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Sensors 2008, 8(2), 1321-1342; doi:10.3390/s8021321
Article

The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data

1
, 2,*  and 2
Received: 28 December 2007; Accepted: 19 February 2008 / Published: 22 February 2008
(This article belongs to the Special Issue Remote Sensing of Natural Resources and the Environment)
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Abstract: Spectral mixing is a problem inherent to remote sensing data and results in fewimage pixel spectra representing "pure" targets. Linear spectral mixture analysis isdesigned to address this problem and it assumes that the pixel-to-pixel variability in ascene results from varying proportions of spectral endmembers. In this paper we present adifferent endmember-search algorithm called the Successive Projection Algorithm (SPA).SPA builds on convex geometry and orthogonal projection common to other endmembersearch algorithms by including a constraint on the spatial adjacency of endmembercandidate pixels. Consequently it can reduce the susceptibility to outlier pixels andgenerates realistic endmembers.This is demonstrated using two case studies (AVIRISCuprite cube and Probe-1 imagery for Baffin Island) where image endmembers can bevalidated with ground truth data. The SPA algorithm extracts endmembers fromhyperspectral data without having to reduce the data dimensionality. It uses the spectralangle (alike IEA) and the spatial adjacency of pixels in the image to constrain the selectionof candidate pixels representing an endmember. We designed SPA based on theobservation that many targets have spatial continuity (e.g. bedrock lithologies) in imageryand thus a spatial constraint would be beneficial in the endmember search. An additionalproduct of the SPA is data describing the change of the simplex volume ratio between successive iterations during the endmember extraction. It illustrates the influence of a newendmember on the data structure, and provides information on the convergence of thealgorithm. It can provide a general guideline to constrain the total number of endmembersin a search.
Keywords: hyperspectral; spectral unmixing; endmember; simplex hyperspectral; spectral unmixing; endmember; simplex
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Zhang, J.; Rivard, B.; Rogge, D.M. The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data. Sensors 2008, 8, 1321-1342.

AMA Style

Zhang J, Rivard B, Rogge DM. The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data. Sensors. 2008; 8(2):1321-1342.

Chicago/Turabian Style

Zhang, Jinkai; Rivard, Benoit; Rogge, D. M. 2008. "The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data." Sensors 8, no. 2: 1321-1342.


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