Chein-I Chang

Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach

Most applications of hyperspectral imagery require processing techniques which achieve two fundamental goals: 1) detect and classify the constituent materials for each pixel in the scene; 2) reduce the data volume/dimensionality, without loss of critical information, so that it can be processed efficiently and assimilated by a human analyst. The authors describe a technique which simultaneously reduces the data dimensionality, suppresses undesired or interfering spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel vector onto a subspace which is orthogonal to the undesired signatures. This operation is an optimal interference suppression process in the least squares sense. Once the interfering signatures have been nulled, projecting the residual onto the signature of interest maximizes the signal-to-noise ratio and results in a single component image that represents a classification for the signature of interest. The orthogonal subspace projection (OSP) operator can be extended to k-signatures of interest, thus reducing the dimensionality of k and classifying the hyperspectral image simultaneously. The approach is applicable to both spectrally pure as well as mixed pixels. >

Estimation of number of spectrally distinct signal sources in hyperspectral imagery

With very high spectral resolution, hyperspectral sensors can now uncover many unknown signal sources which cannot be identified by visual inspection or a priori. In order to account for such unknown signal sources, we introduce a new definition, referred to as virtual dimensionality (VD) in this paper. It is defined as the minimum number of spectrally distinct signal sources that characterize the hyperspectral data from the perspective view of target detection and classification. It is different from the commonly used intrinsic dimensionality (ID) in the sense that the signal sources are determined by the proposed VD based only on their distinct spectral properties. These signal sources may include unknown interfering sources, which cannot be identified by prior knowledge. With this new definition, three Neyman-Pearson detection theory-based thresholding methods are developed to determine the VD of hyperspectral imagery, where eigenvalues are used to measure signal energies in a detection model. In order to evaluate the performance of the proposed methods, two information criteria, an information criterion (AIC) and minimum description length (MDL), and the factor analysis-based method proposed by Malinowski, are considered for comparative analysis. As demonstrated in computer simulations, all the methods and criteria studied in this paper may work effectively when noise is independent identically distributed. This is, unfortunately, not true when some of them are applied to real image data. Experiments show that all the three eigenthresholding based methods (i.e., the Harsanyi-Farrand-Chang (HFC), the noise-whitened HFC (NWHFC), and the noise subspace projection (NSP) methods) produce more reliable estimates of VD compared to the AIC, MDL, and Malinowskis empirical indicator function, which generally overestimate VD significantly. In summary, three contributions are made in this paper, 1) an introduction of the new definition of VD, 2) three Neyman-Pearson detection theory-based thresholding methods, HFC, NWHFC, and NSP derived for VD estimation, and 3) experiments that show the AIC and MDL commonly used in passive array processing and the second-order statistic-based Malinowskis method are not effective measures in VD estimation.

Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis

In hyperspectral image analysis, the principal components analysis (PCA) and the maximum noise fraction (MNF) are most commonly used techniques for dimensionality reduction (DR), referred to as PCA-DR and MNF-DR, respectively. The criteria used by the PCA-DR and the MNF-DR are data variance and signal-to-noise ratio (SNR) which are designed to measure data second-order statistics. This paper presents an independent component analysis (ICA) approach to DR, to be called ICA-DR which uses mutual information as a criterion to measure data statistical independency that exceeds second-order statistics. As a result, the ICA-DR can capture information that cannot be retained or preserved by second-order statistics-based DR techniques. In order for the ICA-DR to perform effectively, the virtual dimensionality (VD) is introduced to estimate number of dimensions needed to be retained as opposed to the energy percentage that has been used by the PCA-DR and MNF-DR to determine energies contributed by signal sources and noise. Since there is no prioritization among components generated by the ICA-DR due to the use of random initial projection vectors, we further develop criteria and algorithms to measure the significance of information contained in each of ICA-generated components for component prioritization. Finally, a comparative study and analysis is conducted among the three DR techniques, PCA-DR, MNF-DR, and ICA-DR in two applications, endmember extraction and data compression where the proposed ICA-DR has been shown to provide advantages over the PCA-DR and MNF-DR.

A New Growing Method for Simplex-Based Endmember Extraction Algorithm

A new growing method for simplex-based endmember extraction algorithms (EEAs), called simplex growing algorithm (SGA), is presented in this paper. It is a sequential algorithm to find a simplex with the maximum volume every time a new vertex is added. In order to terminate this algorithm a recently developed concept, virtual dimensionality (VD), is implemented as a stopping rule to determine the number of vertices required for the algorithm to generate. The SGA improves one commonly used EEA, the N-finder algorithm (N-FINDR) developed by Winter, by including a process of growing simplexes one vertex at a time until it reaches a desired number of vertices estimated by the VD, which results in a tremendous reduction of computational complexity. Additionally, it also judiciously selects an appropriate initial vector to avoid a dilemma caused by the use of random vectors as its initial condition in the N-FINDR where the N-FINDR generally produces different sets of final endmembers if different sets of randomly generated initial endmembers are used. In order to demonstrate the performance of the proposed SGA, the N-FINDR and two other EEAs, pixel purity index, and vertex component analysis are used for comparison

An information-theoretic approach to spectral variability, similarity, and discrimination for hyperspectral image analysis

A hyperspectral image can be considered as an image cube where the third dimension is the spectral domain represented by hundreds of spectral wavelengths. As a result, a hyperspectral image pixel is actually a column vector with dimension equal to the number of spectral bands and contains valuable spectral information that can be used to account for pixel variability, similarity and discrimination. We present a new hyperspectral measure, the spectral information measure (SIM), to describe spectral variability and two criteria, spectral information divergence and spectral discriminatory probability for spectral similarity and discrimination, respectively. The spectral information measure is an information-theoretic measure which treats each pixel as a random variable using its spectral signature histogram as the desired probability distribution. Spectral information divergence (SID) compares the similarity between two pixels by measuring the probabilistic discrepancy between two corresponding spectral signatures. The spectral discriminatory probability calculates spectral probabilities of a spectral database (library) relative to a pixel to be identified so as to achieve material identification. In order to compare the discriminatory power of one spectral measure relative to another, a criterion is also introduced for performance evaluation, which is based on the power of discriminating one pixel from another relative to a reference pixel. The experimental results demonstrate that the new hyperspectral measure can characterize spectral variability more effectively than the commonly used spectral angle mapper (SAM).

Automatic spectral target recognition in hyperspectral imagery

Automatic target recognition (ATR) in hyperspectral imagery is a challenging problem due to recent advances of remote sensing instruments which have significantly improved sensors spectral resolution. As a result, small and subtle targets can be uncovered and extracted from image scenes, which may not be identified by prior knowledge. In particular, when target size is smaller than pixel resolution, target recognition must be carried out at subpixel level. Under such circumstance, traditional spatial-based image processing techniques are generally not applicable and may not perform well if they are applied. The work presented here investigates this issue and develops spectral-based algorithms for automatic spectral target recognition (ASTR) in hyperspectral imagery with no required a priori knowledge, specifically, in reconnaissance and surveillance applications. The proposed ASTR consists of two stage processes, automatic target generation process (ATGP) followed by target classification process (TCP). The ATGP generates a set of targets from image data in an unsupervised manner which will subsequently be classified by the TCP. Depending upon how an initial target is selected in ATGP, two versions of the ASTR can be implemented, referred to as desired target detection and classification algorithm (DTDCA) and automatic target detection and classification algorithm (ATDCA). The former can be used to search for a specific target in unknown scenes while the latter can be used to detect anomalies in blind environments. In order to evaluate their performance, a comparative and quantitative study using real hyperspectral images is conducted for analysis.

A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification

Band selection for remotely sensed image data is an effective means to mitigate the curse of dimensionality. Many criteria have been suggested in the past for optimal band selection. In this paper, a joint band-prioritization and band-decorrelation approach to band selection is considered for hyperspectral image classification. The proposed band prioritization is a method based on the eigen (spectral) decomposition of a matrix from which a loading-factors matrix can be constructed for band prioritization via the corresponding eigenvalues and eigenvectors. Two approaches are presented, principal components analysis (PCA)-based criteria and classification-based criteria. The former includes the maximum-variance PCA and maximum SNR PCA, whereas the latter derives the minimum misclassification canonical analysis (MMCA) (i.e., Fishers discriminant analysis) and subspace projection-based criteria. Since the band prioritization does not take spectral correlation into account, an information-theoretic criterion called divergence is used for band decorrelation. Finally, the band selection can then be done by an eigenanalysis based band prioritization in conjunction with a divergence-based band decorrelation. It is shown that the proposed band-selection method effectively eliminates a great number of insignificant bands. Surprisingly, the experiments show that with a proper band selection, less than 0.1 of the total number of bands can achieve comparable performance using the number of full bands. This further demonstrates that the band selection can significantly reduce data volume so as to achieve data compression.

Anomaly detection and classification for hyperspectral imagery

Anomaly detection becomes increasingly important in hyperspectral image analysis, since hyperspectral imagers can now uncover many material substances which were previously unresolved by multispectral sensors. Two types of anomaly detection are of interest and considered in this paper. One was previously developed by Reed and Yu to detect targets whose signatures are distinct from their surroundings. Another was designed to detect targets with low probabilities in an unknown image scene. Interestingly, they both operate the same form as does a matched filter. Moreover, they can be implemented in real-time processing, provided that the sample covariance matrix is replaced by the sample correlation matrix. One disadvantage of an anomaly detector is the lack of ability to discriminate the detected targets from another. In order to resolve this problem, the concept of target discrimination measures is introduced to cluster different types of anomalies into separate target classes. By using these class means as target information, the detected anomalies can be further classified. With inclusion of target discrimination in anomaly detection, anomaly classification can be implemented in a three-stage process, first by anomaly detection to find potential targets, followed by target discrimination to cluster the detected anomalies into separate target classes, and concluded by a classifier to achieve target classification. Experiments show that anomaly classification performs very differently from anomaly detection.

Constrained band selection for hyperspectral imagery

Constrained energy minimization (CEM) has shown effective in hyperspectral target detection. It linearly constrains a desired target signature while minimizing interfering effects caused by other unknown signatures. This paper explores this idea for band selection and develops a new approach to band selection, referred to as constrained band selection (CBS) for hyperspectral imagery. It interprets a band image as a desired target signature vector while considering other band images as unknown signature vectors. As a result, the proposed CBS using the concept of the CEM to linearly constrain a band image, while also minimizing band correlation or dependence provided by other band images, is referred to as CEM-CBS. Four different criteria referred to as Band Correlation Minimization (BCM), Band Correlation Constraint (BCC), Band Dependence Constraint (BDC), and Band Dependence Minimization (BDM) are derived for CEM-CBS.. Since dimensionality resulting from conversion of a band image to a vector may be huge, the CEM-CBS is further reinterpreted as linearly constrained minimum variance (LCMV)-based CBS by constraining a band image as a matrix where the same four criteria, BCM, BCC, BDC, and BDM, can be also used for LCMV-CBS. In order to determine the number of bands required to select p, a recently developed concept, called virtual dimensionality, is used to estimate the p. Once the p is determined, a set of p desired bands can be selected by the CEM/LCMV-CBS. Finally, experiments are conducted to substantiate the proposed CEM/LCMV-CBS four criteria, BCM, BCC, BDC, and BDM, in comparison with variance-based band selection, information divergence-based band selection, and uniform band selection.

Constrained subpixel target detection for remotely sensed imagery

Target detection in remotely sensed images can be conducted spatially, spectrally or both. The difficulty of detecting targets in remotely sensed images with spatial image analysis arises from the fact that the ground sampling distance is generally larger than the size of targets of interest in which case targets are embedded in a single pixel and cannot be detected spatially. Under this circumstance target detection must be carried out at subpixel level and spectral analysis offers a valuable alternative. In this paper, the problem of subpixel spectral detection of targets in remote sensing images is considered, where two constrained target detection approaches are studied and compared. One is a target abundance-constrained approach, referred to as nonnegatively constrained least squares (NCLS) method. It is a constrained least squares spectral mixture analysis method which implements a nonnegativity constraint on the abundance fractions of targets of interest. Another is a target signature-constrained approach, called constrained energy minimization (CEM) method. It constrains the desired target signature with a specific gain while minimizing effects caused by other unknown signatures. A quantitative study is conducted to analyze the advantages and disadvantages of both methods. Some suggestions are further proposed to mitigate their disadvantages.