{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T17:50:48Z","timestamp":1772905848622,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T00:00:00Z","timestamp":1523491200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Multi-spectral imaging using a camera with more than three channels is an efficient method to acquire and reconstruct spectral data and is used extensively in tasks like object recognition, relighted rendering, and color constancy. Recently developed methods are used to only guide content-dependent filter selection where the set of spectral reflectances to be recovered are known a priori. We present the first content-independent spectral imaging pipeline that allows optimal selection of multiple channels. We also present algorithms for optimal placement of the channels in the color filter array yielding an efficient demosaicing order resulting in accurate spectral recovery of natural reflectance functions. These reflectance functions have the property that their power spectrum statistically exhibits a power-law behavior. Using this property, we propose power-law based error descriptors that are minimized to optimize the imaging pipeline. We extensively verify our models and optimizations using large sets of commercially available wide-band filters to demonstrate the greater accuracy and efficiency of our multi-spectral imaging pipeline over existing methods.<\/jats:p>","DOI":"10.3390\/s18041172","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T12:19:27Z","timestamp":1523535567000},"page":"1172","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Optimized Multi-Spectral Filter Array Based Imaging of Natural Scenes"],"prefix":"10.3390","volume":"18","author":[{"given":"Yuqi","family":"Li","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Ningbo University, Ningbo 315000, China"},{"name":"College of Computer Science and Technology, Zhejiang University, Hangzhou 310000, China"}]},{"given":"Aditi","family":"Majumder","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Irvine, CA 92697-3425, USA"}]},{"given":"Hao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Irvine, CA 92697-3425, USA"}]},{"given":"M.","family":"Gopi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Irvine, CA 92697-3425, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1007\/s11263-008-0176-y","article-title":"Multi-Spectral Imaging by Optimized Wide Band Illumination","volume":"86","author":"Chi","year":"2010","journal-title":"Int. J. Comput. Vis."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Arad, B., and Ben-Shahar, O. (2017, January 21\u201326). Filter Selection for Hyperspectral Estimation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/ICCV.2017.342"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1364\/JOSAA.9.000507","article-title":"Spectral Reflectance of Natural Objects: How Many Basis Functions Are Necessary?","volume":"9","author":"Dannemiller","year":"1992","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1364\/JOSAA.17.000218","article-title":"Color Signals in Natural Scenes: Characteristics of Reflectance Spectra and Effects of Natural Illuminants","volume":"17","author":"Chiao","year":"2000","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"17439","DOI":"10.1364\/OE.19.017439","article-title":"Depth-resolved image mapping spectrometer (IMS) with structured illumination","volume":"19","author":"Gao","year":"2011","journal-title":"Opt. Express"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1111\/j.1467-8659.2008.01169.x","article-title":"Agile Spectrum Imaging: Programmable Wavelength Modulation for Cameras and Projectors","volume":"27","author":"Mohan","year":"2008","journal-title":"Comput. Graph. Forum"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wagadarikar, A.A., Pitsianis, N.P., Sun, X., and Brady, D.J. (2008). Spectral Image Estimation for Coded Aperture Snapshot Spectral Imagers. Image Reconstruction from Incomplete Data V, SPIE.","DOI":"10.1117\/12.795545"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"233","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_10","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1111\/cgf.12847","article-title":"Multisampling Compressive Video Spectroscopy","volume":"35","author":"Jeon","year":"2016","journal-title":"Comput. Graph. Forum"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Mitra, K., Cossairt, O., and Veeraraghavan, A. (2014, January 2\u20134). Can We Beat Hadamard Multiplexing? Data Driven Design and Analysis for Computational Imaging Systems. Proceedings of the 2014 IEEE International Conference on Computational Photography (ICCP), Santa Clara, CA, USA.","DOI":"10.1109\/ICCPHOT.2014.6831800"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1109\/TIP.2010.2046811","article-title":"Generalized assorted pixel camera: Postcapture control of resolution, dynamic range, and spectrum","volume":"19","author":"Yasuma","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1145\/2010324.1964960","article-title":"Switchable primaries using shiftable layers of color filter arrays","volume":"30","author":"Sajadi","year":"2011","journal-title":"ACM Trans. Graph."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3048","DOI":"10.1109\/TIP.2015.2436342","article-title":"A Practical One-Shot Multispectral Imaging System Using a Single Image Sensor","volume":"24","author":"Monno","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3190","DOI":"10.1109\/TIP.2010.2051622","article-title":"Selection of Optimal Spectral Sensitivity Functions for Color Filter Arrays","volume":"19","author":"Parmar","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Sadeghipoor, Z., Lu, Y.M., and S\u00fcsstrunk, S. (2012, January 22\u201326). Optimum spectral sensitivity functions for single sensor color imaging. Proceedings of the IS&T\/SPIE Electronic Imaging, Burlingame, CA, USA.","DOI":"10.1117\/12.907904"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Park, J.I., Lee, M.H., Grossberg, M.D., and Nayar, S.K. (2007, January 14\u201321). Multispectral Imaging using Multiplexed Illumination. Proceedings of the 2007 IEEE 11th International Conference on Computer Vision, Rio de Janeiro, Brazil.","DOI":"10.1109\/ICCV.2007.4409090"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1364\/AO.53.000634","article-title":"Channel selection for multispectral color imaging using binary differential evolution","volume":"53","author":"Shen","year":"2014","journal-title":"Appl. Opt."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1364\/JOSAA.24.000942","article-title":"Selecting algorithms, sensors, and linear bases for optimum spectral recovery of skylight","volume":"24","author":"Valero","year":"2007","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"013201","DOI":"10.1117\/1.2159480","article-title":"Optimization of Spectral Sensitivities with Gaussian Distribution Functions for a Color Image Acquisition Device in the Presence of Noise","volume":"45","author":"Shimano","year":"2006","journal-title":"Opt. Eng."},{"key":"ref_21","unstructured":"Monno, Y., Kitao, T., Tanaka, M., and Okutomi, M. (October, January 30). Optimal Spectral Sensitivity Functions for a Single-Camera One-Shot Multispectral Imaging System. Proceedings of the 19th IEEE International Conference on Image Processing, Orlando, FL, USA."},{"key":"ref_22","first-page":"1530","article-title":"Fourier spectral filter array for optimal multispectral imaging","volume":"25","author":"Jia","year":"2016","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"21626","DOI":"10.3390\/s141121626","article-title":"Multispectral Filter Arrays: Recent Advances and Practical Implementation","volume":"14","author":"Lapray","year":"2014","journal-title":"Sensors"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Li, Y., Wang, C., Zhao, J., and Yuan, Q. (2018). Efficient spectral reconstruction using a trichromatic camera via sample optimization. Vis. Comput., 1\u201311.","DOI":"10.1007\/s00371-017-1469-3"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Shinoda, K., Hamasaki, T., Hasegawa, M., Kato, S., and Ortega, A. (2013, January 8\u201311). Quality metric for filter arrangement in a multispectral filter array. Proceedings of the Picture Coding Symposium (PCS), San Jose, CA, USA.","DOI":"10.1109\/PCS.2013.6737705"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3550","DOI":"10.1109\/TIP.2006.877476","article-title":"Binary tree-based generic demosaicking algorithm for multispectral filter arrays","volume":"15","author":"Miao","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1109\/TIP.2016.2634120","article-title":"Adaptive multispectral demosaicking based on frequency-domain analysis of spectral correlation","volume":"26","author":"Jaiswal","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"982","DOI":"10.1109\/TCI.2017.2691553","article-title":"Multispectral demosaicing using pseudo-panchromatic image","volume":"3","author":"Mihoubi","year":"2017","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1111\/cgf.12717","article-title":"Practical Low-Cost Recovery of Spectral Power Distributions","volume":"35","author":"Kunkel","year":"2016","journal-title":"Comput. Graph. Forum"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3211","DOI":"10.1364\/JOSAA.24.003211","article-title":"Recovery of spectral reflectances of objects being imaged by multispectral cameras","volume":"24","author":"Shimano","year":"2007","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Chakrabarti, A., and Zickler, T. (2011, January 20\u201325). Statistics of Real-World Hyperspectral Images. Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Colorado Springs, CO, USA.","DOI":"10.1109\/CVPR.2011.5995660"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1364\/JOSAA.6.000318","article-title":"Characteristic spectra of Munsell colors","volume":"6","author":"Parkkinen","year":"1989","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1364\/JOSA.67.000779","article-title":"Counting metameric object-color stimuli using frequency-limited spectral reflectance functions","volume":"67","author":"Stiles","year":"1977","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_34","unstructured":"Goldstein, E.B., and Brockmole, J. (2016). Sensation and Perception, Cengage Learning."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1088\/0954-898X_14_3_302","article-title":"Statistics of Natural Image Categories","volume":"14","author":"Torralba","year":"2003","journal-title":"Netw. Comput. Neural Syst."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Hyvarinen, A., Hurri, J., and Hoyer, P.O. (2009). Natural Image Statistics, Springer.","DOI":"10.1007\/978-1-84882-491-1"},{"key":"ref_37","unstructured":"Pouli, F., Cunningham, D.W., and Reinhard, E. (2018, April 10). Image Statistics and their Applications in Computer Graphics. Available online: https:\/\/s3.amazonaws.com\/academia.edu.documents\/44894836\/Image_Statistics_and_their_Applications_20160419-16347-1hlzcca.pdf?AWSAccessKeyId=AKIAIWOWYYGZ2Y53UL3A&Expires=1523335119&Signature=52fMxbpkPhRptNNF0p6pfPLE58A%3D&response-content-disposition=inline%3B%20filename%3DImage_statistics_and_their_applications.pdf."},{"key":"ref_38","unstructured":"(2016, February 01). Spectral Database of CAVE Laboratory, Columbia University. Available online: http:\/\/www.cs.columbia.edu\/CAVE\/databases\/multispectral\/."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1109\/TCE.2005.1561853","article-title":"Color Filter Arrays: Design and Performance Analysis","volume":"51","author":"Lukac","year":"2005","journal-title":"IEEE Trans. Consum. Electron."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2780","DOI":"10.1109\/TIP.2006.877315","article-title":"The Design and Evaluation of a Generic Method for Generating Mosaicked Multispectral Filter Arrays","volume":"15","author":"Miao","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Takamatsu, J., Matsushita, Y., Ogasawara, T., and Ikeuchi, K. (2010, January 13\u201318). Estimating Demosaicing Algorithms using Image Noise Variance. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA.","DOI":"10.1109\/CVPR.2010.5540200"},{"key":"ref_42","first-page":"1848","article-title":"Recovery of Spectral Reflectances of Objects Being Imaged Without Prior Knowledge","volume":"15","author":"Shimano","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S1076-5670(10)62005-8","article-title":"Comparison of Color Demosaicing Methods","volume":"162","author":"Losson","year":"2010","journal-title":"Adv. Imag. Electron. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"68221J","DOI":"10.1117\/12.766768","article-title":"Image demosaicing: A systematic survey","volume":"Volume 6822","author":"Li","year":"2008","journal-title":"Visual Communications and Image Processing 2008"},{"key":"ref_45","unstructured":"Kennedy, J. (December, January 27). Particle Swarm Optimization. Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia."},{"key":"ref_46","unstructured":"Kennedy, J., and Eberhart, R.C. (1997, January 12\u201315). A discrete binary version of the particle swarm algorithm. Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, Orlando, FL, USA."},{"key":"ref_47","unstructured":"(2016, February 01). Spectral Database of Spectral Color Research Group, University of Eastern Finland. Available online: https:\/\/www.uef.fi\/spectral\/spectral-database."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Monno, Y., Tanaka, M., and Okutomi, M. (2011, January 11\u201314). Multispectral demosaicking using adaptive kernel upsampling. Proceedings of the 18th IEEE International Conference on Image Processing, Brussels, Belgium.","DOI":"10.1109\/ICIP.2011.6116337"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Monno, Y., Kiku, D., Kikuchi, S., Tanaka, M., and Okutomi, M. (2014, January 27\u201330). Multispectral demosaicking with novel guide image generation and residual interpolation. Proceedings of the IEEE International Conference on Image Processing (ICIP), Paris, France.","DOI":"10.1109\/ICIP.2014.7025129"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TSP.2008.2007095","article-title":"Sensor Selection via Convex Optimization","volume":"57","author":"Joshi","year":"2009","journal-title":"IEEE Trans. Signal Process"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1172\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:00:25Z","timestamp":1760194825000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/4\/1172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,12]]},"references-count":50,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["s18041172"],"URL":"https:\/\/doi.org\/10.3390\/s18041172","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,12]]}}}