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

Implementation strategies for hyperspectral unmixing using Bayesian source separation

Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical non-negativity of spectra and abundances has to be ensured, such in remote sensing. Moreover, it is sensible to impose a sum-to-one (full additivity) constraint to the estimated source abundances in each pixel. Even though non-negativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms has been so far limited by high computation time and large memory requirements due to the Markov chain Monte Carlo calculations. An implementation strategy which allows one to apply these algorithms on a full hyperspectral image, as typical in Earth and Planetary Science, is introduced. Effects of pixel selection, the impact of such sampling on the relevance of the estimated component spectra and abundance maps, as well as on the computation times, are discussed. For that purpose, two different dataset have been used: a synthetic one and a real hyperspectral image from Mars.Comment: 10 pages, 6 figures, submitted to IEEE Transactions on Geoscience and Remote Sensing in the special issue on Hyperspectral Image and Signal Processing (WHISPERS

Nonlinear unmixing of hyperspectral images: Models and algorithms

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid, and other nonlinear models need to be considered, for instance, when there are multiscattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this article, we present an overview of recent advances in nonlinear unmixing modeling

Automated lithological mapping using airborne hyperspectral thermal infrared data: A case study from Anchorage Island, Antarctica

The thermal infrared portion of the electromagnetic spectrum has considerable potential for mineral and lithological mapping of the most abundant rock-forming silicates that do not display diagnostic features at visible and shortwave infrared wavelengths. Lithological mapping using visible and shortwave infrared hyperspectral data is well developed and established processing chains are available, however there is a paucity of such methodologies for hyperspectral thermal infrared data. Here we present a new fully automated processing chain for deriving lithological maps from hyperspectral thermal infrared data and test its applicability using the first ever airborne hyperspectral thermal data collected in the Antarctic. A combined airborne hyperspectral survey, targeted geological field mapping campaign and detailed mineralogical and geochemical datasets are applied to small test site in West Antarctica where the geological relationships are representative of continental margin arcs. The challenging environmental conditions and cold temperatures in the Antarctic meant that the data have a significantly lower signal to noise ratio than is usually attained from airborne hyperspectral sensors. We applied preprocessing techniques to improve the signal to noise ratio and convert the radiance images to ground leaving emissivity. Following preprocessing we developed and applied a fully automated processing chain to the hyperspectral imagery, which consists of the following six steps: (1) superpixel segmentation, (2) determine the number of endmembers, (3) extract endmembers from superpixels, (4) apply fully constrained linear unmixing, (5) generate a predictive classification map, and (6) automatically label the predictive classes to generate a lithological map. The results show that the image processing chain was successful, despite the low signal to noise ratio of the imagery; reconstruction of the hyperspectral image from the endmembers and their fractional abundances yielded a root mean square error of 0.58%. The results are encouraging with the thermal imagery allowing clear distinction between granitoid types. However, the distinction of fine grained, intermediate composition dykes is not possible due to the close geochemical similarity with the country rock

Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package

Spectral pixels are often a mixture of the pure spectra of the materials, called endmembers, due to the low spatial resolution of hyperspectral sensors, double scattering, and intimate mixtures of materials in the scenes. Unmixing estimates the fractional abundances of the endmembers within the pixel. Depending on the prior knowledge of endmembers, linear unmixing can be divided into three main groups: supervised, semi-supervised, and unsupervised (blind) linear unmixing. Advances in Image processing and machine learning substantially affected unmixing. This paper provides an overview of advanced and conventional unmixing approaches. Additionally, we draw a critical comparison between advanced and conventional techniques from the three categories. We compare the performance of the unmixing techniques on three simulated and two real datasets. The experimental results reveal the advantages of different unmixing categories for different unmixing scenarios. Moreover, we provide an open-source Python-based package available at https://github.com/BehnoodRasti/HySUPP to reproduce the results

GPU Parallel Implementation of Dual-Depth Sparse Probabilistic Latent Semantic Analysis for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is an important task for remotely sensed hyperspectral (HS) data exploitation. It comprises the identification of pure spectral signatures (endmembers) and their corresponding fractional abundances in each pixel of the HS data cube. Several methods have been developed for (semi-) supervised and automatic identification of endmembers and abundances. Recently, the statistical dual-depth sparse probabilistic latent semantic analysis (DEpLSA) method has been developed to tackle the HU problem as a latent topic-based approach in which both endmembers and abundances can be simultaneously estimated according to the semantics encapsulated by the latent topic space. However, statistical models usually lead to computationally demanding algorithms and the computational time of the DEpLSA is often too high for practical use, in particular, when the dimensionality of the HS data cube is large. In order to mitigate this limitation, this article resorts to graphical processing units (GPUs) to provide a new parallel version of the DEpLSA, developed using the NVidia compute device unified architecture. Our experimental results, conducted using four well-known HS datasets and two different GPU architectures (GTX 1080 and Tesla P100), show that our parallel versions of the DEpLSA and the traditional pLSA approach can provide accurate HU results fast enough for practical use, accelerating the corresponding serial versions in at least 30x in the GTX 1080 and up to 147x in the Tesla P100 GPU, which are quite significant acceleration factors that increase with the image size, thus allowing for the possibility of the fast processing of massive HS data repositories

Regularization approaches to hyperspectral unmixing

We consider a few different approaches to hyperspectral unmixing of remotely sensed imagery which exploit and extend recent advances in sparse statistical regularization, handling of constraints and dictionary reduction. Hyperspectral unmixing methods often use a conventional least-squares based lasso which assumes that the data follows the Gaussian distribution, we use this as a starting point. In addition, we consider a robust approach to sparse spectral unmixing of remotely sensed imagery which reduces the sensitivity of the estimator to outliers. Due to water absorption and atmospheric effects that affect data collection, hyperspectral images are prone to have large outliers. The framework comprises of several well-principled penalties. A non-convex, hyper-Laplacian prior is incorporated to induce sparsity in the number of active pure spectral components, and total variation regularizer is included to exploit the spatial-contextual information of hyperspectral images. Enforcing the sum-to-one and non-negativity constraint on the models parameters is essential for obtaining realistic estimates. We consider two approaches to account for this: an iterative heuristic renormalization and projection onto the positive orthant, and a reparametrization of the coefficients which gives rise to a theoretically founded method. Since the large size of modern spectral libraries cannot only present computational challenges but also introduce collinearities between regressors, we introduce a library reduction step. This uses the multiple signal classi fication (MUSIC) array processing algorithm, which both speeds up unmixing and yields superior results in scenarios where the library size is extensive. We show that although these problems are non-convex, they can be solved by a properly de fined algorithm based on either trust region optimization or iteratively reweighted least squares. The performance of the different approaches is validated in several simulated and real hyperspectral data experiments