Abstract
Gaussian mixture model (GMM) has been one of the most representative models for hyperspectral unmixing while considering endmember variability. However, the GMM unmixing models only have proper smoothness and sparsity prior constraints on the abundances and thus do not take into account the possible local spatial correlation. When the pixels that lie on the boundaries of different materials or the inhomogeneous region, the abundances of the neighboring pixels do not have those prior constraints. Thus, we propose a novel GMM unmixing method based on superpixel segmentation (SS) and low-rank representation (LRR), which is called GMM-SS-LRR. we adopt the SS in the first principal component of HSI to get the homogeneous regions. Moreover, the HSI to be unmixed is partitioned into regions where the statistical property of the abundance coefficients have the underlying low-rank property. Then, to further exploit the spatial data structure, under the Bayesian framework, we use GMM to formulate the unmixing problem, and put the low-rank property into the objective function as a prior knowledge, using generalized expectation maximization to solve the objection function. Experiments on synthetic datasets and real HSIs demonstrated that the proposed GMM-SS-LRR is efficient compared with other current popular methods.
Highlights
In the last few decades, Hyperspectral image (HSI) has received considerable attention in the field of earth observation and geoinformation science
For the real HSI, the extracted endmembers E are generally distinct from each other and the number of bands L is usually larger than the total number of the endmember R, which makes the rank(E) = R, and rank(Z) = k ≤ min(R, N); according to Theorem 1, we can get rank(Z) = rank(A), since adopting the principal component analysis (PCA) and superpixel segmentation (SS), the original HSI has been cut into different regions, and the columns of Z are highly correlated, which means that the matrix Z is low rank, the abundance matrix A in each homogeneous regions is low rank
Comparing them with the ground truth, we can see that beta compositional model (BCM) and normal compositional model (NCM) both failed to estimate the pure pixels of corn, and, as for the lettuce 4wk, the abundance maps of Gaussian mixture model (GMM), NCM and BCM were mixed with the endmember corn
Summary
In the last few decades, Hyperspectral image (HSI) has received considerable attention in the field of earth observation and geoinformation science. GMM method assumes that the endmember mnj follows the GMM distribution and noise nn follows the Gaussian distribution: p(nn) := N (nn|0, D), where D is the noise covariance matrix, and with proper abundances constraint under the Bayesian framework to lead the conditional density function to a standard MAP problem. The performance of those methods in this category is often dependent on the initial value of parameters, but does not rely on the large-scale spectral database, which is the research hotspot for the endmember variability problem.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
