An ADMM-based algorithm with minimum dispersion regularization for on-line blind unmixing of hyperspectral images

Pushbroom imaging systems are emerging techniques for real-time acquisition of hyperspectral images. These systems are frequently used in industrial applications to control and sort products on-the-fly. In this paper, the online hyperspectral image blind unmixing is addressed. We propose a new on-line method based on Alternating Direction Method of Multipliers (ADMM) approach, adapted to pushbroom imaging systems. Because of the generally ill-posed nature of the unmixing problem, we impose a minimum endmembers dispersion regularization to stabilize the solution; this regularization can be interpreted as a convex relaxation of the minimum volume regularization and therefore, presents interesting optimization properties. The proposed algorithm presents faster convergence rate and lower computational complexity compared to the algorithms based on multiplicative update rules. Experimental results on synthetic and real datasets, and comparison to state-of-the-art algorithms, demonstrate the effectiveness of our method in terms of rapidity and accuracy.