{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:44:06Z","timestamp":1767339846378,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,3,12]],"date-time":"2023-03-12T00:00:00Z","timestamp":1678579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"],"award-info":[{"award-number":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Lab of Intelligent and Green Flexographic Printing","award":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"],"award-info":[{"award-number":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"]}]},{"name":"Qilu University of Technology (Shandong Academy of Sciences) Pilot Project for Integrating Science, Education, and Industry","award":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"],"award-info":[{"award-number":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"]}]},{"name":"Shandong Province Higher Educational Science and Technology Program","award":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"],"award-info":[{"award-number":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"]}]},{"name":"State Key Laboratory of Biobased Material and Green Papermaking, Qilu University of Technology, Shandong Academy of Sciences","award":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"],"award-info":[{"award-number":["ZR2020MF091","ZBKT202101","2022PX078","J17KA178","ZZ20210108"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The similarity between samples is an important factor for spectral reflectance recovery. The current way of selecting samples after dividing dataset does not take subspace merging into account. An optimized method based on subspace merging for spectral recovery is proposed from single RGB trichromatic values in this paper. Each training sample is equivalent to a separate subspace, and the subspaces are merged according to the Euclidean distance. The merged center point for each subspace is obtained through many iterations, and subspace tracking is used to determine the subspace where each testing sample is located for spectral recovery. After obtaining the center points, these center points are not the actual points in the training samples. The nearest distance principle is used to replace the center points with the point in the training samples, which is the process of representative sample selection. Finally, these representative samples are used for spectral recovery. The effectiveness of the proposed method is tested by comparing it with the existing methods under different illuminants and cameras. Through the experiments, the results show that the proposed method not only shows good results in terms of spectral and colorimetric accuracy, but also in the selection representative samples.<\/jats:p>","DOI":"10.3390\/s23063056","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T03:28:33Z","timestamp":1678678113000},"page":"3056","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Optimized Method Based on Subspace Merging for Spectral Reflectance Recovery"],"prefix":"10.3390","volume":"23","author":[{"given":"Yifan","family":"Xiong","sequence":"first","affiliation":[{"name":"Faculty of Light Industry, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangyuan","family":"Wu","sequence":"additional","affiliation":[{"name":"Faculty of Light Industry, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaozhou","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Biobased Material and Green Papermaking, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"28273","DOI":"10.1364\/OE.25.028273","article-title":"Optimized method for spectral reflectance reconstruction from camera responses","volume":"25","author":"Liang","year":"2017","journal-title":"Opt. Express"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8461","DOI":"10.1364\/AO.56.008461","article-title":"Self-training-based spectral image reconstruction for art paintings with multispectral imaging","volume":"56","author":"Xu","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Liu, Q., Huang, Z., Pointer, M.R., and Luo, M.R. (2019). Optimizing the Spectral Characterisation of a CMYK Printer with Embedded CMY Printer Modelling. Appl. Sci., 9.","DOI":"10.3390\/app9245308"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s00339-011-6689-1","article-title":"Advances in multispectral and hyperspectral imaging for archaeology and art conservation","volume":"106","author":"Liang","year":"2011","journal-title":"Appl. Phys. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1179\/174313110X12771950995716","article-title":"An introduction to hyperspectral imaging and its application for security, surveillance and target acquisition","volume":"58","author":"Yuen","year":"2013","journal-title":"Imaging Sci. J."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Lin, Y.T., and Finlayson, G.D. (2020). Physically Plausible Spectral Reconstruction. Sensors, 20.","DOI":"10.3390\/s20216399"},{"key":"ref_7","unstructured":"Depeursinge, C.D., Everdell, N.L., Vitkin, I.A., Styles, I.B., Claridge, E., Hebden, J.C., and Calcagni, A.S. (2009, January 14\u201317). Multispectral imaging of the ocular fundus using LED illumination. Proceedings of the Novel Optical Instrumentation for Biomedical Applications IV, Munich, German."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7902","DOI":"10.3390\/s130607902","article-title":"Estimation of melanin and hemoglobin using spectral reflectance images reconstructed from a digital RGB image by the Wiener estimation method","volume":"13","author":"Nishidate","year":"2013","journal-title":"Sensors"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"14934","DOI":"10.1364\/OE.24.014934","article-title":"Improved method for skin reflectance reconstruction from camera images","volume":"24","author":"Xiao","year":"2016","journal-title":"Opt. Express"},{"key":"ref_10","first-page":"9","article-title":"Conservation-restoration of Textile Materials from Romanian Medieval Art Collections","volume":"60","author":"Octaviana","year":"2009","journal-title":"Rev. De Chim. Buchar. Orig. Ed."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"86196","DOI":"10.1109\/ACCESS.2020.2992326","article-title":"Detection of Oil-Containing Dressing on Salad Leaves Using Multispectral Imaging","volume":"8","author":"Raju","year":"2020","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1002\/col.21763","article-title":"Comparative Performance Analysis of Spectral Estimation Algorithms and Computational Optimization of a Multispectral Imaging System for Print Inspection","volume":"39","author":"Valero","year":"2012","journal-title":"Color Res. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1002\/col.22231","article-title":"A strategy toward spectral and colorimetric color reproduction using ordinary digital cameras","volume":"43","author":"Fairchild","year":"2018","journal-title":"Color Res. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1002\/col.20613","article-title":"Using weighted pseudo-inverse method for reconstruction of reflectance spectra and analyzing the dataset in terms of normality","volume":"36","author":"Babaei","year":"2011","journal-title":"Color Res. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1002\/col.20086","article-title":"A review of principal component analysis and its applications to color technology","volume":"30","author":"Tzeng","year":"2005","journal-title":"Color Res. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"085208","DOI":"10.1088\/1612-202X\/ab2b36","article-title":"Reflectance spectra recovery from a single RGB image by adaptive compressive sensing","volume":"16","author":"Wu","year":"2019","journal-title":"Laser Phys. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"095201","DOI":"10.1088\/1612-202X\/ac1276","article-title":"Spectral sparse recovery form a single RGB image","volume":"18","author":"Wu","year":"2021","journal-title":"Laser Phys. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1134\/S1054661807020101","article-title":"Wiener estimation method in estimating of spectral reflectance from RGB images","volume":"17","author":"Stigell","year":"2007","journal-title":"Pattern Recognit. Image Anal."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, H., Wu, Z., Zhang, L., and Parkkinen, J. (2013, January 15\u201318). SR-LLA: A novel spectral reconstruction method based on locally linear approximation. Proceedings of the 2013 IEEE International Conference on Image Processing, Melbourne, Australia.","DOI":"10.1109\/ICIP.2013.6738418"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, L., Sole, A., and Hardeberg, J.Y. (2022). Densely Residual Network with Dual Attention for Hyperspectral Reconstruction from RGB Images. Remote Sens., 14.","DOI":"10.3390\/rs14133128"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Xiong, Y., Wu, G., Li, X., Niu, S., and Han, X. (2021, January 10\u201312). Spectral reflectance recovery using convolutional neural network. Proceedings of the International Conference on Optoelectronic Materials and Devices (ICOMD 2021), Guangzhou, China.","DOI":"10.1117\/12.2628555"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Arad, B., Timofte, R., Yahel, R., Morag, N., Bernat, A., Cai, Y., Lin, J., Lin, Z., Wang, H., and Zhang, Y. (2022, January 18\u201324). NTIRE 2022 Spectral Recovery Challenge and Data Set. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA.","DOI":"10.1109\/CVPRW56347.2022.00103"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lin, Y.-T., and Finlayson, G.D. (2021). On the optimization of regression-based spectral reconstruction. Sensors, 21.","DOI":"10.3390\/s21165586"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Liu, Z., Xiao, K., Pointer, M.R., Liu, Q., Li, C., He, R., and Xie, X. (2021). Spectral Reconstruction Using an Iteratively Reweighted Regulated Model from Two Illumination Camera Responses. Sensors, 21.","DOI":"10.3390\/s21237911"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, S., Xiao, K., and Li, P. (2023). Spectra Reconstruction for Human Facial Color from RGB Images via Clusters in 3D Uniform CIELab* and Its Subordinate Color Space. Sensors, 23.","DOI":"10.3390\/s23020810"},{"key":"ref_26","unstructured":"Jon, Y., and Hardeberg, P.D. (2001). Acquisition and Reproduction of Color Images: Colorimetric and Multispectral Approaches, Universal-Publishers."},{"key":"ref_27","unstructured":"Mohammadi, M., Nezamabadi, M., Berns, R., and Taplin, L. (2005, January 8\u201313). A prototype calibration target for spectral imaging. Proceedings of the Tenth Congress of the International Colour Association Granada, Granada, Spain."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"481","DOI":"10.2352\/J.ImagingSci.Technol.(2006)50:5(481)","article-title":"Methods for Optimal Color Selection","volume":"50","author":"Cheung","year":"2006","journal-title":"J. Imaging Sci. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2494","DOI":"10.1364\/AO.47.002494","article-title":"Optimal selection of representative colors for spectral reflectance reconstruction in a multispectral imaging system","volume":"47","author":"Shen","year":"2008","journal-title":"Appl. Opt."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1002\/col.22718","article-title":"Optimal selection of representative samples for efficient digital camera-based spectra recovery","volume":"47","author":"Liang","year":"2022","journal-title":"Color Res. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1364\/JOSAA.25.000371","article-title":"Reconstructing spectral reflectance by dividing spectral space and extending the principal components in principal component analysis","volume":"25","author":"Zhang","year":"2008","journal-title":"J. Opt. Soc. Am. A Opt. Image. Sci. Vis."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"095201","DOI":"10.1088\/1612-2011\/13\/9\/095201","article-title":"A method for selecting training samples based on camera response","volume":"13","author":"Zhang","year":"2016","journal-title":"Laser Phys. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1051286","DOI":"10.3389\/fpsyg.2022.1051286","article-title":"Optimized clustering method for spectral reflectance recovery","volume":"13","author":"Xiong","year":"2022","journal-title":"Front. Psychol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5165","DOI":"10.1364\/OE.27.005165","article-title":"Spectra estimation from raw camera responses based on adaptive local-weighted linear regression","volume":"27","author":"Liang","year":"2019","journal-title":"Opt. Express"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1016\/j.ijleo.2015.03.026","article-title":"Reconstruction of spectral color information using weighted principal component analysis","volume":"126","author":"Wu","year":"2015","journal-title":"Optik"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1111\/j.1520-6378.1994.tb00053.x","article-title":"Measurement and analysis of object reflectance spectra","volume":"19","author":"Vrhel","year":"1994","journal-title":"Color Res. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"25830","DOI":"10.1364\/OE.389614","article-title":"Sequential adaptive estimation for spectral reflectance based on camera responses","volume":"28","author":"Wang","year":"2020","journal-title":"Opt. Express"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1364\/AO.53.000709","article-title":"Adaptive global training set selection for spectral estimation of printed inks using reflectance modeling","volume":"53","author":"Eckhard","year":"2014","journal-title":"Appl. Opt."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1109\/TCI.2018.2855445","article-title":"Spectral Reflectance Recovery From a Single RGB Image","volume":"4","author":"Fu","year":"2018","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Jiang, J., Liu, D., Gu, J., and S\u00fcsstrunk, S. (2013, January 15\u201317). What is the space of spectral sensitivity functions for digital color cameras?. Proceedings of the IEEE Workshop on Applications of Computer Vision (WACV), Clearwater Beach, FL, USA.","DOI":"10.1109\/WACV.2013.6475015"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/6\/3056\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:53:21Z","timestamp":1760122401000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/6\/3056"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,12]]},"references-count":40,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["s23063056"],"URL":"https:\/\/doi.org\/10.3390\/s23063056","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,3,12]]}}}