Tucker tensor decomposition with rank estimation for sparse hyperspectral unmixing

Hyperspectral image unmixing gives increasing focus on the structural integrity of the spatial-spectral information. A large number of methods exploit the sparse and low-rank properties of the abundance vectors, abundance matrices and abundance maps, which are first-order or second-order structures, and are hard to preserve the integrated structure of the abundance. The abundance tensor formed by overlapping the abundance maps of endmembers sequentially is a more appropriate expression of the abundance. However, hyperspectral unmixing studies based on the abundance tensor are still in the minority, and most of these methods either inherently degrade the tensor structure to some extent, which is hard to distinguish the low-rankness of different dimensions; or are based on tensor decomposition methods, which always require a pre-estimation of the tensor rank, thus the unmixing accuracy depends on the rank estimation. In this article, we propose an unmixing model on tensor framework, in which the abundance tensor is approximated by a truncated Tucker tensor decomposition (TTD). Since the generated factor matrices are relatively low-rank, the low-rankness exploration of the abundance tensor is achieved potentially by this way. Moreover, we further improve the unmixing performance by a suitable rank estimation. The more flexible algorithm Tucker tensor decomposition with rank estimation for sparse hyperspectral unmixing (TTDRE) is proposed to differentiate the low-rankness of different dimensions of the abundance tensor while preserving the structural integrity. Experiments on synthetic and real data illustrate the effectiveness of our method.