A Generalized Multiscale Bundle-Based Hyperspectral Sparse Unmixing
  Algorithm
Luciano Carvalho Ayres Ricardo Augusto Borsoi José Carlos Moreira Bermudez Sérgio José Melo de Almeida
In hyperspectral sparse unmixing, a successful approach employs spectral
bundles to address the variability of the endmembers in the spatial domain.
However, the regularization penalties usually employed aggregate substantial
computational complexity, and the solutions are very noise-sensitive. We
generalize a multiscale spatial regularization approach to solve the unmixing
problem by incorporating group sparsity-inducing mixed norms. Then, we propose
a noise-robust method that can take advantage of the bundle structure to deal
with endmember variability while ensuring inter- and intra-class sparsity in
abundance estimation with reasonable computational cost. We also present a
general heuristic to select the \emph{most representative} abundance estimation
over multiple runs of the unmixing process, yielding a solution that is robust
and highly reproducible. Experiments illustrate the robustness and consistency
of the results when compared to related methods.