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求解大规模线性问题的张量GMRES算法
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Abstract:
彩色图像和视频通常可以被描述为高阶张量。本文基于三阶张量t-积，讨论了Krylov子空间方法用以解决图像恢复中的大规模线性问题。本文通过张量GMRES算法构建Krylov子空间，将大规模线性问题转换为小规模问题，且构建的子空间始终保持张量的空间结构。数值例子和彩色图像修复的应用说明了算法的有效性。
Color images and video sequences can typically be characterized as higher-order tensors. This paper investigates Krylov subspace methods based on the third-order tensor t-product for solving large-scale linear systems arising in image restoration. This paper employs the tensor GMRES algorithm to construct the Krylov subspace, effectively reducing large-scale linear problems to manageable small-scale formulations, while consistently preserving the spatial architecture of tensors within the constructed subspace. Numerical experiments and applications in color image inpainting demonstrate the efficacy of the proposed methodology.
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