Inertia-Constrained Pixel-by-Pixel Nonnegative Matrix Factorisation: a Hyperspectral Unmixing Method Dealing with Intra-class Variability

Blind source separation is a common processing tool to analyse the constitution of pixels of hyperspectral images. Such methods usually suppose that pure pixel spectra (endmembers) are the same in all the image for each class of materials. In the framework of remote sensing, such an assumption is no more valid in the presence of intra-class variabilities due to illumination conditions, weathering, slight variations of the pure materials, etc... In this paper, we first describe the results of investigations highlighting intra-class variability measured in real images. Considering these results, a new formulation of the linear mixing model is presented leading to two new methods. Unconstrained Pixel-by-pixel NMF (UP-NMF) is a new blind source separation method based on the assumption of a linear mixing model, which can deal with intra-class variability. To overcome UP-NMF limitations an extended method is proposed, named Inertia-constrained Pixel-by-pixel NMF (IP-NMF). For each sensed spectrum, these extended versions of NMF extract a corresponding set of source spectra. A constraint is set to limit the spreading of each source's estimates in IP-NMF. The methods are tested on a semi-synthetic data set built with spectra extracted from a real hyperspectral image and then numerically mixed. We thus demonstrate the interest of our methods for realistic source variabilities. Finally, IP-NMF is tested on a real data set and it is shown to yield better performance than state of the art methods

Robust Linear Spectral Unmixing using Anomaly Detection

This paper presents a Bayesian algorithm for linear spectral unmixing of hyperspectral images that accounts for anomalies present in the data. The model proposed assumes that the pixel reflectances are linear mixtures of unknown endmembers, corrupted by an additional nonlinear term modelling anomalies and additive Gaussian noise. A Markov random field is used for anomaly detection based on the spatial and spectral structures of the anomalies. This allows outliers to be identified in particular regions and wavelengths of the data cube. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding a joint linear unmixing and anomaly detection algorithm. Simulations conducted with synthetic and real hyperspectral images demonstrate the accuracy of the proposed unmixing and outlier detection strategy for the analysis of hyperspectral images

A Quantitative Assessment of Forest Cover Change in the Moulouya River Watershed (Morocco) by the Integration of a Subpixel-Based and Object-Based Analysis of Landsat Data

A quantitative assessment of forest cover change in the Moulouya River watershed (Morocco) was carried out by means of an innovative approach from atmospherically corrected reflectance Landsat images corresponding to 1984 (Landsat 5 Thematic Mapper) and 2013 (Landsat 8 Operational Land Imager). An object-based image analysis (OBIA) was undertaken to classify segmented objects as forested or non-forested within the 2013 Landsat orthomosaic. A Random Forest classifier was applied to a set of training data based on a features vector composed of different types of object features such as vegetation indices, mean spectral values and pixel-based fractional cover derived from probabilistic spectral mixture analysis). The very high spatial resolution image data of Google Earth 2013 were employed to train/validate the Random Forest classifier, ranking the NDVI vegetation index and the corresponding pixel-based percentages of photosynthetic vegetation and bare soil as the most statistically significant object features to extract forested and non-forested areas. Regarding classification accuracy, an overall accuracy of 92.34% was achieved. The previously developed classification scheme was applied to the 1984 Landsat data to extract the forest cover change between 1984 and 2013, showing a slight net increase of 5.3% (ca. 8800 ha) in forested areas for the whole region

Large-Scale Urban Impervous Surfaces Estimation Through Incorporating Temporal and Spatial Information into Spectral Mixture Analysis

With rapid urbanization, impervious surfaces, a major component of urbanized areas, have increased concurrently. As a key indicator of environmental quality and urbanization intensity, an accurate estimation of impervious surfaces becomes essential. Numerous automated estimation approaches have been developed during the past decades. Among them, spectral mixture analysis (SMA) has been recognized as a powerful and widely employed technique. While SMA has proven valuable in impervious surface estimation, effects of temporal and spectral variability have not been successfully addressed. In particular, impervious surface estimation is likely to be sensitive to seasonal changes, majorly due to the shadowing effects of vegetation canopy in summer and the confusion between impervious surfaces and soil in winter. Moreover, endmember variability and multi-collinearity have adversely impacted the accurate estimation of impervious surface distribution with coarse resolution remote sensing imagery. Therefore, the main goal of this research is to incorporate temporal and spatial information, as well as geostatistical approaches, into SMA for improving large-scale urban impervious surface estimation. Specifically, three new approaches have been developed in this dissertation to improve the accuracy of large-scale impervious surface estimation. First, a phenology based temporal mixture analysis was developed to address seasonal sensitivity and spectral confusion issues with the multi-temporal MODIS NDVI data. Second, land use land cover information assisted temporal mixture analysis was proposed to handle the issue of endmember class variability through analyzing the spatial relationship between endmembers and surrounding environmental and socio-economic factors in support of the selection of an appropriate number and types of endmember classes. Third, a geostatistical temporal mixture analysis was developed to address endmember spectral variability by generating per-pixel spatial varied endmember spectra. Analysis results suggest that, first, with the proposed phenology based temporal mixture analysis, a significant phenophase differences between impervious surfaces and soil can be extracted and employed in unmxing analysis, which can facilitate their discrimination and successfully address the issue of seasonal sensitivity and spectral confusion. Second, with the analyzed spatial distribution relationship between endmembers and environmental and socio-economic factors, endmember classes can be identified with clear physical meanings throughout the whole study area, which can effectively improve the unmixing analysis results. Third, the use of the spatially varying per-pixel endmember generated from the geostatistical approach can effectively consider the endmember spectra spatial variability, overcome the endmember within-class variability issue, and improve the accuracy of impervious surface estimates. Major contributions of this research can be summarized as follows. First, instead of Landsat Thematic Mapper (TM) images, MODIS imageries with large geographic coverage and high temporal resolution have been successfully employed in this research, thus making timely and regional estimation of impervious surfaces possible. Second, this research proves that the incorporation of geographic knowledge (e.g. phonological knowledge, spatial interaction, and geostatistics) can effectively improve the spectral mixture analysis model, and therefore improve the estimation accuracy of urban impervious surfaces

Improving Hyperspectral Subpixel Target Detection Using Hybrid Detection Space

A Hyper-Spectral Image (HSI) has high spectral and low spatial resolution. As a result, most targets exist as subpixels, which pose challenges in target detection. Moreover, limitation of target and background samples always hinders the target detection performance. In this thesis, a hybrid method for subpixel target detection of an HSI using minimal prior knowledge is developed. The Matched Filter (MF) and Adaptive Cosine Estimator (ACE) are two popular algorithms in HSI target detection. They have different advantages in differentiating target from background. In the proposed method, the scores of MF and ACE algorithms are used to construct a hybrid detection space. First, some high abundance target spectra are randomly picked from the scene to perform initial detection to determine the target and background subsets. Then, the reference target spectrum and background covariance matrix are improved iteratively, using the hybrid detection space. As the iterations continue, the reference target spectrum gets closer and closer to the central line that connects the centers of target and background and resulting in noticeable improvement in target detection. Two synthetic datasets and two real datasets are used in the experiments. The results are evaluated based on the mean detection rate, Receiver Operating Characteristic (ROC) curve and observation of the detection results. Compared to traditional MF and ACE algorithms with Reed-Xiaoli Detector (RXD) background covariance matrix estimation, the new method shows much better performance on all four datasets. This method can be applied in environmental monitoring, mineral detection, as well as oceanography and forestry reconnaissance to search for extremely small target distribution in a large scene

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

Mapping Impervious Surface Using Phenology-Integrated and Fisher Transformed Linear Spectral Mixture Analysis

The impervious surface area (ISA) is a key indicator of urbanization, which brings out serious adverse environmental and ecological consequences. The ISA is often estimated from remotely sensed data via spectral mixture analysis (SMA). However, accurate extraction of ISA using SMA is compromised by two major factors, endmember spectral variability and plant phenology. This study developed a novel approach that incorporates phenology with Fisher transformation into a conventional linear spectral mixture analysis (PF-LSMA) to address these challenges. Four endmembers, high albedo, low albedo, evergreen vegetation, and seasonally exposed soil (H-L-EV-SS) were identified for PF-LSMA, considering the phenological characteristic of Shanghai. Our study demonstrated that the PF-LSMA effectively reduced the within-endmember spectral signature variation and accounted for the endmember phenology effects, and thus well-discriminated impervious surface from seasonally exposed soil, enhancing the accuracy of ISA extraction. The ISA fraction map produced by PF-LSMA (RMSE = 0.1112) outperforms the single-date image Fisher transformed unmixing method (F-LSMA) (RMSE = 0.1327) and the other existing major global ISA products. The PF-LSMA was implemented on the Google Earth Engine platform and thus can be easily adapted to extract ISA in other places with similar climate conditions.Peer Reviewe