Theoretical and experimental Assessment of noise effects on least squares spectral unmixing of hyperspectral images

The problem of input noise affecting the subpixel classification is examined in order to assess its relationship with the output noise. The approach followed in this study was to investigate the output noise level obtained with a least-squares subpixel classification algorithm applied to simulated spectra. The simulation of mixed pixel spectra took into account variable pixel composition and a selectable power of the superimposed noise. Noise was considered a zero-mean stochastic process over wavelength that was assumed to be jointly normal and uncorrelated. The paper outlines the structure and the mathematical properties of the performed unmixing simulations, and clearly shows the relationship between input and output noise. It is shown that a simple exponential law relates with substantial accuracy the standard deviation of input noise to that of the computed subpixel abundances for fully constrained unmixing. As expected, the cases of unconstrained and (abundances sum to one) partially constrained unmixing are controlled by a linear relationship between input and output noise amplitude. The paper also shows the dependence of unmixed abundances and output noise on the spectral similarity of end members involved in the unmixing. Three subpixel classification approaches (unconstrained, partially constrained, and fully constrained algorithms) were investigated.