Elsevier

Pattern Recognition

Volume 48, Issue 10, October 2015, Pages 3216-3226
Pattern Recognition

Segmented minimum noise fraction transformation for efficient feature extraction of hyperspectral images

https://doi.org/10.1016/j.patcog.2015.04.013Get rights and content

Highlights

  • A segmented minimum noise fraction (MNF) transformation is proposed for efficient feature extraction of hyperspectral images (HSIs).

  • The proposed method significantly reduces the transformation time in comparison with the conventional MNF.

  • The class separability of the extracted features is improved.

  • The extracted features by SMNF even exhibit higher classification accuracy compared with the PCA or MNF.

Abstract

In this paper, a segmented minimum noise fraction (MNF) transformation is proposed for efficient feature extraction of hyperspectral images (HSIs). The original bands can be partitioned into several highly correlated subgroups based on the correlation matrix image of the hyperspectral data. The MNF is implemented separately on each subgroup of the data, and then, the Bhattacharyya distance is used as the band separability measure for feature extraction. Consequently, the extracted features can then be significantly classified using state-of-art classifiers, i.e., k-NN or SVM. Experiments on two benchmark HSIs collected by AVIRIS and ROSIS demonstrate that the proposed method significantly reduces the transformation time in comparison with the conventional MNF. The Fisher scalars’ criterion shows that the class separability with the segmented MNF is the best, and the extracted features even exhibit higher classification accuracy compared with the PCA or MNF.

Introduction

Supervised classification has been widely used in the classification of hyperspectral images (HSIs), but it also faces challenges associated with the high dimensionality of the data and the limited availability of training samples [1]. It has been demonstrated that the original spectral features contain high redundancy; specifically, there is a high correlation between adjacent bands, and the number of the original spectral features may be too high for classification purposes [2]. In addition, the original spectral features may not be the most effective features for separating the objects of interest from others. Furthermore, supervised classification often requires a large amount of available training samples to define the classes, which is an expensive and laborious task that is sometimes even infeasible. The so-called Hughes phenomenon illustrates the relationship among the accuracy, the features and the number of training samples [3]. This phenomenon suggests that there is an optimal measurement complexity for a fixed number of training samples. Too many spectral bands or too many brightness levels per spectral band are undesirable from the perspective of expected classification accuracy.

To address these issues, feature extraction techniques have been developed such that an effective set of features can be identified prior to classification. The goal of feature extraction approaches is to reduce the dimensionality of the input space to better exploit the available (limited) training samples. Principal components analysis (PCA) has become the standard tool for reducing the dimensionality of hyperspectral remote-sensing data [2], [4], [5], [6]. In PCA, the hyperspectral data are projected onto a new space in which the first few components account for most of the total information in the data, and therefore, only the first few features can be retained. However, because the noise variance is not the same in all bands, the principal components transform does not always produce images that exhibit steadily decreasing image quality with increasing number of components [7]. Thus, rather than choosing new components to maximize variance, as the principal components transform does, the minimum noise fraction (MNF) chooses new components to maximize the signal-to-noise ratio [7]. Noise can be effectively removed from hyperspectral data by transforming to the MNF space, smoothing or rejecting the noisiest components, and then retransforming to the original space. In this way, considerably more intense smoothing can be applied to the MNF components with high noise and low signal content than could be applied to each band of the original data.

For low-dimensionality data, dimensionality reduction can be achieved relatively easily using feature extraction techniques, e.g., via MNF transformation to enhance class separability with fewer features. However, MNF-based feature extraction will be a time-consuming task for hyperspectral data with high dimensionality because the best subset of features cannot be extracted until an exhaustive search of all the feature subset combinations has been performed [8]. Thus, implementing MNF with a high-dimensional data-set imposes a high computational load.

The feature extraction step with the MNF transformation consists of mapping the input vector of an image xRn (n spectral bands) onto a new feature description zRm (lower dimensionality m) that is more suitable for the given task. The linear projectionz=WTxis commonly used for this purpose. The projection is given by the matrix W[n×m] of normalized eigenvectors of the image covariance matrix. The MNF is a representative of the unsupervised learning method, which yields the linear projection Eq. (1); it provides a new feature space z; and its first components m are the best choice of linear functions for reconstructing the original data.

Note that the linear projection given by Eq. (1) is a time-consuming task that requires n×n multiplications and n×(n1) additions per pixel. The computational load of this task leads to an inefficient transform of the complete hyperspectral data. Moreover, the task can be biased to the high-variance bands. For example, the shapes of the hyperspectral data recorded by the airborne visible/infrared imaging spectrometer (AVIRIS) or reflective optics imaging spectrographic system (ROSIS) are affected by the solar spectrum. This indicates that a spectral weighting is imposed. Consequently, the variances of the spectral bands in the short wavelength region are considerably higher than those of the remaining bands if the data are not calibrated. Therefore, the conventional MNF will be dominated by the visible and near-infrared bands.

In this paper, a segmented minimum noise fraction (SMNF) transformation is proposed. The original bands can be partitioned into several highly correlated subgroups based on the correlation of hyperspectral bands, and the MNF is implemented separately on each subgroup of data. The Bhattacharyya distance is used as the band separability measure for feature extraction. The proposed SMNF significantly reduces the computational time, and it even exhibits higher classification accuracy compared with the conventional MNF.

Section snippets

Correlation matrix images

Let TX={x1,,xl} be a set of training vectors from the n-dimensional input space of hyperspectral data. The total mean vector μ and covariance matrix Σ are defined asμ=1li=1lxiandΣ=1l1i=1l(xiμ)(xiμ)TA quantity closely related to the covariance matrix Σ is the correlation matrix R, and its elements are determined byρij=vijviivjjwhere vij are the elements of Σ and vii and vjj are the variances of the ith and jth bands of data, which describe the correlation between the i band and the j band.

Experimental demonstration and analysis

In this section, several experiments are conducted on two benchmark datasets that have been preprocessed by de-noising and atmospheric or geometric correction to assess the effectiveness of the proposed SMNF method through comparison with the PCA and MNF. To make the experiments more reasonable, the features are extracted from the aforementioned strategies into both k-NN and SVM classifiers.

Conclusion

The proposed segmented MNF strategy is an efficient feature extraction method for hyperspectral images through the use of the correlation matrix image of hyperspectral data. The Bhattacharyya distance can be used as the band separability measure for feature extraction after the MNF is implemented separately on each subgroup of data. The proposed scheme significantly reduces the computational time, the Fisher scalars’ criterion shows that the class separability with the proposed SMNF is the

Conflict of interest

None declared.

Acknowledgment

This work was supported in part by the National Natural Science Foundation of China under Grant 61331021, in part by the National Defence Pre-research Foundation of China under Grant 9140XXX0283, and in part by the Shenzhen Science and Technology Projection under Grant JCYJ20130408173025036 and Grant JCYJ20130326112132687.

Guan Lixin received the B.S. degree from the School of Information Engineering, Nanchang University, Nanchang, China, in 1998, the M.S. degree in communication and information from Tianjin University, Tianjin, China, in 2006, he is currently pursuing the Ph.D. degree in information and communication engineering from the ATR Key Laboratory of National Defense Technology, Shenzhen University, Shenzhen, China. He has been an associate Professor with the School of Physics and Electronic

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Guan Lixin received the B.S. degree from the School of Information Engineering, Nanchang University, Nanchang, China, in 1998, the M.S. degree in communication and information from Tianjin University, Tianjin, China, in 2006, he is currently pursuing the Ph.D. degree in information and communication engineering from the ATR Key Laboratory of National Defense Technology, Shenzhen University, Shenzhen, China. He has been an associate Professor with the School of Physics and Electronic Information, Gannan Normal University, Ganzhou, China, since 2009.

His current research interests include intelligent information processing, machine learning and their applications to hyperspectral classification.

Xie WeiXin received the B.S. degree in signal and information processing from Xidian University, in 1965. He was a visiting scholar at University of Pennsylvania, U.S.A. from 1981 to 1983, and from 1989 to 1990. He has been a professor of Xidian University since 1986. He was the vice-president of Xidian University from 1992 to 1996, and the president of Shenzhen University from 1996 to 2005.

Currently, Prof. Xie is the chairman of the Academic Committee of Shenzhen University, and the chairman of the Signal Processing branch of the Chinese Institute of Electronics. He is the EB member of Scichina the primary editor of the Chinese Journal of Signal Processing, and the vice editor of Chinese Journal of Electronics.

Pei Jihong received the B.S. degree at Beihang University in 1989, and the M.S. degree at Xidian University in 1994, and the Ph.D. degree at Xidian University in 1998. Currently, he is a professor of Shenzhen University.

His research interests include intelligent information processing, pattern recognition, video image analysis, and image analysis.

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