Michael E. Winter

A proof of the N-FINDR algorithm for the automated detection of endmembers in a hyperspectral image

N-FINDR, an automated end-member detection and unmixing algorithm, was first proposed four years ago. Since then, the algorithm has been used successfully in a number of situations. The apparent success of the N-FINDR algorithm is a strong motivator for a complete review of its approach, from its assumptions to its implementation details. This paper reviews the approach used in N-FINDR, and makes a theoretical argument that the algorithm works. The algorithm can be proven to work perfectly on theoretically perfect data. Moreover, N-FINDR can be shown to have good (although imperfect) convergence properties with non-ideal data.

Using endmembers as a coordinate system in hyperspectral imagery

The linear mixing model (LMM) is a well-known and useful method for decomposing spectra in a hyperspectral image into the sum of their constituents, or endmembers. Mathematically, if the spectra are represented as n-dimensional vectors, then the LMM implies that the set of endmembers defines a basis or coordinate system for the set of spectra. Because the endmembers themselves are generally not orthogonal, the geometry (distances, difference angles, etc.) is changed by moving from band space to endmember space. We explore some of the differences between the two coordinate systems, and show in particular that the difference in angle measurements leads to an improved method for subpixel target detection.

Two years of operations of AHI: an LWIR hyperspectral imager

The Airborne Hyperspectral Imager (AHI) system is a long- wave infrared imaging spectrometer originally designed to detect the presence of buried land mines. Subsequent work with AHI has shown the utility of the long-wave infrared for other applications. The AHI system has been used successfully in the detection of buried land mines using infrared absorption features of disturbed soil. Gas detection was also shown to be feasible, with gas absorption being clearly visible in the thermal IR. This allowed the mapping of a gas release using a matched filter. Geological mapping using AHI can be performed using the thermal band absorption features of different minerals. A large-scale geological map was obtained over a dry lake area in California using a mosaic of AHI flightlines, including mineral spectra and relative abundance maps.

Recent results from AHI: a LWIR hyperspectral imager

The University of Hawaii AHI LWIR hyperspectral sensor has been in active use for several years. Since previous publications the sensor characteristics have evolved, and new applications have been encountered. This paper reviews the current status of the sensor and its characteristics, reviews a gas detection experiment conducted using natural sulfur dioxide emitted from a Hawaiian volcano, and test images from a hyperspectral polarization upgrade.

Calibration of the University of Hawaii's airborne hyperspectral imager

The University of Hawaii’s Airborne Hyperspectral Imager (AHI) consists of a long-wave infrared pushbroom hyperspectral imager and a boresighted 3-color visible high resolution CCD linescan camera. A new data system was added to the AHI in a recent upgrade of the sensor, resulting in the ability to collect data at full resolution in 256 spectral channels. This upgrade motivated the design of a new calibration procedure that removes image distortion and bad pixels from the produced imagery. The approach used is a novel method using a runtime-calculated transform. This transform describes the means of converting the distorted AHI focal plane into a corrected “virtual” AHI focal plane. The transform is formulated using several spatial-statistical assumptions as to the way information varies on the focal plane, and is based on geostatistical interpolation techniques. This transform removes the distortion present in the AHI imager and delivers high quality imagery.

Tradeoffs for real-time hyperspectral analysis

There has been considerable interest in the application of real-time processing techniques to the problem of hyperspectral scene analysis. Recent satellite and aircraft systems can produce data at a rate far faster than the data can be analyzed by interactive computer procedures. Automated and fast procedures for preparing the data for analyst inspection are required for even laboratory use of the large quantities of data. In addition, there are several real-time applications where the data must be processed as it is being acquired. A typical application is a computing system on-board an airplane for operator analysis of the scene as the hyperspectral sensor collects data. In this paper the possible tradeoffs fore rapid analysis are discussed, including choice of algorithm, possible dimensionality reduction, and reduced display level. A real time anomaly detection processing system based on the N- FINDR algorithm has been designed and implemented for the Night Vision Imaging Spectrometer (NVIS). The N-FINDR algorithm is a linear unmixing based algorithm that automatically finds spectral endmembers. The algorithm works by inflating a simplex inside the data, beginning with a random set of pixels. Once these endmember spectra have been found, the image cube can be unmixed using a least-squares approach into a map of fractional abundances of each endmember material in each pixel. In addition to the N-FINDR algorithm, the real-time processing system performs calibration, bad pixel removal, and display of selected fraction planes. The real-time processor is implemented in a commercial Pentium IV computer.

Examining hyperspectral unmixing error reduction due to stepwise unmixing

Unmixing hyperspectral images inherently transfers error from the original hyperspectral image to the unmixed fraction plane image. In essence by reducing the entire information content of an image down to a handful of representative spectra a significant amount of information is lost. In an image with low spectral diversity that obeys the linear mixture model (such as a simple geologic scene), this loss is negligible. However there exist inherent problems in unmixing a hyperspectral image where the actual number of spectrally distinct items in the image exceeds the resolving ability of an unmixing algorithm given sensor noise. This process is demonstrated here with a simple statistical analysis. Stepwise unmixing, where a subset of end-members is used to unmix each pixel provides a means of mitigating this error. The simplest case of stepwise unmixing, constrained unmixing, is statistically examined here. This approach provides a significant reduction in unmixed image error with a corresponding increase in goodness of fit. Some suggestions for future algorithms are presented.

Dimensionality reduction in hyperspectral imagery

In this paper we examine how the projection of hyperspectral data into smaller dimensional subspaces can effect the propagation of error. In particular, we show that the nonorthogonality of endmembers in the linear mixing model can cause small changes in band space (as, for example, from the addition of noise) to lead to relatively large changes in the estimated abundance coefficients. We also show that increasing the number of endmembers can actually lead to an increase in the amount of possible error.

Autonomous determination of endmembers in high spatial and spectral resolution data

Recently, new hyperspectral sensors have become available that provide both high spatial resolution and high spectral resolution. These characteristics combined with high signal to noise ratio allow the differentiation of vegetation or mineral types based upon the spectra of small patches of the surface. In this paper, automated endmember determination methods are applied to high spatial and spectral resolution data from two new sensors, TRWIS III and NVIS. Both of these sensors are high quality low noise pushbroom imaging spectrometers that acquire data at 5 to 6 nm resolution from 400 to 2450 nm. The data sets collected will be used for two different applications of the automated determination of endmembers: scene material classification and the detection of spectral anomalies. The NVIS hyperspectral data was collected from approximately 6000 ft above ground level over Cuprite, Nevada, resulting in a footprint of approximately two meters. The TRWIS III data was collected from 1500 meters altitude over mixed agriculture backgrounds in Ventura County, California, a largely agricultural area about 100 km from Los Angeles. After calibration and other preprocessing steps, the data in each case was processed using the N-FINDR algorithm, which extracts endmembers based upon the geometry of convex sets. Once these endmember spectra are found, the image cube can be unmixed into fractional abundances of each material in each pixel. The results of processing this high spatial and spectral resolution data for these two different applications will be presented.

Improved error mitigation in endmember unmixing of hyperspectral images via image partitioning of targetlike spectral anomalies

Hyperspectral images can be conveniently and quickly interpreted by detecting spectral endmembers present in the image and unmixing the image in terms of those endmembers. However, spectral diversity common in hyperspectral images leads to high errors in the unmixing process by increasing the likelihood that spectral anomalies will be detected as endmembers. We have developed an algorithm to detect target-like spectral anomalies in the image which are likely to detrimentally interfere with the endmember detection process. The hyperspectral image is preprocessed by detecting target-like spectra and masking them from the subsequent endmember detection analysis. By partitioning target-like spectra from the scene, a set of spectral endmembers is detected which can be used to more accurately unmix the image. The vast majority of data in the original image can be interpreted in terms of these detected spectral endmembers. The few spectra which represent the bulk of the spectral diversity in the scene can then be interpreted individually.