A comparative study of linear and nonlinear anomaly detectors for hyperspectral imagery

Hirsh Goldberg; Nasser M. Nasrabadi

doi:10.1117/12.719932

7 May 2007 A comparative study of linear and nonlinear anomaly detectors for hyperspectral imagery

Hirsh Goldberg, Nasser M. Nasrabadi

Proceedings Volume 6565, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIII; 656504 (2007) https://doi.org/10.1117/12.719932
Event: Defense and Security Symposium, 2007, Orlando, Florida, United States

Abstract

In this paper we implement various linear and nonlinear subspace-based anomaly detectors for hyperspectral imagery. First, a dual window technique is used to separate the local area around each pixel into two regions - an inner-window region (IWR) and an outer-window region (OWR). Pixel spectra from each region are projected onto a subspace which is defined by projection bases that can be generated in several ways. Here we use three common pattern classification techniques (Principal Component Analysis (PCA), Fisher Linear Discriminant (FLD) Analysis, and the Eigenspace Separation Transform (EST)) to generate projection vectors. In addition to these three algorithms, the well-known Reed-Xiaoli (RX) anomaly detector is also implemented. Each of the four linear methods is then implicitly defined in a high- (possibly infinite-) dimensional feature space by using a nonlinear mapping associated with a kernel function. Using a common machine-learning technique known as the kernel trick all dot products in the feature space are replaced with a Mercer kernel function defined in terms of the original input data space. To determine how anomalous a given pixel is, we then project the current test pixel spectra and the spectral mean vector of the OWR onto the linear and nonlinear projection vectors in order to exploit the statistical differences between the IWR and OWR pixels. Anomalies are detected if the separation of the projection of the current test pixel spectra and the OWR mean spectra are greater than a certain threshold. Comparisons are made using receiver operating characteristics (ROC) curves.

Citation Download Citation

Hirsh Goldberg and Nasser M. Nasrabadi "A comparative study of linear and nonlinear anomaly detectors for hyperspectral imagery", Proc. SPIE 6565, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIII, 656504 (7 May 2007); https://doi.org/10.1117/12.719932

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available