Chao-Cheng Wu

A New Growing Method for Simplex-Based Endmember Extraction Algorithm

A new growing method for simplex-based endmember extraction algorithms (EEAs), called simplex growing algorithm (SGA), is presented in this paper. It is a sequential algorithm to find a simplex with the maximum volume every time a new vertex is added. In order to terminate this algorithm a recently developed concept, virtual dimensionality (VD), is implemented as a stopping rule to determine the number of vertices required for the algorithm to generate. The SGA improves one commonly used EEA, the N-finder algorithm (N-FINDR) developed by Winter, by including a process of growing simplexes one vertex at a time until it reaches a desired number of vertices estimated by the VD, which results in a tremendous reduction of computational complexity. Additionally, it also judiciously selects an appropriate initial vector to avoid a dilemma caused by the use of random vectors as its initial condition in the N-FINDR where the N-FINDR generally produces different sets of final endmembers if different sets of randomly generated initial endmembers are used. In order to demonstrate the performance of the proposed SGA, the N-FINDR and two other EEAs, pixel purity index, and vertex component analysis are used for comparison

Fast Algorithms to Implement N-FINDR for Hyperspectral Endmember Extraction

The N-finder algorithm (N-FINDR) suffers from several issues in its practical implementation. One is its search region which is usually the entire data space. Another related issue is its excessive computation. A third issue is its use of random initial conditions which causes inconsistency in final results that can not be reproducible if a search for endmembers is not exhaustive. This paper resolves the first two issues by developing two approaches to speed-up of the N-FINDR computation while implementing a recently developed random pixel purity index (RPPI) to alleviate the third issue. First of all, it narrows down the search region for the N-FINDR to a feasible range, called region of interest (ROI), where two ways are proposed, data sphering/thresholding and RPPI, to be used as a pre-processing to find a desired ROI. Second, three methods are developed to reduce computing load of simplex volume computation by simplifying matrix determinant. Third, to further reduce computational complexity three sequential N-FINDR algorithms are implemented by finding one endmember after another in sequence instead of finding all endmembers together at once. The conducted experiments demonstrate that while the proposed fast algorithms can greatly reduce computational complexity, their performance remains as good as the N-FINDR is and is not compromised by reduction of the search region to an ROI.

Real-Time Simplex Growing Algorithms for Hyperspectral Endmember Extraction

The simplex growing algorithm (SGA) was recently developed as an alternative to the N-finder algorithm (N-FINDR) and shown to be a promising endmember extraction technique. This paper further extends the SGA to a versatile real-time (RT) processing algorithm, referred to as RT SGA, which can effectively address the following four major issues arising in the practical implementation for N-FINDR: (1) use of random initial endmembers which causes inconsistent final results; (2) high computational complexity which results from an exhaustive search for finding all endmembers simultaneously; (3) requirement of dimensionality reduction because of large data volumes; and (4) lack of RT capability. In addition to the aforementioned advantages, the proposed RT SGA can also be implemented by various criteria in endmember extraction other than the maximum simplex volume.

Component Analysis-Based Unsupervised Linear Spectral Mixture Analysis for Hyperspectral Imagery

Two of the most challenging issues in the unsupervised linear spectral mixture analysis (ULSMA) are: 1) determining the number of signatures to form a linear mixing model; and 2) finding the signatures used to unmix data. These two issues do not occur in supervised LSMA since the target signatures are assumed to be known a priori. With recent advances in hyperspectral sensor technology, many unknown and subtle signal sources can now be uncovered and revealed and such signal sources generally cannot be identified by prior knowledge. Even when they can, the obtained knowledge may not be reliable, accurate, or complete. As a consequence, the resulting unmixed results may be misleading. This paper addresses these issues by introducing a new concept of inter-band spectral information (IBSI), which can be used to categorize signatures into background and target classes in terms of their sample spectral statistics. It then develops a component analysis (CA)-based ULSMA where two classes of signatures can be extracted directly from the data by two different CA-based transforms without requiring prior knowledge. In order to substantiate the utility of the proposed approach, synthetic images are used for experiments and real images are further used for validation.

Random Pixel Purity Index

Endmember extraction has received increasing interest in hyperspectral image analysis. One widely used endmember extraction algorithm is pixel purity index (PPI), which finds endmembers via a set of random vectors, called skewers. Several issues arise in its implementation. One is the prior knowledge of the number of skewers K required to be used. Second, due to random nature in skewers, the final results are inconsistent and unreproducible. Third, it needs to know the number of dimensions to be retained after dimensionality reduction. Fourth, it needs to preset a cutoff threshold to extract potential endmembers. Finally, it involves human intervention to manually select final endmembers. This letter derives a random PPI (RPPI) to resolve the aforementioned issues. It considers the result produced by PPI using a random set of initial vectors as skewers as a realization of a random algorithm. From a statistical signal processing view point, if endmembers are crucial in terms of information, they should occur in realizations produced by PPI regardless of what set is chosen for skewers. By virtue of this assumption, the proposed RPPI is developed and validated by experiments.

Sequential N-FINDR algorithms

N-finder algorithm (N-FINDR) is probably one of most popular and widely used algorithms used for endmember extraction. Three major obstacles need to be overcome in its practical implementation. One is that the number of endmembers must be known a priori. A second one is the use of random initial endmembers to initialize N-FINDR, which results in inconsistent final results of extracted endmembers. A third one is its very expensive computational cost caused by an exhaustive search. While the first two issues can be resolved by a recently developed concept, virtual dimensionality (VD) and custom-designed initialization algorithms respectively, the third issue seems to remain challenging. This paper addresses the latter issue by re-designing N-FINDR which can generate one endmember at a time sequentially in a successive fashion to ease computational complexity. Such resulting algorithm is called SeQuential N-FINDR (SQ N-FINDR) as opposed to the original N-FINDR referred to as SiMultaneous N-FINDR (SM N-FINDR) which generates all endmembers simultaneously at once. Two variants of SQ N-FINDR can be further derived to reduce computational complexity. Interestingly, experimental results show that SQ N-FINDR can perform as well as SM-N-FINDR if initial endmembers are appropriately selected.

Linear Spectral Mixture Analysis Based Approaches to Estimation of Virtual Dimensionality in Hyperspectral Imagery

Virtual dimensionality (VD) is a new concept which was originally developed for estimating the number of spectrally distinct signatures present in hyperspectral data. The effectiveness of the VD is determined by the technique used for VD estimation. This paper develops an orthogonal subspace projection (OSP) technique to estimate the VD. The idea is derived from linear spectral mixture analysis where a data sample vector is modeled as a linear mixture of a finite set of what is called as virtual endmembers in this paper. A similar idea was also previously investigated by the signal subspace estimate (SSE) and was later improved by hyperspectral signal subspace identification by minimum error (HySime), where the minimum mean squared error is used as a criterion to determine the VD. Interestingly, with an appropriate interpretation, the proposed OSP technique includes the SSE/HySime as its special case. In order to demonstrate its utility, experiments using synthetic images and real image data sets are conducted for performance analysis.

Improved Process for Use of a Simplex Growing Algorithm for Endmember Extraction

A recent paper by Chang develops a new algorithm, called the simplex growing algorithm, which has shown promise in end member extraction. There is an erroneous description made for one of synthetic image experiments. While making a simple correction would have sufficed, a series of studies has led to interesting and intriguing results on how to determine an appropriate number of end members p, how to design a better end member extraction algorithm, and how to use an effective technique to perform dimensionality reduction.

Real-time causal processing of anomaly detection for hyperspectral imagery

Anomaly detection generally requires real-time processing to find targets on a timely basis. However, for an algorithm to be implemented in real time, the used data samples can be only those up to the data sample being visited; no future data samples should be involved in the data processing. Such a property is generally called causality, which has unfortunately received little interest thus far in real-time hyperspectral data processing. This paper develops causal processing to perform anomaly detection that can be also implemented in real time. The ability of real-time causal processing is derived from the concept of innovations used to derive a Kalman filter via a recursive causal update equation. Specifically, two commonly used anomaly detectors, sample covariance matrix (K)-based Reed-Xiaoli detector (RXD), called K-RXD, and sample correlation matrix (R)-based RXD, called R-RXD, are derived for their real-time causal processing versions. To substantiate their utility in applications of anomaly detection, real image data sets are conducted for experiments.

Exploration of methods for estimation of number of endmembers in hyperspectral imagery

An endmember is an idealized, pure signature for a class and provides crucial information for hyperspectral image analysis. Recently, endmember extraction has received considerable attention in hyperspectral imaging due to significantly improved spectral resolution where the likelihood of a hyperspectral image pixel uncovered by a hyperspectral image sensor as an endmember is substantially increased. Many algorithms have been proposed for this purpose. One great challenge in endmember extraction is the determination of number of endmembers, p required for an endmember extraction algorithm (EEA) to generate. Unfortunately, this issue has been overlooked and avoided by making an empirical assumption without justification. However, it has been shown that an appropriate selection of p is critical to success in extracting desired endmembers from image data. This paper explores methods available in the literature that can be used to estimate the value, p. These include the commonly used eigenvalue-based energy method, An Information criterion (AIC), Minimum Description Length (MDL), Gershgorin radii-based method, Signal Subspace Estimation (SSE) and Neyman-Pearson detection method in detection theory. In order to evaluate the effectiveness of these methods, two sets of experiments are conducted for performance analysis. The first set consists of synthetic imagebased simulations which allow us to evaluate their performance with a priori knowledge, while the second set comprising of real hyperspectral image experiments which demonstrate utility of these methods in real applications.