Dimitris G. Manolakis

Detection algorithms for hyperspectral imaging applications

We introduce key concepts and issues including the effects of atmospheric propagation upon the data, spectral variability, mixed pixels, and the distinction between classification and detection algorithms. Detection algorithms for full pixel targets are developed using the likelihood ratio approach. Subpixel target detection, which is more challenging due to background interference, is pursued using both statistical and subspace models for the description of spectral variability. Finally, we provide some results which illustrate the performance of some detection algorithms using real hyperspectral imaging (HSI) data. Furthermore, we illustrate the potential deviation of HSI data from normality and point to some distributions that may serve in the development of algorithms with better or more robust performance. We therefore focus on detection algorithms that assume multivariate normal distribution models for HSI data.

Hyperspectral subpixel target detection using the linear mixing model

Relative to multispectral sensing, hyperspectral sensing can increase the detectability of pixel and subpixel size targets by exploiting finer detail in the spectral signatures of targets and natural backgrounds. Over the past several years, different algorithms for the detection of full-pixel or subpixel targets with known spectral signature have been developed. The authors take a closer and more in-depth look at the class of subpixel target detection algorithms that explore the linear mixing model (LMM) to characterize the targets and the interfering background. Sensor noise is modeled as a Gaussian random vector with uncorrelated components of equal variance. The paper makes three key contributions. First, it provides a complete and self-contained theoretical derivation of a subpixel target detector using the generalized likelihood ratio test (GLRT) approach and the LMM. Some other widely used algorithms are obtained as byproducts. The performance of the resulting detector, under the postulated model, is discussed in great detail to illustrate the effects of the various operational factors. Second, it introduces a systematic approach to investigate how well the adopted model characterizes the data, and how robust the detection algorithm is to model-data mismatches. Finally, it compares the derived algorithms with regard to two desirable properties: capacity to operate in constant false alarm rate mode and ability to increase the separation between target and background.

A recursive modified Gram-Schmidt algorithm for least- squares estimation

This paper presents a recursive form of the modified Gram-Schmidt algorithm (RMGS). This new recursive least-squares (RLS) estimation algorithm has a computational complexity similar to the conventional RLS algorithm, but is more robust to roundoff errors and has a highly modular structure, suitable for VLSI implementation. Its properties and features are discussed and compared to other LS estimation algorithms.

Detection algorithms for hyperspectral imaging applications: a signal processing perspective

The purpose of this paper is to present a unified, simplified, and concise, overview of spectral target detection algorithms for hyperspectral imaging applications. We focus on detection algorithms derived using established statistical techniques and whose performance is predictable under reasonable assumptions about hyperspectral imaging data. The emphasis on a signal processing perspective helps to, better understand the strengths and limitations of each algorithm, avoid unrealistic performance expectations, and apply an algorithm properly and sensibly.

Numerically robust least-squares lattice-ladder algorithms with direct updating of the reflection coefficients

New time-recursive equations are derived for the reflection coefficients and the ladder gains in the a priori and a posteriori forms of the exact least-squares (LS) lattice-ladder filtering algorithms. The numerical accuracy of the LS lattice-ladder algorithms obtained by use of these new direct time update equations is analyzed and compared to the accuracy resulting from the conventional LS lattice-ladder algorithms. The analysis and a number of simulation results which are presented lead us to conclude that the new a priori and a posteriori forms of the LS lattice-ladder algorithms yield superior performance.

Detection Algorithms in Hyperspectral Imaging Systems: An Overview of Practical Algorithms

Hyperspectral imaging applications are many and span civil, environmental, and military needs. Typical examples include the detection of specific terrain features and vegetation, mineral, or soil types for resource management; detecting and characterizing materials, surfaces, or paints; the detection of man-made materials in natural backgrounds for the purpose of search and rescue; the detection of specific plant species for the purposes of counter narcotics; and the detection of military vehicles for the purpose of defense and intelligence. The objective of this article is to provide a tutorial overview of detection algorithms used in current hyperspectral imaging systems that operate in the reflective part of the spectrum (0.4 - 24 μm.) The same algorithms might be used in the long-wave infrared spectrum; however, the phenomenology is quite different. The covered topics and the presentation style have been chosen to illustrate the strong couplings among the underlying phenomenology, the theoretical framework for algorithm development and analysis, and the requirements of practical applications.

Algorithm taxonomy for hyperspectral unmixing

In this paper, we introduce a set of taxonomies that hierarchically organize and specify algorithms associated with hyperspectral unmixing. Our motivation is to collectively organize and relate algorithms in order to assess the current state-of-the-art in the field and to facilitate objective comparisons between methods. The hyperspectral sensing community is populated by investigators with disparate scientific backgrounds and, speaking in their respective languages, efforts in spectral unmixing developed within disparate communities have inevitably led to duplication. We hope our analysis removes this ambiguity and redundancy by using a standard vocabulary, and that the presentation we provide clearly summarizes what has and has not been done. As we shall see, the framework for the taxonomies derives its organization from the fundamental, philosophical assumptions imposed on the problem, rather than the common calculations they perform, or the similar outputs they might yield.

Taxonomy of detection algorithms for hyperspectral imaging applications

A unified, simplified, and concise overview of spectral target detection algorithms for hyperspectral imaging applications is presented. We focus on detection algorithms derived using established statistical techniques and whose performance is predictable under reasonable assumptions about hyperspectral imaging data. The emphasis on a signal processing perspective enables us to better understand the strengths and limitations of each algorithm, avoid unrealistic performance expectations, and apply an algorithm properly and sensibly.

Efficient recursive in order least squares FIR filtering and prediction

This paper is concerned with the efficient determination of the optimum, in the least squares sense, FIR filter on the basis of data samples of the input and desired response signals, by procedures recursive in the filter order. This situation typically arises when no a priori statistics are available and the system order is not known. The general multiinput-multioutput (multichannel) case is considered here and a fast algorithm is presented requiring for single channel signals approximately 2S + 15m multiplications (mps) per order m, S being the number of samples. In the special case of linear prediction it calls for about S + 12m mps. Hence it offers a computational reduction of 5m and 2m mps in comparison to the methods of Marple [1] and Morf et al. [2], respectively. Additionally, the proposed scheme is inherently symmetric and is suited very well to initialization of fast sequential algorithms as well as algorithms searching for the optimum lag filter.

Modeling hyperspectral imaging data

Developing proper models for hyperspectral imaging (HSI) data allows for useful and reliable algorithms for data exploitation. These models provide the foundation for development and evaluation of detection, classification, clustering, and estimation algorithms. To date, real world HSI data has been modeled as a single multivariate Gaussian, however it is well known that real data often exhibits non-Gaussian behavior with multi-modal distributions. Instead of the single multivariate Gaussian distribution, HSI data can be model as a finite mixture model, where each of the mixture components need not be Gaussian. This paper will focus on techniques used to segment HSI data into homogenous clusters. Once the data has been segmented, each individual cluster can be modeled, and the benefits provided by the homogeneous clustering of the data versus non-clustering explored. One of the promising techniques uses the Expectation-Maximization (EM) algorithm to cluster the data into Elliptically Contoured Distributions (ECDs). A larger family of distributions, the family of ECDs includes the mutlivariate Gaussian distribution and exhibits most of its properties. ECDs are uniquely defined by their multivariate mean, covariance and the distribution of its Mahalanobis (or quadratic) distance metric. This metric lets multivariate data be identified using a univariate statistic and can be adjusted to more closely match the longer tailed distributions of real data. This paper will focus on three issues. First, the definition of the multivariate Elliptically Contoured Distribution mixture model will be developed. Second, various techniques will be described that segment the mixed data into homogeneous clusters. Most of this work will focus on the EM algorithm and the multivariate t-distribution, which is a member of the family of ECDs and provides longer tailed distributions than the Gaussian. Lastly, results using HSI data from the AVIRIS sensor will be shown, and the benefits of clustered data will be presented.