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Joint Within-Class Collaborative Representation for Hyperspectral Image Classification
Wei Li, Member, IEEE, and Qian Du, Senior Member, IEEE
Abstract—Representation-based classification has gained great interest recently. In this paper, we extend our previous work in collaborative representation-based classification to spatially joint versions. This is due to the fact that neighboring pixels tend to belong to the same class with high probability. Specifically, neighboring pixels near the test pixel are simultaneously represented via a joint collaborative model of linear combinations of labeled samples, and the weights for representation are estimated by an -minimization derived closed-form solution.
Experimental results confirm that the proposed joint withinclass collaborative representation outperforms other state-of-theart techniques, such as joint sparse representation and support vector machines with composite kernels.
Index Terms—Collaborative representation, hyperspectral image, pattern classification, spatial correlation.
H YPERSPECTRAL IMAGERY (HSI) obtained byremote-sensing systems is a 3-D data cube with both spatial and spectral coordinates. Typically, hyperspectral data consist of hundreds of narrow contiguous wavelength bands which include detailed spectral information about the materials in the scene. Taking advantage of the rich spectral information, numerous classification algorithms using hyperspectral data have been developed for a variety of applications –, such as land use analysis, pollution monitoring, etc.
With the advance of sensor technology, hyperspectral images with high spatial resolution are continually becoming more available. Compared to the classifiers solely using spectral signatures –, recent research efforts using joint spatial-spectral featuresmay improve classification accuracy –, particularly when dealing with high-spatial-resolution images. For instance, morphological profile (MP) generated by the morphological operators (e.g., opening and closing), which is widely used for modeling structural information, has been introduced in .
Texture features , -D Gabor wavelets , and 3-D gray level co-occurrence matrices (GLCM)  have also been investigated for hyperspectral image classification. Aforementioned classification methods mainly explore the joint spectral-spatial features in HSI, followed by a pixel-wise classifier. Another widely used strategy is to include the spatial information in a post-processing step. For instance, Markov random field (MRF) ,  is amodel to incorporate the spatial-context information based on the results of support vector machine (SVM)  classifier, namely SVM-MRF. In addition, researchers have taken into account simultaneous spectral and spatial information within the designed classifier. In , themethodexploited the properties of Mercer’s conditions to construct a family of composite kernels (CKs) for the combination of both spectral and spatial information. A simple CK naturally comes from the concatenation of nonlinear transformations of spectral and contextual signatures, and the resulting classifier is referred to as SVM-CK.Note that the spatial feature in SVM-CK is simply the neighbor average of a small window, and the use of such a feature does not necessarily increase the dimensionality of the feature space.
Deviated from traditional classifiers with the training-testing fashion, sparse representation has been proposed for classification. In , a pixel to be classified is sparsely approximated by labeled samples, and it is assigned to the class whose labeled samples provide the smallest representation error. In , two joint sparsity models have also been proposed to incorporate the contextual information: in one joint model called simultaneous orthogonal matching pursuit (SOMP), pixels in a small neighborhood around the test pixel are simultaneously represented by linear combinations of labeled samples, whereas in the other model called OMP with smoothing (OMP-S), the smoothing constraint is imposed to force the vector Laplacian of the approximations to be zero. The ideas were extended to anomaly detection  and kernel version of joint sparsity model for hyperspectral image classification has been discussed in .
It has been argued that it is the “collaborative” nature of the approximation instead of “competitive” nature imposed by sparseness constraint that actually improves the classification accuracy . Thus, a collaborative representation based classifier, called nearest regularized subspace (NRS), was proposed in  for hyperspectral image classification. The essence of NRS classifier is an penalty in the style of a distance-weighted
Tikhonov regularization . The distance-weighted measurement enforces a structure of weight vector; compared to sparserepresentation-based approach, the weights can be simply estimated through a closed-form solution, resulting in much lower computational cost.
However, the NRS classifier was originally designed to be a pixel-wise classifier—only the spectral signature has been exploited while ignoring the spatial information at neighboring
Manuscript received August 29, 2013; revised December 08, 2013; accepted
February 16, 2014. This work was supported by the National Natural Science
Foundation of China under Grant NSFC-61302164.
W. Li is with the College of Information Science and Technology, Beijing
University of Chemical Technology, Beijing 100029, China (e-mail: firstname.lastname@example.org).
Q. Du is with the Department of Electrical and Computer Engineering,
Mississippi State University, Mississippi State, MS 39762 USA (e-mail: email@example.com).
Digital Object Identifier 10.1109/JSTARS.2014.2306956
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