Does Independent Component Analysis Play a~Role in Unmixing Hyperspectral Data?

Abstract

Abstract-Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2) sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.Index Terms-Independent component analysis (ICA), independent factor analysis (IFA), mixture of Gaussians, unmixing hyperspectral data.

Dimensionality reduction for hyperspectral imagery based on fastica

“…3(b) shows the six ICs obtained by the proposed method, where the different targets were detected and extracted in separate components for classification. The six ICs represent grass, towers, vegetation, trees, hay-window and corns respectively [15] . The corresponding six ICs produced by the proposed method without MNF is given in Fig.…”

Indirect rock type modeling using geostatistical simulation of independent components in Nohkouhi volcanogenic massive sulfide deposit, Iran

“…ICA has been used in many different fields such as face recognition (Bartlett et al 2002;Déniz et al 2003;Draper et al 2003;Kim et al 2005), image classification (Chen and Zhang, 1999;Lee and Lewicki, 2002;Bigdely-Shamlo et al 2002), text classification (Pu and Yang, 2006), seismic signal processing (Acernese and Ciaramella, 2003), and hyperspectral data processing (Chiang et al 2000;Fiori, 2003;Nascimento and Dias, 2005;Gholami et al, 2012). Iwamori and Albarède (2008) and Iwamori et al (2010) used Fast ICA to extract independent features of isotopic data of oceanic basalts to illuminate global geochemical structure and mantle dynamics.…”

Null Subspace Analysis for Spectral Unmixing in Hyperspectral Remote Sensing

“…It extracts endmembers and obtains abundance fractions simultaneity, by maximizing the nongaussianity measure. However there are always mistakes in ICA [14].Sum to one least square [15], non-negative constrain least square(NNLS) [16] [17] and full constrain least square(FCLS) [18] are the approaches of abundance inverse, based on the classic solution to least square problem. They consider the physics constrained conditions in LMM and introduce these conditions to the solution of least square.…”