This work revisits coupled tensor decomposition (CTD)-based hyperspectral super-resolution (HSR). HSR aims at fusing a pair of hyperspectral and multispectral images to recover a super-resolution image (SRI). The vast majority of the HSR approaches take a low-rank matrix recovery perspective. The challenge is that theoretical guarantees for recovering the SRI using low-rank matrix models are either elusive or derived under stringent conditions. A couple of recent CTD-based methods ensure recoverability for the SRI under relatively mild conditions, leveraging on algebraic properties of the canonical polyadic decomposition (CPD) and the Tucker decomposition models, respectively. However, the latent factors of both the CPD and Tucker models have no physical interpretations in the context of spectral image analysis, which makes incorporating prior information challenging---but using priors is often essential for enhancing performance in noisy environments. This work employs an idea that models spectral images as tensors following the block-term decomposition model with multilinear rank-$(L_r, L_r, 1)$ terms (i.e., the LL1 model) and formulates the HSR problem as a coupled LL1 tensor decomposition problem. Similar to the existing CTD approaches, recoverability of the SRI is shown under mild conditions. More importantly, the latent factors of the LL1 model can be interpreted as the key constituents of spectral images, i.e., the endmembers' spectral signatures and abundance maps. This connection allows us to easily incorporate prior information for performance enhancement. A flexible algorithmic framework that can work with a series of structural information is proposed to take advantage of the model interpretability. The effectiveness is showcased using simulated and real data.

中文翻译：

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通过可解释的块项张量建模实现高光谱超分辨率

这项工作重新审视了基于耦合张量分解 (CTD) 的高光谱超分辨率 (HSR)。HSR 旨在融合一对高光谱和多光谱图像以恢复超分辨率图像 (SRI)。绝大多数 HSR 方法都采用低秩矩阵恢复的观点。挑战在于，使用低秩矩阵模型恢复 SRI 的理论保证要么难以捉摸，要么在严格条件下推导出来。最近的几种基于 CTD 的方法分别利用典型多元分解 (CPD) 和 Tucker 分解模型的代数特性，确保了 SRI 在相对温和的条件下的可恢复性。然而，CPD 和 Tucker 模型的潜在因素在光谱图像分析的背景下没有物理解释，这使得合并先验信息具有挑战性——但使用先验通常对于提高嘈杂环境中的性能至关重要。这项工作采用了一种想法，即按照具有多线性秩-$(L_r, L_r, 1)$ 项（即 LL1 模型）的块项分解模型将光谱图像建模为张量，并将 HSR 问题表述为耦合的 LL1 张量分解问题。与现有的 CTD 方法类似，SRI 的可恢复性在温和条件下显示。更重要的是，LL1 模型的潜在因素可以解释为光谱图像的关键组成部分，即端元的光谱特征和丰度图。这种联系使我们能够轻松地合并先验信息以提高性能。提出了一种可以处理一系列结构信息的灵活算法框架，以利用模型的可解释性。使用模拟和真实数据展示了有效性。