Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing
The block-term tensor decomposition model with multilinear rank-<inline-formula><tex-math notation="LaTeX">$(L_{r},L_{r},1)$</tex-math></inline-formula> terms (or the “<inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</t...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2023-01-01
|
| Series: | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10022317/ |
| _version_ | 1811168714063609856 |
|---|---|
| author | Meng Ding Xiao Fu Xi-Le Zhao |
| author_facet | Meng Ding Xiao Fu Xi-Le Zhao |
| author_sort | Meng Ding |
| collection | DOAJ |
| description | The block-term tensor decomposition model with multilinear rank-<inline-formula><tex-math notation="LaTeX">$(L_{r},L_{r},1)$</tex-math></inline-formula> terms (or the “<inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula> tensor decomposition” in short) offers a valuable alternative formulation for <italic>hyperspectral unmixing</italic> (HU), which ensures the identifiability of the endmembers/abundances in cases where classic matrix factorization (MF) approaches cannot provide such guarantees. However, the existing <inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula>-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 <inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula> 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 <italic>gradient projection</italic> (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 <inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula>-decomposition-based HU algorithms. |
| first_indexed | 2024-04-10T16:31:23Z |
| format | Article |
| id | doaj.art-7c6f90a000fa49efa82a3e4da45000bc |
| institution | Directory Open Access Journal |
| issn | 2151-1535 |
| language | English |
| last_indexed | 2024-04-10T16:31:23Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing |
| spelling | doaj.art-7c6f90a000fa49efa82a3e4da45000bc2023-02-09T00:00:14ZengIEEEIEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing2151-15352023-01-01161691170910.1109/JSTARS.2023.323865310022317Fast and Structured Block-Term Tensor Decomposition for Hyperspectral UnmixingMeng Ding0https://orcid.org/0000-0002-8670-0846Xiao Fu1https://orcid.org/0000-0003-4847-9586Xi-Le Zhao2https://orcid.org/0000-0002-6540-946XSchool of Mathematics, Southwest Jiaotong University, Chengdu, ChinaSchool of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, USASchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, ChinaThe block-term tensor decomposition model with multilinear rank-<inline-formula><tex-math notation="LaTeX">$(L_{r},L_{r},1)$</tex-math></inline-formula> terms (or the “<inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula> tensor decomposition” in short) offers a valuable alternative formulation for <italic>hyperspectral unmixing</italic> (HU), which ensures the identifiability of the endmembers/abundances in cases where classic matrix factorization (MF) approaches cannot provide such guarantees. However, the existing <inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula>-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 <inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula> 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 <italic>gradient projection</italic> (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 <inline-formula><tex-math notation="LaTeX">${\mathsf{LL1}}$</tex-math></inline-formula>-decomposition-based HU algorithms.https://ieeexplore.ieee.org/document/10022317/Hyperspectral unmixingstructured block-term tensor decompositionalternating gradient projection |
| spellingShingle | Meng Ding Xiao Fu Xi-Le Zhao Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing Hyperspectral unmixing structured block-term tensor decomposition alternating gradient projection |
| title | Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing |
| title_full | Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing |
| title_fullStr | Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing |
| title_full_unstemmed | Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing |
| title_short | Fast and Structured Block-Term Tensor Decomposition for Hyperspectral Unmixing |
| title_sort | fast and structured block term tensor decomposition for hyperspectral unmixing |
| topic | Hyperspectral unmixing structured block-term tensor decomposition alternating gradient projection |
| url | https://ieeexplore.ieee.org/document/10022317/ |
| work_keys_str_mv | AT mengding fastandstructuredblocktermtensordecompositionforhyperspectralunmixing AT xiaofu fastandstructuredblocktermtensordecompositionforhyperspectralunmixing AT xilezhao fastandstructuredblocktermtensordecompositionforhyperspectralunmixing |