Graph regularization-based joint nonnegative representation for the classification of hyperspectral images

摘要

The hyperspectral image classification methods based on sparse representation and collaborative representation have achieved some satisfactory results. However, some of the representation coefficients obtained from them may be negative, which is physically difficult to explain. In addition, existing methods do not consider the local geometric relationships between pixels. To address these problems, this paper proposes a joint nonnegative representation model based on the graph regularization for the hyperspectral image classification. First, for a testing pixel, the similarity between the neighbouring pixels and the testing pixel is used to collect some neighbouring pixels in a window centred at a testing pixel and construct a new neighbourhood pixel set. Each pixel in this neighbourhood pixel set is approximated by a nonnegative linear combination of training pixels from a given over-completed training pixel set. The nonnegative constraint here can ensure to some extent that the representation coefficients of those homogeneous training pixels of the testing pixel from the same class are nonnegative, while ones of those heterogeneous training pixels from different classes are as close to zero as possible. Thus, the obtained coefficients are sparse and physically explicable. Secondly, in order to preserve the manifold structure of training pixels, we also introduce a graph-based regularization constraint. Compared with some other existing methods, our model can obtain a sparse and more discriminative representation coefficient. Furthermore, it can also reveal the local structure of training pixels. The alternative iteration optimization algorithm is devised to solve the proposed model and gives its closed-form solutions in each iteration. Experiment results on four remote sensing image data sets show the superiority of the proposed method.