Robust linear unmixing with enhanced sparsity

Spectral unmixing is a central problem in hyperspectral imagery. It is usually assuming a linear mixture model. Solving this inverse problem, however, can be seriously impacted by a wrong estimation of the number of endmembers, a bad estimation of the endmembers themselves, the spectral variability of the endmembers or the presence of nonlinearities. These problems can result in a too large number of retained endmembers. We propose to tackle this problem by introducing a new formulation for robust linear unmixing enhancing sparsity. With a single tuning parameter the optimization leads to a range of behaviors: from the standard linear model (low sparsity) to a hard classification (maximal sparsity : only one endmember is retained per pixel). We solve the proposed new functional using a computationally efficient proximal primal dual method. The experimental study, including both realistic simulated data and real data demonstrates the versatility of the proposed approach.