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Nonnegative matrix factorization (NMF) and its numerous variants have been extensively studied and used in hyperspectral unmixing (HU). With the aid of the designed deep structure, deep NMF-based methods demonstrate advantages in exploring the hierarchical features of complex data. However, a noise corruption problem commonly exists in hyperspectral data and severely degrades the unmixing performance of deep NMF-based methods when applied to HU. In this study, we propose an ℓ 2 , 1 norm-based robust deep nonnegative matrix factorization ( ℓ 2 , 1 -RDNMF) for HU, which incorporates an ℓ 2 , 1 norm into the two stages of the deep structure to achieve robustness. The multiplicative updating rules of ℓ 2 , 1 -RDNMF are efficiently learned and provided. The efficiency of the presented method is verified in experiments using both synthetic and genuine data. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is a crucial technique for exploiting remotely sensed hyperspectral data, which aims at estimating a set of spectral signatures, called endmembers and their corresponding proportions, called abundances. The performance of HU is often seriously degraded by various kinds of noise existing in hyperspectral images (HSIs). Most of existing robust HU methods are based on the assumption that noise or outlier only exists in one kind of formulation, e.g., band noise or pixel noise. However, in real-world applications, HSIs are unavoidably corrupted by noisy bands and noisy pixels simultaneously, which require robust HU in both the spatial dimension and spectral dimension. Meanwhile, the sparsity of abundances is an inherent property of HSIs and different regions in an HSI may possess various sparsity levels across locations. This article proposes a correntropy-based spatial-spectral robust sparsity-regularized unmixing model to achieve 2-D robustness and adaptive weighted sparsity constraint for abundances simultaneously. The updated rules of the proposed model are efficient to be implemented and carried out by a half-quadratic technique. The experimental results obtained by both synthetic and real hyperspectral data demonstrate the superiority of the proposed method compared to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is a crucial technique for exploiting remotely sensed hyperspectral data, which aims to estimate a set of spectral signatures, called endmembers and their corresponding proportions, called abundances. Nonnegative matrix factorization (NMF) and its various robust extensions have been widely applied to HU. Most existing robust NMF methods consider that noises only exist in one kind of formulation. However, the hyperspectral images (HSIs) are unavoidably corrupted by noisy bands and noisy pixels simultaneously in the real applications. This paper proposes a novel spectral–spatial robust NMF model by incorporating $\ell _{2,1}$ norm and $\ell _{1,2}$ norm, which achieves robustness to band noise and pixel noise simultaneously. The Huber’s M-estimator is integrated into the proposed model to achieve better assignations of weights for each pixel and band with various noise intensities, which avoids the singularity problem and effectively improves the unmixing performance. The elegant updating rules of the proposed spectral–spatial robust model are also efficiently learned and provided. Experiments are conducted on both synthetic and real hyperspectral data sets. The experimental results demonstrate the effectiveness of the proposed methods in unmixing performance. [ABSTRACT FROM AUTHOR]