光谱学与光谱分析, 2019, 39 (5): 1551, 网络出版: 2019-05-13  

MCR-BANDS用于高光谱成像分辨中旋转模糊度的评估

Evaluation of Rotation Ambiguity by MCR-BANDS on Hyperspectral Imaging
作者单位
首都师范大学化学系, 北京 100048
摘要
自建模曲线分辨用来将双线性光谱数据矩阵分解成具有明确物理或化学意义的曲线, 一方面反映了复杂体系中各个主成分对应的纯光谱, 同时也能够解析得到其对应的相对浓度。 这一方法在高光谱解析中充分发挥了其优势, 成为了高光谱分析中的重要方法之一。 然而, 双线性结构数据多元分辨模型在约束不充分的条件下往往不能获得唯一解, 这一问题是由顺序模糊、 尺度模糊和旋转模糊引起, 其中旋转模糊最难消除。 在高光谱成像中, 如果不能明确浓度分布情况, 将导致在成像领域难以确认目标的准确位置或形貌。 为了充分了解旋转模糊带来的影响, 评估非唯一解情况下可行解的范围, 并进一步为实际应用中需要解析获得的每个主成分的纯光谱或波谱信号, 以及其对应的浓度信息提供客观的评估依据, 在以往的研究中, 研究人员分别使用网格法、 蒙特卡洛法进行抽样, 以计算曲线分辨结果中可行解的范围, 也有科研人员使用了几何多边形内部和外围面积的形式表示结果, 但是这些结果往往面临运算时间过长, 或者无法实现高维可视化而不适用于大于四个主成分的数据等问题, 而且通常这些方法很难将曲线分辨过程中施加的除非负约束之外的其他约束方法加以利用, 导致可行解范围计算不准确。 为了解决以上问题, 采用MCR-BANDS对MCR-ALS(多元曲线分辨-交替最小二乘)分辨获得的结果进行了旋转模糊程度的评估, 并将其应用到遥感高光谱成像的解析中。 首先以美国地质勘探局矿物光谱库中的纯光谱为基础的模拟数据集对MCR-ALS和MCR-BANDS的结果进行了评测, 在模拟数据中能够方便地控制噪声的影响, 控制选取主成分之间的纯光谱差异、 仿照真实环境中浓度渐变特征等因素, 考查了特定条件下MCR结果中旋转模糊的水平。 随后为了证实所用方法的可行性, 进一步采用MCR-ALS分析了机载可见/红外成像光谱仪(AVIRIS)获得的遥感高光谱图像数据, 并首次采用MCR-BANDS对MCR-ALS的分辨结果的旋转模糊进行了分析, 实现了对遥感高光谱数据成像浓度分布的受到旋转模糊影响的可视化表示。 可以发现真实解和MCR-ALS获得的可行解均在MCR-BANDS计算得到的可行解范围之内。 结果表明, MCR-BANDS方法基于最大和最小的信号贡献对旋转模糊的范围进行计算, 能够适用于不同主成分的体系中, 并且完美对接MCR-ALS中使用到的诸如非负、 单峰、 封闭和选择性约束等。 MCR-BANDS的分析结果可以为MCR-ALS的解析结果提供相应的旋转模糊水平估计, 有利于对MCR-ALS结果的解释; 在充分约束条件下, 能够有效减少甚至消除旋转模糊对MCR-ALS分辨结果的影响, 为精确确定遥感高光谱中解析得到的目标物位置提供了客观的范围。
Abstract
Self-modeling curve resolution can resolve the bilinear spectral datasets as the profiles of pure signal and their contributions which can be explained easily in physical and chemical meaning. With the advantage that their results can provide the pure spectra and the corresponding relative concentrations in the analyzed complex systems, MCR methods have been widely applied in the analysis of hyperspectral imaging. However, when the constraints applied are not strong enough, multivariate curve resolution models for bilinear data always suffer the problem of order ambiguity, scale ambiguity and rotation ambiguity which induce non-unique solution. Rotation ambiguity is the most difficult to be removed. To investigate the level of rotation ambiguity and provide the range of feasible solutions, in the published works, the researcher used grid search or Monte Carlo random sampling to display some feasible solutions fulfill the bilinear model under certain constraints. In this way, the concentrations and pure spectra results resolved by MCR can be better explained for their application by providing a range of feasible solutions. Polygons projected by feasible solutions based on geometry were also employed to illustrate the feasible solutions and the extension of rotation ambiguity. These methods normally are time consuming and cannot be used in the system with more than four components. More importantly, they cannot apply different constraints based on the properties of the analyzed samples, except non-negativity. In this work, we applied MCR-BANDS to evaluate the level of rotation ambiguity for resolved by MCR-ALS on the remote sensing hyperspectral imaging. In the first part, the mineral spectra selected from United States Geological Survey Committee were used for simulating a hyperspectral imaging dataset. In the simulated dataset, the noise level can be controlled and the differences of the spectral features between different components were easily identified. The concentrations of different components were simulated the real conditions, with gradual changes in the space. The rotation ambiguity was evaluated in the simulated data by using MCR-BANDS. To better explain the application of MCR-BANDS, this method was used to analyze a remote sensing dataset collected by Airborne Visible Infrared Imaging Spectrometer (AVIRIS), and the affection of rotation ambiguity on different components was visually displayed as concentration distributions in maps. The results show that MCR-BANDS can provide the level of feasible solutions of MCR-ALS by using maximum and minimum signal contribution functions (SCCF). This method can be applied to the system with any number of components, and can use almost all of the constraints which are chosen in MCR-ALS, like non-negativity, unimodality, closure, selectivity/local rank etc. The concentration distribution results from maximum and minimum SCCF are helpful to locate the specific targets in the remote sensing hyperspectral imaging.

邵常艳, 张欣, 张卓勇. MCR-BANDS用于高光谱成像分辨中旋转模糊度的评估[J]. 光谱学与光谱分析, 2019, 39(5): 1551. SHAO Chang-yan, ZHANG Xin, ZHANG Zhuo-yong. Evaluation of Rotation Ambiguity by MCR-BANDS on Hyperspectral Imaging[J]. Spectroscopy and Spectral Analysis, 2019, 39(5): 1551.

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