A Multitemporal Linear Spectral Unmixing: An Iterative Approach Accounting For Abundance Variations

In this work, we propose an iterative approach for a multitemporal spectral unmixing. We represent temporal variations in abundances as the Dirichlet-Markov process in the linear mixing model. Our work is based on the observation that the end-members can be extracted bandwise from the multitemporal data. It accounts for temporal variations in abundances resulting in better estimates of unmixed components. Given the temporal dataset, we first resort to principal component analysis (PCA) to obtain an initial number of spectrally distinct signatures. A set of initial endmembers and their abundances are estimated using the standard least-squares approach. We then propose an approach to carry out bandwise endmember extraction making use of the initial (temporal) abundances and spatial/temporal information. This results in a constrained estimate giving improved endmembers. These are then incorporated in our data-driven approach for abundance estimation to overcome ill-posedness. Subsequently, the number of endmembers is iteratively refined in a feedback mechanism based on the data reconstruction error obtained using the estimated/improved unmixed components. We show the mean-squared convergence of the proposed approach. In this paper, the obtained results are demonstrated by showing few results on synthetically generated hyperspectral data.