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

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

Super-Resolution for Hyperspectral and Multispectral Image Fusion Accounting for Seasonal Spectral Variability

Image fusion combines data from different heterogeneous sources to obtain more precise information about an underlying scene. Hyperspectral-multispectral (HS-MS) image fusion is currently attracting great interest in remote sensing since it allows the generation of high spatial resolution HS images, circumventing the main limitation of this imaging modality. Existing HS-MS fusion algorithms, however, neglect the spectral variability often existing between images acquired at different time instants. This time difference causes variations in spectral signatures of the underlying constituent materials due to different acquisition and seasonal conditions. This paper introduces a novel HS-MS image fusion strategy that combines an unmixing-based formulation with an explicit parametric model for typical spectral variability between the two images. Simulations with synthetic and real data show that the proposed strategy leads to a significant performance improvement under spectral variability and state-of-the-art performance otherwise

Hyperspectral image unmixing with LiDAR data-aided spatial regularization

Spectral unmixing (SU) methods incorporating the spatial regularizations have demonstrated increasing interest. Although spatial regularizers that promote smoothness of the abundance maps have been widely used, they may overly smooth these maps and, in particular, may not preserve edges present in the hyperspectral image. Existing unmixing methods usually ignore these edge structures or use edge information derived from the hyperspectral image itself. However, this information may be affected by the large amounts of noise or variations in illumination, leading to erroneous spatial information incorporated into the unmixing procedure. This paper proposes a simple yet powerful SU framework that incorporates external data [i.e. light detection and ranging (LiDAR) data]. The LiDAR measurements can be easily exploited to adjust the standard spatial regularizations applied to the unmixing process. The proposed framework is rigorously evaluated using two simulated data sets and a real hyperspectral image. It is compared with methods that rely on spatial information derived from a hyperspectral image. The results show that the proposed framework can provide better abundance estimates and, more specifically, can significantly improve the abundance estimates for the pixels affected by shadows

Unmixing dynamic PET images with variable specific binding kinetics

To analyze dynamic positron emission tomography (PET) images, various generic multivariate data analysis techniques have been considered in the literature, such as principal component analysis (PCA), independent component analysis (ICA), factor analysis and nonnegative matrix factorization (NMF). Nevertheless, these conventional approaches neglect any possible nonlinear variations in the time activity curves describing the kinetic behavior of tissues with specific binding, which limits their ability to recover a reliable, understandable and interpretable description of the data. This paper proposes an alternative analysis paradigm that accounts for spatial fluctuations in the exchange rate of the tracer between a free compartment and a specifically bound ligand compartment. The method relies on the concept of linear unmixing, usually applied on the hyperspectral domain, which combines NMF with a sum-to-one constraint that ensures an exhaustive description of the mixtures. The spatial variability of the signature corresponding to the specific binding tissue is explicitly modeled through a perturbed component. The performance of the method is assessed on both synthetic and real data and is shown to compete favorably when compared to other conventional analysis methods

Modeling spatial and temporal variabilities in hyperspectral image unmixing

Acquired in hundreds of contiguous spectral bands, hyperspectral (HS) images have received an increasing interest due to the significant spectral information they convey about the materials present in a given scene. However, the limited spatial resolution of hyperspectral sensors implies that the observations are mixtures of multiple signatures corresponding to distinct materials. Hyperspectral unmixing is aimed at identifying the reference spectral signatures composing the data -- referred to as endmembers -- and their relative proportion in each pixel according to a predefined mixture model. In this context, a given material is commonly assumed to be represented by a single spectral signature. This assumption shows a first limitation, since endmembers may vary locally within a single image, or from an image to another due to varying acquisition conditions, such as declivity and possibly complex interactions between the incident light and the observed materials. Unless properly accounted for, spectral variability can have a significant impact on the shape and the amplitude of the acquired signatures, thus inducing possibly significant estimation errors during the unmixing process. A second limitation results from the significant size of HS data, which may preclude the use of batch estimation procedures commonly used in the literature, i.e., techniques exploiting all the available data at once. Such computational considerations notably become prominent to characterize endmember variability in multi-temporal HS (MTHS) images, i.e., sequences of HS images acquired over the same area at different time instants. The main objective of this thesis consists in introducing new models and unmixing procedures to account for spatial and temporal endmember variability. Endmember variability is addressed by considering an explicit variability model reminiscent of the total least squares problem, and later extended to account for time-varying signatures. The variability is first estimated using an unsupervised deterministic optimization procedure based on the Alternating Direction Method of Multipliers (ADMM). Given the sensitivity of this approach to abrupt spectral variations, a robust model formulated within a Bayesian framework is introduced. This formulation enables smooth spectral variations to be described in terms of spectral variability, and abrupt changes in terms of outliers. Finally, the computational restrictions induced by the size of the data is tackled by an online estimation algorithm. This work further investigates an asynchronous distributed estimation procedure to estimate the parameters of the proposed models