We consider the decomposition of a data matrix assumed to be a superposition of a low-rank matrix and a component which is sparse in a known dictionary, using a convex demixing method. We consider two sparsity structures for the sparse factor of the dictionary sparse component, namely entry-wise and column-wise sparsity, and provide a unified analysis, encompassing both undercomplete and the overcomplete dictionary cases, to show that the constituent matrices can be successfully recovered under some relatively mild conditions on incoherence, sparsity, and rank. We leverage these results to localize targets of interest in a hyperspectral (HS) image based on their spectral signature(s) using the a priori known characteristic spectral responses of the target. We corroborate our theoretical results and analyze target localization performance of our approach via experimental evaluations and comparisons to related techniques.

中文翻译：

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基于字典的鲁棒 PCA 泛化及其在高光谱成像中的目标定位应用

我们考虑使用凸解混合方法分解假设为低秩矩阵和已知字典中稀疏分量的叠加的数据矩阵。我们考虑字典稀疏分量的稀疏因子的两种稀疏结构，即 entry-wise 和 column-wise 稀疏性，并提供统一的分析，包括不完整和过完整字典情况，以表明可以成功恢复组成矩阵在一些相对温和的条件下，不连贯性、稀疏性和秩。我们利用这些结果，使用目标的先验已知特征光谱响应，根据其光谱特征在高光谱 (HS) 图像中定位感兴趣的目标。