Reweighted local collaborative sparse regression for hyperspectral unmixing

Abstract Sparse unmixing is based on the assumption that each mixed pixel in the hyperspectral image can be expressed in the form of linear combinations of known pure signatures in the spectral library. Collaborative sparse regression improves the unmixing results by solving a joint sparse regression problem, where the sparsity is simultaneously imposed to all pixels in the data set. However, hyperspectral images exhibit rich spatial correlation that can be exploited to better estimate endmember abundances. The work, based on the iterative reweighted algorithm and local collaborative sparse unmixing, utilized a reweighted local collaborative sparse unmixing (RLCSU). The simultaneous utilization of iterative reweighted minimization and local collaborative sparse unmixing (including spectral information and spatial information in the formulation, respectively) significantly improved the sparse unmixing performance. The optimization problem was simply solved by the variable splitting and augmented Lagrangian algorithm. Our experimental results were obtained by using both simulated and real hyperspectral data sets. The proposed RLCSU algorithm obtain better signal-to-reconstruction error (SRE, measured in dB) results than LCSU and CLSUnSAL algorithms in all considered signal-to-noise ratio (SNR) levels, especially in the case of low noise values. The RLCSU algorithm obtains a better SRE(dB) result (30.01) than LCSU (20.08) and CLSUnSAL (17.28) algorithms for the simulated data 1 with SNR = 50 dB. It demonstrated that the proposed method is an effective and accurate spectral unmixing algorithm.