Hyperspectral unmixing with _q regularization

Hyperspectral unmixing is an important technique for analyzing remote sensing images. In this paper, we consider and examine the l_q, 0 ≤ q ≤ 1 penalty on the abundances for promoting sparse unmixing of hyperspectral data. We also apply a first-order roughness penalty to promote piecewise smooth endmembers. A novel iterative algorithm for simultaneously estimating the endmembers and the abundances is developed and tested both on simulated and two real hyperspectral data sets. We present an extensive simulation study where we vary both the SNR and the sparsity of the simulated data and identify the model parameters that minimize the reconstruction errors and the spectral angle distance. We show that choosing 0 ≤ q ≤ 1 can outperform the l₁ penalty when the SNR is low or the sparsity of the underlying model is high. We also examine the effects of the imposing the abundance sum constraint using a real hyperspectral data set.