MESMA, subpixel analysis, spectral mixing/unmixing
Multiple Endmember Spectral Mixture Analysis (MESMA) is a technique for estimating the proportion of each pixel that is covered by a series of known cover types - in other words, it seeks to determine the likely composition of each image pixel. Pixels that contain more than one cover type are called mixed pixels. “Pure” pixels contain only one feature or class. For example, a mixed pixel might contain vegetation, bare ground, and soil crust. A pure pixel would contain only one feature, such as vegetation. Mixed pixels can cause problems in traditional image classifications (e.g., supervised or unsupervised classification) because the pixel belongs to more than one class but can be assigned to only a single class. One way to address the problem of mixed pixels is to use subpixel analysis with hyperspectral imagery.
Subpixel analysis methods determines the component parts of mixed pixels by predicting the proportion of a pixel that belongs to a particular class or feature based on the spectral characteristics of its endmembers. It converts radiance to fractions of spectral endmembers that correspond to features on the ground.
Spectral endmembers are the “pure” spectra corresponding to each of the land cover classes. Ideally, spectral endmembers account for most of the image’s spectral variability and serve as a reference to determine the spectral make up of mixed pixels. Thus the definition of land cover classes, and selection of appropriate endmembers for each of these classes, are both critical in MESMA. Endmembers obtained from the actual image are generally preferred because no calibration is needed between selected endmembers and the measured spectra. These endmembers are assumed to represent the purest pixels in the image.
Selecting endmembers for natural systems can be exceedingly difficult because:
MESMA differs from other spectral mixture analysis such as Spectral Mixture Analysis (SMA) because it allows the number and the quantity of endmembers to vary pixel by pixel. SMA models pixel spectra as a linear combination of spectral signatures from two or more ground components. However, spectral mixture analysis does not account for the absence of one of the surface features or spectral variation within pure materials since it utilizes an invariable set of surface features. Unlike SMA, MESMA permits endmembers to vary on a per pixel basis. This technique uses whichever model that has the smallest root mean square error (RMSE) when compared to the spectral curve of the pixel.
MESMA was formulated by D.A. Roberts and colleagues using Airborne Visible Infrared Imaging Spectrometer (AVIRIS) imagery of chaparral in California's Santa Monica Mountains.
“The technique models remotely measured spectral data as linear combinations of pure spectra, called endmembers, while allowing the types and number of endmembers to vary on a per pixel basis. In this manner, vegetation is characterized by a unique set of endmembers as well as by the fractions. Reference endmembers were selected from a library of field and laboratory measured spectra of leaves, canopies, nonphotosynthetic materials (e.g. stems) and soils and used to develop a series of candidate models. Each candidate model was applied to the image, then, on per pixel basis, assessed in terms of fractions, root mean squared (RMS) error and residuals. If a model met all criteria, it was listed as a candidate for that pixel” (Roberts et al., 1998, p. 267).
The fundamental education for MESMA is
where a mixed pixel Liλ from location i is modeled as the sum of N endmembers, Lkλ, each covering a fraction fki of the pixel. The residual term εiλ describes the unmodeled portion of the radiance, and the chosen model for each pixel is the one that minimizes the root mean squared error (RMSE) over the included number of bands used in unmixing, B:
Hyperspectral imagery is recommended for MESMA. The following programs offer subpixel analysis capability:
Dennison, P.E., and Roberts, D.A. 2003. Endmember Selection for Multiple Endmember Spectral Mixture Analysis using Endmember Average RSME. Remote Sensing of Environment, 87(2-3), pp. 123-135. DOI: 10.1016/S0034-4257(03)00135-4.
Quintano , C., Fernández-Manso, A., Shimabukuro, Y.E., Pereira, G. 2012. Spectral unmixing. International Journal of Remote Sensing, 33(17). DOI: 10.1080/01431161.2012.661095.
Roberts, D.A., Gardner, M., Church, R., Ustin, S., Scheer, G., Green, R.O. 1998. Mapping chaparral in the Santa Monica Mountains using Multiple Endmember Spectral Mixture models. Remote Sensing of Environment, 65(3), pp. 267-279, ISSN 0034-4257, DOI: 10.1016/S0034-4257(98)00037-6. http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/20241/1/98-1135.pdf
Eckmann, T.C., Roberts, D.A., Still, C.J. 2008. Using multiple endmember spectral mixture analysis to retrieve subpixel fire properties from MODIS. Remote Sensing of Environment, 112(10), pp. 3773-3783. DOI: 10.1016/j.rse.2008.05.008.
Okin, G.S., Roberts, D.A., Murray, B., Okin, W. 2001. Practical limits on hyperspectral vegetation discrimination in arid and semiarid environments. Remote Sensing of Environment, 77(2), pp. 212-225. DOI: 10.1016/S0034-4257(01)00207-3 ftp://popo.jpl.nasa.gov/pub/docs/workshops/99_docs/46.pdf
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