Spectral unmixing is a consequential preprocessing task in hyperspectral image interpretation. With the help of large spectral libraries, unmixing is equivalent to finding the optimal subset of the library entries that can best model the image. Sparse regression techniques have been widely used to solve this optimization problem, since the number of materials present in a scene is usually small. However, the high mutual coherence of library signatures negatively affects the sparse unmixing performance. To cope with this challenge, a new algorithm called spectral-spatial low-rank sparse unmixing (SSLRSU) is established. In this article, the double weighting factors under the l ₁ framework aim to improve the row sparsity of the abundance matrix and the sparsity of each abundance map. Meanwhile, the low-rank regularization term exploits the low-dimensional structure of the image, which makes for accurate endmember identification from the spectral library. The underlying optimization problem can be solved by the alternating direction method of multipliers efficiently. The experimental results, conducted by using both synthetic and real hyperspectral data, uncover that the proposed SSLRSU strategy can get accurate unmixing results over those given by other advanced sparse unmixing strategies.

Recently, many variational models involving high order derivatives have been widely used in image processing, because they can reduce staircase effects during noise elimination. However, it is very challenging to construct efficient algorithms to obtain the minimizers of original high order functionals. In this paper, we propose a new linearized augmented Lagrangian method for Euler's elastica image denoising model. We detail the procedures of finding the saddle-points of the augmented Lagrangian functional. Instead of solving associated linear systems by FFT or linear iterative methods (e.g., the Gauss-Seidel method), we adopt a linearized strategy to get an iteration sequence so as to reduce computational cost. In addition, we give some simple complexity analysis for the proposed method. Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method, and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.

Integrating a low-spatial-resolution hyperspectral image (LR-HSI) with a high-spatial-resolution multispectral image (HR-MSI) is recognized as a valid method for acquiring HR-HSI. Among the current fusion approaches, the tensor ring (TR) decomposition-based method has received growing attention owing to its superior performance in preserving the spatial-spectral correlation. Based on TR decomposition, the degradation model is developed via the spectral and spatial cores in TR. Here, we study the low-rankness of TR factors from the TNN perspective and consider the mode-2 logarithmic TNN (LTNN) on each TR factor. A novel fusion model is proposed by incorporating this LTNN regularization and the weighted total variation which is to promote the continuity of HR-HSI in the spatial-spectral domain. Meanwhile, we have devised a proximal alternating minimization algorithm to solve the proposed model. The experimental results indicate that our method improves the visual quality and exceeds the existing state-of-the-art fusion approaches concerning various quantitative metrics.

Sparse unmixing plays a crucial role in the field of hyperspectral image unmixing technology, leveraging the availability of pre-existing endmember spectral libraries. In recent years, there has been a growing trend in incorporating spatial information from hyperspectral images into sparse unmixing models. There is a strong spatial correlation between pixels in hyperspectral images (that is, the spatial information is very rich), and many sparse unmixing algorithms take advantage of this to improve the sparse unmixing effect. Since hyperspectral images are susceptible to noise, the feature separability of ground objects is reduced, which makes most sparse unmixing methods and models face the risk of degradation or even failure. To address this challenge, a novel robust dual spatial weighted sparse unmixing algorithm (RDSWSU) has been proposed for hyperspectral image unmixing. This algorithm effectively utilizes the spatial information present in the hyperspectral images to mitigate the impact of noise during the unmixing process. For the proposed RDSWSU algorithm, which is based on ${\mathsf{\ell }}_1$ sparse unmixing framework, a pre-calculated superpixel spatial weighting factor is used to smooth the noise, so as to maintain the original spatial structure of hyperspectral images. The RDSWSU algorithm, which builds upon the ${\mathsf{\ell }}_1$ sparse unmixing framework, employs a pre-calculated spatial weighting factor at the superpixel level. This factor aids in noise smoothing and helps preserve the inherent spatial structure of hyperspectral images throughout the unmixing process. Additionally, another spatial weighting factor is utilized in the RDSWSU algorithm to capture the local smoothness of abundance maps at the sub-region level. This factor helps enhance the representation of piecewise smooth variations within different regions of the hyperspectral image. Specifically, the combination of these two spatial weighting factors in the RDSWSU algorithm results in an enhanced sparsity of the abundance matrix. The RDSWSU algorithm, which is a sparse unmixing model, offers an effective solution using the alternating direction method of multiplier (ADMM) with reduced requirements for tuning the regularization parameter. The proposed RDSWSU method outperforms other advanced sparse unmixing algorithms in terms of unmixing performance, as demonstrated by the experimental results on synthetic and real hyperspectral datasets.