Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing
Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing
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DOI：
10.1109/jstars.2023.3238653
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发表时间：
2022-05
影响因子：
5.5
通讯作者：
Meng Ding;Xiao Fu;Xile Zhao
中科院分区：
文献类型：
--
作者：
Meng Ding;Xiao Fu;Xile Zhao
带多线性秩-$（L_{r}，L_{r}，1）$项的块项张量分解模型（简称“${\mathsf{LL 1}}$张量分解”）为高光谱解混（HU）提供了一种有价值的替代公式，在经典矩阵分解（MF）方法不能提供这种保证的情况下，它确保了端元/丰度的可识别性。然而，现有的基于${\mathsf{LL 1}}$张量分解的HU算法使用张量的三因子参数化（即，高光谱图像立方体），这导致难以合并HU中出现的结构先验信息。因此，他们的算法往往表现出高的每次迭代的复杂性和缓慢的收敛。本文重点介绍HU中结构约束和正则化项下的${\mathsf{LL 1}}$张量分解。我们的算法使用的张量模型的两个因素重新参数化。与基于MF的方法一样，因子对应于HU背景下的端元和丰度。因此，所提出的框架是自然的，将物理动机的先验在HU。为了解决公式化的优化问题，提出了一种基于两块交替梯度投影（GP）的算法。提出了精心设计的投影求解器，以实现GP算法具有相对较低的每次迭代的复杂度。提出了一种基于外推的加速策略来加速GP算法。这种外推多块算法在文献中只具有渐近收敛保证。我们的分析表明，该算法收敛到附近的一个稳定点在有限的迭代，在合理的条件下。实验结果表明，与现有的基于${\mathsf{LL 1}}$-分解的HU算法相比，该算法具有数量级的加速比和可观的HU性能增益.
The block-term tensor decomposition model with multilinear rank-$(L_{r},L_{r},1)$ terms (or the “${\mathsf{LL1}}$ tensor decomposition” in short) offers a valuable alternative formulation for hyperspectral unmixing (HU), which ensures the identifiability of the endmembers/abundances in cases where classic matrix factorization (MF) approaches cannot provide such guarantees. However, the existing ${\mathsf{LL1}}$-tensor-decomposition-based HU algorithms use a three-factor parameterization of the tensor (i.e., the hyperspectral image cube), which causes difficulties in incorporating structural prior information arising in HU. Consequently, their algorithms often exhibit high per-iteration complexity and slow convergence. This article focuses on ${\mathsf{LL1}}$ tensor decomposition under structural constraints and regularization terms in HU. Our algorithm uses a two-factor reparameterization of the tensor model. Like in the MF-based approaches, the factors correspond to the endmembers and abundances in the context of HU. Thus, the proposed framework is natural to incorporate physics-motivated priors in HU. To tackle the formulated optimization problem, a two-block alternating gradient projection (GP)-based algorithm is proposed. Carefully designed projection solvers are proposed to implement the GP algorithm with a relatively low per-iteration complexity. An extrapolation-based acceleration strategy is proposed to expedite the GP algorithm. Such an extrapolated multiblock algorithm only had asymptotic convergence assurances in the literature. Our analysis shows that the algorithm converges to the vicinity of a stationary point within finite iterations, under reasonable conditions. Empirical study shows that the proposed algorithm often attains orders-of-magnitude speedup and substantial HU performance gains compared with the existing ${\mathsf{LL1}}$-decomposition-based HU algorithms.