{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:04Z","timestamp":1760242744500,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2016,5,21]],"date-time":"2016-05-21T00:00:00Z","timestamp":1463788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The nonuniformity of the spatial response to surface radiation is a fundamental characteristic of all airborne and spaceborne sensors that inevitably introduces uncertainty into the estimation of object proportions by the spectral unmixing of mixed pixels. Simulated data of the surface radiation distribution and a TM (thematic mapper) response matrix were developed and utilized to imitate the generation of mixed pixels and the extraction of the object proportion via a Monte Carlo simulation, and then, the nonuniformity effect of a sensor\u2019s PSF (point spread function) was explored. The following conclusions were drawn: (1) given a nonuniform spatial response of a sensor to a surface scene with a constant object proportion and various object distribution patterns, the mixed pixel DN (digital number) of a remotely-sensed image becomes a random variable, which causes a PSF nonuniform effect on the object proportion extraction; (2) for the estimated object proportion, the corresponding true object proportion appears with a random variation; its upper and lower bounds take on an asymmetrical spindle shape; and models of these bound curves at any probability level were established; (3) there exists a negative linear relationship between the bias of the spectral unmixing and the estimated proportion; the bias is zero at an estimated proportion of 50%, and when the estimated proportions are approximately 100% and 0%, the object proportion is overestimated by 0.78% and underestimated by 0.78%, respectively; (4) the relationship between the standard deviation of the spectral unmixing and the estimated proportion follows a symmetrical polynomial function opening downward; the standard deviation reaches a maximum of 4.4% at the estimated proportion of 50%, and when the estimated proportion is approximately 100% or 0%, the standard deviation is a minimum, 1.05%. The above findings contribute to a comprehensive understanding of the PSF nonuniformity effect, have the potential to compensate for the bias of proportion estimation and present its confidence interval at any probability level.<\/jats:p>","DOI":"10.3390\/rs8050437","type":"journal-article","created":{"date-parts":[[2016,5,24]],"date-time":"2016-05-24T09:05:05Z","timestamp":1464080705000},"page":"437","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Simulation of the Impact of a Sensor\u2019s PSF on Mixed Pixel Decomposition: 1. Nonuniformity Effect"],"prefix":"10.3390","volume":"8","author":[{"given":"Chao","family":"Xu","sequence":"first","affiliation":[{"name":"Northeast Institute of Geography and Agroecology, Chinese Academy of Sciences, Changchun 130102, China"},{"name":"College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Zhaoli","family":"Liu","sequence":"additional","affiliation":[{"name":"Northeast Institute of Geography and Agroecology, Chinese Academy of Sciences, Changchun 130102, China"}]},{"given":"Guanglei","family":"Hou","sequence":"additional","affiliation":[{"name":"Northeast Institute of Geography and Agroecology, Chinese Academy of Sciences, Changchun 130102, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0034-4257(86)90018-0","article-title":"On the nature of models in remote sensing","volume":"20","author":"Strahler","year":"1986","journal-title":"Remote Sens. Environ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1080\/014311697219015","article-title":"The pixel: A snare and a delusion","volume":"18","author":"Fisher","year":"1997","journal-title":"Int. J. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1080\/014311698214848","article-title":"Review article Synergy in remote sensing-what\u2019s in a pixel?","volume":"19","author":"Cracknell","year":"1998","journal-title":"Int. J. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5307","DOI":"10.1080\/01431161.2012.661095","article-title":"Spectral unmixing","volume":"33","author":"Quintano","year":"2012","journal-title":"Int. J. Remote Sens."},{"key":"ref_5","unstructured":"Duran, O., and Petrou, M. (2004). Mixed Pixel Classification in Remote Sensing\u2014Literature Survey, School of Electronics and Physical Sciences, University of Surrey."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Manslow, J.F., and Nixon, M.S. (2002). On the Ambiguity Induced by a Remote Sensor\u2019s PSF, Wiley.","DOI":"10.1002\/0470035269.ch4"},{"key":"ref_7","unstructured":"McGillem, C., Anuta, P., Malaret, E., and Yu, K. (1983). Estimation of a Remote Sensing System Point-Spread Function from Measured Imagery, LARS Technical Reports."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"864","DOI":"10.1109\/TGRS.1985.289472","article-title":"The Landsat sensors\u2019 spatial responses","volume":"6","author":"Markham","year":"1985","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1080\/014311600210641","article-title":"Beware of per-pixel characterization of land cover","volume":"21","author":"Townshend","year":"2000","journal-title":"Int. J. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1109\/TGRS.2006.886182","article-title":"Spatial PSF Nonuniformity Effects in Airborne Pushbroom Imaging Spectrometry Data","volume":"45","author":"Nieke","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1109\/36.239899","article-title":"Improved estimation of fraction images using partial image restoration","volume":"31","author":"Wu","year":"1993","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/S0034-4257(01)00298-X","article-title":"Impact of sensor\u2019s point spread function on land cover characterization: Assessment and deconvolution","volume":"80","author":"Huang","year":"2002","journal-title":"Remote Sens. Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2137","DOI":"10.1080\/01431160701395310","article-title":"Estimation of sensor point spread function by spatial subpixel analysis","volume":"29","author":"Kaiser","year":"2008","journal-title":"Int. J. Remote Sens."},{"key":"ref_14","unstructured":"Turner, M.G., Gardner, R.H., and O\u2019neill, R.V. (2001). Landscape Ecology in Theory and Practice, Springer."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4567","DOI":"10.1080\/01431160802609726","article-title":"Impact of point spread function of MSG-SEVIRI on active fire detection","volume":"30","author":"Calle","year":"2009","journal-title":"Int. J. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1117\/12.7976678","article-title":"Measurement of the Landsat Thematic Mapper modulation transfer function using an array of point sources","volume":"27","author":"Rauchmiller","year":"1988","journal-title":"Opt. Eng."},{"key":"ref_17","unstructured":"Cliff, A.D., and Ord, J.K. (1981). Spatial Processes: Models and Applications, Pion Press."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Pont, W.F., Schwartz, C.R., Crist, E.P., and Kenton, A.C. (1995, January 17\u201321). Sensor point spread function effects on the statistics of multispectral target signatures. Proceedings of the SPIE\u2019s 1995 Symposium on OE\/Aerospace Sensing and Dual Use Photonics, International Society for Optics and Photonics, Orlando, FL, USA.","DOI":"10.1117\/12.211296"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3142","DOI":"10.1364\/AO.21.003142","article-title":"Image sampling, reconstruction, and the effect of sample-scene phasing","volume":"21","author":"Park","year":"1982","journal-title":"Appl. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"923","DOI":"10.14358\/PERS.73.8.923","article-title":"Variability in soft classification prediction and its implications for sub-pixel scale change detection and super resolution mapping","volume":"8","author":"Foody","year":"2007","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1016\/j.rse.2011.03.003","article-title":"Endmember variability in spectral mixture analysis: A review","volume":"115","author":"Somers","year":"2011","journal-title":"Remote Sens. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/8\/5\/437\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:24:18Z","timestamp":1760210658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/8\/5\/437"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,21]]},"references-count":21,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2016,5]]}},"alternative-id":["rs8050437"],"URL":"https:\/\/doi.org\/10.3390\/rs8050437","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2016,5,21]]}}}