多端元光谱混合分析综述

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基于多源光谱特征融合技术的花生油掺伪检测

基于多源光谱特征融合技术的花生油掺伪检测涂斌;陈志;彭博;郑晓;宋志强;尹成;曾路路;何东平【摘要】以拉曼、近红外2种光谱特征融合结合化学计量学方法对花生油掺伪进行了定量分析.分别用激光拉曼、激光近红外光谱仪采集134个掺伪油样本的光谱数据,采用SPXY算法对样本集进行划分.拉曼光谱(Ram)和近红外光谱(near infrared spectroscopy,NIR)数据进行预处理后,采用后向间隔偏最小二乘法(BiPLS)和联合间隔偏最小二乘法(synergy interval partial least squares,SiPLS)分别提取2种光谱的特征波长;将提取的特征波长融合,结合支持向量机回归(SVR)建立数学模型,采用网格搜索算法(CV)对SVR模型的参数组合(C,g)值寻优,建立最优参数模型.研究表明:建立的Ram-NIR-SVR模型能够实现花生油中掺杂油脂含量的快速准确预测,预测集和校正集的相关系数R分别达到0.98和0.99,均方根误差(MSE)低于2.38E-3;对比不同特征波长提取方法,并与单光谱分析技术比较,可以看出,数据融合技术能够增强模型预测能力,减小模型参数,有利于模型的实际应用,体现了2种光谱很好的互补性.表明光谱分析结合数据融合技术对食用油真实性综合鉴别具有重要意义.【期刊名称】《食品与发酵工业》【年(卷),期】2016(042)004【总页数】5页(P169-173)【关键词】花生油;拉曼光谱;近红外光谱;定量分析;数据融合;支持向量机回归【作者】涂斌;陈志;彭博;郑晓;宋志强;尹成;曾路路;何东平【作者单位】武汉轻工大学机械工程学院,湖北武汉,430023;武汉轻工大学机械工程学院,湖北武汉,430023;武汉轻工大学机械工程学院,湖北武汉,430023;武汉轻工大学机械工程学院,湖北武汉,430023;武汉轻工大学机械工程学院,湖北武汉,430023;武汉轻工大学机械工程学院,湖北武汉,430023;武汉轻工大学机械工程学院,湖北武汉,430023;武汉轻工大学食品科学与工程学院,湖北武汉,430023【正文语种】中文食用油可以为人体提供所需的不饱和脂肪酸、维生素等，属于日常生活用品，连续几年销量超过2 000 万t [1-2]。

分层多个端元光谱混合分析

Hierarchical Multiple Endmember Spectral Mixture Analysis (MESMA)of hyperspectral imagery for urban environmentsJonas Franke a ,⁎,Dar A.Roberts b ,1,Kerry Halligan c ,2,Gunter Menz d ,3aUniversity of Bonn,Center for Remote Sensing of Land Surfaces (ZFL),Walter-Flex-Strasse 3,D-53113Bonn,GermanybUniversity of California,Santa Barbara,Department of Geography,1832Ellison Hall,UC Santa Barbara,Santa Barbara,CA 93106-4060,United States cSanborn Map Company,610SW Broadway,Suite 310,Portland,OR 97205,United States dUniversity of Bonn,Department of Geography,Remote Sensing Research Group (RSRG),Meckenheimer Allee 166,53115Bonn,Germanya b s t r a c ta r t i c l e i n f o Article history:Received 15December 2008Received in revised form 27March 2009Accepted 28March 2009Keywords:Multiple Endmember Spectral Mixture Analysis (MESMA)Hyperspectral Mapper (HyMap)UrbanLand cover HyperspectralImaging spectrometry Endmember selection Hierarchical classi ﬁcationRemote sensing has considerable potential for providing accurate,up-to-date information in urban areas.Urban remote sensing is complicated,however,by very high spectral and spatial complexity.In this paper,Multiple Endmember Spectral Mixture Analysis (MESMA)was applied to map urban land cover using HyMap data acquired over the city of Bonn,Germany.MESMA is well suited for urban environments because it allows the number and types of endmembers to vary on a per-pixel basis,which allows controlling the large spectral variability in these environments.We employed a hierarchical approach,in which MESMA was applied to map four levels of complexity ranging from the simplest level consisting of only two classes,impervious and pervious,to 20classes that differentiated material composition and plant species.Lower levels of complexity,mapped at the highest accuracies,were used to constrain spatially models at higher levels of complexity,reducing spectral confusion between materials.A spectral library containing 1521endmembers was created from the HyMap data.Three endmember selection procedures,Endmember Average RMS (EAR),Minimum Average Spectral Angle (MASA)and Count Based Endmember Selection (COB),were used to identify the most representative endmembers for each level of bined two-,three-or four-endmember models –depending on the hierarchical level –were applied,and the highest endmember fractions were used to assign a land cover class.Classi ﬁcation accuracies of 97.2%were achieved for the two lowest complexity levels,consisting of impervious and pervious classes,and a four class map consisting of vegetation,bare soil,water and built-up.At the next level of complexity,consisting of seven classes including trees,grass,bare soil,river,lakes/basins,road and roof/building,classi ﬁcation accuracies remained high at 81.7%with most classes mapped above 85%accuracy.At the highest level,consisting of 20land cover classes,a 75.9%classi ﬁcation accuracy was achieved.The ability of MESMA to incorporate within-class spectral variability,combined with a hierarchical approach that uses spatial information from one level to constrain model selection at a higher level of complexity was shown to be particularly well suited for urban environments.©2009Elsevier Inc.All rights reserved.1.IntroductionCurrent and accurate information about urban composition is critical for urban planning,disaster response and improved environ-mental management.Remote sensing has the potential to provide the necessary information about urban infrastructure,socio-economic attributes and environmental conditions at a diversity of scales (Jensen &Cowen,1999;Small,2001).As a result,an increasing num-ber of studies have focused on remote sensing of urban environments and their land cover (e.g.,Ben-Dor et al.,2001,Herold &Roberts,2005;Powell et al.,2007;Small,2001,2003,2005).Urban remote sensing is complicated by the complexity of urban environments which includes considerable spectral diversity at very ﬁne spatial scales (Powell et al.,2007;Small,2001,2005).Spectrally,urban areas are complicated by the presence of numerous spectrally unique materials,and the presence of spectrally ambiguous materials,such as dark-shingles and asphalt roads (Herold et al.,2003a ).Other factors further complicate analysis,including non-Lambertian beha-vior of urban materials that leads to high within-class spectral variability (Herold et al.,2004),3-dimensional heterogeneity of urban areas (Herold et al.,2003a )and material aging,which causes spectral changes (Herold &Roberts,2005).As a result,urban environments exhibit a high dimensionality in spectral space (Small,2001,2005).Remote Sensing of Environment 113(2009)1712–1723⁎Corresponding author.Tel.:+49228734023;fax:+49228736857.E-mail addresses:jonasfranke@uni-bonn.de (J.Franke),dar@(D.A.Roberts),halligan.kerry@ (K.Halligan),g.menz@uni-bonn.de (G.Menz).1Tel.:+18058932276;fax:+18058933146.2Tel.:+15032288708;fax:+15032288751.3Tel.:+49228739700;fax:+49228739702.0034-4257/$–see front matter ©2009Elsevier Inc.All rights reserved.doi:10.1016/j.rse.2009.03.018Contents lists available at ScienceDirectRemote Sensing of Environmentj o u r n a l h o m e p a g e :w ww.e l s ev i e r.c o m /l o c a t e /rs eSome studies,therefore,have focused on the spectral separability of urban materials for land cover mapping,using sensors such as the Airborne Visible Near Infrared Imaging Spectrometer (AVIRIS)(Hepner et al.,1998;Hepner &Chen,2001;Herold et al.,2004)or the Compact Airborne Spectrographic Imager (CASI)(Ben-Dor et al.,2001).Herold et al.(2004)concluded that the current knowledge about urban materials and their separation based on spectral characteristics is inadequate.In addition to the large diversity of urban materials,improved knowledge about spatio-temporal changes in urban vegetation cover is important to determine and model urban environmental conditions (Ridd,1995;Small,2001).Limitations of remote sensing techniques for urban mapping in the spatial dimension,as observed in previous studies (Powell et al.,2007;Small,2001,2005),resulting from coarse spatial resolutions of sensors such as Landsat Enhanced Thematic Mapper (ETM+),can potentially be overcome by novel analysis techniques.For urban applications,a spatial resolution of at least 5m is required,in order to adequately capture urban structures (Small,2003).However,due to the high spatial variability of urban structure with spectrally heterogeneous materials close to each other,mixed pixels are still common in images covering urban areas (Powell et al.,2007).Spectral mixture analyses (SMA)can potentially solve some of the problems associated with the spectral heterogeneity of urban surfaces (Small,2001).However,simple mixing models,which consist of a single set of endmembers applied to an entire scene,are potentially not appropriate for urban areas because they cannot account for considerable within-class variability (Rashed et al.,2003;Roessner et al.,2001).To overcome this limitation,Song (2005)proposed Bayesian spectral mixture analysis (BSMA),in which endmembers are not treated as constants.Multiple Endmember Spectral Mixture Analysis (MESMA;Roberts et al.,1998)represents an alternative approach,in which the number and types of endmembers are allowed to vary on a per-pixel basis,thereby accounting for urban spectral heterogeneity.Forexample,Fig.1.Location of the study area of Bonn in Germany.Shaded relief data set with the river Rhine given in blue,combined with a swath of true-color HyMap data acquired on May 28,2005indicating the landscapestructure.Fig.2.Hierarchical structure of the Multiple Endmember Spectral Mixture Analysis giving 4levels of different complexity.1713J.Franke et al./Remote Sensing of Environment 113(2009)1712–1723MESMA has been used to map vegetation,impervious and soil frac-tions in a number of urban areas,including the city of Manaus,Brazil (Powell et al.,2007)and Los Angeles (Rashed et al.,2003).Object-oriented approaches also have considerable potential for mapping urban areas at high accuracy (Herold et al.,2003b ).Benediktsson et al.(2005)also discuss the importance of spatial and spectral information describing a morphological method for a joint spatial/spectral classi ﬁer for urban environments.Roessner et al.(2001)incorporated spatial context to improve endmember selection to iteratively unmix hyperspectral data covering an urban area.In this study,we propose hierarchical MESMA,in which different models are used for different levels of complexity,and in which highly accurate models at the lowest level of complexity are used to spatially constrain models at higher levels of complexity.We tested this approach using HyMap data acquired over the city of Bonn,Germany.Our objectives were thereby to (i)demonstrate the potential of MESMA for mapping urban land cover at various levels of detail ranging from imperviousness to material discrimination,(ii)determine materials or land covers with a high degree of spectral confusion (iii)incorporate spatial constraints into MESMA to improve classi ﬁcation accuracies and thus (iv)to prove this hierarchical MESMA approach for urban environments.2.Methodology 2.1.Study area and dataThis study focused on an urban transect in the region of Bonn,Germany.The city of Bonn is located in Western Germany along the river Rhine,approximately 30km southeast of the city of Cologne.Bonn represents a typical large German city with a popu-lation of 320,000.The city dates from Roman times and contains a medieval city center with large 19th and 20th century urban exten-sions.Bonn is situated in generally level terrain at an average elevation of 55m above sea level.Although the city includes a few taller buildings (e.g.,the 165m Posttower)it is dominated by 3–5stories commercial and residential structures as well as 1and 2ﬂoor family houses,principally located in residential areas that are concentrically arranged around the town center.The Bonn area is characterized by highly diverse land cover types and complex urban material compositions.Fig.1shows the Bonn study site location and an airborne Hyperspectral Mapper (HyMap)subscene acquired on 28/05/2005covering a representative NW –SE cross-section of the city,emphasiz-ing the highly diverse land use regime present within the study area.A number of urban land covers are shown:residential areas (with differing densities and socio-economic structures),mixed-use areas,and commercial and industrial districts.Non-urban land cover types include water bodies,green vegetation and bare soils.The speci ﬁc urban materials present in the Bonn region result from centuries of urban development combined with local traditional in ﬂuences.The diversity of building materials found in the area includes asphalt and cobblestone road surfaces,as well as roofs composed of slate,metal,glass,gravel,bitumen,plastics and a number of types and colors of composite shingles.Old houses in the historic town center typically have shingle roofs composed of dark slate from the nearby Rhenish Slate Mountains.Predominant vegetation types in the studyareaFig.3.Work ﬂow of the hierarchical MESMA.1714J.Franke et al./Remote Sensing of Environment 113(2009)1712–1723include European chestnut,linden and other mixed deciduous trees, as well as riparian areas that are mostly covered with grass.Airborne Hyperspectral Mapper(HyMap)data were acquired on 28/05/2005.The HyMap-system is a whisk-broom scanner with an ax-head double mirror which acquires126spectral bands with a bandwidth of16nm(in the VIS and NIR region)in the spectral range between450nm and2480nm.HyMap is typically operated at altitudes between2000and5000m agl and has an instantaneous ﬁeld of view(IFOV)of2.5mr along track and2.0mr across track by a ﬁeld of view(FOV)of±30°(Cocks et al.,1998).The chosen conﬁgura-tion resulted in a nominal ground IFOV of4.0m.HyVista Corp.and the German Aerospace Center(DLR)carried out the pre-processing of the HyMap data.The validation of the atmospheric corrections using ATCOR4(Richter and Schlaepfer,2002)was performed against in-situ measurements obtained with an ASD FieldSpec Pro spectroradiometer (Analytical Spectral Devices Inc.,Boulder,Co,USA).During further pre-processing,26bands showing high levels of noise,especially those near the water absorption features at1400and1900nm,were removed from the data to improve overall image quality.2.2.Endmember selectionThe quality of SMA results,in general,is highly dependent on the availability of representative endmembers(Tompkins et al.,1997). Endmembers used in SMA can either be derived from image pixels or from a spectral library that contains reference endmembers derived from measurements taken in theﬁeld,laboratory,from radiative trans-fer models(Sonnentag et al.,2007)or derived from other images.The advantage of image endmembers is that they can be collected at the same scale as the image and are easier to associate with image features (Rashed et al.,2003).In addition,image endmembers have the advantage of being canopy-scale spectra,incorporating the effects of non-linear mixing which may be present,especially in vegetation surfaces,at the leaf-scale.Several approaches for the selection of optimal/representative endmembers from images have been devel-oped.One example is the Pixel Purity Index(PPI),described by Boardman et al.(1995).Recently,several endmember selection approaches have been proposed for MESMA,in which a spectral library is analyzed to identify the subset of spectra that are most representative of a speciﬁc class,and least confused with members outside that class. Examples include Count-based Endmember Selection(CoB)(Roberts et al.,2003),Endmember Average Root Mean Square Error(EAR) (Dennison&Roberts,2003)and the Minimum Average Spectral Angle (MASA)(Dennison et al.,2004).In contrast to the PPI,these approaches require knowledge about the spectral characteristics to assign each spectrum to a particular ing CoB,optimal endmembers are identiﬁed as those spectra within a spectral library that model the greatest number of spectra within a speciﬁc class while meeting other selection criteria,including fractional constraints(i.e.fractions are required to be between0and100%),andﬁt constraints based on RMSE and spectral residuals(Roberts et al.,2003).CoB provides several quality parameters that allow for a ranking of representative endmembers.The in-CoB parameter reports the total number of spectra modelled within the class,whereas the out-CoB reports the total number of models outside of the class.A high in-CoB with a low out-CoB represents an excellent endmember choice.EAR calculates the average RMSE produced by a spectrum when it is used to model all other members of its class.The optimum spectrum produces the lowest averageRMSE.Fig.4.Merged classiﬁcation result of level1as derived from two-and three-endmember model MESMA,showing impervious and pervious surfaces in the area of Bonn with an overall classiﬁcation accuracy of97.2%.1715J.Franke et al./Remote Sensing of Environment113(2009)1712–1723The MASA calculates the average spectral angle between a reference spectrum (candidate model)and all other spectra within the same class.The best endmember is selected as the one that produces the lowest average spectral angle (Dennison et al.,2004).In this study,a comprehensive survey of the area of Bonn was conducted,in order to identify representative surface types and to ﬁnd locations suitable for developing a spectral library from the image.A Differential Global Position System (Trimble GeoExplorerXT with a Trimble GeoBeacon receiver)was used to collect reference data with a high spatial accuracy.Three to ﬁve Regions of interest (ROI),consisting of around 30pixels per ROI were selected in the HyMap image for each endmember type.A random sample of all ROIs was extracted,to develop a spectral library consisting of 1521spectra with 1384pixels set aside for validation of the MESMA results.The spectral library was developed using ‘VIPER-tools ’,an ENVI add on ( ),and all relevant metadata added.For each hierarchical MESMA level,separate spectral libraries were created containing optimal/most representative endmembers with low probability of confusion with other endmember classes,characterized by low EAR or MASA values or high in-Cob values.These metrics were calculated with the ‘VIPER-tools ’and endmembers were consecutively sorted by their metric values.The spectra selection should be done on a case by case basis,depending on the users'objective.A number of different strategies may be employed.In our study,most of our selections were from the top candidates of each metric.2.3.Hierarchical Multiple Endmember Spectral Mixture Analysis (MESMA)Linear SMA assumes that a mixed spectrum can be modeled as a linear combination of pure spectra,known as endmembers (Adams et al.,1986).Under ideal conditions,the most accurate fractional estimates can be achieved using the minimum number of end-members required to account for spectral variability within a mixed pixel (Sabol et al.,1992).Fractional errors occur either when too few endmembers are used,resulting in spectral information that cannot be accounted for by the existing endmembers,or too many,in which case minor departures between measured and modelled spectra are often assigned to an endmember that is used in the model,but not actually present (Roberts et al.,1998).Urban environments are particularly dif ﬁcult for a simple mixture model because a single endmember cannot account for considerable spectral variation within a class.In contrast,MESMA can account for within-class variability and thus is likely to be more suitable for urban remote sensing.Typically,MESMA is applied by running numerous models for a pixel and selecting one model based on its ability to meet selection criteria and produce the best ﬁt,typically a minimum RMS (Painter et al.,1998).Selection criteria include fractional constraints (minimum and maximum fraction constrains),maximum allowable shade fraction,RMSE constraints and a residual constraint set to remove any model that exceeds a threshold over a range of ing this approach,pixel-scale limits in spectral dimensionality are recognized while also accounting for considerable spectral variability within a scene.The constraints for the models are variably selectable,whereby MESMA can also be run in an unconstrained mode.Roberts et al.(1998)found that with the ﬂexible MESMA approach,a majority of pixels in an image could be modeled with only two-endmember models.Powell and Roberts (2008)found that natural landscapes in Brazil required only two-endmember models,disturbed regions required three-and urban areas required four-endmembermodels.Fig.5.Classi ﬁcation result of level 2displays the land cover classes ‘Vegetation ’,‘Built-up ’,‘Bare soil ’and ‘Water body ’in the urban area of Bonn with an overall classi ﬁcation accuracy of 97.2%.1716J.Franke et al./Remote Sensing of Environment 113(2009)1712–1723In this study,a hierarchically structured MESMA was realized,whereby two-,three-or four-endmember models were uniquely tailored for four different levels of complexity (Fig.2).At the lowest level only two broad classes were mapped,impervious and pervious.At level 2,four land cover classes were mapped;at the third level,the land cover classes were subdivided into up to two categories,such as grass and trees,roads vs.roof materials and lake vs.river.At the highest level of complexity,20classes of speci ﬁc materials or tree species were mapped (Fig.2).The basic idea of hierarchical MESMA was to use the result from one level as a spatial constraint for the next level,taking advantage of higher classi ﬁcation accuracies achieved at lower levels of complexity to improve accuracies at higher levels.For example,models for level 2were constrained by results from level one,where vegetation,bare soil and water bodies are restricted to areas mapped as pervious,and built-up is restricted to the impervious class.In this case,the results for level 1and level 2are the same for impervious and built-up.MESMAs of levels 1and 2were run unconstrained and as spatial constraints only those masks were used,in cases when classi ﬁcation accuracy was greater than 85%at a lower level.MESMAs of level 3were run partially constrained (minimum and maximum allowable fractions were constrained).By using spatial information at one level for the analysis of the next level,high classi ﬁcation accuracies achieved at the lower levels should therefore improve accuracies at higher levels.The work ﬂow of this hierarchical MESMA is displayed in Fig.3.For MESMA of the imperviousness at level 1,30two-endmember models were used,whereby the ﬁrst spectral library contained 30representative endmembers (15representing pervious and 15representing impervious surfaces)determined by EAR,MASA and Cob and the second spectral library contained shade.In addition,a three-endmember model was applied with 15pervious endmembers in the ﬁrst library,15impervious endmembers in the second and shade in the third spectral library resulting in 225models.The RMSE change between the results of the two-and three-endmember model results was calculated afterwards.In cases where the RMSE did not change more than 0.1between both results,the result of the two-endmember model was chosen.The three-endmember model was only selected where a third endmember was needed to drop the RMSE (RMSE change N 0.1).Both MESMA classi ﬁcation results (classes were assigned to the highest endmember fraction)were merged to the two ﬁnal classes impervious and pervious.MESMA of the second level discriminated 4different land cover classes by the use of 30two-endmember models similar to level 1.MESMA was run in an unconstrained mode,whereas the analysis was spatially constrained,because the land cover classes vegetation,bare soil and water body were only analyzed for pervious areas as identi ﬁed at the ﬁrst level.Due to the fact that spatial constraints were used,the land cover class ‘Built-up ’at level 2is the same as the impervious class from level 1.Over most parts of the region RMSE values at level 2were low,which indicates that this level could be successfully modeled with only two-endmember models.MESMA at the third level determined dominant surface types including trees,grass,bare soils,rivers,lakes/basins,roads and roofs/buildings.First,69two-endmember models were used,applied to each land cover mask as derived from the results of level 2(excepting bare soil).MESMA was run in a partially constrained mode (minimum and maximum allowable fraction values were constrained).A four-endmember model was run additionally in order to improve discrimi-nation between vegetation types as well as roads androofs/buildings.Fig.6.Classi ﬁcation result of level 3as derived from two-and four-endmember model MESMA that gives the dominant surface types trees,grass,bare soils,rivers,lakes/basins,roads and roofs/buildings with an overall classi ﬁcation accuracy of 81.7%.1717J.Franke et al./Remote Sensing of Environment 113(2009)1712–1723The so called V–I–S model was proposed by Ridd(1995),which divides urban areas into three physically based classes,vegetation, impervious surfaces and soil.In the present study,theﬁrst spectral library contained12vegetation endmembers,the second library contained14endmembers representing impervious surfaces,the third library contained3soil endmembers and the fourth spectral library contained shade resulting in504models.Classes were assigned to the highest endmember fractions.The RMSE was used as a constraint for each class.Due to a signiﬁcant confusion between soil and red-shingle roofs,a maximum RMSE of0.025was applied as a constraint for the soil class.All pixels with dominant soil fractions and RMSE values greater than0.1,were assigned to the roof class.If no model met all these constraints,the pixel was left unmodeled/ unclassiﬁed.The classiﬁcation result of level3was merged from the results of the two-endmember and four-endmember models.MESMA of level4discriminated20different materials or vegetation species as shown in Fig.2.Due to the fact that the classes ‘River’,‘Lakes/Basins’and‘Bare soil’were alreadyﬁnal classes at level 2or3with classiﬁcation accuracies higher than85%,the information for these classes was taken from those levels,respectively.212two-endmember models were used for the MESMA applied at level4. MESMA was run in an unconstrained mode similar to level2.48two-endmember models were used for all vegetated pixels as identiﬁed at level3and164two-endmember models were used for all pixels not classiﬁed as water,vegetated or bare soil at level3.Results of the discrimination of vegetation species and urban materials as obtained from MESMAs of level4were merged withﬁnal classes already obtained at levels2and3.Minor classiﬁcation errors were present in some buildings,represented by individual pixels of a different class imbedded within an otherwise compact building object.To reduce this type of error,the building classes were smoothed using a3⁎3 majorityﬁlter to remove single-pixel errors within buildings.All other classes remained unﬁltered.Classiﬁcation results of each hierarchical level were compared to the random sample of validation pixels,in order to assess classiﬁcation accuracy,whereby the total sample size of1384pixel splits–depending on the hierarchical level–to theﬁnal classes.3.Results and discussionFigs.4–7show the classiﬁcation results of the4hierarchical levels. The MESMA results of levels1to3(Figs.4–6)reveal the spatial structure of the urban area of Bonn with mostly impervious areas in the central business district(CBD)in the northern part of the scene close to the Rhine River and in the strongly industrial area in the northwest.Residential areas,in contrast,are clearly distinguishable by a higher percentage of vegetated areas.In the southern part of the scene,the densely vegetated recreation area‘Rheinaue’is obvious, which also acts as a naturalﬂoodplain for the Rhine River,which occasionallyﬂoods.Observing the result of hierarchical MESMA level 4(Fig.7),a detailed insight into the urban spatial structure is given. Considering object sizes and roof materials,the industrial area in the northwest is clearly distinguishable from the CBD.In addition,larger objects with different roof materials are obvious in the southern part of the scene as well,that indicate the area of governmental buildings, museums,headquarters of organizations and companies etc.The spatial distribution of vegetation species also gives detailed informa-tion about urban environmental condition.The V–I–S modelas Fig.7.Classiﬁcation result of level4that shows different materials and vegetation species in20classes of the urban area of Bonn with an overall classiﬁcation accuracy of75.9%. 1718J.Franke et al./Remote Sensing of Environment113(2009)1712–1723described above is displayed in Fig.8,which shows the fractions of vegetation,impervious surfaces and soil as a false-color RGB as derived by the four-endmember models at level 3.A mask considering maximum allowable fractions and RMSE constraints was thereby applied.Error matrices were calculated using ground reference data for each hierarchical level (Tables 1–4).The overall classi ﬁcation accuracies were 97.2%for level 1(kappa coef ﬁcient of 0.94)and level 2(kappa coef ﬁcient of 0.95),81.7%for level 3(kappa coef ﬁcient of 0.75)and 75.9%(kappa coef ﬁcient of 0.74)for hierarchical level 4.Only minor confusion occurred at level 1between the classes impervious and pervious (Table 1).The high accuracies of 95.4%and 100%respectively could be on the one hand achieved due to the selection of highly representative endmembers using EAR,MASA and CoB and on the other hand due to the fact that results of the two-and three-endmember models were merged,depending on the RMSE change.The endmember selection approaches selected the following repre-sentative endmembers:for pervious surfaces,10vegetation end-members,2water and 3soil endmembers (Fig.9a);for impervioussurfaces,3road endmembers and 12roof endmembers (Fig.9b).Using the RMSE change between the results of the two-and three-endmember models was very suitable for identifying pixels that required a third endmember to drop the RMSE and improved ac-curacies.In particular,the models cardboard roof/shade as well as grass/shade in the two-endmember MESMA had the highest frequency within these pixels with high RMSE change.At level 2,4different land cover classes were discriminated by 30two-endmember models,whose endmembers were speci ﬁcally selected by the mentioned endmember selection procedures.Some confusion was evident for bare soil,in which 23.4%of the cases were mis-classi ﬁed as built-up area (Table 2).The class ‘Bare soil ’had a comparatively low sample size in the validation data (47)since it already is a ﬁnal class at level 2(total sample size splits down to the ﬁnal classes).Almost no confusion occurred for the other classes at level 2,whereby the classes ‘Vegetation ’and ‘Water body ’were almost perfectly classi ﬁed with accuracies of 99.8%and100%.Fig.8.False-color image giving the fractions of vegetation,impervious surfaces and soil as derived from MESMA by using four-endmember models (V –I –S model)at level 3.Black pixels give areas where the maximum allowable fractions or the RMSE exceed the set constraints.Table 1Error matrix of the level 1classi ﬁcation result and ground truth data gives the percentage of classi ﬁcation accuracy and mis ﬁt.Classi ﬁed/ground truth Pervious Impervious Sample size 513871Pervious 100.0 4.6Impervious0.095.4Table 2Error matrix of the level 2classi ﬁcation result and ground truth data gives the percentage of classi ﬁcation accuracy and mis ﬁt.Classi ﬁed/ground truth Vegetation Bare soil Built-up Water body Sample size 3984787168Vegetation 99.70.00.90.0Bare soil 0.076.6 2.20.0Built-up 0.323.496.90.0Water body0.00.00.0100.01719J.Franke et al./Remote Sensing of Environment 113(2009)1712–1723。

基于丰度划分的高光谱遥感图像解混

基于丰度划分的高光谱遥感图像解混余淞淞【摘要】高光谱遥感成像技术能够获取目标区域丰富的光谱信息和空间信息。

混合像元现象在遥感图像中普遍存在，处理遥感图像解混问题是提高地物识别精度的前提。

由于端元光谱可变性的存在，传统的基于单一单元光谱的线性解混方法解混精度难以达到应用要求。

对多端元光谱策略进行分析，并给出一种基于丰度划分的高光谱解混算法，对实际光谱数据进行试验并取得较好效果。

%Hyperspectral remote sensing imagery provides rich spectral information and space information about the place of interest. Mixed pixels happen in spectral images frequently, which reduce the classification accuracy of ground truth. Due to spectral variability, early spectral unmixing methods using one pixel as endmember ectral unmixing can't provide enough performance for applications. Pays more attention to the multiple endmember spectral analysis, and proposes an unmixing method based on abundance division. Experiments on real hyper-spectal images show high performance.【期刊名称】《现代计算机（普及版）》【年(卷),期】2015(000)003【总页数】3页(P74-76)【关键词】高光谱;混合像元;光谱解混;丰度划分【作者】余淞淞【作者单位】同济大学电子信息与工程学院，上海 201804【正文语种】中文随着世界科技发展，遥感技术日益成熟，已经成为对地观测的重要手段之一。

基于面向对象的多端元光谱混合分析方法

端元光谱混合分析方法的效率，本文提出了基于面向对象的多端元光谱混合分析方法。首先利用面向对象的分析方
法对研究区遥感影像进行分类，得到分类结果图；然后对分类结果图中包含多种土地覆盖类型的对象进行多端元光
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刘正春，卢帅，张辉
（１．山西农业大学资源环境学院，山西太谷０３０８０１；２．山西省科技情报研究所，山西太原０３０００１）
摘要：为了充分利用中等分辨率遥感影像的空间、纹理和光谱信息，解决影像中存在的大量混合像元问题，提高多
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混合像元分解研究综述——端元内光谱差异问题

混合像元分解研究综述——端元内光谱差异问题或叫做端元变异，端元不稳定(Endmember variation)。

一般的混合像元分解算法假设相同地物都有相同的光谱特征，因而对整幅图像采用相同的端元光谱。

但由于同物异谱现象的存在，端元的光谱并非恒定的值，这就是端元内光谱差异现象。

这种现象的存在常常会导致分解结果的误差。

目前，解决该问题的方法可以分为四类：(1) 多端元方法多端元方法指对每一类地物选取多个端元光谱参与混合像元分解。

其中最典型的方法是由Roberts等(1998)[49]提出的MESMA(Multiple Endmember Spectral Mixture Analysis)方法。

该方法首先为每类地物选取多条光谱，并以此生成多个端元组合（每个端元组合由不同地物中的某一条光谱组成），接着对每个像元寻找最小二乘法误差最小的端元组合，进而求出每个像元的端元比例。

该方法在很多研究中被证实是十分有效的[50-54]。

Bateson等(2000)[55]提出了一种端元束的方法，该方法对每类地物生成端元束（一个端元束由许多同一类地物的光谱组成），将所有端元束的光谱作为端元进行混合像元分解。

因为端元数目超过光谱波段数，方程组欠定，所以只能求解出每一类地物（也就是一个端元束内所有光谱的比例之和）的最小值和最大值，再对其作平均得到每类地物的比例。

该方法的优点在于可以得到每类地物比例的误差范围。

多端元方法机制明确，但计算复杂，耗时过长。

(2) 光谱变换在很多情况下，同类地物的光谱的差别来自绝对值的变化，而光谱形状是相似的。

因此通过对光谱进行一定的变换可以减少端元的光谱差异。

Wu（2003）[56]提出将光谱除以各个波段的均值，再作混合像元分解，并应用于城市监测；Garcia-Haro等（2005）[57]将光谱作标准化后再作混合像元分解；Asner等(2003)[58]将光谱作微分后再作混合像元分解。

Juan Pablo Guerschman等(2009)[59]利用原始光谱计算出归一化差分植被指数（Normalized Difference VegetationIndex, NDVI）和纤维素吸收指数（Cellulose Absorption Index，CAI），假设两个指数也满足线性混合模型，利用两个指数求得光合植被、非光合植被及裸土的比例。

混合光谱分解模型研究

混合光谱分解模型研究摘要：对有限波段的混合光谱遥感数据而言，端元的选取及其端元数量对模型精度有重要的影响。

随着高光谱平台的发展和数据不断进入各种行业领域，研究人员开始使用高光谱影像进行混合像元分解提取不同组分。

但是由于高光谱相邻波段的高度相关性，导致不同地物光谱特征的可分维度没有得到实质性提高，因此在利用LSMA算法进行混合光谱分解时，端元光谱的数量还是受到一定的限制。

正是受限于混合像元分解的端元数量，导致LSMA在城市地表组分的分解精度不高，因此在探索如何阐明端元变化对模型精度影响方面有了很多探索性研究，如对端元进行归一化处理；多端元混合像元分解模型（MESAM）得以发展并被广泛应用。

混合光谱解析方法由于LSMA算法在解析的过程中不能使用过多的端元，端元过多或者过少都会引起模型精度大大降低。

而MESAM的出现恰恰是为了解决LSMA的弊端，其基本思想是每个像素在使用类似LSMA的算法进行混合像元分解的过程中，端元的数量和类型可根据需求进行组合。

换而言之，一个像素内的地物可能是由纯地物组成，也可能是由两种地物组成，或者是三种甚至是4中及其以上多的地物组成，在应用MESMA解析过程中，会根据像素内实际地物的多少进行端元选取（一个、两个、三个、四个的端元），最终实现混合像元解析。

于此对应，Maselli(1998, 2001)也发展了一种基于端元正交映射的多端元混合光谱分解模型（MSOD），其基本思想与MESMA相似，但是要对每个端元的光谱进行Gram-Schmidt投影转化，然后将每个像素的光谱进行同样的投影变换，最后光谱的分解在斯密特投影空间进行。

近来，Deng &Wu (2012, 2013)通过穗帽变换，构建了BCI光谱转化模型，并在BCI光谱转化空间内实现了混合光谱分解，并与其他模型反演效果进行了对照，该方法的应用前景还需要进一步验证。

混合光谱的解析方法的另一个发展方向就是采用智能算法进行像元内的地物组分反演。

基于端元变化的两种混合像元分解算法比较研究

基于端元变化的两种混合像元分解算法比较研究
段金亮;王杰;文星跃
【期刊名称】《资源开发与市场》
【年(卷),期】2017(033)006
【摘要】光谱混合分析对提高遥感影像分类具有重要意义,其中端元变化处理是提高解混精度的关键.目前,许多算法被用来解决端元变化,但仍存在一些问题有待解决,如算法运行效率慢、忽略端元的高阶交互、像元空间邻城信息缺失.结合IDL和MATLAB混合编程,利用确定性模型中的交替最小角度法和统计性模型中考虑高阶项的非线性算法对Hyperion影像进行端元变化解混,再利用概率松弛标记法对像元补充空间邻域信息.试验结果表明:当某种地物类别所占面积较大时,确定性与统计性模型都能获得较高的解混精度;当地物类别所占面积较小时,确定性模型的解混精度高于统计性模型;补充像元空间邻域信息对解混结果有很好的校正.
【总页数】6页(P651-655,封2)
【作者】段金亮;王杰;文星跃
【作者单位】西华师范大学国土资源学院,四川南充637009;西华师范大学国土资源学院,四川南充637009;西华师范大学国土资源学院,四川南充637009
【正文语种】中文
【中图分类】TP751.1
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1.基于非线性降维的高光谱混合像元分解算法 [J], 唐晓燕;高昆;倪国强
2.基于修正MCMC的端元可变的混合像元分解算法 [J], 胡霞;宋现锋;牛海山
3.一种端元变化的神经网络混合像元分解方法 [J], 吴柯;张良培;李平湘
4.端元光谱变化与混合像元分解精度的关系研究 [J], 吴波;周小成;赵银娣
5.基于超像素的流形正则化稀疏约束NMF混合像元分解算法 [J], 李登刚; 陈香香; 李华丽; 王忠美
因版权原因，仅展示原文概要，查看原文内容请购买。

光谱解混[整理版]

光谱解混定义：Spectral unmixing is the procedure by which the measured spectrum of a mixed pixel is decomposed into a collection of constituent spectra，or endmembers，and a set of corresponding fractions，or abundances，that indicate the proportion of each endmember present in the pixel.【spectral unmixing，2002】光谱混叠产生原因：First, if the spatial resolution of a sensor is low enough that disparate materials can jointly occupy a single pixel, the resulting spectral measurement will be some composite of the individual spectra. This is the case for remote sensing platforms flying at a high altitude or performing wide-area surveillance, where low spatial resolution is common. Second, mixed pixels can result when distinct materials are combined into a homogeneous mixture. This circumstance can occur independent of the spatial resolution of the sensor.光谱混合模型：混合像元分解模型可以分为两类，即线性光谱混合模型( LSMM，Linear Spectral Mixture Model) 和非线性光谱混合模型( NLSMM，Nonlinear Spectral Mixture Model) LSMM假定像元光谱是各组分光谱的线性组合，而NLSMM则认为像元光谱是各组分光谱按照非线性关系综合而成的。

浅谈光谱混合的基本原理及相关模型

浅谈光谱混合的基本原理及相关模型摘要：本文主要是研究基于可变端元的线性模型。

而线性混合模型一般可以分为三种情形：无约束的线性混合模型，部分约束的线性混合模型和全约束混合模型，线性解混就是在已知所有端元的情况下求出它们图像的各个象元中所占的比例，从而得到反应每个端元在图像中分布情况的比例系数图。

关键词：局部；高光谱；可变端元；丰度；混合象元Abstract: this paper is mainly based on the research of the linear model variable $. And general mixed-linear model can be divided into three categories: unconstrained linear mixed model, part of the constraint mixed-linear model and the constraint mixture model, linear solution is known in the mix all the yuan for them out of each image as the proportion of yuan, and get a response in the image yuan each end of the proportion of the distribution coefficient graph.Key words: local; Hyperspectral; Variable end yuan; Abundance; Mixed like yuan1 混合象元的形成遥感器所获取的地面反射或发射光谱信号是以象元为单元为单位记录的。

它是象元所对应的地表物质光谱信号的综合。

图像中每个象元所对应的地表，往往包含不同的覆盖类型，他们有着不同的光谱响应特征。

遥感影像的光谱混合分析技术

遥感影像的光谱混合分析技术在当今的科技领域，遥感技术正发挥着日益重要的作用，而其中的光谱混合分析技术更是成为了研究的焦点之一。

遥感影像就像是从太空中为我们拍摄的地球“照片”，但这些“照片”蕴含着远比我们肉眼所见更为丰富和复杂的信息。

光谱混合分析技术，则是帮助我们解读这些信息的一把关键“钥匙”。

要理解光谱混合分析技术，首先得明白什么是光谱。

简单来说，光谱就像是每种物质独特的“指纹”。

不同的物体，由于其组成成分和物理化学特性的差异，在接收和反射光线时会表现出特定的光谱特征。

比如，植被在特定的光谱波段会有明显的反射特征，而水体、土壤等也各自有着独特的光谱表现。

当我们通过遥感卫星或飞机获取到某个区域的影像时，所得到的往往不是单一物体的纯净光谱信息，而是多种物体混合在一起的复杂信号。

这就好比在一张照片中，既有草地、又有树木、还有建筑物和道路。

光谱混合分析技术的任务，就是要从这种复杂的混合信号中，分解出不同物体各自的贡献比例和成分信息。

那么，为什么要进行光谱混合分析呢？这其中有着多方面的重要意义。

从资源管理的角度来看，通过准确分析遥感影像中的土地利用类型和植被覆盖情况，我们可以更好地规划和保护自然资源。

比如，能够清晰地了解某个区域的森林面积是否在减少，或者哪些地方的耕地受到了侵蚀。

在环境监测方面，它可以帮助我们监测水体的污染程度、大气中污染物的分布等。

例如，通过分析光谱特征，我们可以判断出某片水域中的藻类含量是否超标，或者某个区域的大气中是否存在过量的颗粒物。

对于城市规划，光谱混合分析能够提供关于城市土地利用、建筑物分布和基础设施状况的详细信息。

这有助于合理规划城市的发展，优化交通布局，提高城市的生活质量。

在农业领域，它可以用于评估农作物的生长状况、监测病虫害的发生，从而为精准农业提供有力的支持。

比如，通过分析遥感影像中农田的光谱特征，农民可以知道哪些区域的作物缺水、缺肥，以便及时采取措施。

实现光谱混合分析的方法有多种，其中较为常见的包括线性光谱混合模型和非线性光谱混合模型。

红外光谱多元分析理论、方法及应用

判别分析
根据已知类别的样本数据，建立判别函数，用于预测新样本的类别。
聚类分析
将相似性较高的样本归为同一类，用于未知样本的分类和识别。
红外光谱与多元分析的结合
数据预处理
在将红外光谱数据输入多元分析方法之前，需要进行数据预处理，如平滑、基线校正、归一化等，以提高数据的准确性和可靠性。
特征提取
利用多元分析方法对预处理后的红外光谱数据进行特征提取，提取出能够反映不同样品差异的关键特征。
了一种可靠的手段。
案例二
总结词
无损、原位
VS
详细描述
在生物大分子结构的研究中，红外光谱多元分析技术发挥了重要作用。该技术可以在不破坏生物样品的情况下，对生物大分子进行原位分析，获得其结构和动态信息。这为生物科学研究提供了重要的实验手段。
案例三
总结词
实时、在线
详细描述
红外光谱多元分析技术还可用于实时、在线监测大气污染物。通过测量大气中污染物的红外光谱，可以快速确定污染物的种类和浓度，为大气污染治理提供科学依据。这种方法的实时性和在线性使其成为大气污染监测的理想选择。
详细描述
在红外光谱多元分析中，判别分析法可用于建立分类模型，根据已知类别样品的红外光谱特征，构建判别函数，对未知类别的样品进行分类预测，实现样品的快速分类和鉴别。
03
红外光谱多元分析应用
在化学领域的应用
化学成分鉴定
红外光谱能够检测化学物质分子中的特定振动模式，通过比对标准谱图数据库，可以确定化学物质的成分。
THANKS
谢谢您的观看
样品处理要求高
红外光谱分析需要样品纯净度高，无杂质干扰，对样品处理要求较高。
定量分析精度低

端元可变的高光谱图像解混算法研究

端元可变的高光谱图像解混算法研究光谱解混是高光谱图像众多应用中需要解决的一个关键问题。

传统的光谱解混方法假定每类地物仅有一种端元光谱, 其端元集是固定的。

由于地物的复杂多样性和成像条件的影响, 高光谱图像“同物异谱〞和“异物同谱〞现象普遍存在, 从而导致对所有像元用固定的端元集进行解混精度受限。

因此, 研究端元可变的高光谱图像解混算法对提高高光谱图像的应用具有重要的意义。

本文针对端元可变的端元束提取以及多端元光谱混合分析算法展开研究, 主要研究内容如下:(1) 针对现有的基于光谱信息和空间信息的端元束提取方法没有充分考虑冗余端元的去除, 导致后续光谱解混误差增加和光谱解混复杂度较高的问题, 提出了一种基于超像素分割和像元纯度指数的端元束提取方法。

首先通过PPI 提取初始候选端元, 每个超像素内保存一个候选端元并以超像素为邻域计算其均质性指数,对保存的端元根据其均质性指数进行筛选, 通过聚类得到每类地物的端元束, 并进一步去除类内冗余端元。

仿真和真实数据实验结果说明, 所提出的方法能有效提取可变端元且能降低后续光谱解混的复杂度。

(2) 针对基于超像素分割和纯像元指数的端元束提取算法无法有效解决含多种植被和植被与其他地物致密混合的城市高光谱数据的问题,提出了基于植被指数分析和PPI 结合超像素分割的端元束提取方法。

对PPI 提取并经超像素分析保存的端元集, 根据植被指数分为植被端元、含植被的混合端元和其他端元三类。

纯植被端元集利用其最大光谱值分成两类, 其他端元集那么先利用均质性指数进行筛选,再通过聚类得到每类地物的端元束, 通过一系列实验验证了该算法的有效性。

(3) 多端元光谱混合分析同样是解决光谱可变性的有效手段。

为了在降低光谱混合分析时间复杂度的同时提高其精度, 提出了一种由粗到细的多端元光谱混合分析算法。

该算法首先基于扩展的端元集对每个像元进行全约束光谱混合粗分析, 确定含所有地物的初始端元集,在此根底上进一步进行精细光谱混合分析, 迭代光谱混合分析构建端元子集, 最终根据重构误差变化量确定各个像元的最优端元集。

优化端元提取方法的高光谱混合像元分解

优化端元提取方法的高光谱混合像元分解高光谱混合像元分解是一种常用的遥感数据分析方法，可以用于提取地物信息和监测环境变化。

在实际应用中，为了提高分解结果的准确性和可靠性，需要进行端元提取的优化。

端元提取是指从高光谱数据中选择代表地物的像元进行分解。

传统的端元提取方法主要基于经验或人工选择，存在以下问题：首先，传统方法需要人工选择代表地物样本进行端元提取，这种方式受主观因素干扰较大，容易引入误差。

为了减少主观因素的干扰，可以使用统计学方法来进行自动化的端元提取。

常用的统计学方法有聚类分析、主成分分析和最大似然分类等。

其次，传统方法在进行端元提取时通常只考虑了光谱信息，而忽略了空间信息。

然而，地物的空间分布特征对端元提取和混合像元分解结果的准确性和可靠性有重要影响。

因此，应该将空间信息考虑进来，可以利用地物边界信息和多源遥感数据进行融合，以提高端元提取的准确性。

此外，高光谱混合像元分解还需要考虑混合像元的数量和选择。

传统方法通常假设混合像元是由两个或三个端元组成的，但实际情况往往更为复杂，混合像元可能由多个端元组成。

因此，可以利用自适应光谱混合方法，对混合像元数量进行估计，并选择最优的混合像元组合来进行分解。

最后，在进行端元提取和混合像元分解时还应考虑光谱响应的非线性和光谱混叠的影响。

非线性效应会导致混合像元分解结果的偏差，光谱混叠则会造成端元提取的困难。

因此，可以利用非线性光谱混合像元分解方法和反混叠技术，来克服这些问题，提高分解结果的准确性。

综上所述，优化端元提取方法的高光谱混合像元分解可以使用统计学方法进行自动化的端元提取，同时考虑空间信息和光谱非线性效应等因素。

通过合理选择混合像元数量和采用反混叠技术，可以提高分解结果的准确性和可靠性，从而更好地应用于地物信息提取和环境监测等领域。

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多端元光谱混合分析综述戚文超;张霞;岳跃民【摘要】多端元光谱混合分析是一种端元可变的线性光谱混合分析方法,通过由不同种类和数量的纯净像元(端元)构成的端元组合,对混合像元进行分解.针对每类地物,该方法可以采用多条同种端元光谱进行解混,在一定程度上克服了同种地物的光谱变异问题,能够提高解混的精度.本文对多端元光谱混合分析的具体方法进行综述.首先,基于对多端元解混研究现状的深入分析,归纳了多端元光谱混合分析的基本流程.其次,对多端元解混涉及的端元选取方法进行总结,分别概述了图像端元和参考端元扩充的策略及优化的指标;在此基础上,系统论述了端元光谱库构建主要途径及其优缺点,并指出针对特定的研究区域最佳端元模型确定的方法.最后,提出多端元光谱混合分析存在的问题并给出相应的解决方案.【期刊名称】《遥感信息》【年(卷),期】2016(031)005【总页数】8页(P11-18)【关键词】多端元光谱混合分析;端元提取;端元扩充及优化;端元库构建;端元模型【作者】戚文超;张霞;岳跃民【作者单位】中国科学院遥感与数字地球研究所,北京100101;中国科学院大学,北京100049;中国科学院遥感与数字地球研究所,北京100101;中国科学院亚热带农业生态过程重点实验室,长沙410125【正文语种】中文【中图分类】P237因遥感传感器空间分辨率的限制和地物特征光谱的异质性，中等或低空间分辨率影像的像元中往往出现光谱混合现象，给遥感解译造成困扰。

为消除混合像元造成的影响，通常采用传统线性光谱混合分析模型(固定端元)对遥感影像进行混合像元分解。

但由于该模型未能充分考虑遥感数据光谱维类内光谱的可变性[1]，造成端元分解过剩(解混结果中端元数目远远大于端元的真实数目)以及用太少的端元进行解混导致精度不高的问题[2-3]。

为此，1988年Roberts等提出了多端元光谱混合分析(Multiple Endmember Spectral Mixture Analysis，MESMA)[4]。

多端元光谱混合分析(MESMA)方法是基于构成每个混合像元的端元种类及数量都是可变的，将像元光谱视为端元光谱的线性混合，利用不同地物光谱构成多种端元模型(允许每种地物选取多条光谱)，并对混合像元运行所有可能的端元组合模型，通过最优端元判断准则(如比例约束、均方根误差约束、残差约束)，挑选出适合每个像元的最佳端元模型，反演出像元中每个端元的分量[5]。

目前，基于中低空间分辨率的高光谱遥感数据，MESMA已被广泛应用于复杂多样的地理环境分析，其中包括地物组成信息的提取和土地覆盖分类[6]，不透水区域、雪颗粒以及火的尺寸制图[7-8],城市热岛效应和土地利用及空气污染的关系研究等[9]。

如Eckmann等[10]基于夜间ASTER影像，运用MESMA对研究区中亚像元级火的尺寸和温度进行估计，反演出混合像元中发光燃烧体、发烟燃烧体以及非燃烧体三种端元的丰度，促进火灾的监测和预报。

但解混精度受太阳光辐射和云层的影响较大。

赵莲等[11]基于端元在空间分布的聚类特征，采用格网的形式，运用MESMA 提取研究区冬小麦种植面积，消除端元分解过剩造成的影响，但其未能解决各格网分解结果的不连续及如何确定格网尺寸等问题。

刘正春等[12]基于TM遥感影像，采用光谱归一化的多端元解混方法，对研究区内的土地覆盖信息进行定量提取。

研究结果表明，与传统固定端元形式的线性光谱混合分析方法相比，该方法能够获得更高的解混精度，更有利于复杂多样的城市地区的混合像元分解。

由以上分析知，MESMA能更好地解释城市景观、森林、农场、沙漠、半干旱地区[13]、湖泊等研究区地物类内光谱的异质性，更适合在地表类型复杂多变的地区进行土地利用/覆盖信息的提取。

但由于用于解混的可变端元数目增多，MESMA也存有一定的问题，如解混效率低、解混过程复杂等[14-15]。

为对多端元解混做进一步研究，本文对多端元光谱混合分析过程中涉及的主要步骤进行了归纳与总结，多端元光谱混合分析示意图如图1所示。

由图1知，MESMA首先需要获得用于解混的初始端元，其中包括图像端元和参考端元。

其次，对获得的初始端元进行扩充，并采用一定的指标对扩充后的端元进行优化。

基于优化后的端元，可采用图像端元、参考端元或两种端元相结合的3种方式构建端元光谱库。

最后，从端元光谱库中挑选不同的端元组合模型进行解混，并依据端元模型优化指标确定多端元光谱混合分析的最佳端元模型。

为了确定影像中构成混合像元的端元数目、类型，以及与之相对应的端元光谱信息，在采用“图像端元”进行多端元光谱混合分析前，应对影像进行端元提取。

首先，在端元提取的过程中，涉及的估算端元数目的方法有主成分分析法(PCA)、虚拟维度法(VD)、HySime方法、噪声白化HFC[16-17]，以及根据影像MNF(最小噪声分离)变换后的特征值分布转折点的情况确定端元的数目等[18]。

一般情况下，研究区端元数目取决于波段去相关处理后的独立波段数，与研究区影像中大部分像元的具体情况、端元的种类以及遥感影像数据的信息量(影像的光谱维数)有关[19]。

基于估算的端元数目，可通过端元提取算法确定初始端元集。

根据影像中纯净端元的存在与否，端元提取算法包括端元识别算法和端元生成算法两大类。

其中，端元识别算法主要包括纯净像元指数(PPI)、顶点成分分析(VCA)、自动形态学端元提取算法(AMEE)、N-FINDR算法以及连续最大角锥算法(SMACC)等；端元生成算法主要包括迭代误差分析(IEA)、极小体积变换(MVT)、凸锥分析算法(CCA)和迭代限制端元(ICE)算法等[20-21]。

其中，端元生成算法提取端元的精度高于端元识别算法，但端元生成算法的运行效率较低[22]。

针对多端元光谱混合分析，目前常用的端元提取方法大致分为两类：1)首先采用最小噪声分离(MNF)变换对影像进行去相关处理，以消除噪声的影响。

其次，运用纯净像元指数法对去噪后的像元进行筛选。

最后，基于筛选结果，利用ENVI中的N 维可视化工具进行初始端元的选取。

2)基于影像对象的光谱、纹理、形状以及坡度等相关信息，采用支持向量机算法或最大似然算法对遥感影像进行监督分类。

综合考虑研究区实际情况和分类后土地覆盖类型，并结合不同地物光谱的反射差异来初选端元[23]。

如崔天翔等[24]针对湿地植被类型复杂多样的特点，通过采用MNF 变换、纯净像元指数PPI计算以及人机交互端元选取等一系列运算，构建五端元模型对研究区植被覆盖度进行估算。

廖春华等[25]将研究区的HIS数据进行MNF 变换，通过纯净像元指数和端元均方根误差相结合的方法提取端元光谱，实现了新疆石河子地区植被覆盖度的反演。

Wang等[26]采用MNF变化对影像进行去相关处理并计算PPI指数，利用N维可视化识别工具来提取植被和非植被端元，并采用RMSE指标将相似度较高的罂粟和小麦分离出来。

刘正春等[27]采用面向对象的分析方法对研究区影像进行监督分类，对分类结果图中的多种土地覆盖类型进行多端元光谱混合分析，成功获取各种土地覆盖类别的丰度图和分解残差图。

在端元提取的过程中，由于不同的研究区域内的地表成分各异，端元选择还要充分考虑图像地物类型和地物覆盖度的影响，一般提取影像中同类单一地物覆盖度大于75%的像元光谱用于解混，以减小解混误差[28]。

经以上端元提取步骤处理后，可以得到研究区每类地物的初始端元，其中包括端元的数目，端元的类型以及每种端元的光谱信息，为下一步端元的扩充和优化做准备。

对于每类物质，端元集应包含足够数量的端元以充分代表地物的光谱变化，故端元的数量应足够多；但端元增多不仅会增大端元间的干扰因素，而且端元模型数量成倍增加，降低了解混算法运行的效率，所以端元的数量又应充分的少[29-30]。

因此，在运用多端元光谱混合分析进行解混时，一般先采用一定的方法对初始端元进行扩充(包含所有可能典型地物并考虑同物异谱)，然后再采用一定的优化指标对扩充后的端元进行优化。

端元扩充的方法主要分为两大类：1)针对“图像端元”，可结合地面实际情况，将可能包含的地物类型的标准光谱库光谱经过插值或截取的方法对初始端元库进行扩充，或通过设定光谱角阈值对提取的初始端元进行扩充[31]。

2)针对采用野外实地测量的光谱或在实验室条件下对样本进行光谱反射率测量[32]获得的“参考端元”，可结合传感器光谱响应函数对参考光谱进行重采样，使其光谱分辨率及光谱范围与待解混影像一致，然后综合考虑外界条件(如矿物的风化水平)对地物光谱的影响，采用不同的梯度对端元光谱进行扩充[33]。

端元优化的方法主要有以下几种：最小平均光谱角法(MASA)、端元均方根误差法(EAR)、类别均方根误差法(CAR)、光谱角与光谱距离法(SASD)以及计数端元选择法(CoB)等。

其中，CoB最早是由Roberts于2003年提出的，用于从某一地物端元集中挑选最优端元光谱来模拟实际地物的该类别像元[34]。

在计数端元选择法(CoB)中，候选端元组合根据3个约束条件(丰度、RMSE、残差)来判断该端元组合分解类别中其他光谱的拟合度，记录下每条端元光谱被模拟为类内(in-CoB)及类外(out-CoB)的次数，理想的端元应具有最高in_CoB值及最低out_CoB值[35-36]。

为衡量光谱的普适性，一般采用计数指数(Count Based Index，CoBI)来挑选最优端元，且优先挑选同时具有高CoBI和in_CoB的端元。

如Liu和Yang[37]运用纯净像元指数法提取影像端元，借助"VIPER_Tools"工具，采用CoB和EAR指标来优选端元，并以RMSE作为最佳模型的评价指标，进行植被信息提取的研究。

Michishita等[38]指出不同的影像端元优化的指标不同，如TM影像端元优选的指标是In_CoB、Out_CoB、CoBI和EAR，而CoBI、EAR和MASA是MODIS影像端元优选的指标。

Wu等[39]通过决策树分类并结合归一化差值指数NDVI和生物物理成分指数BCI的方法提取端元，采用EAR指数优化端元，对城市不透水表面进行空间约束下的多端元解混研究。

经扩充和优化后的端元的光谱具有最大的类间差异性和最小的类内异质性，既能显著区别于其他类别，也能最佳地代表同类别地物光谱响应特征。

利用优化后的端元构建端元库，可提高多端元光谱混合分析的精度。

构建端元光谱库的方法大致可分为以下4种[40]：1)采用野外测量的地物光谱或者基于现存的地物波谱信息库构建“参考端元库”。

2)运用端元提取算法从研究区影像中提取的影像端元，并对其进行微调与优化，以此来建立“图像端元库”。

如李晓雪等[41]将草地类型图和土地利用分类图分别与影像叠加选择感兴趣区域ROI，建立图像端元库。