Anisotropic Tensor Deconvolution of Hyperspectral Images
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915736747769856 |
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| author | Wang, Xinjue Wang, Xiuheng Ollila, Esa Vorobyov, Sergiy A. |
| author_facet | Wang, Xinjue Wang, Xiuheng Ollila, Esa Vorobyov, Sergiy A. |
| contents | Hyperspectral image (HSI) deconvolution is a challenging ill-posed inverse problem, made difficult by the data's high dimensionality.We propose a parameter-parsimonious framework based on a low-rank Canonical Polyadic Decomposition (CPD) of the entire latent HSI $\mathbf{\mathcal{X}} \in \mathbb{R}^{P\times Q \times N}$.This approach recasts the problem from recovering a large-scale image with $PQN$ variables to estimating the CPD factors with $(P+Q+N)R$ variables.This model also enables a structure-aware, anisotropic Total Variation (TV) regularization applied only to the spatial factors, preserving the smooth spectral signatures.An efficient algorithm based on the Proximal Alternating Linearized Minimization (PALM) framework is developed to solve the resulting non-convex optimization problem.Experiments confirm the model's efficiency, showing a numerous parameter reduction of over two orders of magnitude and a compelling trade-off between model compactness and reconstruction accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11694 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Anisotropic Tensor Deconvolution of Hyperspectral Images Wang, Xinjue Wang, Xiuheng Ollila, Esa Vorobyov, Sergiy A. Image and Video Processing Computer Vision and Pattern Recognition Machine Learning Signal Processing Hyperspectral image (HSI) deconvolution is a challenging ill-posed inverse problem, made difficult by the data's high dimensionality.We propose a parameter-parsimonious framework based on a low-rank Canonical Polyadic Decomposition (CPD) of the entire latent HSI $\mathbf{\mathcal{X}} \in \mathbb{R}^{P\times Q \times N}$.This approach recasts the problem from recovering a large-scale image with $PQN$ variables to estimating the CPD factors with $(P+Q+N)R$ variables.This model also enables a structure-aware, anisotropic Total Variation (TV) regularization applied only to the spatial factors, preserving the smooth spectral signatures.An efficient algorithm based on the Proximal Alternating Linearized Minimization (PALM) framework is developed to solve the resulting non-convex optimization problem.Experiments confirm the model's efficiency, showing a numerous parameter reduction of over two orders of magnitude and a compelling trade-off between model compactness and reconstruction accuracy. |
| title | Anisotropic Tensor Deconvolution of Hyperspectral Images |
| topic | Image and Video Processing Computer Vision and Pattern Recognition Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2601.11694 |