{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T18:07:20Z","timestamp":1770833240586,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T00:00:00Z","timestamp":1659657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science, Technology and Space, Israel","award":["3-18410"],"award-info":[{"award-number":["3-18410"]}]},{"name":"Ministry of Science, Technology and Space, Israel","award":["3-13351"],"award-info":[{"award-number":["3-13351"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Designing and optimizing systems by end-to-end deep learning is a recently emerging field. We present a novel physics-constrained autoencoder (PyCAE) for the design and optimization of a physically realizable sensing model. As a case study, we design a compressive hyperspectral imaging system for remote sensing based on this approach, which allows capturing hundreds of spectral bands with as few as four compressed measurements. We demonstrate our deep learning approach to design spectral compression with a spectral light modulator (SpLM) encoder and a reconstruction neural network decoder. The SpLM consists of a set of modified Fabry\u2013P\u00e9rot resonator (mFPR) etalons that are designed to have a staircase-shaped geometry. Each stair occupies a few pixel columns of a push-broom-like spectral imager. The mFPR\u2019s stairs can sample the earth terrain in along-track scanning from an airborne or spaceborne moving platform. The SpLM is jointly designed with an autoencoder by a data-driven approach, while spectra from remote sensing databases are used to train the system. The SpLM\u2019s parameters are optimized by integrating its physically realizable sensing model in the encoder part of the PyCAE. The decoder part of the PyCAE implements the spectral reconstruction.<\/jats:p>","DOI":"10.3390\/rs14153766","type":"journal-article","created":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T04:16:55Z","timestamp":1660018615000},"page":"3766","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Learned Design of a Compressive Hyperspectral Imager for Remote Sensing by a Physics-Constrained Autoencoder"],"prefix":"10.3390","volume":"14","author":[{"given":"Yaron","family":"Heiser","sequence":"first","affiliation":[{"name":"Electro-Optics and Photonics Department, School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel"}]},{"given":"Adrian","family":"Stern","sequence":"additional","affiliation":[{"name":"Electro-Optics and Photonics Department, School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,5]]},"reference":[{"key":"ref_1","first-page":"37","article-title":"Advances in Hyperspectral Image and Signal Processing: A Comprehensive Overview of the State of the Art","volume":"5","author":"Ghamisi","year":"2017","journal-title":"GRSM"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Li, Z., Huang, L., and He, J. (2019). A Multiscale Deep Middle-level Feature Fusion Network for Hyperspectral Classification. Remote Sens., 11.","DOI":"10.3390\/rs11060695"},{"key":"ref_3","first-page":"6690","article-title":"Deep Learning for Hyperspectral Image Classification: An Overview","volume":"57","author":"Li","year":"2019","journal-title":"IEEE Trans."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2047","DOI":"10.1038\/s41377-022-00743-6","article-title":"Spectral imaging with deep learning","volume":"11","author":"Huang","year":"2022","journal-title":"Light Sci. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.neucom.2021.03.035","article-title":"A survey: Deep learning for hyperspectral image classification with few labeled samples","volume":"448","author":"Jia","year":"2021","journal-title":"Neurocomputing"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Heiser, Y., Oiknine, Y., and Stern, A. (2019). Compressive Hyperspectral Image Reconstruction with Deep Neural Networks, SPIE.","DOI":"10.1117\/12.2522122"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"35811","DOI":"10.1364\/OE.27.035811","article-title":"DeepCubeNet: Reconstruction of spectrally compressive sensed hyperspectral images with deep neural networks","volume":"27","author":"Gedalin","year":"2019","journal-title":"Opt. Express"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"041406","DOI":"10.1117\/1.JEI.30.4.041406","article-title":"Deep neural network classification in the compressively sensed spectral image domain","volume":"30","author":"Cohen","year":"2021","journal-title":"J. Electron. Imaging"},{"key":"ref_9","first-page":"2152","article-title":"DARecNet-BS: Unsupervised Dual-Attention Reconstruction Network for Hyperspectral Band Selection","volume":"18","author":"Roy","year":"2021","journal-title":"LGRS"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.eswa.2019.04.006","article-title":"Hyperspectral imagery classification based on semi-supervised 3-D deep neural network and adaptive band selection","volume":"129","author":"Sellami","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1007\/s12517-021-06984-w","article-title":"Band selection strategies for hyperspectral image classification based on machine learning and artificial intelligent techniques\u2013Survey","volume":"14","author":"Sawant","year":"2021","journal-title":"Arab. J. Geosci."},{"key":"ref_12","first-page":"3","article-title":"Spectral Imaging for Remote Sensing","volume":"14","author":"Shaw","year":"2003","journal-title":"Linc. Lab. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"090901","DOI":"10.1117\/1.OE.52.9.090901","article-title":"Review of snapshot spectral imaging technologies","volume":"52","author":"Hagen","year":"2013","journal-title":"Opt. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Eismann, M.T. (2012). Hyperspectral Remote Sensing, SPIE.","DOI":"10.1117\/3.899758"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Manolakis, D.G., Lockwood, R.B., and Cooley, T.W. (2016). Hyperspectral Imaging Remote Sensing: Physics, Sensors, and Algorithms, Cambridge University Press.","DOI":"10.1017\/CBO9781316017876"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0034-4257(93)90012-M","article-title":"The airborne visible\/infrared imaging spectrometer (AVIRIS)","volume":"44","author":"Vane","year":"1993","journal-title":"Remote Sens. Environ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"10286","DOI":"10.3390\/rs61110286","article-title":"Landsat-8 operational land imager design, characterization, and performance","volume":"6","author":"Knight","year":"2014","journal-title":"Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Thenkabail, P.S., and Lyon, J.G. (2016). Hyperspectral Remote Sensing of Vegetation, CRC Press.","DOI":"10.1201\/b11222"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.buildenv.2017.05.027","article-title":"High-resolution spectral mapping of urban thermal properties with Unmanned Aerial Vehicles","volume":"121","author":"Gaitani","year":"2017","journal-title":"Build. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Gupta, R.P. (2017). Remote Sensing Geology, Springer.","DOI":"10.1007\/978-3-662-55876-8"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.isprsjprs.2007.09.006","article-title":"Relationships between the mineralogical and chemical composition of tropical soils and topography from hyperspectral remote sensing data","volume":"63","author":"Formaggio","year":"2008","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5201","DOI":"10.1080\/01431160412331270803","article-title":"A review of satellite and airborne sensors for remote sensing based detection of minefields and landmines","volume":"25","author":"Maathuis","year":"2004","journal-title":"Int. J. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Schott, J.R. (2007). Remote Sensing: The Image Chain Approach, Oxford University Press on Demand.","DOI":"10.1093\/oso\/9780195178173.001.0001"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"C2-171","DOI":"10.1051\/jphyscol:1967230","article-title":"Conclusions on multiplex methods","volume":"28","author":"Fellgett","year":"1967","journal-title":"J. Phys. Colloq."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2015.12.004","article-title":"A review of snapshot multidimensional optical imaging: Measuring photon tags in parallel","volume":"616","author":"Gao","year":"2016","journal-title":"Phys. Rep."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Griffiths, P.R., and De Haseth, J.A. (2007). Fourier Transform Infrared Spectrometry, John Wiley & Sons.","DOI":"10.1002\/047010631X"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Foken, T. (2021). Springer Handbook of Atmospheric Measurements, Springer.","DOI":"10.1007\/978-3-030-52171-4"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"111717","DOI":"10.1117\/1.OE.51.11.111717","article-title":"Remote sensing of gases by hyperspectral imaging: System performance and measurements Remote sensing of gases by hyperspectral imaging: System performance and measurements","volume":"51","author":"Sabbah","year":"2012","journal-title":"Opt. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4763","DOI":"10.1063\/1.1146154","article-title":"A review of spaceborne infrared Fourier transform spectrometers for remote sensing","volume":"66","author":"Persky","year":"1995","journal-title":"Rev. Sci. Instrum."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5894","DOI":"10.1364\/AO.50.005894","article-title":"Experimental results from an airborne static Fourier transform imaging spectrometer","volume":"50","author":"Ferrec","year":"2011","journal-title":"Appl. Opt."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1364\/OL.15.000652","article-title":"Liquid-crystal imaging Fourier-spectrometer array","volume":"15","author":"Itoh","year":"1990","journal-title":"Opt. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"23524","DOI":"10.1038\/srep23524","article-title":"Miniature Compressive Ultra-spectral Imaging System Utilizing a Single Liquid Crystal Phase Retarder","volume":"6","author":"August","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"8446","DOI":"10.1364\/OE.24.008446","article-title":"Along-track scanning using a liquid crystal compressive hyperspectral imager","volume":"24","author":"Oiknine","year":"2016","journal-title":"Opt. Express"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1364\/OPTICA.4.000400","article-title":"High-resolution hyperspectral imaging with cascaded liquid crystal cells","volume":"4","author":"Jullien","year":"2017","journal-title":"Optica"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Oiknine, Y., August, I., Farber, V., Gedalin, D., and Stern, A. (2018). Compressive Sensing Hyperspectral Imaging by Spectral Multiplexing with Liquid Crystal. J. Imaging, 5.","DOI":"10.3390\/jimaging5010003"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Stern, A. (2016). Optical Compressive Imaging, CRC Press.","DOI":"10.1201\/9781315371474"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3455","DOI":"10.1038\/s41598-020-60413-8","article-title":"Dual-camera design for hyperspectral and panchromatic imaging, using a wedge shaped liquid crystal as a spectral multiplexer","volume":"10","author":"Shmilovich","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5042","DOI":"10.1364\/OL.43.005042","article-title":"Multi-aperture snapshot compressive hyperspectral camera","volume":"43","author":"Oiknine","year":"2018","journal-title":"Opt. Lett."},{"key":"ref_39","unstructured":"(2022, July 07). Hyperspectral Remote Sensing Scenes\u2014Grupo de Inteligencia Computacional (GIC). Available online: https:\/\/www.ehu.eus\/ccwintco\/index.php\/Hyperspectral_Remote_Sensing_Scenes."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1364\/OL.42.000025","article-title":"Compressive sensing resonator spectroscopy","volume":"42","author":"Oiknine","year":"2017","journal-title":"Opt. Lett."},{"key":"ref_41","unstructured":"Hinton, G., Srivastava, N., and Swersky, K. (2012). Neural Networks for Machine Learning, Coursera."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1162\/089976699300016412","article-title":"Estimating or Propagating Gradients through Stochastic Neurons for Conditional Computation","volume":"11","author":"Bengio","year":"1999","journal-title":"Neural Comput."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.neucom.2019.05.006","article-title":"DR2-Net: Deep Residual Reconstruction Network for image compressive sensing","volume":"359","author":"Yao","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3365","DOI":"10.1109\/TPAMI.2020.2982166","article-title":"Deep learning for image super-resolution: A survey","volume":"43","author":"Wang","year":"2020","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Zhao, J., Kechasov, D., Rewald, B., Bodner, G., Verheul, M., Clarke, N., and Clarke, J.L. (2020). Deep Learning in Hyperspectral Image Reconstruction from Single RGB images\u2014A Case Study on Tomato Quality Parameters. Remote Sens., 12.","DOI":"10.3390\/rs12193258"},{"key":"ref_47","unstructured":"Proakis, J.G., and Manolakis, D.K. (2007). Digital Signal Processing: Principles, Algorithms, and Applications, Pearson. [4th ed.]."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3766\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:04:54Z","timestamp":1760141094000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3766"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,5]]},"references-count":47,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["rs14153766"],"URL":"https:\/\/doi.org\/10.3390\/rs14153766","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,5]]}}}