Using random matrix theory to determine the intrinsic dimension of a hyperspectral image

Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process, since under- or over- estimation of this number may lead to incorrect unmixing for unsupervised methods. In this thesis we introduce a new method for determining the intrinsic dimension, using recent advances in Random Matrix Theory (RMT). This method is not sensitive to non-i.i.d. and correlated noise, and it is entirely unsupervised and free from any user-determined parameters. The new RMT method is mathematically derived, and robustness tests are run on synthetic data to determine how the results are a ected by: image size; noise levels; noise variability; noise approximation; spectral characteristics of the endmembers, etc. Success rates are determined for many di erent synthetic images, and the method is compared to two principal state of the art methods, Noise Subspace Projection (NSP) and HySime. All three methods are then tested on twelve real hyperspectral images, including images acquired by satellite, airborne and land-based sensors. When images that were acquired by di erent sensors over the same spatial area are evaluated, RMT gives consistent results, showing the robustness of this method to sensor characterisics

Graph Laplacian for Image Anomaly Detection

Reed-Xiaoli detector (RXD) is recognized as the benchmark algorithm for image anomaly detection; however, it presents known limitations, namely the dependence over the image following a multivariate Gaussian model, the estimation and inversion of a high-dimensional covariance matrix, and the inability to effectively include spatial awareness in its evaluation. In this work, a novel graph-based solution to the image anomaly detection problem is proposed; leveraging the graph Fourier transform, we are able to overcome some of RXD's limitations while reducing computational cost at the same time. Tests over both hyperspectral and medical images, using both synthetic and real anomalies, prove the proposed technique is able to obtain significant gains over performance by other algorithms in the state of the art.Comment: Published in Machine Vision and Applications (Springer

Estimating the Intrinsic Dimension of Hyperspectral Images Using a Noise-Whitened Eigengap Approach

International audienceLinear mixture models are commonly used to represent a hyperspectral data cube as linear combinations of endmember spectra. However, determining the number of endmembers for images embedded in noise is a crucial task. This paper proposes a fully automatic approach for estimating the number of endmembers in hyperspectral images. The estimation is based on recent results of random matrix theory related to the so-called spiked population model. More precisely, we study the gap between successive eigenvalues of the sample covariance matrix constructed from high-dimensional noisy samples. The resulting estimation strategy is fully automatic and robust to correlated noise owing to the consideration of a noise-whitening step. This strategy is validated on both synthetic and real images. The experimental results are very promising and show the accuracy of this algorithm with respect to state-of-the-art algorithms

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

A convex formulation for hyperspectral image superresolution via subspace-based regularization

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe

Experimental Study of Hierarchical Clustering for Unmixing of Hyperspectral Images

[EN] Estimation of the number of materials that are present in a hyperspectral image is a necessary step in many hyperspectral image processing algorithms, including classification and unmixing. Previously, we presented an algorithm that estimated the number of materials in the image using clustering principles. This algorithm is an iterative approach with two input parameters: the initial number of materials (P0) and the number of materials added in each iteration (¿). Since the choice of P0 and ¿ can have a large impact on the estimation accuracy. In this paper, we made an experimental study of the effect of these parameters on the algorithm performance. Thus, we show that the choice of a large ¿ can significantly reduce the estimation accuracy. These results can help to make an appropriate choice of these two parameters.This research has been supported by Generalitat Valenciana, grant PROMETEO 2019/109.Prades Nebot, J.; Salazar Afanador, A.; Safont, G.; Vergara Domínguez, L. (2021). Experimental Study of Hierarchical Clustering for Unmixing of Hyperspectral Images. IEEE. 1-5. https://doi.org/10.1109/ICARES53960.2021.96652011

Estimation of the Number of Endmembers in Hyperspectral Images Using Agglomerative Clustering

[EN] Many tasks in hyperspectral imaging, such as spectral unmixing and sub-pixel matching, require knowing how many substances or materials are present in the scene captured by a yperspectral image. In this paper, we present an algorithm that estimates the number of materials in the scene using agglomerative clustering. The algorithm is based on the assumption that a valid clustering of the image has one cluster for each different material. After reducing the dimensionality of the hyperspectral image, the proposed method obtains an initial clustering using K-means. In this stage, cluster densities are estimated using Independent Component Analysis. Based on the K-means result, a model-based agglomerative clustering is performed, which provides a hierarchy of clusterings. Finally, a validation algorithm selects a clustering of the hierarchy; the number of clusters it contains is the estimated number of materials. Besides estimating the number of endmembers, the proposed method can approximately obtain the endmember (or spectrum) of each material by computing the centroid of its corresponding cluster. We have tested the proposed method using several hyperspectral images. The results show that the proposed method obtains approximately the number of materials that these images contain.This work was supported by Spanish Administration (Ministerio de Ciencia, Innovacion y Universidades) and European Union (FEDER) under grant TEC2017-84743-P.Prades Nebot, J.; Safont Armero, G.; Salazar Afanador, A.; Vergara Domínguez, L. (2020). Estimation of the Number of Endmembers in Hyperspectral Images Using Agglomerative Clustering. Remote Sensing. 12(21):1-22. https://doi.org/10.3390/rs12213585S122122