Robust Constrained Hyperspectral Unmixing Using Reconstructed-Image Regularization

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.