  Hyperspectral (HS) unmixing is the process of decomposing an HS image into
material-specific spectra (endmembers) and their spatial distributions
(abundance maps). Existing unmixing methods have two limitations with respect
to noise robustness. First, if the input HS image is highly noisy, even if the
balance between sparse and piecewise-smooth regularizations for abundance maps
is carefully adjusted, noise may remain in the estimated abundance maps or
undesirable artifacts may appear. Second, existing methods do not explicitly
account for the effects of stripe noise, which is common in HS measurements, in
their formulations, resulting in significant degradation of unmixing
performance when such noise is present in the input HS image. To overcome these
limitations, we propose a new robust hyperspectral unmixing method based on
constrained convex optimization. Our method employs, in addition to the two
regularizations for the abundance maps, regularizations for the HS image
reconstructed by mixing the estimated abundance maps and endmembers. This
strategy makes the unmixing process much more robust in highly-noisy scenarios,
under the assumption that the abundance maps used to reconstruct the HS image
with desirable spatio-spectral structure are also expected to have desirable
properties. Furthermore, our method is designed to accommodate a wider variety
of noise including stripe noise. To solve the formulated optimization problem,
we develop an efficient algorithm based on a preconditioned primal-dual
splitting method, which can automatically determine appropriate stepsizes based
on the problem structure. Experiments on synthetic and real HS images
demonstrate the advantages of our method over existing methods.
