Nonlinear unmixing of hyperspectral images: Models and algorithms

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling

Residual Component Analysis of Hyperspectral Images - Application to Joint Nonlinear Unmixing and Nonlinearity Detection

International audienceThis paper presents a nonlinear mixing model for joint hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are linear combinations of known pure spectral components corrupted by an additional nonlinear term, affecting the end members and contaminated by an additive Gaussian noise. A Markov random field is considered for nonlinearity detection based on the spatial structure of the nonlinear terms. The observed image is segmented into regions where nonlinear terms, if present, share similar statistical properties. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint nonlinear unmixing and nonlinearity detection algorithm. The performance of the proposed strategy is first evaluated on synthetic data. Simulations conducted with real data show the accuracy of the proposed unmixing and nonlinearity detection strategy for the analysis of hyperspectral images

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Spectral Mixture Analysis as a Unified Framework for the Remote Sensing of Evapotranspiration

This study illustrates a unified, physically-based framework for mapping landscape parameters of evapotranspiration (ET) using spectral mixture analysis (SMA). The framework integrates two widely used approaches by relating radiometric surface temperature to subpixel fractions of substrate (S), vegetation (V), and dark (D) spectral endmembers (EMs). Spatial and temporal variations in these spectral endmember fractions reflect process-driven variations in soil moisture, vegetation phenology, and illumination. Using all available Landsat 8 scenes from the peak growing season in the agriculturally diverse Sacramento Valley of northern California, we characterize the spatiotemporal relationships between each of the S, V, D land cover fractions and apparent brightness temperature (T) using bivariate distributions in the ET parameter spaces. The dark fraction scales inversely with shortwave broadband albedo (ρ < −0.98), and show a multilinear relationship to T. Substrate fraction estimates show a consistent (ρ ≈ 0.7 to 0.9) linear relationship to T. The vegetation fraction showed the expected triangular relationship to T. However, the bivariate distribution of V and T shows more distinct clustering than the distributions of Normalized Difference Vegetation Index (NDVI)-based proxies and T. Following the Triangle Method, the V fraction is used with T to compute the spatial maps of the ET fraction (EF; the ratio of the actual total ET to the net radiation) and moisture availability (Mo; the ratio of the actual soil surface evaporation to potential ET at the soil surface). EF and Mo estimates derived from the V fraction distinguish among rice growth stages, and between rice and non-rice agriculture, more clearly than those derived from transformed NDVI proxies. Met station-based reference ET & soil temperatures also track vegetation fraction-based estimates of EF & Mo more closely than do NDVI-based estimates of EF & Mo. The proposed approach using S, V, D land cover fractions in conjunction with T (SVD+T) provides a physically-based conceptual framework that unifies two widely-used approaches by simultaneously mapping the effects of albedo and vegetation abundance on the surface temperature field. The additional information provided by the third (Substrate) fraction suggests a potential avenue for ET model improvement by providing an explicit observational constraint on the exposed soil fraction and its moisture-modulated brightness. The structures of the T, EF & Mo vs SVD feature spaces are complementary and that can be interpreted in the context of physical variables that scale linearly and that can be represented directly in process models. Using the structure of the feature spaces to represent the spatiotemporal trajectory of crop phenology is possible in agricultural settings, because variations in the timing of planting and irrigation result in continuous trajectories in the physical parameter spaces that are represented by the feature spaces. The linear scaling properties of the SMA fraction estimates from meter to kilometer scales also facilitate the vicarious validation of ET estimates using multiple resolutions of imagery

Nonlinear Hyperspectral Unmixing With Robust Nonnegative Matrix Factorization

International audienceWe introduce a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. The new model extends the commonly used linear mixing model by introducing an additional term accounting for possible nonlinear effects, that are treated as sparsely distributed additive outliers.With the standard nonnegativity and sum-to-one constraints inherent to spectral unmixing, our model leads to a new form of robust nonnegative matrix factorization with a group-sparse outlier term. The factorization is posed as an optimization problem which is addressed with a block-coordinate descent algorithm involving majorization-minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods

Multiscale Imaging of Evapotranspiration

Evapotranspiration (ET; evaporation + transpiration) is central to a wide range of biological, chemical, and physical processes in the Earth system. Accurate remote sensing of ET is challenging due to the interrelated and generally scale dependent nature of the physical factors which contribute to the process. The evaporation of water from porous media like sands and soils is an important subset of the complete ET problem. Chapter 1 presents a laboratory investigation into this question, examining the effects of grain size and composition on the evolution of drying sands. The effects of composition are found to be 2-5x greater than the effects of grain size, indicating that differences in heating caused by differences in reflectance may dominate hydrologic differences caused by grain size variation. In order to relate the results of Chapter 1 to the satellite image archive, however, the question of information loss between hyperspectral (measurements at 100s of wavelength intervals) laboratory measurements and multispectral (≤ 12 wavelength intervals) satellite images must be addressed. Chapter 2 focuses on this question as applied to substrate materials such as sediment, soil, rock, and non-photosynthetic vegetation. The results indicate that the continuum that is resolved by multispectral sensors is sufficient to resolve the gradient between sand-rich and clay-rich soils, and that this gradient is also a dominant feature in hyperspectral mixing spaces where the actual absorptions can be resolved. Multispectral measurements can be converted to biogeophysically relevant quantities using spectral mixture analysis (SMA). However, retrospective multitemporal analysis first requires cross-sensor calibration of the mixture model. Chapter 3 presents this calibration, allowing multispectral image data to be used interchangeably throughout the Landsat 4-8 archive. In addition, a theoretical explanation is advanced for the observed superior scaling properties of SMA-derived fraction images over spectral indices. The physical quantities estimated by the spectral mixture model are then compared to simultaneously imaged surface temperature, as well as to the derived parameters of ET Fraction and Moisture Availability. SMA-derived vegetation abundance is found to produce substantially more informative ET maps, and SMA-derived substrate fraction is found to yield a surprisingly strong linear relationship with surface temperature. These results provide context for agricultural applications. Chapter 5 investigates the question of mapping and monitoring rice agricultural using optical and thermal satellite image time series. Thermal image time series are found to produce more accurate maps of rice presence/absence, but optical image time series are found to produce more accurate maps of rice crop timing. Chapter 6 takes a more global approach, investigating the spatial structure of agricultural networks for a diverse set of landscapes. Surprisingly consistent scaling relations are found. These relations are assessed in the context of a network-based approach to land cover analysis, with potential implications for the scale dependence of ET estimates. In sum, this thesis present a novel approach to improving ET estimation based on a synthesis of complementary laboratory measurements, satellite image analysis, and field observations. Alone, each of these independent sources of information provides novel insights. Viewed together, these insights form the basis of a more accurate and complete geophysical understanding of the ET phenomenon