Generalized linear mixing model accounting for endmember variability

Endmember variability is an important factor for accurately unveiling vital information relating the pure materials and their distribution in hyperspectral images. Recently, the extended linear mixing model (ELMM) has been proposed as a modification of the linear mixing model (LMM) to consider endmember variability effects resulting mainly from illumination changes. In this paper, we further generalize the ELMM leading to a new model (GLMM) to account for more complex spectral distortions where different wavelength intervals can be affected unevenly. We also extend the existing methodology to jointly estimate the variability and the abundances for the GLMM. Simulations with real and synthetic data show that the unmixing process can benefit from the extra flexibility introduced by the GLMM

Hyperspectral unmixing with spectral variability using a perturbed linear mixing model

International audienceGiven a mixed hyperspectral data set, linear unmixing aims at estimating the reference spectral signatures composing the data-referred to as endmembers-their abundance fractions and their number. In practice, the identified endmembers can vary spectrally within a given image and can thus be construed as variable instances of reference endmembers. Ignoring this variability induces estimation errors that are propagated into the unmixing procedure. To address this issue, endmember variability estimation consists of estimating the reference spectral signatures from which the estimated endmembers have been derived as well as their variability with respect to these references. This paper introduces a new linear mixing model that explicitly accounts for spatial and spectral endmember variabilities. The parameters of this model can be estimated using an optimization algorithm based on the alternating direction method of multipliers. The performance of the proposed unmixing method is evaluated on synthetic and real data. A comparison with state-of-the-art algorithms designed to model and estimate endmember variability allows the interest of the proposed unmixing solution to be appreciated

Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing model and the pure-pixel assumption. We present a family of fast recursive algorithms, and prove they are robust under any small perturbations of the input data matrix. This family generalizes several existing hyperspectral unmixing algorithms and hence provides for the first time a theoretical justification of their better practical performance.Comment: 30 pages, 2 figures, 7 tables. Main change: Improvement of the bound of the main theorem (Th. 3), replacing r with sqrt(r

Self-Dictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search are Related

This paper considers a recently emerged hyperspectral unmixing formulation based on sparse regression of a self-dictionary multiple measurement vector (SD-MMV) model, wherein the measured hyperspectral pixels are used as the dictionary. Operating under the pure pixel assumption, this SD-MMV formalism is special in that it allows simultaneous identification of the endmember spectral signatures and the number of endmembers. Previous SD-MMV studies mainly focus on convex relaxations. In this study, we explore the alternative of greedy pursuit, which generally provides efficient and simple algorithms. In particular, we design a greedy SD-MMV algorithm using simultaneous orthogonal matching pursuit. Intriguingly, the proposed greedy algorithm is shown to be closely related to some existing pure pixel search algorithms, especially, the successive projection algorithm (SPA). Thus, a link between SD-MMV and pure pixel search is revealed. We then perform exact recovery analyses, and prove that the proposed greedy algorithm is robust to noise---including its identification of the (unknown) number of endmembers---under a sufficiently low noise level. The identification performance of the proposed greedy algorithm is demonstrated through both synthetic and real-data experiments

Spectral unmixing approach in hyperspectral remote sensing: a tool for oil palm mapping

Las plantaciones de palma de aceite típicamente abarcan grandes áreas, por esto, la teledetección remota se ha convertido en una herramienta útil para el monitoreo avanzado de este cultivo. Este trabajo revisa y evalúa dos enfoques para analizar las plantaciones de palma de aceite a partir de datos de teledetección remota hiperespectral: desmezclado espectral lineal y variabilidad espectral. Además, se propone un marco computacional basado en el desmezclado espectral para la estimación de las fracciones de abundancias de cultivos de palma de aceite. Este enfoque también considera la variabilidad espectral de las firmas en las imágenes hiperespectrales. El marco computacional propuesto modifica el modelo de mezcla lineal mediante la introducción de un vector de pesos, de manera que se puedan identificar las bandas espectrales que menos contribuyen a la estimación de fracciones de abundancias erróneas. Este enfoque aprovecha la detección de los árboles de palma de aceite, ya que permite diferenciarlos de otros materiales en términos de fracciones de abundancia. Los resultados experimentales obtenidos a partir de datos de teledetección remota hiperespectral en el rango de 410-990 nm, muestran mejoras de un 8.18 % en la métrica de Precisión del Usuario (Uacc) en la identificación de palmas de aceite por el marco propuesto con respecto a los métodos tradicionales de desmezclado espectral; el método propuesto logró un 95 % de Uacc. Esto confirma las capacidades del marco computacional formulado y facilita la gestión y el monitoreo de grandes áreas de plantaciones de palma de aceite.Oil palm plantations typically span large areas; therefore, remote sensing has become a useful tool for advanced oil palm monitoring. This work reviews and evaluates two approaches to analyze oil palm plantations based on hyperspectral remote sensing data: linear spectral unmixing and spectral variability. Moreover, a computational framework based on spectral unmixing for the estimation of fractional abundances of oil palm plantations is proposed in this study. Such approach also considers the spectral variability of hyperspectral image signatures. More specifically, the proposed computational framework modifies the linear mixing model by introducing a weighting vector, so that the spectral bands that contribute the least to the estimation of erroneous fractional abundances can be identified. This approach improves palm detection as it allows to differentiate them from other materials in terms of fractional abundances. Experimental results obtained from hyperspectral remote sensing data in the range 410-990 nm show improvements of 8.18 % in User Accuracy (Uacc) in the identification of oil palms by the proposed framework with respect to traditional unmixing methods. Thus, the proposed method achieved a 95% Uacc. This confirms the capabilities of the proposed computational framework and facilitates the management and monitoring of large areas of oil palm plantations

SULoRA: Subspace Unmixing with Low-Rank Attribute Embedding for Hyperspectral Data Analysis

To support high-level analysis of spaceborne imaging spectroscopy (hyperspectral) imagery, spectral unmixing has been gaining significance in recent years. However, from the inevitable spectral variability, caused by illumination and topography change, atmospheric effects and so on, makes it difficult to accurately estimate abundance maps in spectral unmixing. Classical unmixing methods, e.g. linear mixing model (LMM), extended linear mixing model (ELMM), fail to robustly handle this issue, particularly facing complex spectral variability. To this end, we propose a subspace-based unmixing model using low-rank learning strategy, called subspace unmixing with low-rank attribute embedding (SULoRA), robustly against spectral variability in inverse problems of hyperspectral unmixing. Unlike those previous approaches that unmix the spectral signatures directly in original space, SULoRA is a general subspace unmixing framework that jointly estimates subspace projections and abundance maps in order to find a ‘raw’ subspace which is more suitable for carrying out the unmixing procedure. More importantly, we model such ‘raw’ subspace with low-rank attribute embedding. By projecting the original data into a low-rank subspace, SULoRA can effectively address various spectral variabilities in spectral unmixing. Furthermore, we adopt an alternating direction method of multipliers (ADMM) based to solve the resulting optimization problem. Extensive experiments on synthetic and real datasets are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods

Sequential Dimensionality Reduction for Extracting Localized Features

Linear dimensionality reduction techniques are powerful tools for image analysis as they allow the identification of important features in a data set. In particular, nonnegative matrix factorization (NMF) has become very popular as it is able to extract sparse, localized and easily interpretable features by imposing an additive combination of nonnegative basis elements. Nonnegative matrix underapproximation (NMU) is a closely related technique that has the advantage to identify features sequentially. In this paper, we propose a variant of NMU that is particularly well suited for image analysis as it incorporates the spatial information, that is, it takes into account the fact that neighboring pixels are more likely to be contained in the same features, and favors the extraction of localized features by looking for sparse basis elements. We show that our new approach competes favorably with comparable state-of-the-art techniques on synthetic, facial and hyperspectral image data sets.Comment: 24 pages, 12 figures. New numerical experiments on synthetic data sets, discussion about the convergenc