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Sparse unmixing (SU) algorithms use the existing spectral library as prior knowledge to analyze the endmembers and estimate abundance maps. The majority of SU algorithms use loss functions based on the $L_{2,1}$ -norm or $F$ -norm to minimize reconstruction error. They have different advantages and shortcomings. In short, $F$ -norm has a differentiable characteristic, and it is easy to minimize as a loss function. However, it is very sensitive to heavy noise and outliers. While the $L_{2,1}$ -norm emphasizes the reconstruction error on each band and is robust to noise with different intensities in different bands. But the $L_{2,1}$ -norm is nondifferentiable at zero-point. This article introduces an adaptive loss function based on the $\sigma $ -norm for SU, which combines the advantages of the $L_{2,1}$ -norm and $F$ -norm. The adaptive loss function is related to a nonnegative parameter $\sigma $. By adjusting the parameter $\sigma $ , the adaptive loss function can approach the $F$ -norm or $L_{2,1}$ -norm. To the best of our knowledge, it is the first time to apply an adaptive loss function to SU. Moreover, the adaptive loss function is globally differentiable, and we propose an optimization algorithm for the adaptive loss function and verify its convergence. Experiments on real-world and synthetic HSIs show that the adaptive loss function effectively enhances the performance of the SU algorithms. [ABSTRACT FROM AUTHOR]

Hyperspectral image super-resolution (SR) methods based on deep learning have achieved significant progress recently. However, previous methods lack the joint analysis between spectrum and horizontal or vertical direction. Besides, when both 2D and 3D convolution are in the network, the existing models cannot effectively combine the two. To address these issues, in this article, we propose a novel hyperspectral image SR method by exploring the relationship between 2D/3D convolution (ERCSR). Our method alternately employs 2D and 3D units to solve the problem of structural redundancy by sharing spatial information during reconstruction for existing model, which can enhance the learning ability of 2D spatial domain. Importantly, compared with the network using 3D units, i.e., 2D units are replaced by 3D units, it can not only reduce the size of the model but also improve the performance of the model. Furthermore, to exploit the spectrum fully, the split adjacent spatial and spectral convolution (SAEC) is designed to parallelly explore information between spectrum and horizontal or vertical direction in space. Experiments on widely used benchmark datasets demonstrate that the proposed approach outperforms state-of-the-art SR algorithms across different scales in terms of quantitative and qualitative analysis. [ABSTRACT FROM AUTHOR]

The fusion of a low-spatial-resolution hyperspectral image (HSI) (LR-HSI) with its corresponding high-spatial-resolution multispectral image (MSI) (HR-MSI) to reconstruct a high-spatial-resolution HSI (HR-HSI) has been a significant subject in recent years. Nevertheless, it is still difficult to achieve the cross-mode information fusion of spatial mode and spectral mode when reconstructing HR-HSI for the existing methods. In this article, based on a convolutional neural network (CNN), an interpretable spatial–spectral reconstruction network (SSR-NET) is proposed for more efficient HSI and MSI fusion. More specifically, the proposed SSR-NET is a physical straightforward model that consists of three components: 1) cross-mode message inserting (CMMI); this operation can produce the preliminary fused HR-HSI, preserving the most valuable information of LR-HSI and HR-MSI; 2) spatial reconstruction network (SpatRN); the SpatRN concentrates on reconstructing the lost spatial information of LR-HSI with the guidance of spatial edge loss (Lspat); and 3) spectral reconstruction network (SpecRN); the SpecRN pays attention to reconstruct the lost spectral information of HR-MSI under the constraint of spatial edge loss ({Lspec). Comparative experiments are conducted on six HSI data sets of Urban, Pavia University (PU), Pavia Center (PC), Botswana, Indian Pines (IP), and Washington DC Mall (WDCM), and the proposed SSR-NET achieves the superior or competitive results in comparison with seven state-of-the-art methods. The code of SSR-NET is available at https://github.com/hw2hwei/SSRNET. [ABSTRACT FROM AUTHOR]

Band selection is one of the most important technique in the reduction of hyperspectral image (HSI). Different from traditional feature selection problem, an important characteristic of it is that there is usually strong correlation between neighboring bands, that is, bands with close indexes. Aiming to fully exploit this prior information, a novel band selection method called optimal neighborhood reconstruction (ONR) is proposed. In ONR, band selection is considered as a combinatorial optimization problem. It evaluates a band combination by assessing its ability to reconstruct the original data, and applies a noise reducer to minimize the influence of noisy bands. Instead of using some approximate algorithms, ONR exploits a recurrence relation that underlies the optimization target to obtain the optimal solution in an efficient way. Besides, we develop a parameter selection approach to automatically determine the parameter of ONR, ensuring it is adaptable to different data sets. In experiments, ONR is compared with some state-of-the-art methods on six HSI data sets. The results demonstrate that ONR is more effective and robust than the others in most of the cases. [ABSTRACT FROM AUTHOR]