Hyperspectral Unmixing Based on Constrained Bilinear or Linear-Quadratic Matrix Factorization

Unsupervised hyperspectral unmixing methods aim to extract endmember spectra and infer the proportion of each of these spectra in each observed pixel when considering linear mixtures. However, the interaction between sunlight and the Earth’s surface is often very complex, so that observed spectra are then composed of nonlinear mixing terms. This nonlinearity is generally bilinear or linear quadratic. In this work, unsupervised hyperspectral unmixing methods, designed for the bilinear and linear-quadratic mixing models, are proposed. These methods are based on bilinear or linear-quadratic matrix factorization with non-negativity constraints. Two types of algorithms are considered. The first ones only use the projection of the gradient, and are therefore linked to an optimal manual choice of their learning rates, which remains the limitation of these algorithms. The second developed algorithms, which overcome the above drawback, employ multiplicative projective update rules with automatically chosen learning rates. In addition, the endmember proportions estimation, with three alternative approaches, constitutes another contribution of this work. Besides, the reduction of the number of manipulated variables in the optimization processes is also an originality of the proposed methods. Experiments based on realistic synthetic hyperspectral data, generated according to the two considered nonlinear mixing models, and also on two real hyperspectral images, are carried out to evaluate the performance of the proposed approaches. The obtained results show that the best proposed approaches yield a much better performance than various tested literature methods.

Characterizing low-temperature aqueous alteration of Mars-analog basalts from Mauna Kea at multiple scales

We performed a multi-scale characterization of aqueous alteration of Mars analog basaltic rock from a Mauna Kea drill core using high-resolution visible and short-wave infrared (VIS-SWIR) spectral imaging, scanning electron microscopy, X-ray diffraction, and point VIS-SWIR spectra. Several types of smectites, zeolites, and primary minerals were identified. Mineral classes were mapped in cut sections extracted from the drill core and used to represent the range of alteration products seen in field data collected over 1000 m depth (Calvin et al. 2020). Ten distinct spectral end-members identified in the cut sections were used to map the field point spectra. Trioctahedral Fe- and Mg-rich smectites were present toward the top of the zone of analysis (972 m below the surface) and increased in abundance toward the bottom of the drill core (1763 m depth). The mineralogy demonstrates a general trend of discontinuous alteration that increases in intensity with depth, with less pervasive phyllosilicate alteration at the top, several zones of different mixtures of zeolites toward the center, followed by more abundant phyllosilicates in the lowest sections. Distinctly absent are Fe-Mg phyllosilicates other than smectites, as well as carbonates, sulfates, and Al phyllosilicates such as kaolinite or illite. Furthermore, hematite was only detected in two of 24 samples. The suite of assemblages points to aqueous alteration at low-to-moderate temperatures at neutral to basic pH in low-oxygen conditions, with little evidence of extensive surface interaction, presenting a possible analog for an early Mars subsurface environment. We also present a library of VIS-SWIR spectra of the analyzed cut sections, including both spatial averages (i.e., unweighted linear mixtures) of spectral images of each cut section and single point spectra of the cut sections. This will allow for consideration of nonlinear mixing effects in point spectra of these assemblages from natural surfaces in future terrestrial or planetary work.

An Alternative Approach to Mapping Pigments in Paintings With Hyperspectral Reflectance Image Cubes Using Artificial Intelligence

Spectral imaging modalities, including reflectance and X-ray fluorescence, play an important role in conservation science. In reflectance hyperspectral imaging, the data are classified into areas having similar spectra and turned into labeled pigment maps using spectral features and fusing with other information. Direct classification and labeling remain challenging because many paints are intimate pigment mixtures that require a non-linear unmixing model for a robust solution. Neural networks have been successful in modeling non-linear mixtures in remote sensing with large training datasets. For paintings, however, existing spectral databases are small and do not encompass the diversity encountered. Given that painting practices are relatively consistent within schools of artistic practices, we tested the suitability of using reflectance spectra from a subgroup of well-characterized paintings to build a large database to train a one-dimensional (spectral) convolutional neural network. The labeled pigment maps produced were found to be robust within similar styles of paintings.

Simulation Analysis on Partial Discharge Signals Produced by Multiple Insulation Defects in GIS

In this paper, the simulation analysis on partial discharge (PD) signals produced by multiple insulation defects in gas insulated substation (GIS) has been researched by the simulation software of electromagnetic field (XFDTD). The theoretical analysis and simulation results show that the single partial discharge signal is the linear convolution of the partial discharge current signal and its corresponding impact response in GIS. The mixed partial discharge signals are the linear mixtures of every partial discharge signal.

Nonlinear Interaction Decomposition (NID): A Method for Separation of Cross-frequency Coupled Sources in Human Brain

Cross-frequency coupling (CFC) is a phenomenon through which spatially and spectrally distributed information can be integrated in the brain. There is, however, a lack of methods decomposing brain electrophysiological data into interacting components. Here, we propose a novel framework for detecting such interactions in Magneto- and Electroencephalography (MEG/EEG), which we refer to as Nonlinear Interaction Decomposition (NID). In contrast to all previous methods for separation of cross-frequency (CF) sources in the brain, we propose that the extraction of nonlinearly interacting oscillations can be based on the statistical properties of their linear mixtures. The main idea of NID is that nonlinearly coupled brain oscillations can be mixed in such a way that the resulting linear mixture has a non-Gaussian distribution. We evaluate this argument analytically for amplitude-modulated narrow-band oscillations which are either phase-phase or amplitude-amplitude CF coupled. We validated NID extensively with simulated EEG obtained with realistic head modeling. The method extracted nonlinearly interacting components reliably even at SNRs as small as −15 (dB). Additionally, we applied NID to the resting-state EEG of 81 subjects to characterize CF phase-phase coupling between alpha and beta oscillations. The extracted sources were located in temporal, parietal and frontal areas, demonstrating the existence of diverse local and distant nonlinear interactions in resting-state EEG data.