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Review of Spectral Unmixing for Hyperspectral Imagery

Review of Spectral Unmixing for Hyperspectral Imagery. Lidan Miao Sept. 29, 2005. Motivation. The wide existence of mixed signals In hyperspectral image, the measurement of a single pixel is usually a contribution from several materials ( endmembers ). What is spectral unmixing?

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Review of Spectral Unmixing for Hyperspectral Imagery

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  1. Review of Spectral Unmixingfor Hyperspectral Imagery Lidan Miao Sept. 29, 2005

  2. Motivation • The wide existence of mixed signals • In hyperspectral image, the measurement of a single pixel is usually a contribution from several materials (endmembers). • What is spectral unmixing? • A process by which mixed pixel spectra are decomposed into endmember signatures and their fractional abundances. • Applications • Subpixel detection. • Classification • Material quantification

  3. Data Mixing Model • Linear mixing • Mixing scale is macroscopic and there is negligible interaction among distinct endmembers. • Nonlinear mixing • Mixing scale is microscopic. The incident radiations scattered through multiple bounces involves several endmembers. Linear model Nonlinear model

  4. Linear Mixing Model • Measurement model • Observation vector • Material signature matrix • Abundance fractions • Nonnegative and sum-to-one constraints

  5. Unmixing Algorithms • Supervised • Obtain M from laboratory data or training samples. • With known M, unmixing is a least square problem. • Not reliable due to spatial and temporal variation in illumination and atmospheric conditions. • Unsupervised • Linear spectral mixture analysis (LSMA) • Two steps: estimate M from given data + inversing. • Independent component analysis (ICA) • How to interpret the system model? • Lagrange constrained neural network (LCNN) • Pixel-based algorithm.

  6. LSMA • Assumptions • There exist at least one pure pixel for each class. • The material signature matrix is the same for all image pixels in the scene. • The number of endmembers can be determined. • Two-step process • Endmember detection • Convex geometry-based approach (MVT, PPI, N-FINDR, VCA) • LSE-based approach (UFCLS, USCLS, UNCLS) • Abundance estimation • Least square method (LSE, SCLS, NCLS, FCLS) • Orthogonal subspace projection (OPS) • Quadratic programming (QP) • Target constrained method (CEM)

  7. Convex Geometry • Convex hull • The set of all convex combinations of point in C. • Simplex • Convex hull of k+1 affinely independent points. • Strong parallelism between LSMA and CG. • Endmember detection is equivalent to identifying vertices. Simplex in R2 Convex hull in R2

  8. LSE-based Approach • Minimize the LSE between the linear mixture model and estimated measurements. • Select the brightest pixel as the first endmember,after each iteration, select the most distinct pixel as new endmember. • Use currently selected endmembers to unmix and calculate LSE.

  9. ICA • System model • Application • Blind source separation (BSS) and deconvolution. • Assumption • Mutually independent sources. • Permutation and scaling problem: • This compromises its application in spectral unmixing

  10. ICA in Spectral Unmixing • Two interpretations of system model • Vector xi is the stack notation of image of band i. • Column of M is endmember signature. • Vector si is the abundance of endmember i at all pixel positions. • Sources are not mutually independent. • Vector xi is the spectrum of pixel i. • Vector mi is endmember signature. • Row vector si is the abundance of pixel i. • Sources are mutually independent.

  11. LCNN • System model • Pixel-by-pixel processing • Two principles • Maximum entropy • Given incomplete information, maximum entropy is the least bias estimate • Closed system, no energy exchange • Minimum Helmholtz free energy • The minimum free energy is achieved at thermal equilibrium state. • Open system, nonzero energy exchange

  12. Minimum Energy-based LCNN • Objective function • Nonlinear programming formulation • The problem in objective function cannot be solved by learning algorithm.

  13. Selection of spectral signatures Ground truth Abundance map Endmember signatures Generation of simulated scene Unmixing algorithm Extracted endmembers Estimated abundance Evaluation System • 1. Evaluation of abundance fraction • Root mean square error (RMSE) • Fractional abundance angle distance (FAAD) • 2. Evaluation of endmember signature • Spectral angle distance (SAD) • Spectral information divergence (SID) 2 1

  14. Simulated Data

  15. Unmixing Results (1)

  16. Unmixing Result (2) • There exist pure pixels in the scene (SNR=30dB) VCA USCLS

  17. Unmixing Result (3) • There are no pure pixels in the scene (SNR=30dB) VCA USCLS

  18. Unmixing Result (4)

  19. Experiments on Real Data (1) VCA N-FINDR

  20. Experiments on Real Data (2) USCLS FastICA

  21. Conclusion • Convex geometry-based methods can successfully extract endmembers. • ICA is not a robust algorithm for spectral unmixing. • More works on LCNN. • Spatial information? • Redefine the objective function?

  22. To be continued ...

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