Sparse and Low-Rank Constrained Tensor Factorization for Hyperspectral Image Unmixing

Abstract

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.

Superpixel-Based Weighted Collaborative Sparse Regression and Reweighted Low-Rank Representation for Hyperspectral Image Unmixing

“…1) Samson Data: the data are generated by the SAMSON sensor [14]. It contains 156 channels with the wavelengths from 0.401 ~ 0.889𝜇𝑚 .…”

“…Several spectral unmixing approaches based on geometry [7]- [9], statistics [10], [11], nonnegative matrix factorization (NMF) [12]- [14] and sparse regression [5], [15] are mainly introduced in LMM. Although geometry and statistics approaches are simple and fast, the presence of pure materials assumptions in hyperspectral data are usually required and accompanied with higher computational complexity.…”

“…Recently, Low-Rank Representation (LRR) has received considerable attention for better learning the spatial-spectral low dimensional embedding [14], [36]. The joint sparse and low-rank learning (J-SLoL) [37] method is introduced for spectral unmixing by sharing sparse coefficients and performing low-rank constraints.…”

SSCU-Net: Spatial–Spectral Collaborative Unmixing Network for Hyperspectral Images

“…On the other hand, in [24] and [25], a weighted sparse unmixing framework with weighted l 1 norm is proposed, which penalizes the nonzero elements in the abundance matrix by introducing one or more weighting factors. Meanwhile, a variety of spatial and/or spectral weighted regularizers [26]- [30] have also been proposed to introduce related spatial and spectral information in HSI to improve the unmixing results.…”

Hyperspectral Sparse Unmixing With Spectral-Spatial Low-Rank Constraint

“…The high spatial correlation of the image implies the low rankness of the abundance matrix [26]. Accordingly, when the low-rank constraint is imposed on the abundance matrix, the low-dimensional subspace structure of the image will be well preserved [27]. More recently, the sparsity and lowrank constraints [28] were simultaneously imposed on the abundance matrix to reduce the solution space.…”