Joana Frontera-Pons

False-alarm regulation for target detection in hyperspectral imaging

Classical target detection schemes are usually obtained deriving the likelihood ratio under Gaussian hypothesis and replacing the unknown background parameters by their estimates. In this paper, the adaptive versions of the classical Matched Filter and the Normalized Matched Filter are analyzed for the case when the mean vector of the background is unknown and has to be estimated jointly with the covariance matrix, as it is the case in hyperspectral imaging. More precisely, theoretical closed form expressions for false-alarm regulation are derived and these results are extended to non-Gaussian cases using robust estimation procedures. Finally, simulations validate the theoretical contribution.

Robust anomaly detection in Hyperspectral Imaging

Anomaly Detection methods are used when there is not enough information about the target to detect. These methods search for pixels in the image with spectral characteristics that differ from the background. The most widespread detection test, the RX-detector, is based on the Mahalanobis distance and on the background statistical characterization through the mean vector and the covariance matrix. Although non-Gaussian distributions have already been introduced for background modeling in Hyperspectral Imaging, the parameters estimation is still performed using the Maximum Likelihood Estimates for Gaussian distribution. This paper describes robust estimation procedures more suitable for non-Gaussian environment. Therefore, they can be used as plug-in estimators for the RX-detector leading to some great improvement in the detection process. This theoretical improvement has been evidenced over two real hyperspectral images.

Hyperspectral Anomaly Detectors Using Robust Estimators

Anomaly detection methods are devoted to target detection schemes in which no a priori information about the spectra of the targets of interest is available. This paper reviews classical anomaly detection schemes such as the widely spread Reed-Xiaoli detector and some of its variations. Moreover, the Mahalanobis distance-based detector, rigorously derived from a Kellys test-based approach, is analyzed and its exact distribution is derived when both mean vector and covariance matrix are unknown and have to be estimated. Although, most of these techniques are based on Gaussian distribution, we also propose here ways to extend them to non-Gaussian framework. For this purpose, elliptical distributions are considered for background statistical characterization. Through this assumption, this paper describes robust estimation procedures (M-estimators of location and scale) more suitable for non-Gaussian environment. We show that using them as plug-in estimators in anomaly detectors leads to some great improvement in the detection process. Finally, the theoretical contribution is validated through simulations and on real hyperspectral scenes.

A class of robust estimates for detection in hyperspectral images using elliptical distributions background

When dealing with impulsive background echoes, Gaussian model is no longer pertinent. We study in this paper the class of elliptically contoured (EC) distributions. They provide a multivariate location-scatter family of distributions that primarily serve as long tailed alternatives to the multivariate normal model. They are proven to represent a more accurate characterization of HSI data than models based on the multivariate Gaussian assumption. For data in ℝk, robust proposals for the sample covariance estimate are the M-estimators. We have also analyzed the performance of an adaptive non- Gaussian detector built with these improved estimators. Constant False Alarm Rate (CFAR) is pursued to allow the detector independence of nuisance parameters and false alarm regulation.

Adaptive Nonzero-Mean Gaussian Detection

Classical target detection schemes are usually obtained by deriving the likelihood ratio under Gaussian hypothesis and replacing the unknown background parameters by their estimates. In most applications, interference signals are assumed to be Gaussian with zero mean [or with a known mean vector (MV)] and with an unknown covariance matrix (CM). When the MV is unknown, it has to be jointly estimated with the CM. In this paper, adaptive versions of the classical matched filter (MF) and the normalized MF, as well as two versions of the Kelly detector are first derived and then analyzed for the case where the MV of the background is unknown. More precisely, theoretical closed-form expressions for false alarm (FA) regulation are derived and the constant FA rate property is pursued to allow the detector to be independent of nuisance parameters. Finally, the theoretical contributions are validated through simulations.

Robust detection using M-estimators for hyperspectral imaging

Hyperspectral data have been proved not to be multivariate normal but long tailed distributed. In order to take into account these features, the family of elliptical contoured distributions is proposed to describe noise statistical behavior. Although non-Gaussian models are assumed for background modeling and detectors design, the parameters estimation is still performed using classical Gaussian based estimators; as for the covariance matrix, generally determined according to the SCM approach. We discuss here the class of M-estimators as a robust alternative for background statistical characterization and highlight their outcome when used in an adaptive GLRT-LQ detector.

Binary partition trees-based robust adaptive hyperspectral RX anomaly detection

The Reed-Xiaoli (RX) is considered as the benchmark algorithm in multidimensional anomaly detection (AD). However, the RX detector performance decreases when the statistical parameters estimation is poor. This could happen when the background is non-homogeneous or the noise independence assumption is not fulfilled. For a better performance, the statistical parameters are estimated locally using a sliding window approach. In this approach, called adaptive RX, a window is centered over the pixel under the test (PUT), so the background mean and covariance statistics are estimated using the data samples lying inside the windows spatial support, named the secondary data. Sometimes, a smaller guard window prevents those pixels close to the PUT to be used, in order to avoid the presence of outliers in the statistical estimation. The size of the window is chosen large enough to ensure the invertibility of the covariance matrix and small enough to justify both spatial and spectral homogeneity. We present here an alternative methodology to select the secondary data for a PUT by means of a binary partition tree (BPT) representation of the image. We test the proposed BPT-based adaptive hyperspectral RX AD algorithm using a real dataset provided by the Target Detection Blind Test project.

Performance analysis of robust detectors for hyperspectral imaging

When accounting for heterogeneity and non-Gaussianity of real hyperspectral data, elliptical distributions provide reliable models for background characterization. Through these assumptions, this paper highlights the fact that robust estimation procedures are an interesting alternative to classical methods and can bring some great improvement to the detection process. The goal of this paper is then not only to recall well-known methodologies of target detection but also to propose ways to extend them for taking into account the heterogeneity and non-Gaussianity of the hyperspectral images.

Morphological operators for images valued on the sphere

The lack of a natural ordering on the sphere presents an inherent problem when defining morphological operators extended to unit sphere. We analyze here the notion of averaging over the unit sphere to obtain a local origin which can used to formulate ordering based operators. The notion of local supremum and infimum is introduced, which allows to define the dilation and erosion for images valued on the sphere. The algorithms are illustrated using polarimetric images.

Robust ANMF Detection in Noncentered Impulsive Background

One of the most general and acknowledged models for background statistics characterization is the family of elliptically symmetric distributions. They account for heterogeneity and non-Gaussianity of real data. Today, although nonGaussian models are assumed for background modeling and design of detectors, the parameters estimation is usually performed using classical Gaussian-based estimators. This letter analyzes robust estimation techniques in a nonGaussian environment and highlights their interest as an alternative to classical procedures for target detection purposes. The goal of this letter is to extend well-known detection methodologies to nonGaussian framework, when the statistical mean is nonnull and unknown. Furthermore, a theoretical closed-form expression for false-alarm regulation is derived and the Constant False Alarm Rate property is pursued to allow the detector to be independent of nuisance parameters. The experimental validation is conducted on simulations.