A novel nonlinear hyperspectral unmixing approach for images of oil spills at sea

Hyperspectral remote sensing is currently being used to detect and monitor marine oil spills that cause damage to the environment. However, nonlinear interactions of oil and water make it difficult to extract their fractional abundances from the spectral response. Improving the modelling of nonlinear hyperspectral mixtures, which is required for a thorough and reliable characterization of the materials in an image, remains a challenging yet fundamental task. This study proposes a new model that combines polynomial and trigonometric systems to understand the nonlinear effects of oil and water spectral response. Although the model is nonlinear, unmixing is performed by solving a linear problem, thus allowing fast computation. Compared to classic polynomial models, the details of nonlinear interactions are better expressed and quantified, and the reconstruction accuracy and endmember abundance estimation are improved for both synthetic and real datasets. Both the polynomial and trigonometric parts of the model play important roles in characterizing nonlinearities, with statistically linear dependence areas covering more than 90% and 30%, respectively, in oil spill images sampled after the Deepwater Horizon explosion. Analysis of the experimental results suggests that the proposed model provides an efficient and accurate unmixing method that can be used to help design oil spill response plans.