Semi-supervised hyperspectral image classification based on a Markov random field and sparse multinomial logistic regression

This paper introduces a new semi-supervised classification and segmentation approach tailored to hyperspectral images. The posterior distributions of the classes are modeled by the multinomial logistic regression. The contextual information inherent to the spatial configuration of the image pixels is modeled by a Multi-Level Logistic (MLL) Markov-Gibbs random field. The multinomial logistic regressors, assumed to be random vectors with independent Lapla-cian components, are learned using the recently introduced LOR-SAL algorithm. The maximum a posteriori (MAP) segmentation is computed via the α-Expansion algorithm, a powerful graph cut based approach to integer optimization. The effectiveness of the proposed methodology is illustrated by classifying simulated and real data sets. Comparisons with state-of-art methods are also included.