Endmember Finding Research Articles

Editorial for Special Issue “Advances in Hyperspectral Data Exploitation”

Hyperspectral imaging (HSI) has emerged as a promising, advanced technology in remote sensing and has demonstrated great potential in the exploitation of a wide variety of data. In particular, its capability has expanded from unmixing data samples and detecting targets at the subpixel scale to finding endmembers, which generally cannot be resolved by multispectral imaging. Accordingly, a wealth of new HSI research has been conducted and reported in the literature in recent years. The aim of this Special Issue “Advances in Hyperspectral Data Exploitation“ is to provide a forum for scholars and researchers to publish and share their research ideas and findings to facilitate the utility of hyperspectral imaging in data exploitation and other applications. With this in mind, this Special Issue accepted and published 19 papers in various areas, which can be organized into 9 categories, including I: Hyperspectral Image Classification, II: Hyperspectral Target Detection, III: Hyperspectral and Multispectral Fusion, IV: Mid-wave Infrared Hyperspectral Imaging, V: Hyperspectral Unmixing, VI: Hyperspectral Sensor Hardware Design, VII: Hyperspectral Reconstruction, VIII: Hyperspectral Visualization, and IX: Applications.

Improving Spectral-Based Endmember Finding by Exploring Spatial Context for Hyperspectral Unmixing

Hyperspectral unmixing, which intends to decompose mixed pixels into a collection of endmembers weighted by their corresponding fraction abundances, has been widely utilized for remote sensing image exploitation. Recent studies have revealed that spatial context of pixels is important complemental information for hyperspectral image processing. However, many well-known endmember finding (EF) algorithms identify spectrally pure spectra from hyperspectral images according to spectral information only, resulting in limited accuracy of hyperspectral unmixing application since they ignore spatial distribution or structure information in the image. Therefore, in this article, several novel spatial exploiting (SE) strategies are proposed to improve the performance of the well-known spectral-based EF (sEF) algorithms by integrating spatial information. Three different spatial exploiting strategies are designed to use pixel spatial context, by which the spectral variation of pixels can be alleviated to improve the performance of hyperspectral unmixing. Specifically, in pixel domain, the pixels are linearly reconstructed using their neighbors in which the spatially derived factor to weight the importance of the spectral information is generated using local linear representation and local sparse representation, while in the feature domain, pixels are revised using dominated features of neighboring pixels in singular value decomposition. The proposed spatial exploiting strategies can not only be used as a preprocessing stage to revise pixels for sEF algorithms, but also be used as a postprocessing step to revise endmembers found via sEF algorithms. Finally, experimental results on both synthetic and real hyperspectral datasets demonstrate that the proposed SE strategies can certainly improve the performance of several well-known sEF algorithms, and obtain more accurate unmixing results than several state-of-the-art spatial preprocessing methods.

N-FINDER for Finding Endmembers in Compressively Sensed Band Domain

N-finder algorithm (N-FINDR) has been widely used for finding endmembers in hyperspectral imagery. Since N-FINDR must find all endmembers simultaneously, it requires exhausting all possible $p$ -endmember combinations among the entire data samples with $p$ being the number of endmembers required to be found. Accordingly, directly implementing N-FINDR is practically infeasible. To mitigate this dilemma, two recently developed algorithms called sequential N-FINDR (SQ N-FINDR) and successive N-FINDR (SC N-FINDR) were developed. However, even such an exhaustive search issue can be resolved numerically, another challenging issue for N-FINDR, which remains unsolved, is spectral dimensionality reduction. Because a $p$ -vertex simplex is embedded in a ( $p-1$ )-dimensional spectral data space, N-FINDR does not require full spectral dimensionality to calculate simplex volume (SV). This article presents a compressive sensing (CS) approach to N-FINDR that can find a $p$ -vertex simplex with the maximal SV by SQ/SC N-FINDR in a compressively sensed band domain (CSBD). In particular, to make this idea work, a new CS-based property called restricted SV property (RSVP) can be shown to be preserved in CSBD via a sensing matrix. It is this property that allows what N-FINDR and SQ/SC N-FINDR can achieve in the original data space (ODS) to be also achieved in CSBD. To further show the utility of SQ/SC N-FINDR in both ODS and CSBD as well as SV preserved by RSVP, a series of experiments are conducted for performance analysis.

ASSESSING AND COMPARING THE PERFORMANCE OF ENDMEMBER EXTRACTION METHODS IN MULTIPLE CHANGE DETECTION USING HYPERSPECTRAL DATA

Abstract. Endmember extraction is a process to identify the hidden pure source signals from the mixture. Endmember finding has become increasingly important in hyperspectral data exploitation because endmembers can be used to specify unknown particular spectral classes. This paper evaluates the change detection problem in bi-temporal hyperspectral remote sensing images using the unmixing process. A complete spectral unmixing process contains estimating the number of endmembers, endmember extraction and abundance estimation. Endmember extraction is a vital step in spectral unmixing of hyperspectral images. Hyperspectral change detection by unmixing has the potential to provide subpixel information from hyperspectral images. In this study, four methods including Simplex Identification via variable Splitting and Augmented Lagrangian (SISAL), N-finder algorithm (N-FINDR), Vertex Component Analysis (VCA), and Fast algorithm for linearly Unmixing (FUN) are used to produce multiple change detection maps. This paper explores and compares the performance of these methods in multiple change detection. The empirical results reveal the superiority of the FUN method in providing multiple change map with an overall accuracy of 87% and a kappa coefficient of 0.70.

A Novel Endmember Extraction Method Using Sparse Component Analysis for Hyperspectral Remote Sensing Imagery

The spectral unmixing technique is an effective method of solving the mixed pixel problem in the hyperspectral remote sensed imagery. During the process, endmember extraction algorithm (EEA) is significant for the creation of material abundance maps. However, the traditional EEAs are not very reliable due to the low resolution of sensor and the complex diversity of land cover feature distribution. In addition, the mutually independent assumption of the endmember corresponding abundance will be affected accordingly. In order to overcome the above limitations, a novel endmember extraction method using sparse component analysis for hyperspectral remote sensing imagery (EESCA) has been presented in this paper. EESCA assumes that each pixel in the image scene is a sparse linear mixture of all endmembers. First, the hyperline clustering algorithm is incorporated to consider the subspace clustering of all pixels after the initialization of endmember mixing matrix. It enlarges differences among ground objects and helps finding endmembers with smaller spectrum divergences. After that, the K-SVD is proposed to search the real endmembers for sparse representations with coefficients summarized in the mixing matrix. The method transfers the pure endmember extraction problem into an optimization problem by minimizing the residual errors. The four state-of-the art methods are implemented to make comparisons with the performance of EESCA. The robustness of the proposed algorithm is verified through both simulated images and real satellite images. Experimental results show that the EESCA outperforms other methods in spectral angle distance and root-mean-square error, and especially could identify accurate endmembers for ground objects with smaller spectrum divergences.

Endmember search and proportion estimates from airborne hyperspectral surveys

ABSTRACTThe estimation of areas of land-cover elements is required for many natural resource management programmes and is also used by the mineral and petroleum resource communities either for detection of mineral abundances or monitoring of environmental remediation and other off-site impacts. When the identification of many constituent elements is desired, remote sensors that possess many spectral bands are often deployed, providing data that can be used in a spectroscopic (or other) analysis. At the size of a (remotely sensed) ground sample (represented as an image pixel), which with current technology is typically a few metres, the sample is heterogeneous and typically composed of several biological and geological constituents. It is of interest to first identify the constituent elements and their number and, second, to estimate their relative abundance. When no suitable spectral library is available for a particular data set, an exploratory approach using a blind unmixing method may be used to detect and estimate the endmembers themselves – an exploratory approach because there is no guarantee that the spectral endmembers fitted using blind unmixing will correspond to the ‘pure’ materials of interest to a particular application. Further, if employing a blind unmixing technique to each image in a large multi-image survey independently, there is no guarantee that compatible sets of endmembers will be found to produce maps that are seamless across contiguous images. The aim of this article is to examine the potential for applying blind unmixing at the whole-of-survey level as a way to finding endmembers and proportion maps that are cross-swath consistent and broadscale applicable. We demonstrate that a mosaic of many radiometrically block-adjusted swaths of data from the HyMap airborne hyperspectral imager (HyVista Corporation) can be unmixed as a single image using the Iterated Constrained Endmembers blind unmixing algorithm. The major endmembers are validated against available Analytical Spectral Devices ground spectra and broadscale abundance maps of the type targeted by both vegetation and soil mapping communities are produced.

A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FurthestSum initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

Recursive Geometric Simplex Growing Analysis for Finding Endmembers in Hyperspectral Imagery

Simplex growing algorithm (SGA) is an endmember finding algorithm which searches for endmembers one after another by growing simplexes one vertex at a time via maximizing simplex volume (SV). Unfortunately, several issues arise in calculating SV. One is the use of dimensionality reduction (DR) because the dimensionality of a simplex is usually much smaller than data dimensionality. Second, calculating SV requires calculating the determinant of an ill-ranked matrix in which case singular value decomposition (SVD) is generally required to perform DR. Both approaches generally do not produce true SV. Finally, the computing time becomes excessive and numerically instable as the number of endmembers grows. This paper develops a new theory, called geometric simplex growing analysis (GSGA), to resolve these issues. It can be considered as an alternative to SGA from a rather different point of view. More specifically, GSGA looks into the geometric structures of a simplex whose volume can be actually calculated by multiplication of its base and height. As a result, it converts calculating maximal SV to finding maximal orthogonal projection as its maximal height becomes perpendicular to its base. To facilitate GSGA in practical applications, GSGA is further used to extend SGA to recursive geometric simplex growing algorithm (RGSGA) which allows GSGA to be implemented recursively in a similar manner that a Kalman filter does. Consequently, RGSGA can be very easily implemented with significant saving of computing time. Best of all, RGSGA is also shown to be most efficient and effective among all SGA-based variants.

Comparative Study and Analysis Among ATGP, VCA, and SGA for Finding Endmembers in Hyperspectral Imagery

Endmember finding has become increasingly important in hyperspectral data exploitation because endmembers can be used to specify unknown particular spectral classes. Pixel purity index (PPI) and N-finder algorithm (N-FINDR) are probably the two most widely used techniques for this purpose where many currently available endmember finding algorithms are indeed derived from these two algorithms and can be considered as their variants. Among them are three well-known algorithms derived from imposing different abundance constraints, that is, abundance-unconstrained automatic target generation process (ATGP), abundance nonnegativity constrained vertex component analysis (VCA), and fully abundance constrained simplex growing algorithm (SGA). This paper explores relationships among these three algorithms and further shows that theoretically they are essentially the same algorithms in the sense of design rationale. The reason that these three algorithms perform differently is not because they are different algorithms, but rather because they use different preprocessing steps, such as initial conditions and dimensionality reduction transforms.

Recursive Orthogonal Projection-Based Simplex Growing Algorithm

The simplex growing algorithm (SGA) has been widely used for finding endmembers. It can be considered as a sequential version of the well-known endmember finding algorithm, N-finder algorithm (N-FINDR), which finds endmembers one at a time by growing simplexes. However, one of the major hurdles for N-FINDR and SGA is the calculation of simplex volume (SV) which poses a great challenge in designing any algorithm using SV as a criterion for finding endmembers. This paper develops an orthogonal projection (OP)-based SGA (OP-SGA) which essentially resolves this computational issue. It converts the issue of calculating SV to calculating the OP on previously found simplexes without computing matrix determinants. Most importantly, a recursive Kalman filter-like OP-SGA, to be called recursive OP-SGA (ROP-SGA), can be also derived to ease computation. By virtue of ROP-SGA, several advantages and benefits in computational savings and hardware implementation can be gained for which N-FINDR and SGA do not have.

Convex cone volume analysis for finding endmembers in hyperspectral imagery

This paper presents a new approach, called convex cone volume analysis (CCVA), which can be considered as a partially constrained-abundance (abundance non-negativity constraint) technique to find endmembers. It can be shown that finding the maximal volume of a convex cone in the original data space is equivalent to finding the maximal volume of a simplex in a hyperplane. As a result, the CCVA can take advantage of many recently developed fast computational algorithms developed for N-FINDR to derive their counterparts for CCVA.

Design and Development of Iterative Pixel Purity Index

Pixel purity index (PPI) and N-finder algorithm (N-FINDR) are the two most widely used techniques for finding endmembers in hyperspectral imagery. Unfortunately, both of them suffer from two same major issues, inconsistency resulting from random initial conditions and computational complexity resulting from finding all endmembers simultaneously. To resolve these issues, a theory of iterative N-FINDR (IN-FINDR) has been recently developed for N-FINDR via iterative processes. This paper develops various versions of iterative PPI (IPPI), which can be considered as a companion paper of IN-FINDR. The IPPI reinvents a wheel by redesigning various versions of iterative algorithms which implement PPI via two iterative processes, one for data sample vectors and the other for skewers. More specifically, two different iterative versions of IPPI are developed, called progressive IPPI (P-IPPI) and causal IPPI (C-IPPI), which correspond to two versions of IN-FINDR, successive N-FINDR (SC N-FINDR) and sequential N-FINDR (SQ N-FINDR), respectively. Because they are iterative in nature, C-IPPI and P-IPPI can be further extended to process skewer sets in two different fashions, varying skewer set and growing skewer set, to be called varying skewer set C-IPPI (VC-IPPI) and growing skewer set P-IPPI (GP-IPPI). As a result, the fast IPPI (FIPPI) can be shown indeed to be their special case.

FPGA Implementation of the Pixel Purity Index Algorithm for Remotely Sensed Hyperspectral Image Analysis

Hyperspectral imaging is a new emerging technology in remote sensing which generates hundreds of images, at different wavelength channels, for the same area on the surface of the Earth. Over the last years, many algorithms have been developed with the purpose of finding endmembers, assumed to be pure spectral signatures in remotely sensed hyperspectral data sets. One of the most popular techniques has been the pixel purity index (PPI). This algorithm is very time-consuming. The reconfigurability, compact size, and high computational power of Field programmable gate arrays (FPGAs) make them particularly attractive for exploitation in remote sensing applications with (near) real-time requirements. In this paper, we present an FPGA design for implementation of the PPI algorithm. Our systolic array design includes a DMA and implements a prefetching technique to reduce the penalties due to the I/O communications. We have also included a hardware module for random number generation. The proposed method has been tested using real hyperspectral data collected by NASA's Airborne Visible Infrared Imaging Spectrometer over the Cuprite mining district in Nevada. Experimental results reveal that the proposed hardware system is easily scalable and able to provide accurate results with compact size in (near) real-time, which make our reconfigurable system appealing for on-board hyperspectral data processing.