/AO.48.003446","article-title":"Liquid crystal panel for highefficiency barrier type autostereoscopic three-dimensional displays","volume":"48","author":"Chen","year":"2009","journal-title":"Appl. Opt."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2008","DOI":"10.1016\/j.ijleo.2009.07.002","article-title":"Stereo viewing zone in parallax-barrier-based autostereoscopic display","volume":"121","author":"Wang","year":"2010","journal-title":"Optik"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1364\/AO.50.000H87","article-title":"Three-dimensional display technologies of recent interest: Principles, status, and issues [Invited]","volume":"50","author":"Hong","year":"2011","journal-title":"Appl. Opt."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1038\/161777a0","article-title":"A new microscopic principle","volume":"161","author":"Gabor","year":"1948","journal-title":"Nature"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"22603","DOI":"10.1364\/OE.26.022603","article-title":"eHoloNet: A learning-based end-to-end approach for in-line digital holographic reconstruction","volume":"26","author":"Wang","year":"2018","journal-title":"Opt. Exp."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"016004","DOI":"10.1117\/1.AP.1.1.016004","article-title":"End-to-end deep learning framework for digital holographic reconstruction","volume":"1","author":"Ren","year":"2019","journal-title":"Adv. Photonics"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Shevkunov, I., Katkovnik, V., Claus, D., Pedrini, G., Petrov, N.V., and Egiazarian, K. (2019). Spectral object recognition in hyperspectral holography with complex-domain denoising. Sensors, 19.","DOI":"10.3390\/s19235188"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"G197","DOI":"10.1364\/AO.58.00G197","article-title":"3D object recognition through processing of 2D holograms","volume":"58","author":"Bordbar","year":"2019","journal-title":"Appl. Opt."},{"key":"ref_12","first-page":"446","article-title":"La Photographie Integrale","volume":"146","author":"Lippmann","year":"1908","journal-title":"Comp. Ren. Acad. Des Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1364\/JOSA.58.000071","article-title":"Optimum parameters and resolution limitation of integral photography","volume":"58","author":"Burckhardt","year":"1968","journal-title":"J. Opt. Soc. Am."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2034","DOI":"10.1364\/AO.37.002034","article-title":"Gradient index lens array method based on real time integral photography for three dimensional images","volume":"37","author":"Arai","year":"1998","journal-title":"Appl. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1364\/OL.27.000324","article-title":"Improved viewing resolution of three-dimensional integral imaging by use of nonstationary micro-optics","volume":"27","author":"Jang","year":"2002","journal-title":"Opt. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1364\/OL.27.001144","article-title":"Three-dimensional synthetic aperture integral imaging","volume":"27","author":"Jang","year":"2002","journal-title":"Opt. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1996","DOI":"10.1364\/AO.42.001996","article-title":"Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor","volume":"42","author":"Jang","year":"2003","journal-title":"Appl. Opt."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1924","DOI":"10.1364\/OL.28.001924","article-title":"Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with nonuniform focal lengths and aperture sizes","volume":"28","author":"Jang","year":"2003","journal-title":"Opt. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1364\/OPEX.12.000483","article-title":"Three-dimensional volumetric object reconstruction using computational integral imaging","volume":"12","author":"Hong","year":"2004","journal-title":"Opt. Exp."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"9175","DOI":"10.1364\/OPEX.13.009175","article-title":"Formation of real, orthoscopic integral images by smart pixel mapping","volume":"13","author":"Javidi","year":"2005","journal-title":"Opt. Exp."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1109\/JDT.2005.858883","article-title":"Extended depth-of-field 3-D display and visualization by combination of amplitude-modulated microlenses and deconvolution tools","volume":"1","author":"Saavedra","year":"2005","journal-title":"IEEE J. Disp. Tech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"9657","DOI":"10.1364\/OE.14.009657","article-title":"Optically-corrected elemental images for undistorted integral image display","volume":"14","author":"Pons","year":"2006","journal-title":"Opt. Exp."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1109\/JPROC.2006.870696","article-title":"Three-dimensional image sensing, visualization, and processing using integral imaging","volume":"94","author":"Stern","year":"2006","journal-title":"Proc. IEEE"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1109\/MC.2006.270","article-title":"Light fields and computational imaging","volume":"39","author":"Levoy","year":"2006","journal-title":"IEEE Comput. Mag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1109\/JPROC.2009.2016816","article-title":"Progress in 3-D multiperspective display by integral imaging","volume":"97","author":"Saavedra","year":"2009","journal-title":"Proc. IEEE"},{"key":"ref_26","first-page":"556","article-title":"Three-Dimensional Optical Sensing and Visualization Using Integral Imaging","volume":"99","author":"Cho","year":"2010","journal-title":"Proc. IEEE"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.optlaseng.2018.07.016","article-title":"Computational volumetric reconstruction of integral imaging with improved depth resolution considering continuously non-uniform shifting pixels","volume":"111","author":"Cho","year":"2018","journal-title":"Opt. Laser Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4426","DOI":"10.1364\/OE.16.004426","article-title":"Three-dimensional visualization by photon counting computational integral imaging","volume":"16","author":"Tavakoli","year":"2008","journal-title":"Opt. Exp."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1364\/OL.35.001825","article-title":"Three-dimensional photon counting integral using Bayesian estimation","volume":"35","author":"Jung","year":"2010","journal-title":"Opt. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"19681","DOI":"10.1364\/OE.19.019681","article-title":"Three-dimensional photon counting integral imaging reconstruction using penalized maximum likelihood expectation maximization","volume":"19","author":"Aloni","year":"2011","journal-title":"Opt. Exp."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1364\/OL.37.001487","article-title":"Three-dimensional photon counting integral imaging using moving array lens technique","volume":"37","author":"Cho","year":"2012","journal-title":"Opt. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JPHOT.2013.2294625","article-title":"Photon-counting security tagging and verification using optically encoded QR codes","volume":"6","author":"Markman","year":"2013","journal-title":"IEEE. Photonics J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1364\/JOSAA.31.000394","article-title":"Full-phase photon-counting double-random-phase encryption","volume":"31","author":"Markman","year":"2014","journal-title":"JOSA A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"070301","DOI":"10.3788\/COL201513.070301","article-title":"Three-dimensional color photon counting microscopy using Bayesian estimation with adaptive priori information","volume":"13","author":"Cho","year":"2015","journal-title":"Chin. Opt. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1364\/AO.54.001657","article-title":"Photon counting imaging and phase mask multiplexing for multiple images authentication and digital hologram security","volume":"54","author":"Rajput","year":"2015","journal-title":"Appl. Opt."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"025701","DOI":"10.1088\/2040-8986\/abe18a","article-title":"Low-light phase imaging using in-line digital holography and the transport of intensity equation","volume":"23","author":"Gupta","year":"2021","journal-title":"J. Opt."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Jang, J.-Y., and Cho, M. (2023). Lensless three-dimensional imaging under photon-starved conditions. Sensors, 23.","DOI":"10.3390\/s23042336"},{"key":"ref_38","unstructured":"Goodman, J.W. (2015). Statistical Optics, Wiley. [2nd ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2358","DOI":"10.1364\/AO.28.002358","article-title":"Nonlinear joint power spectrum based optical correlation","volume":"28","author":"Javidi","year":"1989","journal-title":"Appl. Opt."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/6\/1731\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:10:30Z","timestamp":1760105430000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/6\/1731"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,7]]},"references-count":39,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["s24061731"],"URL":"https:\/\/doi.org\/10.3390\/s24061731","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2024,3,7]]}}}