LAUSR

An important task of spectral unmixing is to recover the signatures of endmembers from a hyperspectral dataset in which no pure signature is exposed. Most algorithms are based on linear mixing model and require that data should be sufficiently scattered to guarantee model uniqueness. However, data may not be scattered sufficiently enough and become incomplete. In this case, can we still recover the endmembers accurately? Moreover, if we wrongly estimate an endmember, the error may be propagated to other endmembers. For these purposes, we propose a new model, namely, affine simplicial cone (ASC), to capture the local geometric feature of data. This model requires less geometric information and relaxes the conditions of model uniqueness. Then, we present analyses on the error propagation of turbulent endmembers and the condition of local uniqueness. Based on ASC, we present an endmember purification problem to recover only one endmember. In this way, error propagation can be alleviated, and local uniqueness can be easily satisfied. Finally, we develop an endmember purifying algorithm (EPA) to solve this problem. Our experiments demonstrate that the performance of EPA is competitive to the state-of-the-art unmixing algorithms not only for the synthetic datasets but also for the real hyperspectral remote sensing datasets. We can conclude that the ASC model and the EPA algorithm have the potential capability for hyperspectral data exploration.