{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T18:10:21Z","timestamp":1774030221719,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,5,5]],"date-time":"2017-05-05T00:00:00Z","timestamp":1493942400000},"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":["41401517"],"award-info":[{"award-number":["41401517"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Planning Project of Zhejiang Province, China","award":["2015C33223"],"award-info":[{"award-number":["2015C33223"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The component substitution (CS) pansharpening methods have been developed for almost three decades and have become better understood recently by generalizing them into one framework. However, few studies focus on the statistical assumptions implicit in the CS methods. This paper reveals their implicit statistical assumptions from a Bayesian data fusion framework and suggests best practices for histogram matching of the panchromatic image to the intensity image, a weighted summation of the multispectral images, to better satisfy these assumptions. The purpose of histogram matching was found to make the difference between the high-resolution panchromatic and intensity images as small as possible, as one implicit assumption claims their negligible difference. The statistical relationship between the high-resolution panchromatic and intensity images and the relationship between their corresponding low-resolution images are the same, as long as the low resolution panchromatic image is derived by considering the modulation transfer functions of the multispectral sensors. Hence, the histogram-matching equation should be derived from the low-resolution panchromatic and intensity images, but not derived from the high-resolution panchromatic and expanded low-resolution intensity images. Experiments using three example CS methods, each using the two different histogram-matching equations, was conducted on the four-band QuickBird and eight-band WorldView-2 top-of-atmosphere reflectance data. The results verified the best practices and showed that the histogram-matching equation derived from the high-resolution panchromatic and expanded low-resolution intensity images provides more-blurred histogram-matched panchromatic image and, hence less-sharpened pansharpened images than that derived from the low-resolution image pair. The usefulness of the assumptions revealed in this study for method developers is discussed. For example, the CS methods can be improved by satisfying the assumptions better, e.g., classifying the images into homogenous areas before pansharpening, and by changing the assumptions to be more general to address their deficiencies.<\/jats:p>","DOI":"10.3390\/rs9050443","type":"journal-article","created":{"date-parts":[[2017,5,5]],"date-time":"2017-05-05T10:31:08Z","timestamp":1493980268000},"page":"443","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Revealing Implicit Assumptions of the Component Substitution Pansharpening Methods"],"prefix":"10.3390","volume":"9","author":[{"given":"Bin","family":"Xie","sequence":"first","affiliation":[{"name":"Institute of Remote Sensing and Earth Sciences, Hangzhou Normal University, Hangzhou 311121, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4470-3616","authenticated-orcid":false,"given":"Hankui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Geospatial Sciences Center of Excellence, South Dakota State University, Brookings, SD 57007, USA"}]},{"given":"Bo","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Geography and Resource Management, The Chinese University of Hong Kong, Shatin, Hong Kong, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"747","DOI":"10.14358\/PERS.82.10.747","article-title":"Understanding the quality of pansharpening\u2014A lab study","volume":"82","author":"Zhang","year":"2016","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/MGRS.2015.2434351","article-title":"Fusing Landsat and MODIS data for vegetation monitoring","volume":"3","author":"Gao","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Garzelli, A. (2016). A review of image fusion algorithms based on the super-resolution paradigm. Remote Sens., 8.","DOI":"10.3390\/rs8100797"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1109\/36.763269","article-title":"Some terms of reference in data fusion","volume":"37","author":"Wald","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3008","DOI":"10.1109\/JSTARS.2015.2440092","article-title":"Hyper-sharpening: A first approach on SIM-GA data","volume":"8","author":"Selva","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/MGRS.2015.2440094","article-title":"Hyperspectral pansharpening: A review","volume":"3","author":"Loncan","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1109\/TGRS.2007.912448","article-title":"Synthesis of multispectral images to high spatial resolution: A critical review of fusion methods based on remote sensing physics","volume":"46","author":"Thomas","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1109\/TGRS.2014.2361734","article-title":"A critical comparison among pansharpening algorithms","volume":"53","author":"Vivone","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2016.2561021","article-title":"Data fusion and remote sensing: An ever-growing relationship","volume":"4","author":"Schmitt","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Alparone, L., Aiazzi, B., Baronti, S., and Garzelli, A. (2015). Remote Sensing Image Fusion, CRC Press.","DOI":"10.1201\/b18189"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1109\/TGRS.2010.2067219","article-title":"A new pan-sharpening method using a compressed sensing technique","volume":"49","author":"Li","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2664","DOI":"10.1109\/TGRS.2015.2504261","article-title":"Exploiting Joint Sparsity for Pansharpening: The J-SparseFI Algorithm","volume":"54","author":"Zhu","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5425","DOI":"10.1109\/TGRS.2016.2564639","article-title":"Noise Removal from Hyperspectral Image with Joint Spectral\u2014Spatial Distributed Sparse Representation","volume":"54","author":"Li","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1142\/S0218001409007260","article-title":"Facial biometrics using nontensor product wavelet and 2D discriminant techniques","volume":"23","author":"Zhang","year":"2009","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3271","DOI":"10.1109\/TIP.2010.2055570","article-title":"A blind watermarking scheme using new nontensor product wavelet filter banks","volume":"19","author":"You","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.inffus.2004.06.009","article-title":"An IHS and wavelet integrated approach to improve pan-sharpening visual quality of natural colour IKONOS and QuickBird images","volume":"6","author":"Zhang","year":"2005","journal-title":"Inf. Fusion"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"591","DOI":"10.14358\/PERS.72.5.591","article-title":"MTF-tailored multiscale fusion of high-resolution MS and pan imagery","volume":"72","author":"Aiazzi","year":"2006","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1109\/JSTARS.2016.2546061","article-title":"MTF-Based Deblurring Using a Wiener Filter for CS and MRA Pansharpening Methods","volume":"9","author":"Palsson","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3230","DOI":"10.1109\/TGRS.2007.901007","article-title":"Improving component substitution pansharpening through multivariate regression of MS plus Pan data","volume":"45","author":"Aiazzi","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S1566-2535(01)00036-7","article-title":"A new look at IHS-like image fusion methods","volume":"2","author":"Tu","year":"2001","journal-title":"Inf. Fusion"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.cageo.2006.06.008","article-title":"A general framework for component substitution image fusion: An implementation using the fast image fusion method","volume":"33","author":"Dou","year":"2007","journal-title":"Comput. Geosci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7380","DOI":"10.1109\/TGRS.2014.2311815","article-title":"High-fidelity component substitution pansharpening by the fitting of substitution data","volume":"52","author":"Xu","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jel\u00e9nek, J., Kopa\u010dkov\u00e1, V., Kouck\u00e1, L., and Mi\u0161urec, J. (2016). Testing a modified PCA-based sharpening approach for image fusion. Remote Sens., 8.","DOI":"10.3390\/rs8100794"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1109\/TGRS.2016.2606324","article-title":"Sensitivity of pansharpening methods to temporal and instrumental changes between multispectral and panchromatic data sets","volume":"55","author":"Aiazzi","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6828","DOI":"10.3390\/rs70606828","article-title":"A new look at image fusion methods from a Bayesian perspective","volume":"7","author":"Zhang","year":"2015","journal-title":"Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1847","DOI":"10.1109\/TGRS.2008.917131","article-title":"Bayesian data fusion for adaptable image pansharpening","volume":"46","author":"Fasbender","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3834","DOI":"10.1109\/TGRS.2009.2017737","article-title":"Noise-resistant wavelet-based Bayesian fusion of multispectral and hyperspectral images","volume":"47","author":"Zhang","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1924","DOI":"10.1109\/TGRS.2004.830644","article-title":"Application of the stochastic mixing model to hyperspectral resolution enhancement","volume":"42","author":"Eismann","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1109\/TIP.2004.829779","article-title":"MAP estimation for hyperspectral image resolution enhancement using an auxiliary sensor","volume":"13","author":"Hardie","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1080\/19479832.2016.1180326","article-title":"Model-based view at multi-resolution image fusion methods and quality assessment measures","volume":"7","author":"Palubinskas","year":"2016","journal-title":"Int. J. Image Data Fusion"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"7135","DOI":"10.1109\/TGRS.2016.2596290","article-title":"An Integrated Framework for the Spatio\u2013Temporal\u2013Spectral Fusion of Remote Sensing Images","volume":"54","author":"Shen","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","first-page":"1","article-title":"An Adaptive Weighted Tensor Completion Method for the Recovery of Remote Sensing Images with Missing Data","volume":"PP","author":"Ng","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2563","DOI":"10.1109\/TGRS.2015.2503045","article-title":"Spatial methods for multispectral pansharpening: Multiresolution analysis demystified","volume":"54","author":"Alparone","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/0034-4257(87)90015-0","article-title":"The factor of scale in remote sensing","volume":"21","author":"Woodcock","year":"1987","journal-title":"Remote Sens. Environ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"193","DOI":"10.14358\/PERS.74.2.193","article-title":"Multispectral and panchromatic data fusion assessment without reference","volume":"74","author":"Alparone","year":"2008","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_36","unstructured":"Updike, T., and Comp, C. (2010). Radiometric Use of WorldView-2 Imagery, Digital Globe."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhang, H.K., and Roy, D.P. (2016). Computationally inexpensive Landsat 8 operational land imager (OLI) pansharpening. Remote Sens., 8.","DOI":"10.3390\/rs8030180"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1109\/TGRS.2015.2476513","article-title":"Quantitative quality evaluation of pansharpened imagery: Consistency versus synthesis","volume":"54","author":"Palsson","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"6539","DOI":"10.3390\/rs5126539","article-title":"Spatial quality assessment of pan-sharpened high resolution satellite imagery based on an automatically estimated edge based metric","volume":"5","author":"Javan","year":"2013","journal-title":"Remote Sens."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1109\/LGRS.2004.836784","article-title":"A global quality measurement of pan-sharpened multispectral imagery","volume":"1","author":"Alparone","year":"2004","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1109\/LGRS.2009.2022650","article-title":"Hypercomplex quality assessment of multi\/hyperspectral images","volume":"6","author":"Garzelli","year":"2009","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1109\/TGRS.2002.800241","article-title":"Bidirectional NDVI and atmospherically resistant BRDF inversion for vegetation canopy","volume":"40","author":"Gao","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1109\/TGRS.2014.2351754","article-title":"Pansharpening based on semiblind deconvolution","volume":"53","author":"Vivone","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/LGRS.2014.2324817","article-title":"Pansharpening using regression of classified MS and pan images to reduce color distortion","volume":"12","author":"Xu","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1109\/LGRS.2008.2012003","article-title":"A comparison between global and context-adaptive pansharpening of multispectral images","volume":"6","author":"Aiazzi","year":"2009","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1109\/LGRS.2013.2265915","article-title":"A robust image fusion method based on local spectral and spatial correlation","volume":"11","author":"Wang","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2096","DOI":"10.1109\/TGRS.2014.2354471","article-title":"Pansharpening of multispectral images based on nonlocal parameter optimization","volume":"53","author":"Garzelli","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1109\/TGRS.2016.2614367","article-title":"Context-adaptive pansharpening based on image segmentation","volume":"55","author":"Restaino","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Li, H., Jing, L., Wang, L., and Cheng, Q. (2016). Improved pansharpening with un-mixing of mixed MS sub-pixels near boundaries between vegetation and non-vegetation objects. Remote Sens., 8.","DOI":"10.3390\/rs8020083"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"6039","DOI":"10.3390\/rs6076039","article-title":"A parallel computing paradigm for pan-sharpening algorithms of remotely sensed images on a multi-core computer","volume":"6","author":"Yang","year":"2014","journal-title":"Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/5\/443\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:34:48Z","timestamp":1760207688000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/5\/443"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,5]]},"references-count":50,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2017,5]]}},"alternative-id":["rs9050443"],"URL":"https:\/\/doi.org\/10.3390\/rs9050443","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,5]]}}}