Sparse hyperspectral unmixing using an approximate L₀ norm

Sparse unmixing aims at finding an optimal subset of spectral signatures in a large spectral library to effectively model each pixel in the hyperspectral image and compute their fractional abundances. In most previous work concerned with the sparse unmixing, L₂ norm is used to measure the error tolerance and the L₁ norm is added as the sparsity regularization. However, in some applications, using L₁ norm to measure the error tolerance has significant robustness advantages over the L₂ norm. Besides, in some cases, using a smooth function to approximate the L₀ norm can obtain more accurate results than the L₁ norm in the field of sparse regression. Thus, in this paper, we consider the two alternative choices for sparse unmixing. A reweighted iteration algorithm is also proposed so that the unconvex regularizer (smoothed L₀ norm) can be efficiently solved through transforming it into a series of weighted L ₁ regularizer problems. Experimental results on both synthetic and real hyperspectral data demonstrate the efficacy of the new models.