{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T20:18:40Z","timestamp":1774988320946,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2017,12,13]],"date-time":"2017-12-13T00:00:00Z","timestamp":1513123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Chinese University of Hong Kong","award":["444411"],"award-info":[{"award-number":["444411"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Remote sensing provides rich sources of data for the monitoring of land surface dynamics. However, single-sensor systems are constrained from providing spatially high-resolution images with high revisit frequency due to the inherent sensor design limitation. To obtain images high in both spatial and temporal resolutions, a number of image fusion algorithms, such as spatial and temporal adaptive reflectance fusion model (STARFM) and enhanced STARFM (ESTARFM), have been recently developed. To capitalize on information available in a fusion process, we propose a Bayesian data fusion approach that incorporates the temporal correlation information in the image time series and casts the fusion problem as an estimation problem in which the fused image is obtained by the Maximum A Posterior (MAP) estimator. The proposed approach provides a formal framework for the fusion of remotely sensed images with a rigorous statistical basis; it imposes no requirements on the number of input image pairs; and it is suitable for heterogeneous landscapes. The approach is empirically tested with both simulated and real-life acquired Landsat and Moderate Resolution Imaging Spectroradiometer (MODIS) images. Experimental results demonstrate that the proposed method outperforms STARFM and ESTARFM, especially for heterogeneous landscapes. It produces surface reflectances highly correlated with those of the reference Landsat images. It gives spatio-temporal fusion of remotely sensed images a solid theoretical and empirical foundation that may be extended to solve more complicated image fusion problems.<\/jats:p>","DOI":"10.3390\/rs9121310","type":"journal-article","created":{"date-parts":[[2017,12,14]],"date-time":"2017-12-14T04:30:55Z","timestamp":1513225855000},"page":"1310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":125,"title":["A Bayesian Data Fusion Approach to Spatio-Temporal Fusion of Remotely Sensed Images"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2999-1181","authenticated-orcid":false,"given":"Jie","family":"Xue","sequence":"first","affiliation":[{"name":"Department of Geography and Resource Management, The Chinese University of Hong Kong, Hong Kong, China"}]},{"given":"Yee","family":"Leung","sequence":"additional","affiliation":[{"name":"Department of Geography and Resource Management, The Chinese University of Hong Kong, Hong Kong, China"},{"name":"Institute of Future Cities, The Chinese University of Hong Kong, Hong Kong, China"},{"name":"Big Data Decision Analytic Center, The Chinese University of Hong Kong, Hong Kong, China"}]},{"given":"Tung","family":"Fung","sequence":"additional","affiliation":[{"name":"Department of Geography and Resource Management, The Chinese University of Hong Kong, Hong Kong, China"},{"name":"Institute of Future Cities, The Chinese University of Hong Kong, Hong Kong, China"},{"name":"Institute of Environment, Energy and Sustainability, The Chinese University of Hong Kong, Hong Kong, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1080\/014311698215748","article-title":"Review article multisensor image fusion in remote sensing: Concepts, methods and applications","volume":"19","author":"Pohl","year":"1998","journal-title":"Int. J. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1016\/j.rse.2007.08.011","article-title":"The availability of cloud-free landsat etm+ data over the conterminous united states and globally","volume":"112","author":"Ju","year":"2008","journal-title":"Remote Sens. Environ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.inffus.2011.08.001","article-title":"Multisensor data fusion: A review of the state-of-the-art","volume":"14","author":"Khaleghi","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1798","DOI":"10.3390\/rs70201798","article-title":"Comparison of spatiotemporal fusion models: A review","volume":"7","author":"Chen","year":"2015","journal-title":"Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2207","DOI":"10.1109\/TGRS.2006.872081","article-title":"On the blending of the landsat and modis surface reflectance: Predicting daily landsat surface reflectance","volume":"44","author":"Gao","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4367","DOI":"10.1080\/01431161.2013.777488","article-title":"A spatial and temporal reflectance fusion model considering sensor observation differences","volume":"34","author":"Shen","year":"2013","journal-title":"Int. J. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3112","DOI":"10.1016\/j.rse.2008.03.009","article-title":"Multi-temporal modis\u2013landsat data fusion for relative radiometric normalization, gap filling, and prediction of landsat data","volume":"112","author":"Roy","year":"2008","journal-title":"Remote Sens. Environ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.rse.2013.02.007","article-title":"Assessing the accuracy of blending landsat\u2013modis surface reflectances in two landscapes with contrasting spatial and temporal dynamics: A framework for algorithm selection","volume":"133","author":"Emelyanova","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2610","DOI":"10.1016\/j.rse.2010.05.032","article-title":"An enhanced spatial and temporal adaptive reflectance fusion model for complex heterogeneous regions","volume":"114","author":"Zhu","year":"2010","journal-title":"Remote Sens. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6346","DOI":"10.3390\/rs5126346","article-title":"An improved image fusion approach based on enhanced spatial and temporal the adaptive reflectance fusion model","volume":"5","author":"Fu","year":"2013","journal-title":"Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1988","DOI":"10.1016\/j.rse.2009.05.011","article-title":"Generation of dense time series synthetic landsat data through data blending with modis using a spatial and temporal adaptive reflectance fusion model","volume":"113","author":"Hilker","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.rse.2011.10.014","article-title":"Evaluation of landsat and modis data fusion products for analysis of dryland forest phenology","volume":"117","author":"Walker","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_13","first-page":"43","article-title":"Evaluation of long-term ndvi time series derived from landsat data through blending with modis data","volume":"25","author":"Singh","year":"2012","journal-title":"Atm\u00f3sfera"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2499","DOI":"10.1016\/j.rse.2011.05.010","article-title":"Downscaling real-time vegetation dynamics by fusing multi-temporal modis and landsat ndvi in topographically complex terrain","volume":"115","author":"Hwang","year":"2011","journal-title":"Remote Sens. Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.rse.2011.12.016","article-title":"Mapping leaf area index using spatial, spectral, and temporal information from multiple sensors","volume":"119","author":"Gray","year":"2012","journal-title":"Remote Sens. Environ."},{"key":"ref_16","first-page":"59","article-title":"Generation and evaluation of gross primary productivity using landsat data through blending with modis data","volume":"13","author":"Singh","year":"2011","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1856","DOI":"10.3390\/rs4061856","article-title":"Preparing landsat image time series (lits) for monitoring changes in vegetation phenology in queensland, australia","volume":"4","author":"Bhandari","year":"2012","journal-title":"Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1016\/j.rse.2009.03.007","article-title":"A new data fusion model for high spatial- and temporal-resolution mapping of forest disturbance based on landsat and modis","volume":"113","author":"Hilker","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.rse.2013.04.002","article-title":"Toward near real-time monitoring of forest disturbance by fusion of modis and landsat data","volume":"135","author":"Xin","year":"2013","journal-title":"Remote Sens. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1016\/j.foreco.2010.12.020","article-title":"Characterizing stand-replacing disturbance in western alberta grizzly bear habitat, using a satellite-derived high temporal and spatial resolution change sequence","volume":"261","author":"Gaulton","year":"2011","journal-title":"For. Ecol. Manag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1080\/01431161.2016.1271471","article-title":"Improving spatiotemporal reflectance fusion using image inpainting and steering kernel regression techniques","volume":"38","author":"Wu","year":"2017","journal-title":"Int. J. Remote Sens."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"096095","DOI":"10.1117\/1.JRS.9.096095","article-title":"Spatiotemporal image-fusion model for enhancing the temporal resolution of landsat-8 surface reflectance images using modis images","volume":"9","author":"Hazaymeh","year":"2015","journal-title":"J. Appl. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3707","DOI":"10.1109\/TGRS.2012.2186638","article-title":"Spatiotemporal reflectance fusion via sparse representation","volume":"50","author":"Huang","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wei, J., Wang, L., Liu, P., and Song, W. (2016). Spatiotemporal fusion of remote sensing images with structural sparsity and semi-coupled dictionary learning. Remote Sens., 9.","DOI":"10.3390\/rs9010021"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"6791","DOI":"10.1109\/TGRS.2015.2448100","article-title":"An error-bound-regularized sparse coding for spatiotemporal reflectance fusion","volume":"53","author":"Wu","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.rse.2015.11.016","article-title":"A flexible spatiotemporal method for fusing satellite images with different resolutions","volume":"172","author":"Zhu","year":"2016","journal-title":"Remote Sens. Environ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1874","DOI":"10.1016\/j.rse.2009.04.011","article-title":"Downscaling time series of meris full resolution data to monitor vegetation seasonal dynamics","volume":"113","author":"Kaiser","year":"2009","journal-title":"Remote Sens. Environ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.inffus.2015.12.005","article-title":"An improved high spatial and temporal data fusion approach for combining landsat and modis data to generate daily synthetic landsat imagery","volume":"31","author":"Wu","year":"2016","journal-title":"Inf. Fusion"},{"key":"ref_30","first-page":"132","article-title":"Multitemporal fusion of Landsat\/TM and ENVISAT\/MERIS for crop monitoring","volume":"23","author":"Alonso","year":"2013","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"14000","DOI":"10.3390\/rs71014000","article-title":"A spectral unmixing model for the integration of multi-sensor imagery: A tool to generate consistent time series data","volume":"7","author":"Doxani","year":"2015","journal-title":"Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5346","DOI":"10.3390\/rs5105346","article-title":"An enhanced spatial and temporal data fusion model for fusing landsat and modis surface reflectance to generate high temporal landsat-like data","volume":"5","author":"Zhang","year":"2013","journal-title":"Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.rse.2014.09.012","article-title":"A comparison of starfm and an unmixing-based algorithm for landsat and modis data fusion","volume":"156","author":"Gevaert","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Xie, D., Zhang, J., Zhu, X., Pan, Y., Liu, H., Yuan, Z., and Yun, Y. (2016). An improved starfm with help of an unmixing-based method to generate high spatial and temporal resolution remote sensing data in complex heterogeneous regions. Sensors, 16.","DOI":"10.3390\/s16020207"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/LGRS.2015.2402644","article-title":"Spatial and temporal image fusion via regularized spatial unmixing","volume":"12","author":"Xu","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Milisavljevic, N. (2009). Updating scarce high resolution images with time series of coarser images: A bayesian data fusion solution. Sensor and Data Fusion, InTech.","DOI":"10.5772\/102"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Fasbender, D., Obsomer, V., Radoux, J., Bogaert, P., and Defourny, P. (2007, January 18\u201320). Bayesian Data Fusion: Spatial and temporal applications. Proceedings of the 2007 International Workshop on the Analysis of Multi-temporal Remote Sensing Images, Leuven, Belgium.","DOI":"10.1109\/MULTITEMP.2007.4293058"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1080\/2150704X.2013.769283","article-title":"Unified fusion of remote-sensing imagery: Generating simultaneously high-resolution synthetic spatial\u2013temporal\u2013spectral earth observations","volume":"4","author":"Huang","year":"2013","journal-title":"Remote Sens. Lett."},{"key":"ref_39","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_40","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1109\/TGRS.2004.837324","article-title":"Hyperspectral resolution enhancement using high-resolution multispectral imagery with arbitrary response functions","volume":"43","author":"Eismann","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_41","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_42","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1080\/19479832.2010.551522","article-title":"Wavelet-based bayesian fusion of multispectral and hyperspectral images using gaussian scale mixture model","volume":"3","author":"Zhang","year":"2012","journal-title":"Int. J. Image Data Fusion"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1109\/TGRS.2009.2030323","article-title":"Map estimation for multiresolution fusion in remotely sensed images using an igmrf prior model","volume":"48","author":"Joshi","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1109\/JSTSP.2015.2407855","article-title":"Bayesian fusion of multi-band images","volume":"9","author":"Wei","year":"2015","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.patrec.2005.08.010","article-title":"Resolution enhancement via probabilistic deconvolution of multiple degraded images","volume":"27","author":"Flusser","year":"2006","journal-title":"Pattern Recognit. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Akhtar, N., Shafait, F., and Mian, A. (2015, January 7\u201312). Bayesian sparse representation for hyperspectral image super resolution. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA.","DOI":"10.1109\/CVPR.2015.7298986"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2082","DOI":"10.1016\/j.sigpro.2012.01.020","article-title":"A super-resolution reconstruction algorithm for hyperspectral images","volume":"92","author":"Zhang","year":"2012","journal-title":"Signal Process."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.dsp.2012.10.002","article-title":"Bayesian combination of sparse and non-sparse priors in image super resolution","volume":"23","author":"Villena","year":"2013","journal-title":"Digit. Signal Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1364","DOI":"10.1117\/1.1384886","article-title":"Bayesian sensor image fusion using local linear generative models","volume":"40","author":"Sharma","year":"2001","journal-title":"Opt. Eng."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1117\/1.601623","article-title":"High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system","volume":"37","author":"Hardie","year":"1998","journal-title":"Opt. Eng."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"6886","DOI":"10.3390\/rs70606886","article-title":"Characterizing the pixel footprint of satellite albedo products derived from modis reflectance in the Heihe River Basin, China","volume":"7","author":"Peng","year":"2015","journal-title":"Remote Sens."},{"key":"ref_52","unstructured":"Kay, S.M. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall, Inc."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1109\/LGRS.2013.2284282","article-title":"An improved adaptive intensity\u2013hue\u2013saturation method for the fusion of remote sensing images","volume":"11","author":"Leung","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2300","DOI":"10.1109\/TGRS.2002.803623","article-title":"Context-driven fusion of high spatial and spectral resolution images based on oversampled multiresolution analysis","volume":"40","author":"Aiazzi","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"063507","DOI":"10.1117\/1.JRS.6.063507","article-title":"Use of modis and landsat time series data to generate high-resolution temporal synthetic landsat data using a spatial and temporal reflectance fusion model","volume":"6","author":"Wu","year":"2012","journal-title":"J. Appl. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/12\/1310\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:53:54Z","timestamp":1760208834000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/12\/1310"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,13]]},"references-count":55,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["rs9121310"],"URL":"https:\/\/doi.org\/10.3390\/rs9121310","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,13]]}}}