{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:22:16Z","timestamp":1760228536360,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T00:00:00Z","timestamp":1652745600000},"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":["61527802","TCGZ2020C004","202020429036"],"award-info":[{"award-number":["61527802","TCGZ2020C004","202020429036"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014206","name":"National Key Laboratory Foundation of China","doi-asserted-by":"publisher","award":["61527802","TCGZ2020C004","202020429036"],"award-info":[{"award-number":["61527802","TCGZ2020C004","202020429036"]}],"id":[{"id":"10.13039\/501100014206","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Compressed sensing (CS) has been widely used in hyperspectral (HS) imaging to obtain hyperspectral data at a sub-Nyquist sampling rate, lifting the efficiency of data acquisition. Yet, reconstructing the acquired HS data via iterative algorithms is time consuming, which hinders the real-time application of compressed HS imaging. To alleviate this problem, this paper makes the first attempt to adopt convolutional neural networks (CNNs) to reconstruct three-dimensional compressed HS data by backtracking the entire imaging process, leading to a simple yet effective network, dubbed the backtracking reconstruction network (BTR-Net). Concretely, we leverage the divide-and-conquer method to divide the imaging process based on coded aperture tunable filter (CATF) spectral imager into steps, and build a subnetwork for each step to specialize in its reverse process. Consequently, BTR-Net introduces multiple built-in networks which performs spatial initialization, spatial enhancement, spectral initialization and spatial\u2013spectral enhancement in an independent and sequential manner. Extensive experiments show that BTR-Net can reconstruct compressed HS data quickly and accurately, which outperforms leading iterative algorithms both quantitatively and visually, while having superior resistance to noise.<\/jats:p>","DOI":"10.3390\/rs14102406","type":"journal-article","created":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T08:34:29Z","timestamp":1652776469000},"page":"2406","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Backtracking Reconstruction Network for Three-Dimensional Compressed Hyperspectral Imaging"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8277-467X","authenticated-orcid":false,"given":"Xi","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Beijing Institute of Technology Chongqing Innovation Center, Chongqing 401120, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0897-821X","authenticated-orcid":false,"given":"Tingfa","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Beijing Institute of Technology Chongqing Innovation Center, Chongqing 401120, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4345-7938","authenticated-orcid":false,"given":"Yuhan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Beijing Institute of Technology Chongqing Innovation Center, Chongqing 401120, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5072-6198","authenticated-orcid":false,"given":"Axin","family":"Fan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Beijing Institute of Technology Chongqing Innovation Center, Chongqing 401120, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5390-0403","authenticated-orcid":false,"given":"Chang","family":"Xu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Beijing Institute of Technology Chongqing Innovation Center, Chongqing 401120, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6936-9485","authenticated-orcid":false,"given":"Jianan","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Photoelectronic Imaging Technology and System of Ministry of Education of China, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1007\/s12665-011-1112-y","article-title":"Application of hyperspectral remote sensing for environment monitoring in mining areas","volume":"65","author":"Zhang","year":"2012","journal-title":"Environ. Earth Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.rse.2011.07.021","article-title":"Synergies between VSWIR and TIR data for the urban environment: An evaluation of the potential for the Hyperspectral Infrared Imager (HyspIRI) Decadal Survey mission","volume":"117","author":"Roberts","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.patrec.2015.09.010","article-title":"A survey on representation-based classification and detection in hyperspectral remote sensing imagery","volume":"83","author":"Li","year":"2016","journal-title":"Pattern Recognit. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/j.rse.2017.08.020","article-title":"Hyperspectral remote sensing of shallow waters: Considering environmental noise and bottom intra-class variability for modeling and inversion of water reflectance","volume":"200","author":"Jay","year":"2017","journal-title":"Remote Sens. Environ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1896","DOI":"10.1364\/AO.417952","article-title":"Microlens array snapshot hyperspectral microscopy system for the biomedical domain","volume":"60","author":"Yu","year":"2021","journal-title":"Appl. Opt."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5293","DOI":"10.1364\/AO.46.005293","article-title":"Optical architectures for compressive imaging","volume":"46","author":"Neifeld","year":"2007","journal-title":"Appl. Opt."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/MSP.2007.914730","article-title":"Single-pixel imaging via compressive sampling","volume":"25","author":"Duarte","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"B44","DOI":"10.1364\/AO.47.000B44","article-title":"Single disperser design for coded aperture snapshot spectral imaging","volume":"47","author":"Wagadarikar","year":"2008","journal-title":"Appl. Opt."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2661229.2661262","article-title":"Spatial-spectral encoded compressive hyperspectral imaging","volume":"33","author":"Lin","year":"2014","journal-title":"ACM Trans. Graph."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2104","DOI":"10.1109\/TPAMI.2016.2621050","article-title":"Adaptive Nonlocal Sparse Representation for Dual-Camera Compressive Hyperspectral Imaging","volume":"39","author":"Wang","year":"2017","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2197","DOI":"10.1364\/OE.27.002197","article-title":"Channeled compressive imaging spectropolarimeter","volume":"27","author":"Ren","year":"2019","journal-title":"Opt. Express"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"25226","DOI":"10.1364\/OE.26.025226","article-title":"Compressive spectral imaging system based on liquid crystal tunable filter","volume":"26","author":"Wang","year":"2018","journal-title":"Opt. Express"},{"key":"ref_14","first-page":"280","article-title":"Real-time adaptive coded aperture: Application to the compressive spectral imaging system","volume":"Volume 11353","author":"Schelkens","year":"2020","journal-title":"Proceedings of the Optics, Photonics and Digital Technologies for Imaging Applications VI"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1364\/PRJ.377665","article-title":"Super-resolution compressive spectral imaging via two-tone adaptive coding","volume":"8","author":"Xu","year":"2020","journal-title":"Photon. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2992","DOI":"10.1109\/TIP.2007.909319","article-title":"A New TwIST: Two-Step Iterative Shrinkage\/Thresholding Algorithms for Image Restoration","volume":"16","author":"Figueiredo","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/JSTSP.2007.910281","article-title":"Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems","volume":"1","author":"Figueiredo","year":"2007","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yuan, X. (2016, January 25\u201328). Generalized alternating projection based total variation minimization for compressive sensing. Proceedings of the 2016 IEEE International Conference on Image Processing (ICIP), Phoenix, AZ, USA.","DOI":"10.1109\/ICIP.2016.7532817"},{"key":"ref_19","first-page":"9","article-title":"Spectral image estimation for coded aperture snapshot spectral imagers","volume":"Volume 7076","author":"Wagadarikar","year":"2008","journal-title":"Proceedings of the Image Reconstruction from Incomplete Data V"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mousavi, A., and Baraniuk, R.G. (2017, January 5\u20139). Learning to invert: Signal recovery via Deep Convolutional Networks. Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA.","DOI":"10.1109\/ICASSP.2017.7952561"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5117","DOI":"10.1109\/TIT.2016.2556683","article-title":"From Denoising to Compressed Sensing","volume":"62","author":"Metzler","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1266","DOI":"10.1109\/JSTARS.2017.2787483","article-title":"Compressed Sensing Reconstruction of Hyperspectral Images Based on Spectral Unmixing","volume":"11","author":"Wang","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Xue, J., Zhao, Y., Liao, W., and Chan, J.C.W. (2019). Nonlocal Tensor Sparse Representation and Low-Rank Regularization for Hyperspectral Image Compressive Sensing Reconstruction. Remote Sens., 11.","DOI":"10.3390\/rs11020193"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6813","DOI":"10.1109\/TIP.2020.2994411","article-title":"Hyperspectral Image Compressive Sensing Reconstruction Using Subspace-Based Nonlocal Tensor Ring Decomposition","volume":"29","author":"Chen","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Takeyama, S., Ono, S., and Kumazawa, I. (2020). A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization. Remote Sens., 12.","DOI":"10.3390\/rs12213541"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.neunet.2014.09.003","article-title":"Deep learning in neural networks: An overview","volume":"61","author":"Schmidhuber","year":"2015","journal-title":"Neural Netw."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Leibe, B., Matas, J., Sebe, N., and Welling, M. (2016, January 11\u201314). XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks. Proceedings of the Computer Vision\u2014ECCV 201, 14th European Conference, Amsterdam, The Netherlands.","DOI":"10.1007\/978-3-319-46484-8"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1252","DOI":"10.1109\/TMI.2016.2548501","article-title":"Automatic Segmentation of MR Brain Images With a Convolutional Neural Network","volume":"35","author":"Moeskops","year":"2016","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1109\/TMI.2016.2546227","article-title":"Segmenting Retinal Blood Vessels With Deep Neural Networks","volume":"35","author":"Liskowski","year":"2016","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Shi, W., Caballero, J., Husz\u00e1r, F., Totz, J., Aitken, A.P., Bishop, R., Rueckert, D., and Wang, Z. (2016, January 27\u201330). Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network. Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.207"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1109\/TPAMI.2017.2699184","article-title":"DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs","volume":"40","author":"Chen","year":"2018","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1038\/s41377-021-00484-y","article-title":"Unsupervised content-preserving transformation for optical microscopy","volume":"10","author":"Li","year":"2021","journal-title":"Light. Sci. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1038\/s41377-021-00545-2","article-title":"Deeply learned broadband encoding stochastic hyperspectral imaging","volume":"10","author":"Zhang","year":"2021","journal-title":"Light. Sci. Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2257","DOI":"10.1109\/TIP.2018.2884076","article-title":"HyperReconNet: Joint Coded Aperture Optimization and Image Reconstruction for Compressive Hyperspectral Imaging","volume":"28","author":"Wang","year":"2019","journal-title":"IEEE Trans. Image Process."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Miao, X., Yuan, X., Pu, Y., and Athitsos, V. (November, January 27). lambda-Net: Reconstruct Hyperspectral Images From a Snapshot Measurement. Proceedings of the 2019 IEEE\/CVF International Conference on Computer Vision (ICCV), Seoul, Korea.","DOI":"10.1109\/ICCV.2019.00416"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Wang, L., Sun, C., Fu, Y., Kim, M.H., and Huang, H. (2019, January 15\u201320). Hyperspectral Image Reconstruction Using a Deep Spatial-Spectral Prior. Proceedings of the 2019 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00822"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wang, L., Sun, C., Zhang, M., Fu, Y., and Huang, H. (2020, January 13\u201319). DNU: Deep Non-Local Unrolling for Computational Spectral Imaging. Proceedings of the 2020 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00173"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Yang, Y., Xie, Y., Chen, X., and Sun, Y. (2021). Hyperspectral Snapshot Compressive Imaging with Non-Local Spatial-Spectral Residual Network. Remote Sens., 13.","DOI":"10.3390\/rs13091812"},{"key":"ref_39","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_40","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep Residual Learning for Image Recognition. Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_41","unstructured":"Gan, L. (2007, January 1\u20134). Block Compressed Sensing of Natural Images. Proceedings of the 2007 15th International Conference on Digital Signal Processing, Wales, UK."},{"key":"ref_42","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_43","unstructured":"Alsallakh, B., Kokhlikyan, N., Miglani, V., Yuan, J., and Reblitz-Richardson, O. (2020). Mind the Pad\u2013CNNs can Develop Blind Spots. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Arad, B., and Ben-Shahar, O. (2016, January 11\u201314). Sparse Recovery of Hyperspectral Signal from Natural RGB Images. Proceedings of the European Conference on Computer Vision, Amsterdam, The Netherlands.","DOI":"10.1007\/978-3-319-46478-7_2"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/10\/2406\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:13:35Z","timestamp":1760138015000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/10\/2406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,17]]},"references-count":44,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["rs14102406"],"URL":"https:\/\/doi.org\/10.3390\/rs14102406","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,5,17]]}}}