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

Optimal Clustering Framework for Hyperspectral Band Selection

Band selection, by choosing a set of representative bands in hyperspectral image (HSI), is an effective method to reduce the redundant information without compromising the original contents. Recently, various unsupervised band selection methods have been proposed, but most of them are based on approximation algorithms which can only obtain suboptimal solutions toward a specific objective function. This paper focuses on clustering-based band selection, and proposes a new framework to solve the above dilemma, claiming the following contributions: 1) An optimal clustering framework (OCF), which can obtain the optimal clustering result for a particular form of objective function under a reasonable constraint. 2) A rank on clusters strategy (RCS), which provides an effective criterion to select bands on existing clustering structure. 3) An automatic method to determine the number of the required bands, which can better evaluate the distinctive information produced by certain number of bands. In experiments, the proposed algorithm is compared to some state-of-the-art competitors. According to the experimental results, the proposed algorithm is robust and significantly outperform the other methods on various data sets

S^2-Transformer for Mask-Aware Hyperspectral Image Reconstruction

The technology of hyperspectral imaging (HSI) records the visual information upon long-range-distributed spectral wavelengths. A representative hyperspectral image acquisition procedure conducts a 3D-to-2D encoding by the coded aperture snapshot spectral imager (CASSI) and requires a software decoder for the 3D signal reconstruction. By observing this physical encoding procedure, two major challenges stand in the way of a high-fidelity reconstruction. (i) To obtain 2D measurements, CASSI dislocates multiple channels by disperser-titling and squeezes them onto the same spatial region, yielding an entangled data loss. (ii) The physical coded aperture leads to a masked data loss by selectively blocking the pixel-wise light exposure. To tackle these challenges, we propose a spatial-spectral (S^2-) Transformer network with a mask-aware learning strategy. First, we simultaneously leverage spatial and spectral attention modeling to disentangle the blended information in the 2D measurement along both two dimensions. A series of Transformer structures are systematically designed to fully investigate the spatial and spectral informative properties of the hyperspectral data. Second, the masked pixels will induce higher prediction difficulty and should be treated differently from unmasked ones. Thereby, we adaptively prioritize the loss penalty attributing to the mask structure by inferring the pixel-wise reconstruction difficulty upon the mask-encoded prediction. We theoretically discusses the distinct convergence tendencies between masked/unmasked regions of the proposed learning strategy. Extensive experiments demonstrates that the proposed method achieves superior reconstruction performance. Additionally, we empirically elaborate the behaviour of spatial and spectral attentions under the proposed architecture, and comprehensively examine the impact of the mask-aware learning.Comment: 11 pages, 16 figures, 6 tables, Code: https://github.com/Jiamian-Wang/S2-transformer-HS

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio