Adaptive non-local Euclidean medians sparse unmixing for hyperspectral imagery

Sparse unmixing models based on sparse representation theory and a sparse regression model have been successfully applied to hyperspectral remote sensing image unmixing. To better utilize the abundant spatial information and improve the unmixing accuracy, spatial sparse unmixing methods such as the non-local sparse unmixing (NLSU) approach have been proposed. Although the NLSU method utilizes non-local spatial information as the spatial regularization term and obtains a satisfactory unmixing accuracy, the final abundances are affected by the non-local neighborhoods and drift away from the true abundance values when the observed hyperspectral images have high noise levels. Furthermore, NLSU contains two regularization parameters which need to be appropriately set in real applications, which is a difficult task and often has a high computational cost. To solve these problems, an adaptive non-local Euclidean medians sparse unmixing (ANLEMSU) method is proposed to improve NLSU by replacing the non-local means total variation spatial consideration with the non-local Euclidean medians filtering approach. In addition, ANLEMSU utilizes a joint maximum a posteriori (JMAP) strategy to acquire the relationships between the regularization parameters and the estimated abundances, and achieves the fractional abundances adaptively, without the need to set the two regularization parameters manually. The experimental results using both simulated data and real hyperspectral images indicate that ANLEMSU outperforms the previous sparse unmixing algorithms and, hence, provides an effective option for the unmixing of hyperspectral remote sensing imagery.