Regularization approaches to hyperspectral unmixing

We consider a few different approaches to hyperspectral unmixing of remotely sensed imagery which exploit and extend recent advances in sparse statistical regularization, handling of constraints and dictionary reduction. Hyperspectral unmixing methods often use a conventional least-squares based lasso which assumes that the data follows the Gaussian distribution, we use this as a starting point. In addition, we consider a robust approach to sparse spectral unmixing of remotely sensed imagery which reduces the sensitivity of the estimator to outliers. Due to water absorption and atmospheric effects that affect data collection, hyperspectral images are prone to have large outliers. The framework comprises of several well-principled penalties. A non-convex, hyper-Laplacian prior is incorporated to induce sparsity in the number of active pure spectral components, and total variation regularizer is included to exploit the spatial-contextual information of hyperspectral images. Enforcing the sum-to-one and non-negativity constraint on the models parameters is essential for obtaining realistic estimates. We consider two approaches to account for this: an iterative heuristic renormalization and projection onto the positive orthant, and a reparametrization of the coefficients which gives rise to a theoretically founded method. Since the large size of modern spectral libraries cannot only present computational challenges but also introduce collinearities between regressors, we introduce a library reduction step. This uses the multiple signal classi fication (MUSIC) array processing algorithm, which both speeds up unmixing and yields superior results in scenarios where the library size is extensive. We show that although these problems are non-convex, they can be solved by a properly de fined algorithm based on either trust region optimization or iteratively reweighted least squares. The performance of the different approaches is validated in several simulated and real hyperspectral data experiments

Assessment of Soil erosion parameters in Costa Rica using reflectance hyperspectral and simulated EnMAP imagery

Soil erosion can be linked to relative fractional cover of photosynthetic-active vegetation, non-photosynthetic-active vegetation and bare soil, and terrain characteristics such as the C and LS factors. This study investigates the capacity of EnMAP imagery to map areas prone to soil erosion in a region near San Jose, Costa Rica, characterized by spatially extensive coffee plantations and grazing in a mountainous terrain. Simulated EnMAP imagery is based on airborne hyperspectral HyMap data. Fractional cover estimates are derived using a Multiple End-member Spectral Mixture Analysis approach. The C and LS factors are derived from a digital elevation model. The analysis was done independently for EnMAP and HyMap, the latter treated as reference data as no ground truth is available. Results demonstrate that with EnMAP imagery it is possible to extract quality endmember classes with important spectral features related to PV, NPV and soil, and be able to estimate relative cover fractions. This spectral information is critical to separate soil and NPV which greatly can impact integrated modelling with terrain characteristics. From a regional perspective EnMAP can be used to highlight specific areas that may be prone to erosion where this information can be extract directly from the imagery using automated processes