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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]

The noise corruption problem commonly exists in hyperspectral images (HSIs) and severely affects the accuracy of hyperspectral unmixing algorithms. The noise formulation existing in HSIs is relatively complex and would change in conjunction with different devices and imaging settings. For real applications, applying denoising approaches without accurate close-to-reality noise modeling before unmixing may not improve, but rather degrade the unmixing performance. This study proposes a robust hyperspectral unmixing method with practical learning-based hyperspectral image denoising. We formulated a close-to-reality noise model for hyperspectral data and provide a calibration approach for the noise parameters. On the basis of the calibrated noise model, synthetic data were generated and used for training a KST-based denoising network. The noisy hyperspectral data were firstly denoised by the trained denoising network and were then used to perform the unmixing process. A variety of unmixing algorithms can be integrated into our method to improve the accuracy of unmixing in noisy situations. In the experiments, several widely used unmixing algorithms were employed to verify the effect of the proposed method. The experimental results on both synthetic and real demonstrated that our proposed method can handle HSI data with various gain settings and helps to improve the unmixing performance effectively. [ABSTRACT FROM AUTHOR]

This paper presents a new parameterized nonlinear least squares (PNLS) algorithm for unsupervised nonlinear spectral unmixing (UNSU). The PNLS-based algorithms transform the original optimization problem with respect to the endmembers, abundances, and nonlinearity coefficients estimation into separate alternate parameterized nonlinear least squares problems. Owing to the Sigmoid parameterization, the PNLS-based algorithms are able to thoroughly relax the additional nonnegative constraint and the nonnegative constraint in the original optimization problems, which facilitates finding a solution to the optimization problems. Subsequently, we propose to solve the PNLS problems based on the Gauss–Newton method. Compared to the existing nonnegative matrix factorization (NMF)-based algorithms for UNSU, the well-designed PNLS-based algorithms have faster convergence speed and better unmixing accuracy. To verify the performance of the proposed algorithms, the PNLS-based algorithms and other state-of-the-art algorithms are applied to synthetic data generated by the Fan model and the generalized bilinear model (GBM), as well as real hyperspectral data. The results demonstrate the superiority of the PNLS-based algorithms. [ABSTRACT FROM AUTHOR]