Hyperspectral Image Segmentation Using a New Spectral Unmixing-Based Binary Partition Tree Representation

International audienceThe Binary Partition Tree (BPT) is a hierarchical region-based representation of an image in a tree structure. BPT allows users to explore the image at different segmentation scales. Often, the tree is pruned to get a more compact representation and so the remaining nodes conform an optimal partition for some given task. Here, we propose a novel BPT construction approach and pruning strategy for hyperspectral images based on spectral unmixing concepts. Linear Spectral Unmixing (LSU) consists of finding the spectral signatures of the materials present in the image (endmembers) and their fractional abundances within each pixel. The proposed methodology exploits the local unmixing of the regions to find the partition achieving a global minimum reconstruction error. Results are presented on real hyperspectral data sets with different contexts and resolutions

Development and testing of improved spectral unmixing techniques

The tradeoff between spatial and spectral resolution gives rise to a finite ground sample size, which produces data with spectrally mixed pixels in a multispectral and hyperspectral systems. Assuming the mixed pixel to be a linear combination of pure spectra known as endmembers, the fractional abundance of the endmembers can be calculated by linear spectral unmixing. Constraints may be placed to force the unmixed fractions to behave realistically. There are also different methods of selecting these endmember spectra, including scene derived and laboratory measured spectra. The stepwise unmixing uses an iterative regression technique to select the optimal endmembers on a per pixel basis. It shows promise of improving the unmixing process by introducing flexibility in endmember selection. However, stepwise procedure has not been rigorously tested, and its parameters are not well characterized. It was the aim of this research to characterize the major parameters of stepwise unmixing, including spectral resolution, library size, F-to-enter/exit, and pixel mixture complexity. In addition to the parametric studies, a comparison between stepwise procedure and hierarchical unmixing was made, as well as applications of unmixing algorithms to non-remote sensing data such as nuclear magnetic resonance (NMR) spectra. The parametric studies were conducted on synthetic data for its advantages of knowing exactly what is in the mixture. The algorithm was also tested with images to confirm the results of the parametric studies. The result showed that the stepwise procedure is capable of results comparable with the best traditional unmixing case

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

Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this paper, we propose to revisit the NMF as a multi-objective problem, in particular a bi-objective one, where the objective functions defined in both input and feature spaces are taken into account. By taking the advantage of the sum-weighted method from the literature of multi-objective optimization, the proposed bi-objective NMF determines a set of nondominated, Pareto optimal, solutions instead of a single optimal decomposition. Moreover, the corresponding Pareto front is studied and approximated. Experimental results on unmixing real hyperspectral images confirm the efficiency of the proposed bi-objective NMF compared with the state-of-the-art methods

Eigenspectra optoacoustic tomography achieves quantitative blood oxygenation imaging deep in tissues

Light propagating in tissue attains a spectrum that varies with location due to wavelength-dependent fluence attenuation by tissue optical properties, an effect that causes spectral corruption. Predictions of the spectral variations of light fluence in tissue are challenging since the spatial distribution of optical properties in tissue cannot be resolved in high resolution or with high accuracy by current methods. Spectral corruption has fundamentally limited the quantification accuracy of optical and optoacoustic methods and impeded the long sought-after goal of imaging blood oxygen saturation (sO2) deep in tissues; a critical but still unattainable target for the assessment of oxygenation in physiological processes and disease. We discover a new principle underlying light fluence in tissues, which describes the wavelength dependence of light fluence as an affine function of a few reference base spectra, independently of the specific distribution of tissue optical properties. This finding enables the introduction of a previously undocumented concept termed eigenspectra Multispectral Optoacoustic Tomography (eMSOT) that can effectively account for wavelength dependent light attenuation without explicit knowledge of the tissue optical properties. We validate eMSOT in more than 2000 simulations and with phantom and animal measurements. We find that eMSOT can quantitatively image tissue sO2 reaching in many occasions a better than 10-fold improved accuracy over conventional spectral optoacoustic methods. Then, we show that eMSOT can spatially resolve sO2 in muscle and tumor; revealing so far unattainable tissue physiology patterns. Last, we related eMSOT readings to cancer hypoxia and found congruence between eMSOT tumor sO2 images and tissue perfusion and hypoxia maps obtained by correlative histological analysis

Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing

In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully-constrained unmixing, with both the non-negativity and sum-to-one constraints, while the second one deals with the non-negativity and the sparsity-promoting of the abundances. The corresponding optimization problems are solved efficiently using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing is robust to outlier bands.Comment: 23 page