Abstract
The Fully Constrained Least Squares (FCLS) method discussed in Chap. 2 is a Linear Spectral Mixture Analysis (LSMA) technique which has been widely used for data unmixing. It assumes that data sample vectors can be represented by a set of signatures via a Linear Mixing Model (LMM) by which data sample vectors can then be unmixed by FCLS in terms of the abundance fractions of these signatures present in the data sample vectors subject to two physical constraints, Abundance Sum-to-one Constraint (ASC) and Abundance Non-negativity Constraint (ANC) imposed on LMM. Because of its use of ASC and ANC, FCLS has also been used to find endmembers in a similar manner to N-FINDR because ASC and ANC can be interpreted as the two abundance constraints used to impose on a simplex. In this case, FCLS is considered as SiMultaneous FCLS Endmember-Finding Algorithm (SM FCLS-EFA) in a similar manner to SiMultaneous N-FINDR (SM N-FINDR). So, in parallel to development of N-FINDR in Chang (2013), this chapter also develops a similar theory for SM FCLS-EFA for finding endmembers. Specifically, two sequential versions of SM FCLS, to be called SeQuential FCLS-EFA (SQ-FCLS-EFA) and SuCcessive FCLS (SC-FCLS-EFA), can also be derived as Endmember-Finding Algorithms (EFAs), both of which can be considered as the counterparts of N-FINDR, SeQuential N-FINDR (SQ N-FINDR), and SuCcessive N-FINDR (SC N-FINDR) in Chap. 6, respectively. However, unlike N-FINDR, which is designed to find pure signatures as endmembers, FCLS-EFA is specifically designed to find signatures that are not necessarily pure but rather spectrally distinct signatures to represent data best in terms of an LMM. So, to reflect its nature more accurately in finding signatures for LMM, the endmembers found by FCLS-EFA are indeed Virtual Signatures (VSs) as defined in Chang et al. (2010). To deal further with random issues in the use of initial conditions, three versions of SM FCLS-EFA—Initialization Driven FCLS-EFA (ID-FCLS-EFA), Iterative FCLS-EFA (IFCLS-EFA) , and Random FCLS-EFA (RFCLS-EFA)—are also developed corresponding to their respective counterparts developed for N-FINDR in Chang (2013), which are Initialization Driven N-FINDR (ID-N-FINDR), Iterative N-FINDR (IN-FINDR), and Random N-FINDR (RN-FINDR).
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References
Chang, C.-I 2003a. Hyperspectral imaging: techniques for spectral detection and classification. Dordrecht: Kluwer Academic/Plenum Publishers.
Chang, C.-I 2003b. How to effectively utilize information to design hyperspectral target detection and classification algorithms. Workshop in honor of Professor David Landgrebe on advances in techniques for analysis of remotely sensed data, NASA Goddard Visitor Center, Washington DC, October 27–28, 2003.
Chang, C.-I 2013. Hyperspectral data processing: algorithm design and analysis. New Jersey: Wiley. 2013.
Chang, C.-I, X. Jiao, Y. Du and M.-L. Chang. 2010. A review of unsupervised hyperspectral target analysis. EURASIP Journal on Advanced in Signal Processing 2010: Article ID 503752, 26 pp. doi:10.1155/2010/503752.
Chang, C.-I, X. Jiao, Y. Du and H.M. Chen. 2011a. Component-based unsupervised linear spectral mixture analysis for hyperspectral imagery. IEEE Transactions on Geoscience and Remote Sensing 49(11): 4123–4137.
Chang, C.-I, W. Xiong, H.M. Chen and J.W. Chai. 2011b, Maximum orthogonal subspace projection to estimating number of spectral signal sources for hyperspectral images. IEEE Journal of Selected Topics in Signal Processing 5(3): 504–520.
Chen, S.-Y., Y. Wang, C.C. Wu, C. Liu, and C.-I Chang. 2014a. Real time causal processing of anomaly detection in hyperspectral imagery. IEEE Transactions on Aerospace and Electronics Systems 50(2): 1511–1534.
Chen, S.Y., D. Paylor and C.-I Chang. 2014b. Anomaly discrimination in hyperspectral imagery. Satellite data compression, communication and processing X (ST146), SPIE international symposium on SPIE sensing technology + applications, Baltimore, MD, May 5–9, 2014.
Chen, S.Y., Y.C. Ouyang and C.-I Chang. 2014c. Recursive unsupervised fully constrained least squares methods. 2014 IEEE international geoscience and remote sensing symposium (IGARSS), Quebec Canada, July 13–18, 2014.
Gao, C., S.-Y. Chen, H.M. Chen, C.C. Wu, C.H. Wen and C.-I Chang. 2015. Fully abundance-constrained endmember finding for hyperspectral images. In 7th workshop on hyperspectral image and signal processing: evolution in remote sensing, (WHISPERS), Tokyo, Japan, June 2–5, 2015.
Harsanyi, J.C., and C.-I Chang. 1994. Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach. IEEE Transactions on Geoscience and Remote Sensing 32(4): 779–785.
Plaza, A., and C.-I Chang. 2006. Impact of initialization on design of endmember extraction algorithms. IEEE Transaction on Geoscience and Remote Sensing 44(11): 3397–3407.
Winter, M.E. 1999a. Fast autonomous spectral endmember determination in hyperspectral data. In Proceedings of 13th international conference on applied geologic remote sensing, Vancouver, B.C., Canada, vol. II, pp. 337–344.
Winter, M.E. 1999b. N-finder: an algorithm for fast autonomous spectral endmember determination in hyperspectral data. In Image spectrometry V, Proceedings of SPIE, vol. 3753, pp. 266–277.
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Chang, CI. (2016). Fully Abundance-Constrained Sequential Endmember Finding: Linear Spectral Mixture Analysis. In: Real-Time Progressive Hyperspectral Image Processing. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6187-7_9
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