论文标题
高光谱超分辨率通过可解释的扩展张量建模
Hyperspectral Super-Resolution via Interpretable Block-Term Tensor Modeling
论文作者
论文摘要
这项工作重新审视了基于基于张量的张量分解(CTD)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方法具有低级别的矩阵恢复观点。面临的挑战是,在严格条件下,使用低级别矩阵模型恢复SRI的理论保证是难以捉摸的。最近的几种基于CTD的方法可确保在相对温和的条件下对SRI的可恢复性,分别利用了规范多核分解(CPD)和Tucker分解模型的代数性质。但是,在光谱图像分析的背景下,CPD和Tucker模型的潜在因素都没有物理解释,这使得将先前的信息纳入挑战 - 但是使用先验对于在嘈杂环境中增强性能至关重要。这项工作采用了一个想法,该想法将光谱图像建模为张张子,遵循具有多线性等级的块期分解模型-A $(l_r,l_r,1)$项(即LL1模型),并将HSR问题作为耦合的LL1张量分解问题提出。与现有的CTD方法相似,在轻度条件下显示了SRI的可恢复性。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,即端成员的光谱特征和丰度图。该连接使我们可以轻松地合并以进行性能增强的信息。提出了一种可以与一系列结构信息一起使用的灵活算法框架,以利用模型的解释性。使用模拟和真实数据显示了有效性。
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.