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 subspace approach to high-resolution magnetic resonance spectroscopic imaging

With its unique capability to obtain spatially resolved biochemical profiles from the human body noninvasively, magnetic resonance spectroscopic imaging (MRSI) has been recognized as a powerful tool for in vivo metabolic studies. However, research and clinical applications of in vivo MRSI have been progressing more slowly than expected. The main reasons for this situation are the problems of long data acquisition time, poor spatial resolution and low signal-to-noise ratio (SNR) for this imaging modality. In the last four decades, significant efforts have been made to improve MRSI, resulting in a large number of fast pulse sequences and advanced image reconstruction methods. However, the existing techniques have yet to offer the levels of improvement in imaging time, spatial resolution and SNR necessary to significantly impact in vivo applications of MRSI. This thesis work develops a new subspace imaging approach to address these technical challenges to enable fast, high-resolution MRSI with high SNR. The proposed approach, coined SPICE (Spectroscopic Imaging by Exploiting Spatiospectral Correlation), is characterized by using a subspace model for integrative data acquisition, processing and image reconstruction. More specifically, SPICE represents the spectroscopic signals in MRSI using the partial separability (PS) model. The PS model implies that the high-dimensional spectroscopic signals reside in a low-dimensional subspace, which enables the design of special sparse sampling strategies for accelerated spatiospectral encoding and special image reconstruction strategies for determining the subspace and reconstructing the underlying spatiospectral function of interest from the sparse data. Using the SPICE framework, new data acquisition and image reconstruction methods are developed to enable high-resolution 1H-MRSI of the brain. We have evaluated SPICE using theoretical analysis, numerical simulations, phantom and in vivo experimental studies. Results obtained from these experiments demonstrate the unprecedented capability of SPICE in achieving accelerated MRSI with simultaneously very high resolution and SNR. We expect SPICE to provide a powerful tool for in vivo metabolic studies with many exciting applications. Furthermore, the SPICE framework also presents new opportunities for future developments in subspace-driven signal generation, signal encoding, data processing and image reconstruction methods to advance the research and clinical applications of high-resolution in vivo MRSI

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Computational Spectral Imaging: A Contemporary Overview

Spectral imaging collects and processes information along spatial and spectral coordinates quantified in discrete voxels, which can be treated as a 3D spectral data cube. The spectral images (SIs) allow identifying objects, crops, and materials in the scene through their spectral behavior. Since most spectral optical systems can only employ 1D or maximum 2D sensors, it is challenging to directly acquire the 3D information from available commercial sensors. As an alternative, computational spectral imaging (CSI) has emerged as a sensing tool where the 3D data can be obtained using 2D encoded projections. Then, a computational recovery process must be employed to retrieve the SI. CSI enables the development of snapshot optical systems that reduce acquisition time and provide low computational storage costs compared to conventional scanning systems. Recent advances in deep learning (DL) have allowed the design of data-driven CSI to improve the SI reconstruction or, even more, perform high-level tasks such as classification, unmixing, or anomaly detection directly from 2D encoded projections. This work summarises the advances in CSI, starting with SI and its relevance; continuing with the most relevant compressive spectral optical systems. Then, CSI with DL will be introduced, and the recent advances in combining the physical optical design with computational DL algorithms to solve high-level tasks