Hyperspectral image classification aims to assign feature labels to each image element in images. Nowadays, several classification techniques are applied in hyperspectral classification, such as support vector machines (SVMs), polynomial logistic regression, and neural networks. In recent years, sparse representation has proven to be a powerful tool for solving problems such as face recognition and image super-resolution. The basic assumption of sparse representation is that if a class has enough training samples, the test samples belonging to this class can be represented by using a linear combination of the training samples from this class. Sparse representation classification obtains the sparse representation parameters by the sparse representation of the test samples and calculates the reconstructed residuals for each class of the training samples, which thus determines the class of the test samples. The sparse representation usually pays more attention to the spatial information of the neighborhood of the test image elements and ignores the spatial information of dictionary atoms. The proposed weighted joint sparse representation hyperspectral image classification algorithm based on the spatial-spectral dictionary (SSD-WJSRC) addresses the problem that the spatial-spectral information of dictionary atoms is underutilized.

SSD-WJSRC algorithm makes full use of the spatial-spectral information of dictionary atoms. Firstly, the superpixel segmentation is performed by using the entropy rate superpixel segmentation (ERS) algorithm on the principal component image to obtain the superpixel segmentation map. Secondly, the spatial-spectral joint distance between the test image elements and the dictionary atoms is calculated, and the spatial-spectral joint distance is jointly determined by the spatial distance and the spectral angle distance. Then, image elements are added in the superpixel neighborhood corresponding to the first K dictionary atoms to the spatial-spectral dictionary as sub-dictionaries. Meanwhile, in the joint sparse model, different weights are used for the superpixel neighborhood image elements of the test image elements, and the weights are calculated from the Gaussian kernel distance, and the Gaussian kernel can be used to capture the distance of nonlinear information to measure the similarity between samples. Finally, a weighted sparse representation model is constructed on the spatial-spectral dictionary, which solves sparse coefficients by using the simultaneous orthogonal matching pursuit (SOMP) algorithm, and the reconstructed residuals are calculated. Furthermore, the classification results are determined.

Several important results are obtained as follows. Firstly, The experimental results from the Indian Pines and Salinas datasets show that the proposed SSD-WJSRC can effectively improve the classification accuracy by 97.60% and 98.01%, respectively. The spatial-spectral constraint is adopted to realize the full utilization of the pixel spatial-spectral information of the dictionary and generate a better expressive spatial-spectral dictionary. The proposed method can also improve the misclassification by using spatial information in the case of high spectral similarity of features (Figs. 6 and 7). Secondly, the proposed method reduces the influence of irrelevant pixels in the neighboring pixels on the sparse model by weighting the neighboring domains and effectively improves the classification accuracy in the neighboring regions of different features and at the edges of the features. When classifying feature types with few samples, the proposed method makes full use of the neighborhood information of the samples to ensure classification accuracy (Figs. 6 and 7). Thirdly, the effects of different balance coefficients, number of superpixels, and sparsity on classification accuracy are also analyzed (Figs. 8-10). Finally, in order to verify the effect of the constructed spatial-spectral dictionary on sparse representation classification, ablation experiments are performed. The classification results obtained with the same selection of test image elements and dictionary atoms are shown in Table 5. It can be seen that there is a certain decrease in classification accuracy without constructing the spatial-spectral dictionary, which proves that the spatial-spectral dictionary can effectively improve classification accuracy.

The proposed SSD-WJSRC makes full use of the spatial and spectral information of the dictionary atoms' neighborhoods. The dictionary atoms with high spatial and spectral similarity to the test pixels are selected as the adaptive dictionary, and the superpixel neighborhoods of the dictionary atoms are extended to an adaptive dictionary to form a spatial-spectral dictionary. Different weights are assigned to the superpixel neighborhoods to reduce the influence of the irrelevant image elements on the sparse representation results, and a weighted sparse representation model is constructed on the spatial-spectral dictionary to obtain the classification results. The simulation results on Indian Pines and Salinas datasets show that the accuracy of the proposed algorithm is higher than that of traditional algorithms such as K-Nearest Neighbor (KNN) algorithm, and it has better classification results with fewer samples than current deep learning methods.