利用结构复杂性实现稳健快速的Hyperspectral Imaging
Exploiting Structural Complexity for Robust and Rapid Hyperspectral Imaging
摘要：
本文提出了几种高光谱图像的光谱去噪和超立方体重建的策略，从有限数量的层析测量。特别是，我们表明，无噪声的光谱数据，当堆叠在整个光谱维度，表现出低秩。另一方面，在相同的表示下，频谱噪声呈现带状结构。出于这一动机，我们表明，去噪的频谱数据和未知的频谱噪声和各自的频带可以同时估计，通过使用低秩和同时稀疏最小化操作，而无需噪声频带的先验知识。这一结果对于高光谱成像应用是新颖的。此外，我们表明，成像的计算机断层成像成像系统（CTIS），可以改善有限的角度断层扫描下，通过使用低秩惩罚。对于这两种情况下，我们利用最近的结果在低秩矩阵完成核范数最小化的理论。
英文摘要：
This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the non-noisy spectral data, when stacked across the spectral dimension, exhibits low-rank. On the other hand, under the same representation, the spectral noise exhibits a banded structure. Motivated by this we show that the de-noised spectral data and the unknown spectral noise and the respective bands can be simultaneously estimated through the use of a low-rank and simultaneous sparse minimization operation without prior knowledge of the noisy bands. This result is novel for for hyperspectral imaging applications. In addition, we show that imaging for the Computed Tomography Imaging Systems (CTIS) can be improved under limited angle tomography by using low-rank penalization. For both of these cases we exploit the recent results in the theory of low-rank matrix completion using nuclear norm minimization.
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