Third-order tensors have been widely used in hyperspectral remote sensing because of their ability to maintain the three-dimensional structure of hyperspectral images. In recent years, hyperspectral unmixing algorithms based on tensor factorization have emerged, but these decomposition processes may be inconsistent with physical mechanism of unmixing. To solve this problem, this paper proposes a sparse and low-rank constrained tensor factorization unmixing algorithm (SPLRTF) based on a matrix-vector nonnegative tensor factorization (MV-NTF) framework. Considering the fact that each component tensor obtained by the image decomposition contains only one endmember and the corresponding abundance matrix has sparse property, a sparse constraint is imposed to ensure the accuracy of abundance maps. Since abundance maps also have low-rank attribute, in order to avoid the strict low-rank constraint in the original MV-NTF framework, a low-rank tensor regularization is introduced to flexibly express the low-rank characteristics of the abundance tensors, making the resulting abundance maps more in line with the actual scene. Then the optimization problem is solved by using the alternating direction method of multipliers. In experiments, simulated datasets are adopted to demonstrate the effectiveness of the sparse and low-rank constraints of the proposed algorithm, and real datasets from different sensors and different scenarios are used to verify its applicability.
a b s t r a c tNon-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regularized regression, our sparse eigenvalue based conditions are weaker than that of L1-regularization for parameter estimation and sparseness estimation. For the approximate global and approximate stationary (AGAS) solutions, almost the same conditions are also enough. We show that the desired AGAS solutions can be obtained by coordinate descent (CD) based methods. Finally, we perform some experiments to show the performance of CD methods on giving AGAS solutions and the degree of weakness of the estimation conditions required by the sharp concave regularizers.
Sparse unmixing with a semi-supervised fashion has been applied to hyperspectral remote sensing imagery. However, the imprecise spatial contextual information, the lack of global feature and the high mutual coherences of a spectral library greatly limit the performance of sparse unmixing. In order to address these prominent problems, a new paradigm to characterize sparse hyperspectral unmixing is proposed, namely, the superpixel-based weighted collaborative sparse regression and reweighted low-rank representation unmixing (SBWCRLRU). In the method, the weighted collaborative sparse regression explores the pixels shared the same support set to help the sparsity of abundance fraction, and the reweighted low rank representation minimizes the rank of the abundance matrix to promote the spatial consistency of the image. Meanwhile, superpixel segmentation is adopted to cluster the pixels into different spatial homogeneous regions to further improve the unmixing performance. Extensive experiments results conducted on both synthetic and real data demonstrate the effectiveness of the proposed SBWCRLRU. It can not only improve the performance of hyperspectral unmixing but also outperform the existing sparse unmixing approaches.
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