Qian Du

A linear constrained distance-based discriminant analysis for hyperspectral image classification

Abstract Fishers linear discriminant analysis (LDA) is a widely used technique for pattern classification problems. It employs Fishers ratio, ratio of between-class scatter matrix to within-class scatter matrix to derive a set of feature vectors by which high-dimensional data can be projected onto a low-dimensional feature space in the sense of maximizing class separability. This paper presents a linear constrained distance-based discriminant analysis (LCDA) that uses a criterion for optimality derived from Fishers ratio criterion. It not only maximizes the ratio of inter-distance between classes to intra-distance within classes but also imposes a constraint that all class centers must be aligned along predetermined directions. When these desired directions are orthogonal, the resulting classifier turns out to have the same operation form as the classifier derived by the orthogonal subspace projection (OSP) approach recently developed for hyperspectral image classification. Because of that, LCDA can be viewed as a constrained version of OSP. In order to demonstrate its performance in hyperspectral image classification, Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and HYperspectral Digital Imagery Collection Experiment (HYDICE) data are used for experiments.

A comparative study for orthogonal subspace projection and constrained energy minimization

We conduct a comparative study and investigate the relationship between two well-known techniques in hyperspectral image detection and classification: orthogonal subspace projection (OSP) and constrained energy minimization. It is shown that they are closely related and essentially equivalent provided that the noise is white with large SNR. Based on this relationship, the performance of OSP can be improved via data-whitening and noise-whitening processes.

Linear mixture analysis-based compression for hyperspectral image analysis

Due to significantly improved spectral resolution produced by hyperspectral sensors, the band-to-band correlation is generally very high and can be removed without loss of crucial information. Data compression is an effective means to eliminate such redundancy resulting from high interband correlation. In hyperspectral imagery, various information comes from different signal sources, which include man-made targets, natural backgrounds, unknown clutters, interferers, unidentified anomalies, etc. In many applications, whether or not a compression technique is effective is measured by the degree of information loss rather than information recovery. For example, compression of noise or interferers is highly desirable to image analysis and interpretation. In this paper, we present an unsupervised fully constrained least squares (UFCLS) linear spectral mixture analysis (LSMA)-based compression technique for hyperspectral target detection and classification. Unlike most compression techniques, which deal directly with grayscale images, the proposed compression approach generates and encodes the fractional abundance images of targets of interest present in an image scene to achieve data compression. Since the vital information used for image analysis is generally preserved and retained in these fractional abundance images, the loss of information may have little impact on image analysis. On some occasions, it even improves performance analysis. Airborne Visible/InfraRed Imaging Spectrometer (AVIRIS) and Hyperspectral Digital Imagery Collection Experiment (HYDICE) data are used for experiments to evaluate our proposed LSMA-based compression technique used for applications in hyperspectral detection and image classification. The classification results using the original data and the UFCLS-decompressed data are shown to be very close with no visible difference. But a compression ratio for the HYDICE data with water bands removed can achieve as high as 138:1 with peak SNR (PSNR) 33 dB, while a compression ratio of the AVIRIS scene also with water bands removed is 90:1 with PSNR 40 dB.

Automatic target recognition for hyperspectral imagery using high-order statistics

Due to recent advances in hyperspectral imaging sensors many subtle unknown signal sources that cannot be resolved by multispectral sensors can be now uncovered for target detection, discrimination, and identification. Because the information about such sources is generally not available, automatic target recognition (ATR) presents a great challenge to hyperspectral image analysts. Many approaches developed for ATR are based on second-order statistics in the past years. This paper investigates ATR techniques using high order statistics. For ATR in hyperspectral imagery, most interesting targets usually occur with low probabilities and small population and they generally cannot be described by second-order statistics. Under such circumstances, using high-order statistics to perform target detection have been shown by experiments in this paper to be more effective than using second order statistics. In order to further address a challenging issue in determining the number of signal sources needed to be detected, a recently developed concept of virtual dimensionality (VD) is used to estimate this number. The experiments demonstrate that using high-order statistics-based techniques in conjunction with the VD to perform ATR are indeed very effective

Real-time constrained linear discriminant analysis to target detection and classification in hyperspectral imagery

In this paper, we present a constrained linear discriminant analysis (CLDA) approach to hyperspectral image detection and classification as well as its real-time implementation. The basic idea of CLDA is to design an optimal transformation matrix which can maximize the ratio of inter-class distance to intra-class distance while imposing the constraint that different class centers after transformation are along different directions such that different classes can be better separated. The solution turns out to be a constrained version of orthogonal subspace projection (OSP) implemented with a data whitening process. The CLDA approach can be applied to solve both detection and classification problems. In particular, by introducing color for display the classification is achieved with a single classified image where a pre-assigned color is used to display a specified class. The real-time implementation is also developed to meet the requirement of on-line image analysis when the immediate data assessment is critical. The experiments using HYDICE data demonstrate the strength of CLDA approach in discriminating the targets with subtle spectral difference.

A signal-decomposed and interference-annihilated approach to hyperspectral target detection

A hyperspectral imaging sensor can reveal and uncover targets with very narrow diagnostic wavelengths. However, it comes at a price that it can also extract many unknown signal sources such as background and natural signatures as well as unwanted man-made objects, which cannot be identified visually or a priori. These unknown signal sources can be referred to as interferers, which generally play a more dominant role than noise in hyperspectral image analysis. Separating such interferers from signals and annihilating them subsequently prior to detection may be a more realistic approach. In many applications, the signals of interest can be further divided into desired signals for which we want to extract and undesired signals for which we want to eliminate to enhance signal detectability. This paper presents a signal-decomposed and interference-annihilated (SDIA) approach in applications of hyperspectral target detection. It treats interferers and undesired signals as separate signal sources that can be eliminated prior to target detection. In doing so, a signal-decomposed interference/noise (SDIN) model is suggested in this paper. With the proposed SDIN model, the orthogonal subspace projection-based model and the signal/background/noise model can be included as its special cases. As shown in the experiments, the SDIN model-based SDIA approach generally can improve the performance of the commonly used generalized-likelihood ratio test and constrained energy minimization approach on target detection and classification.

Hidden Markov model approach to spectral analysis for hyperspectral imagery

The hidden Markov model (HMM) has been widely used in speech recognition where it models a speech signal as a doubly sto- chastic process with a hidden state process that can be observed only through a sequence of observations. We present a new application of the HMM in hyperspectral image analysis inspired by the analogy be- tween the temporal variability of a speech signal and the spectral vari- ability of a remote sensing image pixel vector. The idea is to model a hyperspectral spectral vector as a stochastic process where the spectral correlation and band-to-band variability are modeled by a hidden Markov process with parameters determined by the spectrum of the vector that forms a sequence of observations. With this interpretation, a new HMM- based spectral measure, referred to as the HMM information divergence (HMMID), is derived to characterize spectral properties. To evaluate the performance of this new measure, it is further compared to two com- monly used spectral measures, Euclidean distance (ED) and the spectral angle mapper (SAM), and the recently proposed spectral information divergence (SID). The experimental results show that the HMMID per- forms better than the other three measures in characterizing spectral information at the expense of computational complexity.

Segmented PCA-based compression for hyperspectral image analysis

Hyperspectral images have high spectral resolution that helps to improve object classification. But its vast data volume also causes problems in data transmission and data storage. Since there is high correlation among spectral bands in a hyperspectral image, how to reduce the data redundancy while keeping the important information for the following data analysis is a challenging task. In this paper, we investigate a compression technique based on segmented Principal Components Analysis (PCA). A hyperspectral image cube is divided into several non-overlapping blocks in accordance with band-to-band cross-correlations, followed by the PCA performed in each block. A major advantage resulting from this approach is computational efficiency. The utility of the proposed segmented PCA-based compression in target dtection and classification will be investigated. The experiments demonstrate that the segmented PCA-based compression generally outperforms PCA-based compression in terms of high detection and classification accuracy on decompressed hyperspectral image data.

Constrained weighted least squares approaches for target detection and classification in hyperspectral imagery

Least squares unmixing methods are widely used to solve linear mixture problems for endmember abundance estimation in hyperspectral imagery. In this paper, a weighted least squares method is introduced as a generalization. When different weight matrix is used, a certain detector or classifier will be resulted. For accurate abundance fraction estimation, a constrained weighted least squares approach is developed by combining sum-to-one and nonnegativity constraints. The experimental results show that when a meaningful weight matrix is applied as a data pre-processing operator, the weighted least squares method will outperform ordinary least squares solution and the constrained methods will outperform unconstrained ones.

Hidden Markov model approaches to hyperspectral image classification

In this paper, we present a hidden Markov model (HMM) approach to hyperspectral image classification. HMMs have been widely used in speech recognition to model a doubly stochastic process with a hidden state process that can be only observed through a sequence of observations. Since the temporal variability of a speech signal is similar to the spectral variability of a remotely sensed image pixel vector, the same idea can be applied to hyperspectral image classification. It makes use of a hidden Markov process to characterize the spectral correlation and band-to-band variability where the model parameters are determined by the spectra of the pixel vectors that form the observation sequences. Experiments demonstrate that the HMM can better describe the unobserved spectral properties so as to improve classification performance.