Error Approximation of Hyperspectral Unmixing via Correntropy-Induced Metric

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In this letter, a sparse-constrained hyperspectral unmixing method via reconstruction error approximation is proposed. In the presented method, all the noises and the outliers are treated as diverse interferences and addressed to minimize the regularization error. Several techniques are involved in our presented approach: 1) to attenuate the interference of noise, an auxiliary variable is introduced; 2) based on the relative noiseless hyperspectral image, a sparse constraint is employed to achieve the sparsity; and 3) besides, the correntropy-induced metric (CIM), instead of the $L_{2}$ - or $L_{2,1}$ -norm loss function, is utilized to measure the quality of the unmixing model approximation. A series of experiments on the synthetic and real hyperspectral images is conducted, and all the experiment results show the efficacy of the proposed approach.