Regularization Parameter Selection in Minimum Volume Hyperspectral Unmixing

高光谱成像 端元 单纯形 正规化(语言学) 计算机科学 数据点 算法 选型 像素 稳健性(进化) 数学优化 数学 人工智能 生物化学 基因 化学 几何学
作者
Lina Zhuang,Chia-Hsiang Lin,Mário A. T. Figueiredo,José M. Bioucas‐Dias
出处
期刊:IEEE Transactions on Geoscience and Remote Sensing [Institute of Electrical and Electronics Engineers]
卷期号:57 (12): 9858-9877 被引量:93
标识
DOI:10.1109/tgrs.2019.2929776
摘要

Linear hyperspectral unmixing (HU) aims at factoring the observation matrix into an endmember matrix and an abundance matrix. Linear HU via variational minimum volume (MV) regularization has recently received considerable attention in the remote sensing and machine learning areas, mainly owing to its robustness against the absence of pure pixels. We put some popular linear HU formulations under a unifying framework, which involves a data-fitting term and an MV-based regularization term, and collectively solve it via a nonconvex optimization. As the former and the latter terms tend, respectively, to expand (reducing the data-fitting errors) and to shrink the simplex enclosing the measured spectra, it is critical to strike a balance between those two terms. To the best of our knowledge, the existing methods find such balance by tuning a regularization parameter manually, which has little value in unsupervised scenarios. In this paper, we aim at selecting the regularization parameter automatically by exploiting the fact that a too large parameter overshrinks the volume of the simplex defined by the endmembers, making many data points be left outside of the simplex and hence inducing a large data-fitting error, while a sufficiently small parameter yields a large simplex making data-fitting error very small. Roughly speaking, the transition point happens when the simplex still encloses the data cloud but there are data points on all its facets. These observations are systematically formulated to find the transition point that, in turn, yields a good parameter. The competitiveness of the proposed selection criterion is illustrated with simulated and real data.

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