Elsevier

Signal Processing

Volume 168, March 2020, 107361
Signal Processing

A sparse tensor-based classification method of hyperspectral image

https://doi.org/10.1016/j.sigpro.2019.107361Get rights and content

Highlights

  • A sparse tensor-based classification method based on Tucker decomposition for HSI.

  • Sparse tensor-based representation extracts joint spatial-spectral tensor features.

  • The principal component analysis removes noise and reduce calculation time.

  • Intrinsic spatial-spectral tensors remove noise and alleviate with-in class variation.

  • The sparse tensor features are classified with state-of-the-art accuracy by SVM.

Abstract

Previous studies have demonstrated that spatial information can provide significant improvement for the accuracy hyperspectral image (HSI) classification. However, it remains a challenging task to extract three-dimensional (3-D) features from HSI directly. In this paper, a sparse tensor-based classification (STC) method for HSI is proposed. Different from the traditional vector-based or matrix-based methods, the STC utilizes tensor technique to extract the joint spatial-spectral tensor features. We exploit the principal component analysis (PCA) and the 3-D intrinsic spatial-spectral tensors of HSI to alleviate within-class spatial-spectral variation, and to improve the classification performance simultaneously. First, the HSI is segmented into a number of overlapping 3-D tensor patches, which are modelled as summation of intrinsic spatial-spectral tensors and corresponding variation tensors in the next step. Second, the intrinsic spatial-spectral tensor is decomposed into three matrices and a core tensor by the Tucker decomposition (TKD). Sparsity constraint is enforced on the core tensor to extract joint sparse spatial-spectral features. We utilize tensor-based dictionary learning algorithm to train three dictionaries, in order to extract more discriminative tensor features for classification. Finally, we use the support vector machine (SVM) to perform the pixel-wise classification. Experimental results on real HSI datasets demonstrate the proposed method can achieve accurate and robust classification results, and can provide competitive results to state-of-the-art methods.

Introduction

Hyperspectral images (HSIs) are usually composed of several hundreds of adjacent and narrow bands from the visible to the near infrared spectral bands for the same scene. They provide rich information of land-covers, and attract wide attention in many applications, such as land use analysis [1], urban mapping [2], military reconnaissance [3], and environment monitoring [4]. In these applications, the basic problem is classification [5], where each pixel in the HSI is assigned to a category.

During the last decade, many reliable classifiers have been designed for HSI classification, such as support vector machine (SVM) [6], [7], [8], random forests [9], decision trees (DT) [10], and sparse representation-based classifiers (SRC) [11], [12], [13], [14], [15], [16], [17]. Among these approaches, SVM is regarded as a simple but powerful classifier, which has been used as the final classifier in many other HSI classification methods [18], [19]. In [20], Kang et al. combined SVM classifier with random walker algorithm to achieve the spatial-spectral classifier. In addition, it is believed that the HSI contains sparse characteristics, thus, the SRC has become popular for HSI classification. Moreover, as an analogy of sparsity, low-rank property has been utilized in HSI classification, such as low-rank representation (LRR) [21], [22], [23], [24]. Recently, with the development of artificial intelligence, researchers are focused on ensemble learning (EL) [25], [26], active learning (AL) [27], [28], and deep learning (DL) [29], [30]. Specially, deep convolutional neural network (CNN) [31], [32], [33], deep recurrent neural networks (RNN) [34], and fully convolutional network (FCN) [35], which belong to deep learning, are state-of-the-art methods.

The HSI is a special image which is composed of spectral and spatial information, specially, spectral information is correlative with spatial information. Therefore, base on the information used, the HSI classification methods can be divided into three categories. The first category only use the spectral information, such as SVM [6], one-dimensional CNN [33], RNN [34] and sparse representation with spectral information [18]. In the second category of methods, researchers utilize various spatial filters, including morphological attribute profiles [36], [37], [38] and Gabor filter [39], [40], to extract spatial features from HSI before pixel-wise classification is performed. The two-dimensional CNN [33] is another method to exploit spatial information for HSI classification. The third category of methods utilize spectral and spatial information. Researchers can combine the spectral and spatial information [41] in classifiers, such as the contextual kernel support vector machine (CSVM) [42], the composite-kernel support vector machine (CKSCM) [42], three-dimensional CNN [33], and spectral-spatial random walker [20], [43]. The spatial information can also be combined with spectral information in the feature extraction process, such as Markov random field (MRF) [44], [45], and linear representation with additional structured priors, including the joint sparsity [19], [46], [47], [48], [49], Laplacian sparsity [50], low-rank prior [23], [24] and group-based sparsity [19], [51]. In [48], [49], the sparse representation of unknown pixel is expressed as a sparse vector whose nonzero entries correspond to the weights of the selected training samples base on joint sparse model. And the sparse representation is solved via simultaneous orthogonal matching pursuit (SOMP). In spatial-aware dictionary learning (SADL) method [19], the pixels of HSI is partitioned into a number of spatial neighborhoods called contextual groups, and the dictionary learning is carried out with a joint sparse regularizer to induce a common sparsity pattern in the sparse coefficients of each contextual groups.

The aforementioned methods are almost vector or matrix techniques, however, HSI is three-dimensional (3-D) data, which belongs to tensor. There is few method that uses tensor techniques to extract spatial-spectral tensor features for HSI classification. While, tensor techniques for HSI have been used in compressed sensing reconstruction [52], and anomaly detection [53]. In [21], He et al. proposed a low-rank tensor learning (lrTL) algorithm, in which the testing tensor samples can be represented by the linear combination of training tensor samples. In [54], Yang et al. proposed a hybrid probabilistic sparse -coding-based classifier with spatial neighbor tensors (HPSCC-SNT) algorithm, but the dictionary used for feature extraction just represents the spectral features. In [55], Zhao et al. proposed a group tensor decomposition method for HSI classification, but the classifier only use the spectral information from the intrinsic spectral component. These methods exploit tensor techniques, but they fail to extract the tensor features, which contain the spatial, spectral and spatial-spectral information.

In this paper, we propose a sparse tensor-based classification (STC) method for HSI. Different from vector-based and matrix-based methods for HSI classification, we acquire the sparse 3-D tensor features from 3-D tensor patches directly. This is the first time to develop Tucker decomposition (TKD) [56] to extract tensor features for HSI classification. In the STC, the principal component analysis (PCA) [57], [58] is utilized to reduce the spectral dimension of HSI. Next, the dimension reduced HSI is normalized and divided into 3-D tensor patches. Then, we use the three-dimensional method of optimal directions (3-D-MOD) dictionary learning algorithm [52] and N-way block orthogonal matching pursuit (NBOMP) [59], [60] to get the tensor-based sparse representation. Finally, the sparse coefficient tensors are utilized in pixel-wise HSI classification.

The contributions of this study can be summarized as the following aspects.

  • 1.

    We use the 3-D tensors as samples, which follow the 3-D attribute of HSI and help to preserve the joint spatial-spectral information. We have verified that the proposed STC method is capable to extract the spatial, spectral, and joint spatial-spectral features, which are effective for classification.

  • 2.

    We extract the tensor features of the HSI by tensor-based representation with a sparsity constraint. The tensor-based dictionaries can represent a 3-D tensor patch as a 3-D sparse coefficient tensor, which is discriminative enough for simple classifier.

  • 3.

    In the proposed method, we use the PCA to remove noise and to reduce the calculation time. Besides, the PCA and the STC are already able to obtain satisfactory classification performance. Furthermore, we extract features from the intrinsic spatial-spectral tensors to remove noise and to alleviate within-class variation.

The remainder of this paper is organized as follows. Introductions to the TKD model, 3-D-MOD, and NBOMP are briefly given in Section 2. The details of the proposed STC method for HSI are described in Section 3. The experimental setup and results are provided in Section 4. Finally, Section 5 concludes this paper.

Section snippets

Related works

In this section, some backgrounds on the TKD [56], and two related algorithms are briefly described.

Proposed method for HSI classification

To overcome the shortcomings of the vector-based and matrix-based methods in HSI classification tasks, we propose the STC. The features extracted by sparse representation are 3-D tensors, which can represent the joint spatial and spectral information completely. Furthermore, we propose a classification method base on the tensor features.

Fig. 1 shows the schematic diagram of the proposed HSI classification method. First, we pad the margin of the whole HSI. We display the 10th spectral bands of

Experimental results and analysis

In this section, we perform a series of experiments on three benchmark HSI datasets to demonstrate the effectiveness of the proposed STC method. First, we analyse the parameters of the proposed classification method, i.e. P (the spatial size of the 3-D tensor patches) and B (the number of preserved PCs). Next, we analyse the influence of PCA for the speed of the proposed STC. Then we compare the classification accuracies of the STC method with several state-of-the-art methods, including the

Conclusion

In this paper, we have proposed a sparse tensor-based classification (STC) method for hyperspectral image (HSI). The STC is based on the Tucker decomposition, as well as utilizes the sparsity of HSI. The dictionary learning method and sparse representation base on tensor are used to obtain the spectral, spatial, and joint spatial-spectral features. The sparse tensor features are classified by the nolinear classifier SVM. Compared with several HSI classification methods, the proposed STC method

Declaration of Competing Interest

The authors declared that they have no conflicts of interest to this work.

Acknowledgments

The authors would like to thank Prof. D. Landgrebe from Pursue University for providing the Indian Pines data and the Prof. Paolo Gamba from Pavia University for providing the University of Pavia and the Center of Pavia data. This work was supported by the National Natural Science Foundation of China under Grant 61174016 and 61876054.

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