Spectral mixture analysis: Linear and semi-parametric full and iterated partial unmixing in multi- and hyperspectral image data

As a supplement or an alternative to classification of hyperspectral image data linear and semi-parametric mixture models are considered in order to o btain estimates of abundance of each class or end-member in pixels with mix ed membership. Full unmixing based on both ordinary least squares (OLS) and non-negative least squares (NNLS), and the partial unmixing methods orthog onal subspace projection (OSP), constrained energy minimization (CEM) and a n eigenvalue formulation alternative are dealt with. The solution to the ei genvalue formulation alternative proves to be identical to the CEM solution . The matrix inversion involved in CEM can be avoided by working on (a subs et of) orthogonally transformed data such as signal maximum autocorrelation factors, MAFs, or signal minimum noise fractions, MNFs. This will also cau se the partial unmixing result to be independent of the noise isolated in t he MAF/MNFs not included in the analysis. CEM and the eigenvalue formulatio n alternative enable us to perform partial unmixing when we know one desire d end-member spectrum only and not the full set of end-member spectra. This is an advantage over full unmixing and OSP. The eigenvalue formulation of CEM inspires us to suggest an iterated CEM scheme. Also the target constrai ned interference minimized filter (TCIMF) is described. Spectral angle mapp ing (SAM) is briefly described. Finally, semi-parametric unmixing (SPU) bas ed on a combined linear and additive model with a non-linear, smooth functi on to represent end-member spectra unaccounted for is introduced. An exampl e with two generated bands shows that both full unmixing, the CEM, the iter ated CEM and TCIMF methods perform well. A case study with a 30 bands subse t of AVIRIS data shows the utility of full unmixing, SAM, CEM and iterated CEM to more realistic data. Iterated CEM seems to suppress noise better tha n CEM. A study with AVIRIS spectra generated from real spectra shows (1) th at ordinary least squares in this case with one unknown spectrum performs b etter than non-negative least squares, and (2) that although not fully sati sfactory the semi-parametric model gives better estimates of end-member abu ndances than the linear model.