Hyperspectral Image Classification with Spatial Filtering and ℓ2,1 Norm

Recently, the sparse representation based classification methods have received particular attention in the classification of hyperspectral imagery. However, current sparse representation based classification models have not considered all the test pixels simultaneously. In this paper, we propose a hyperspectral classification method with spatial filtering and `2,1 norm (SFL) that can deal with all the test pixels simultaneously. The `2,1 norm regularization is used to extract relevant training samples among the whole training data set with joint sparsity. In addition, the `2,1 norm loss function is adopted to make it robust for samples that deviate significantly from the rest of the samples. Moreover, to take the spatial information into consideration, a spatial filtering step is implemented where all the training and testing samples are spatially averaged with its nearest neighbors. Furthermore, the non-negative constraint is added to the sparse representation matrix motivated by hyperspectral unmixing. Finally, the alternating direction method of multipliers is used to solve SFL. Experiments on real hyperspectral images demonstrate that the proposed SFL method can obtain better classification performance than some other popular classifiers.