Discriminative Low-Rank Gabor Filtering for Spectral–Spatial Hyperspectral Image Classification
Spectral–spatial classification of remotely sensed hyperspectral images has attracted a lot of attention in recent years. Although Gabor filtering has been used for feature extraction from hyperspectral images, its capacity to extract relevant information from both the spectral and the spatial domains of the image has not been fully explored yet. In this paper, we present a new discriminative low-rank Gabor filtering (DLRGF) method for spectral–spatial hyperspectral image classification. A main innovation of the proposed approach is that our implementation is accomplished by decomposing the standard 3-D spectral–spatial Gabor filter into eight subfilters, which correspond to different combinations of low-pass and bandpass single-rank filters. Then, we show that only one of the subfilters (i.e., the one that performs low-pass spatial filtering and bandpass spectral filtering) is actually appropriate to extract suitable features based on the characteristics of hyperspectral images. This allows us to perform spectral–spatial classification in a highly discriminative and computationally efficient way, by significantly decreasing the computational complexity (from cubic to linear order) compared with the 3-D spectral–spatial Gabor filter. In order to theoretically prove the discriminative ability of the selected subfilter, we derive an overall classification risk bound to evaluate the discriminating abilities of the features provided by the different subfilters. Our experimental results, conducted using different hyperspectral images, indicate that the proposed DLRGF method exhibits significant improvements in terms of classification accuracy and computational performance when compared with the 3-D spectral–spatial Gabor filter and other state-of-the-art spectral–spatial classification methods.