Joint spectral classification and unmixing using adaptative pixel neighborhoods

A new spatial unmixing algorithm for hyperspectral images is studied. This algorithm is based on the well-known linear mixing model. The spectral signatures (or endmembers) are assumed to be known while the mixture coefficients (or abundances) are estimated by a Bayesian algorithm. As a pre-processing step, an area filter is employed to partition the image into multiple spectrally consistent connected components or adaptative neighborhoods. Then, spatial correlations are introduced by assigning to the pixels of a given neighbourhood the same hidden labels. More precisely, these pixels are modeled using a new prior distribution taking into account spectral similarity between the neighbors. Abundances are reparametrized by using logistic coefficients to handle the associated physical constraints. Other parameters and hyperparameters are assigned appropriate prior distributions. After computing the joint posterior distribution, a hybrid Gibbs algorithm is employed to generate samples that are asymptotically distributed according to this posterior distribution. The generated samples are finally used to estimate the unknown model parameters. Simulations on synthetic data illustrate the performance of the proposed method.