Manifold learning based spectral unmixing of hyperspectral remote sensing data

Nonlinear mixing effects inherent in hyperspectral data are not properly represented in linear spectral unmixing models. Although direct nonlinear unmixing models provide capability to capture nonlinear phenomena, they are difficult to formulate and the results are not always generalizable. Manifold learning based spectral unmixing accommodates nonlinearity in the data in the feature extraction stage followed by linear mixing, thereby incorporating some characteristics of nonlinearity while retaining advantages of linear unmixing approaches. Since endmember selection is critical to successful spectral unmixing, it is important to select proper endmembers from the manifold space. However, excessive computational burden hinders development of manifolds for large-scale remote sensing datasets. This dissertation addresses issues related to high computational overhead requirements of manifold learning for developing representative manifolds for the spectral unmixing task. Manifold approximations using landmarks are popular for mitigating the computational complexity of manifold learning. A new computationally effective landmark selection method that exploits spatial redundancy in the imagery is proposed. A robust, less costly landmark set with low spectral and spatial redundancy is successfully incorporated with a hybrid manifold which shares properties of both global and local manifolds. While landmark methods reduce computational demand, the resulting manifolds may not represent subtle features of the manifold adequately. Active learning heuristics are introduced to increase the number of landmarks, with the goal of developing more representative manifolds for spectral unmixing. By communicating between the landmark set and the query criteria relative to spectral unmixing, more representative and stable manifolds with less spectrally and spatially redundant landmarks are developed. A new ranking method based on the pixels with locally high spectral variability within image subsets and convex-geometry finds a solution more quickly and precisely. Experiments were conducted to evaluate the proposed methods using the AVIRIS Cuprite hyperspectral reference dataset. A case study of manifold learning based spectral unmixing in agricultural areas is included in the dissertation.Remotely sensed data collected by airborne or spaceborne sensors are utilized to quantify crop residue cover over an extensive area. Although remote sensing indices are popular for characterizing residue amounts, they are not effective with noisy Hyperion data because the effect of residual striping artifacts is amplified in ratios involving band differences. In this case study, spectral unmixing techniques are investigated for estimating crop residue as an alternative approach to empirical models developed using band based indices. The spectral unmixing techniques, and especially the manifold learning approaches, provide more robust, lower RMSE estimates for crop residue cover than the hyperspectral index based method for Hyperion data

Arctic lead detection using a waveform mixture algorithm from CryoSat-2 data

We propose a waveform mixture algorithm to detect leads from CryoSat-2 data, which is novel and different from the existing threshold-based lead detection methods. The waveform mixture algorithm adopts the concept of spectral mixture analysis, which is widely used in the field of hyperspectral image analysis. This lead detection method was evaluated with high-resolution (250 m) MODIS images and showed comparable and promising performance in detecting leads when compared to the previous methods. The robustness of the proposed approach also lies in the fact that it does not require the rescaling of parameters (i.e., stack standard deviation, stack skewness, stack kurtosis, pulse peakiness, and backscatter sigma(0)), as it directly uses L1B waveform data, unlike the existing threshold-based methods. Monthly lead fraction maps were produced by the waveform mixture algorithm, which shows interannual variability of recent sea ice cover during 2011-2016, excluding the summer season (i.e., June to September). We also compared the lead fraction maps to other lead fraction maps generated from previously published data sets, resulting in similar spatiotemporal patterns

Analyse de séries temporelles d’images à moyenne résolution spatiale : reconstruction de profils de LAI, démélangeage : application pour le suivi de la végétation sur des images MODIS

This PhD dissertation is concerned with time series analysis for medium spatial resolution (MSR) remote sensing images. The main advantage of MSR data is their high temporal rate which allows to monitor land use. However, two main problems arise with such data. First, because of cloud coverage and bad acquisition conditions, the resulting time series are often corrupted and not directly exploitable. Secondly, pixels in medium spatial resolution images are often “mixed” in the sense that the spectral response is a combination of the response of “pure” elements.These two problems are addressed in this PhD. First, we propose a data assimilation technique able to recover consistent time series of Leaf Area Index from corrupted MODIS sequences. To this end, a plant growth model, namely GreenLab, is used as a dynamical constraint. Second, we propose a new and efficient unmixing technique for time series. It is in particular based on the use of “elastic” kernels able to properly compare time series shifted in time or of various lengths.Experimental results are shown both on synthetic and real data and demonstrate the efficiency of the proposed methodologies.Cette thèse s’intéresse à l’analyse de séries temporelles d’images satellites à moyenne résolution spatiale. L’intérêt principal de telles données est leur haute répétitivité qui autorise des analyses de l’usage des sols. Cependant, deux problèmes principaux subsistent avec de telles données. En premier lieu, en raison de la couverture nuageuse, des mauvaises conditions d’acquisition, ..., ces données sont souvent très bruitées. Deuxièmement, les pixels associés à la moyenne résolution spatiale sont souvent “mixtes” dans la mesure où leur réponse spectrale est une combinaison de la réponse de plusieurs éléments “purs”. Ces deux problèmes sont abordés dans cette thèse. Premièrement, nous proposons une technique d’assimilation de données capable de recouvrer des séries temporelles cohérentes de LAI (Leaf Area Index) à partir de séquences d’images MODIS bruitées. Pour cela, le modèle de croissance de plantes GreenLab estutilisé. En second lieu, nous proposons une technique originale de démélangeage, qui s’appuie notamment sur des noyaux “élastiques” capables de gérer les spécificités des séries temporelles (séries de taille différentes, décalées dans le temps, ...)Les résultats expérimentaux, sur des données synthétiques et réelles, montrent de bonnes performances des méthodologies proposées

Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications

Nonnegative matrix factorization (NMF) has become a workhorse for signal and data analytics, triggered by its model parsimony and interpretability. Perhaps a bit surprisingly, the understanding to its model identifiability---the major reason behind the interpretability in many applications such as topic mining and hyperspectral imaging---had been rather limited until recent years. Beginning from the 2010s, the identifiability research of NMF has progressed considerably: Many interesting and important results have been discovered by the signal processing (SP) and machine learning (ML) communities. NMF identifiability has a great impact on many aspects in practice, such as ill-posed formulation avoidance and performance-guaranteed algorithm design. On the other hand, there is no tutorial paper that introduces NMF from an identifiability viewpoint. In this paper, we aim at filling this gap by offering a comprehensive and deep tutorial on model identifiability of NMF as well as the connections to algorithms and applications. This tutorial will help researchers and graduate students grasp the essence and insights of NMF, thereby avoiding typical `pitfalls' that are often times due to unidentifiable NMF formulations. This paper will also help practitioners pick/design suitable factorization tools for their own problems.Comment: accepted version, IEEE Signal Processing Magazine; supplementary materials added. Some minor revisions implemente

Tensor-based Hyperspectral Image Processing Methodology and its Applications in Impervious Surface and Land Cover Mapping

The emergence of hyperspectral imaging provides a new perspective for Earth observation, in addition to previously available orthophoto and multispectral imagery. This thesis focused on both the new data and new methodology in the field of hyperspectral imaging. First, the application of the future hyperspectral satellite EnMAP in impervious surface area (ISA) mapping was studied. During the search for the appropriate ISA mapping procedure for the new data, the subpixel classification based on nonnegative matrix factorization (NMF) achieved the best success. The simulated EnMAP image shows great potential in urban ISA mapping with over 85% accuracy. Unfortunately, the NMF based on the linear algebra only considers the spectral information and neglects the spatial information in the original image. The recent wide interest of applying the multilinear algebra in computer vision sheds light on this problem and raised the idea of nonnegative tensor factorization (NTF). This thesis found that the NTF has more advantages over the NMF when work with medium- rather than the high-spatial-resolution hyperspectral image. Furthermore, this thesis proposed to equip the NTF-based subpixel classification methods with the variations adopted from the NMF. By adopting the variations from the NMF, the urban ISA mapping results from the NTF were improved by ~2%. Lastly, the problem known as the curse of dimensionality is an obstacle in hyperspectral image applications. The majority of current dimension reduction (DR) methods are restricted to using only the spectral information, when the spatial information is neglected. To overcome this defect, two spectral-spatial methods: patch-based and tensor-patch-based, were thoroughly studied and compared in this thesis. To date, the popularity of the two solutions remains in computer vision studies and their applications in hyperspectral DR are limited. The patch-based and tensor-patch-based variations greatly improved the quality of dimension-reduced hyperspectral images, which then improved the land cover mapping results from them. In addition, this thesis proposed to use an improved method to produce an important intermediate result in the patch-based and tensor-patch-based DR process, which further improved the land cover mapping results

Non-Negative Blind Source Separation Algorithm Based on Minimum Aperture Simplicial Cone

International audienceWe address the problem of Blind Source Separation (BSS) when the hidden sources are Nonnegative (N-BSS). In this case, the scatter plot of the mixed data is contained within the simplicial cone generated by the columns of the mixing matrix. The proposed method, termed SCSA-UNS for Simplicial Cone Shrinking Algorithm for Unmixing Non-negative Sources, aims at estimating the mixing matrix and the sources by fitting a Minimum Aperture Simplicial Cone (MASC) to the cloud of mixed data points. SCSA-UNS is evaluated on both independent and correlated synthetic data and compared to other N-BSS methods. Simulations are also performed on real Liquid Chromatography-Mass Spectrum (LC-MS) data for the metabolomic analysis of a chemical sample, and on real dynamic Positron Emission Tomography (PET) images, in order to study the pharmacokinetics of the [18F]-FDG (FluoroDeoxyGlucose) tracer in the brain

Nonlinear unmixing of Hyperspectral images

Le démélange spectral est un des sujets majeurs de l’analyse d’images hyperspectrales. Ce problème consiste à identifier les composants macroscopiques présents dans une image hyperspectrale et à quantifier les proportions (ou abondances) de ces matériaux dans tous les pixels de l’image. La plupart des algorithmes de démélange suppose un modèle de mélange linéaire qui est souvent considéré comme une approximation au premier ordre du mélange réel. Cependant, le modèle linéaire peut ne pas être adapté pour certaines images associées par exemple à des scènes engendrant des trajets multiples (forêts, zones urbaines) et des modèles non-linéaires plus complexes doivent alors être utilisés pour analyser de telles images. Le but de cette thèse est d’étudier de nouveaux modèles de mélange non-linéaires et de proposer des algorithmes associés pour l’analyse d’images hyperspectrales. Dans un premier temps, un modèle paramétrique post-non-linéaire est étudié et des algorithmes d’estimation basés sur ce modèle sont proposés. Les connaissances a priori disponibles sur les signatures spectrales des composants purs, sur les abondances et les paramètres de la non-linéarité sont exploitées à l’aide d’une approche bayesienne. Le second modèle étudié dans cette thèse est basé sur l’approximation de la variété non-linéaire contenant les données observées à l’aide de processus gaussiens. L’algorithme de démélange associé permet d’estimer la relation non-linéaire entre les abondances des matériaux et les pixels observés sans introduire explicitement les signatures spectrales des composants dans le modèle de mélange. Ces signatures spectrales sont estimées dans un second temps par prédiction à base de processus gaussiens. La prise en compte d’effets non-linéaires dans les images hyperspectrales nécessite souvent des stratégies de démélange plus complexes que celles basées sur un modèle linéaire. Comme le modèle linéaire est souvent suffisant pour approcher la plupart des mélanges réels, il est intéressant de pouvoir détecter les pixels ou les régions de l’image où ce modèle linéaire est approprié. On pourra alors, après cette détection, appliquer les algorithmes de démélange non-linéaires aux pixels nécessitant réellement l’utilisation de modèles de mélange non-linéaires. La dernière partie de ce manuscrit se concentre sur l’étude de détecteurs de non-linéarités basés sur des modèles linéaires et non-linéaires pour l’analyse d’images hyperspectrales. Les méthodes de démélange non-linéaires proposées permettent d’améliorer la caractérisation des images hyperspectrales par rapport au méthodes basées sur un modèle linéaire. Cette amélioration se traduit en particulier par une meilleure erreur de reconstruction des données. De plus, ces méthodes permettent de meilleures estimations des signatures spectrales et des abondances quand les pixels résultent de mélanges non-linéaires. Les résultats de simulations effectuées sur des données synthétiques et réelles montrent l’intérêt d’utiliser des méthodes de détection de non-linéarités pour l’analyse d’images hyperspectrales. En particulier, ces détecteurs peuvent permettre d’identifier des composants très peu représentés et de localiser des régions où les effets non-linéaires sont non-négligeables (ombres, reliefs,...). Enfin, la considération de corrélations spatiales dans les images hyperspectrales peut améliorer les performances des algorithmes de démélange non-linéaires et des détecteurs de non-linéarités. ABSTRACT : Spectral unmixing is one the major issues arising when analyzing hyperspectral images. It consists of identifying the macroscopic materials present in a hyperspectral image and quantifying the proportions of these materials in the image pixels. Most unmixing techniques rely on a linear mixing model which is often considered as a first approximation of the actual mixtures. However, the linear model can be inaccurate for some specific images (for instance images of scenes involving multiple reflections) and more complex nonlinear models must then be considered to analyze such images. The aim of this thesis is to study new nonlinear mixing models and to propose associated algorithms to analyze hyperspectral images. First, a ost-nonlinear model is investigated and efficient unmixing algorithms based on this model are proposed. The prior knowledge about the components present in the observed image, their proportions and the nonlinearity parameters is considered using Bayesian inference. The second model considered in this work is based on the approximation of the nonlinear manifold which contains the observed pixels using Gaussian processes. The proposed algorithm estimates the relation between the observations and the unknown material proportions without explicit dependency on the material spectral signatures, which are estimated subsequentially. Considering nonlinear effects in hyperspectral images usually requires more complex unmixing strategies than those assuming linear mixtures. Since the linear mixing model is often sufficient to approximate accurately most actual mixtures, it is interesting to detect pixels or regions where the linear model is accurate. This nonlinearity detection can be applied as a pre-processing step and nonlinear unmixing strategies can then be applied only to pixels requiring the use of nonlinear models. The last part of this thesis focuses on new nonlinearity detectors based on linear and nonlinear models to identify pixels or regions where nonlinear effects occur in hyperspectral images. The proposed nonlinear unmixing algorithms improve the characterization of hyperspectral images compared to methods based on a linear model. These methods allow the reconstruction errors to be reduced. Moreover, these methods provide better spectral signature and abundance estimates when the observed pixels result from nonlinear mixtures. The simulation results conducted on synthetic and real images illustrate the advantage of using nonlinearity detectors for hyperspectral image analysis. In particular, the proposed detectors can identify components which are present in few pixels (and hardly distinguishable) and locate areas where significant nonlinear effects occur (shadow, relief, ...). Moreover, it is shown that considering spatial correlation in hyperspectral images can improve the performance of nonlinear unmixing and nonlinearity detection algorithms

Hyperspectral Imagery Target Detection Using Improved Anomaly Detection and Signature Matching Methods

This research extends the field of hyperspectral target detection by developing autonomous anomaly detection and signature matching methodologies that reduce false alarms relative to existing benchmark detectors, and are practical for use in an operational environment. The proposed anomaly detection methodology adapts multivariate outlier detection algorithms for use with hyperspectral datasets containing tens of thousands of non-homogeneous, high-dimensional spectral signatures. In so doing, the limitations of existing, non-robust, anomaly detectors are identified, an autonomous clustering methodology is developed to divide an image into homogeneous background materials, and competing multivariate outlier detection methods are evaluated for their ability to uncover hyperspectral anomalies. To arrive at a final detection algorithm, robust parameter design methods are employed to determine parameter settings that achieve good detection performance over a range of hyperspectral images and targets, thereby removing the burden of these decisions from the user. The final anomaly detection algorithm is tested against existing local and global anomaly detectors, and is shown to achieve superior detection accuracy when applied to a diverse set of hyperspectral images. The proposed signature matching methodology employs image-based atmospheric correction techniques in an automated process to transform a target reflectance signature library into a set of image signatures. This set of signatures is combined with an existing linear filter to form a target detector that is shown to perform as well or better relative to detectors that rely on complicated, information-intensive, atmospheric correction schemes. The performance of the proposed methodology is assessed using a range of target materials in both woodland and desert hyperspectral scenes