Marian-Daniel Iordache

Sparse Unmixing of Hyperspectral Data

Linear spectral unmixing is a popular tool in remotely sensed hyperspectral data interpretation. It aims at estimating the fractional abundances of pure spectral signatures (also called as endmembers) in each mixed pixel collected by an imaging spectrometer. In many situations, the identification of the end-member signatures in the original data set may be challenging due to insufficient spatial resolution, mixtures happening at different scales, and unavailability of completely pure spectral signatures in the scene. However, the unmixing problem can also be approached in semisupervised fashion, i.e., by assuming that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance (e.g., spectra collected on the ground by a field spectroradiometer). Unmixing then amounts to finding the optimal subset of signatures in a (potentially very large) spectral library that can best model each mixed pixel in the scene. In practice, this is a combinatorial problem which calls for efficient linear sparse regression (SR) techniques based on sparsity-inducing regularizers, since the number of endmembers participating in a mixed pixel is usually very small compared with the (ever-growing) dimensionality (and availability) of spectral libraries. Linear SR is an area of very active research, with strong links to compressed sensing, basis pursuit (BP), BP denoising, and matching pursuit. In this paper, we study the linear spectral unmixing problem under the light of recent theoretical results published in those referred to areas. Furthermore, we provide a comparison of several available and new linear SR algorithms, with the ultimate goal of analyzing their potential in solving the spectral unmixing problem by resorting to available spectral libraries. Our experimental results, conducted using both simulated and real hyperspectral data sets collected by the NASA Jet Propulsion Laboratorys Airborne Visible Infrared Imaging Spectrometer and spectral libraries publicly available from the U.S. Geological Survey, indicate the potential of SR techniques in the task of accurately characterizing the mixed pixels using the library spectra. This opens new perspectives for spectral unmixing, since the abundance estimation process no longer depends on the availability of pure spectral signatures in the input data nor on the capacity of a certain endmember extraction algorithm to identify such pure signatures.

Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing

Spectral unmixing aims at estimating the fractional abundances of pure spectral signatures (also called endmembers) in each mixed pixel collected by a remote sensing hyperspectral imaging instrument. In recent work, the linear spectral unmixing problem has been approached in semisupervised fashion as a sparse regression one, under the assumption that the observed image signatures can be expressed as linear combinations of pure spectra, known a priori and available in a library. It happens, however, that sparse unmixing focuses on analyzing the hyperspectral data without incorporating spatial information. In this paper, we include the total variation (TV) regularization to the classical sparse regression formulation, thus exploiting the spatial-contextual information present in the hyperspectral images and developing a new algorithm called sparse unmixing via variable splitting augmented Lagrangian and TV. Our experimental results, conducted with both simulated and real hyperspectral data sets, indicate the potential of including spatial information (through the TV term) on sparse unmixing formulations for improved characterization of mixed pixels in hyperspectral imagery.

Collaborative Sparse Regression for Hyperspectral Unmixing

Sparse unmixing has been recently introduced in hyperspectral imaging as a framework to characterize mixed pixels. It assumes that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance (e.g., spectra collected on the ground by a field spectroradiometer). Unmixing then amounts to finding the optimal subset of signatures in a (potentially very large) spectral library that can best model each mixed pixel in the scene. In this paper, we present a refinement of the sparse unmixing methodology recently introduced which exploits the usual very low number of endmembers present in real images, out of a very large library. Specifically, we adopt the collaborative (also called “multitask” or “simultaneous”) sparse regression framework that improves the unmixing results by solving a joint sparse regression problem, where the sparsity is simultaneously imposed to all pixels in the data set. Our experimental results with both synthetic and real hyperspectral data sets show clearly the advantages obtained using the new joint sparse regression strategy, compared with the pixelwise independent approach.

MUSIC-CSR: Hyperspectral Unmixing via Multiple Signal Classification and Collaborative Sparse Regression

Spectral unmixing aims at finding the spectrally pure constituent materials (also called endmembers) and their respective fractional abundances in each pixel of a hyperspectral image scene. In recent years, sparse unmixing has been widely used as a reliable spectral unmixing methodology. In this approach, the observed spectral vectors are expressed as linear combinations of spectral signatures assumed to be known a priori and presented in a large collection, termed spectral library or dictionary, usually acquired in laboratory. Sparse unmixing has attracted much attention as it sidesteps two common limitations of classic spectral unmixing approaches, namely, the lack of pure pixels in hyperspectral scenes and the need to estimate the number of endmembers in a given scene, which are very difficult tasks. However, the high mutual coherence of spectral libraries, jointly with their ever-growing dimensionality, strongly limits the operational applicability of sparse unmixing. In this paper, we introduce a two-step algorithm aimed at mitigating the aforementioned limitations. The algorithm exploits the usual low dimensionality of the hyperspectral data sets. The first step, which is similar to the multiple signal classification array signal processing algorithm, identifies a subset of the library elements, which contains the endmember signatures. Because this subset has cardinality much smaller than the initial number of library elements, the sparse regression we are led to is much more well conditioned than the initial one using the complete library. The second step applies collaborative sparse regression, which is a form of structured sparse regression, exploiting the fact that only a few spectral signatures in the library are active. The effectiveness of the proposed approach, termed MUSIC-CSR, is extensively validated using both simulated and real hyperspectral data sets.

Recent developments in sparse hyperspectral unmixing

This paper explores the applicability of new sparse algorithms to perform spectral unmixing of hyperspectral images using available spectral libraries instead of resorting to well-known endmember extraction techniques widely available in the literature. Our main assumption is that it is unlikely to find pure pixels in real hyperspectral images due to available spatial resolution and mixing phenomena happening at different scales. The algorithms analyzed in our study rely on different principles, and their performance is quantitatively assessed using both simulated and real hyperspectral data sets. The experimental validation of sparse techniques conducted in this work indicates promising results of this new approach to attack the spectral unmixing problem in remotely sensed hyperspectral images.

Hyperspectral unmixingwith sparse group lasso

Sparse unmixing has been recently introduced as a mechanism to characterize mixed pixels in remotely sensed hyperspectral images. It assumes that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance (e.g., spectra collected on the ground by a field spectroradiometer). Unmixing then amounts to finding the optimal subset of signatures in a (potentially very large) spectral library that can best model each mixed pixel in the scene. In available spectral libraries, it is observed that the spectral signatures appear organized in groups (e.g. different alterations of a single mineral in the U.S. Geological Survey spectral library). In this paper, we explore the potential of the sparse group lasso technique in solving hyperspectral unmixing problems. Our introspection in this work is that, when the spectral signatures appear in groups, this technique has the potential to yield better results than the standard sparse regression approach. Experimental results with both synthetic and real hyperspectral data are given to investigate this issue.

On the use of spectral libraries to perform sparse unmixing of hyperspectral data

In recent years, the increasing availability of spectral libraries has opened a new path toward solving the hyperspec-tral unmixing problem in a semi-supervised fashion. The spectrally pure constituent materials (called endmembers) can be derived from a (potentially very large) spectral library and used for unmixing purposes. The advantage of this approach is that the results of the unmixing process do not depend on the availability of pure pixels in the original hyperspectral data nor on the ability of an endmember extraction algorithm to identify such endmembers. However, resulting from the fact that spectral libraries are usually very large, this approach generally results in a sparse solution. In this paper, we investigate the sensitivity of sparse unmixing techniques to certain characteristics of real and synthetic spectral libraries, including parameters such as mutual coherence and spectral similarity between the signatures contained in the library. Our main goal is to illustrate, via detailed experimental assessment, the potential of using spectral libraries to solve the spectral unmixing problem.

Unmixing sparse hyperspectral mixtures

Finding an accurate sparse approximation of a spectral vector described by a linear model, when there is available a library of possible constituent signals (called endmembers or atoms), is a hard combinatorial problem which, as in other areas, has been increasingly addressed. This paper studies the efficiency of the sparse regression techniques in the spectral unmixing problem by conducting a comparison between four different approaches: Moore-Penrose Pseudoinverse, Orthogonal Matching Pursuit (OMP), Iterative Spectral Mixture Analysis (ISMA) and l2 - l1 sparse regression techniques, which are of widespread use in compressed sensing. We conclude that the l2-l1 sparse regression techniques, implemented here by Iterative Shrinkage/Thresholding (TwIST) algorithm, yield the state-of-the-art in the hyperspectral unmixing area.

Atmospheric correction of APEX hyperspectral data

Abstract Atmospheric correction plays a crucial role among the processing steps applied to remotely sensed hyperspectral data. Atmospheric correction comprises a group of procedures needed to remove atmospheric effects from observed spectra, i.e. the transformation from at-sensor radiances to at-surface radiances or reflectances. In this paper we present the different steps in the atmospheric correction process for APEX hyperspectral data as applied by the Central Data Processing Center (CDPC) at the Flemish Institute for Technological Research (VITO, Mol, Belgium). The MODerate resolution atmospheric TRANsmission program (MODTRAN) is used to determine the source of radiation and for applying the actual atmospheric correction. As part of the overall correction process, supporting algorithms are provided in order to derive MODTRAN configuration parameters and to account for specific effects, e.g. correction for adjacency effects, haze and shadow correction, and topographic BRDF correction. The methods and theory underlying these corrections and an example of an application are presented.

Sparse Unmixing-Based Change Detection for Multitemporal Hyperspectral Images

In recent years, the increased availability of spectral libraries has resulted in a growing interest in sparse unmixing, which aims to find an optimal subset of library signatures to represent the pixels of remotely sensed hyperspectral datasets as linear combinations of these signatures. Sparse unmixing sidesteps two important drawbacks of the regular spectral unmixing process, namely the difficulty of estimating the number of endmembers, and the process of extracting the endmembers itself, the result of which will vary according to the utilized extraction method. In this work, sparse unmixing is exploited for the first time in the context of multitemporal hyperspectral data analysis and change detection. Change detection by sparse unmixing based on spectral libraries has the important advantage of providing not only pixel-level but also subpixel-level change information for the hyperspectral data. The changes that occur in multitemporal datasets due to time or as a result of a significant event are revealed, at subpixel-level, as the abundances of underlying endmembers within a pixel, or as variations in the distribution of these endmembers throughout the scene. The proposed approach is validated by experimental studies on both carefully prepared synthetic datasets and real datasets, using different spectral libraries.