IEEE Trans Image Process. 2014 Dec;23(12):5209-21. doi: 10.1109/TIP.2014.2362008.
The acquisition of hundreds of images of a scene, each at a different wavelength, is known as hyperspectral imaging. This high amount of data allows the extraction of much more information from hyperspectral images compared with conventional color images. The forward-looking imaging approach emerged from remote sensing, but is still not very widespread in industrial and other practical applications. Spectral unmixing, in particular, aims at the determination of the components present in a scene as well as the abundance to which each component contributes. This information is valuable, for instance, when discrimination tasks are to be performed. Involving not only spectral, but also spatial information was found to have the potential to improve the unmixing results. Several publications use spatial first-order regularization (closely related to the total variation approach) to incorporate this spatial information. Like in classical image processing, this approach favors piecewise constant pixel transitions. This is why it was proposed in the literature to use second-order regularization instead of first order to approach piecewise-linear transitions. Therefore, we introduce Hessian-based regularization to hyperspectral unmixing and propose an algorithm to calculate the regularized result. We use simulated data and images measured in our laboratory to show that both the first- and second-order approaches share many properties and produce similar results. The second-order approach, however, is more robust and thus more accurate in finding the minimum. Both methods smoothen the images in the case of supervised unmixing (i.e., the component spectra are known beforehand) and enhance unsupervised unmixing (when the spectra are not known).
获取场景的数百张图像，每张图像的波长都不同，这种技术被称为高光谱成像。与传统的彩色图像相比，这种大量的数据允许从高光谱图像中提取更多的信息。前向成像方法起源于遥感，但在工业和其他实际应用中仍然不是很广泛。光谱分解，特别是，旨在确定场景中存在的成分以及每个成分的丰度。例如，当需要执行判别任务时，这些信息非常有价值。事实证明，不仅涉及光谱信息，还涉及空间信息，具有改善解混结果的潜力。有几篇出版物使用空间一阶正则化（与总变差方法密切相关）来合并此空间信息。与经典图像处理一样，这种方法倾向于分段常数像素过渡。这就是为什么在文献中建议使用二阶正则化而不是一阶正则化来逼近分段线性过渡。因此，我们将基于 Hessian 的正则化引入到高光谱分解中，并提出了一种计算正则化结果的算法。我们使用模拟数据和在我们的实验室中测量的图像来表明，一阶和二阶方法都具有许多共同的特性并产生相似的结果。然而，二阶方法在寻找最小值时更稳健，因此更准确。在有监督分解的情况下（即，成分光谱事先已知），这两种方法都可以平滑图像，并且在无监督分解的情况下（当光谱未知时）可以增强分解。
