In recent years, convolutional neural networks (CNNs) have drawn significant attention for the classification of hyperspectral images (HSIs). Due to their self-attention mechanism, the vision transformer (ViT) provides promising classification performance compared to CNNs. Many researchers have incorporated ViT for HSI classification purposes. However, its performance can be further improved because the current version does not use spatial–spectral features. In this article, we present a new morphological transformer (morphFormer) that implements a learnable spectral and spatial morphological network, where spectral and spatial morphological convolution operations are used (in conjunction with the attention mechanism) to improve the interaction between the structural and shape information of the HSI token and theCLStoken. Experiments conducted on widely used HSIs demonstrate the superiority of the proposed morphFormer over the classical CNN models and state-of-the-art transformer models. The source will be made available publicly athttps://github.com/mhaut/morphFormer.

Recently, Collaborative representation (CR) has drawn much attention towards anomaly detection for hyperspectral imagery. Pixels in the background can be represented with spatial neighbors. In CR, an l2norm is implemented for estimating the weight vector in a closed-form solution. In this paper, locality constraints are imposed on the representation framework called collaborative-competitive representation for hyperspectral anomaly detection (CCRD). By incorporating competition among neighboring atoms lying in various subspaces, local information can be incorporated into the global framework of CR. In addition, distance weighted Tikhonov regularization is used to enhance the performance of CCRD, named CCRDT. Moreover, spatial information is used in the objective function of CCRDT, resulting in SCCRDT, to further enhance the performance of anomaly detection. Experimental results on several hyperspectral datasets demonstrate the superiority of proposed methods in comparison to traditional detectors, such as Reed-Xiaoli (RX) algorithm, kernel RX (KRX) algorithm, and existing collaborative representation-based anomaly detectors.

Recently, graph-based methods have drawn increased attention for representing a high-dimensional features into a low- dimensional data. To obtain an optimal transform for the purpose of classification, different collaborative representation-based methods are for dimensionality reduction (DR). In previous work, a spatial-aware collaborative competitive representation (SaCCPGT) based unsupervised method was investigated for DR of hyperspectral imagery (HSI). It incorporates spatial information into the representation framework. However, it can be further enhanced by considering the data manifold structure. In this paper, Laplacian regularized SaCCPGT (LapSaCCPGT) is presented for DR of HSI to better utilize data structure information into the representation framework. The experimental results observed on different hyperspectral datasets demonstrate the superiority of the proposed LapSaCCPGT than the state-of-the-art DR methods.

Recently, graph-based discriminant analysis has drawn much attention in representing a high-dimensional hyperspectral data set using a low-dimensional subspace by defining high-dimensional data structure on a graph. Obtaining optimal representation coefficients for classification purposes are the key in such methods. A closed form solution can be found to solve the problem related to collaborative representation using labeled samples, which offers computational efficiency. There exists an unsupervised approach of collaboration preserving graph embedding (CPGE) for dimensionality reduction (DR), and its performance is further enhanced by imposing locality-preserving constraint in the method called collaboration–competition preserving graph embedding (CCPGE). In this letter, we introduce spatial-aware collaboration–competitive preserving graph embedding with Tikhonov (SaCCPGT) by imposing a spatial regularization term in the objective function of CCPGE with Tikhonov regularization. In this way, spectral and spatial information can be utilized in a closed form solution in the proposed method. Experimental results on different hyperspectral data sets demonstrate the superior performance of the proposed SaCCPGT in comparison to state-of-the-art graph-based discriminant analysis approaches for DR.

Collaborative representation (CR) is an efficient method for hyperspectral image classification. There exists structure-aware CR with Tikhonov regularization (SaCRT) that utilizes the class label information of training samples into estimation of representation coefficients to provide better performance. It can be further enhanced by considering spatial features because neighboring pixels around the central pixel tend to belong to the same class with high probability. In this paper, a modified SaCRT is proposed for hyperspectral image classification. Its performance is analyzed on different types of spatial features (i.e., spatial averaging features), global feature (i.e., Gabor feature), shape features (i.e., derivative of extended morphological profile (DMP) features), and edge preserving feature. In addition, a majority voting-based ensemble technique is used to enhance the performance by combining different features. The experimental results illustrate that the proposed approach can yield better performance in comparison to state-of-the-art classifiers.

Sparse graph-based discriminant analysis has drawn much attention to represent high dimensional data into low-dimensional subspace by using$l_{1}$-norm optimization. There exists sparse and low-rank graph-based discriminant analysis (SLGDA) for incorporating local and global data structure together by combining both sparsity and low-rankness. Deviating from the concept of sparse representation, collaborative and low-rank representation-based discriminant analysis is proposed (CLGDA) in this paper with the assumption that collaboration among atoms is more important to estimate appropriate representation coefficients by accommodating within-class variation. The experimental results obtained on several hyperspectral datasets illustrate the superior classification performance of the proposed CLGDA in comparison to SLGDA and state-of-the-art approaches.