Robust Multiscale Spectral–Spatial Regularized Sparse Unmixing for Hyperspectral Imagery

Abstract

With the aid of endmember spectral libraries, sparse unmixing plays a critical role in interpreting hyperspectral remote sensing data. Integrating spatial clues from hyperspectral data into sparse unmixing frameworks is pivotal for enhancing unmixing capabilities. As such, extracting and harnessing spatial signatures from imagery has emerged as a prevalent tactic to optimize unmixing. In real-world scenarios, hyperspectral images are susceptible to noise, which poses great challenges to the separability of ground objects. As a result, most sparse unmixing models are ill-equipped to handle this issue properly, facing risks of failure. To tackle this challenge, we proposed a sparse unmixing technique with robust multiscale spectral–spatial regularization (RMSR). In the proposed RMSR model, an abundance estimation error reduction regularizer and a spectral–spatial weighted sparse regularizer are consolidated into a unified framework, which excavates the spatial information of the image from multiple perspectives. Specifically, in the first part, the abundance estimation error is defined as the difference between the precomputed abundance maps at the superpixel level and the expected abundances calculated from the original data. Then, the $\ell _{2,1}$ norm is applied to it as a regularization term, which enhances the robustness of the model against image noise and outliers. In the second part, image level spectral weighting coefficients and local spatial weighting terms are leveraged to individually enhance the sparsity of the abundance maps and their piecewise smoothness. The experimental results reveal the algorithm's considerable capabilities in noise immunity and improved unmixing abilities.

Keywords

• Abundance estimation error
• multiscale
• sparse hyperspectral unmixing
• spatial information
• spatial regularization