Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

/pdf/vertex-component-analysis-a-fast-algorithm-to-unmix-1egulrpm76.pdf

Vertex component analysis: a fast algorithm to unmix hyperspectral data

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 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.

/pdf/hyperspectral-unmixing-overview-geometrical-statistical-and-2lb11fr9l4.pdf

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Hyperspectral remote sensing technology has advanced significantly in the past two decades. Current sensors onboard airborne and spaceborne platforms cover large areas of the Earth surface with unprecedented spectral, spatial, and temporal resolutions. These characteristics enable a myriad of applications requiring fine identification of materials or estimation of physical parameters. Very often, these applications rely on sophisticated and complex data analysis methods. The sources of difficulties are, namely, the high dimensionality and size of the hyperspectral data, the spectral mixing (linear and nonlinear), and the degradation mechanisms associated to the measurement process such as noise and atmospheric effects. This paper presents a tutorial/overview cross section of some relevant hyperspectral data analysis methods and algorithms, organized in six main topics: data fusion, unmixing, classification, target detection, physical parameter retrieval, and fast computing. In all topics, we describe the state-of-the-art, provide illustrative examples, and point to future challenges and research directions.

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Hyperspectral Remote Sensing Data Analysis and Future Challenges

https://rslab.disi.unitn.it/papers/R63-RSE-Plaza.pdf

Recent Advances in Techniques for Hyperspectral Image Processing

A Viking Lander 1 image was modeled as mixtures of reflectance spectra of palagonite dust, gray andesitelike rock, and a coarse rocklike soil. The rocks are covered to varying degrees by dust but otherwise appear unweathered. Rocklike soil occurs as lag deposits in deflation zones around stones and on top of a drift and as a layer in a trench dug by the lander. This soil probably is derived from the rocks by wind abrasion and/or spallation. Dust is the major component of the soil and covers most of the surface. The dust is unrelated spectrally to the rock but is equivalent to the global-scale dust observed telescopically. A new method was developed to model a multispectral image as mixtures of end-member spectra and to compare image spectra directly with laboratory reference spectra. The method for the first time uses shade and secondary illumination effects as spectral end-members; thus the effects of topography and illumination on all scales can be isolated or removed. The image was calibrated absolutely from the laboratory spectra, in close agreement with direct calibrations. The method has broad applications to interpreting multispectral images, including satellite images.

Spectral mixture modeling - A new analysis of rock and soil types at the Viking Lander 1 site. [on Mars]

The analysis of hyperspectral data sets requires the determination of certain basis spectra called 'end-members.' Once these spectra are found, the image cube can be 'unmixed' into the fractional abundance of each material in each pixel. There exist several techniques for accomplishing the determination of the end-members, most of which involve the intervention of a trained geologist. Often these-end-members are assumed to be present in the image, in the form of pure, or unmixed, pixels. In this paper a method based upon the geometry of convex sets is proposed to find a unique set of purest pixels in an image. The technique is based on the fact that in N spectral dimensions, the N-volume contained by a simplex formed of the purest pixels is larger than any other volume formed from any other combination of pixels. The algorithm works by 'inflating' a simplex inside the data, beginning with a random set of pixels. For each pixel and each end-member, the end-member is replaced with the spectrum of the pixel and the volume is recalculated. If it increases, the spectrum of the new pixel replaces that end-member. This procedure is repeated until no more replacements are done. This algorithm successfully derives end-members in a synthetic data set, and appears robust with less than perfect data. Spectral end-members have been extracted for the AVIRIS Cuprite data set which closely match reference spectra, and resulting abundance maps match published mineral maps.

N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data

The use of hyperspectral sensors for geological, agricultural and other remote sensing applications is continually increasing. In addition to airborne sensors, there are now at least four hyperspectral satellite sensors under development. These sensors will be producing a near continual stream of high dimensional data, leading to an obvious analysis bottleneck. Much of the planned analysis of hyperspectral image cubes requires the determination of certain basis spectra called 'end-members.' Once these spectra are found, the image cube can be 'unmixed' into fractional abundances of each material in each pixel. There exist several techniques for accomplishing the determination of these end-members, most of which require the intervention of a trained geologist. This process and the associated computations are often time- consuming. There is a need for automated techniques to allow the quick review of data collected by the sensors. Several different approaches to finding end-members in data will be reviewed, including the Pixel Purity Index, Orasis, and the Iterative Error Estimation methods. A new method, called N- FINDR, which extracts end-members based upon the geometry of convex sets, will be discussed in detail. End-member spectra and abundance maps will be compared to USGS results on AVIRIS data. Data examples from AVIRIS will also be used to compare several of the algorithms.

Autonomous hyperspectral end-member determination methods

With the advent of the commercial 3D video card in the mid 1990s, we have seen an order of magnitude performance
increase with each generation of new video cards. While these cards were designed primarily for visualization and video
games, it became apparent after a short while that they could be used for scientific purposes. These Graphical Processing
Units (GPUs) are rapidly being incorporated into data processing tasks usually reserved for general purpose computers.
It has been found that many image processing problems scale well to modern GPU systems. We have implemented four
popular hyperspectral processing algorithms (N-FINDR, linear unmixing, Principal Components, and the RX anomaly
detection algorithm). These algorithms show an across the board speedup of at least a factor of 10, with some special
cases showing extreme speedups of a hundred times or more.

Hyperspectral processing in graphical processing units

Hyperspectral imagers tend to have lower spatial resolution than multispectral ones. This often results in a (sometimes
difficult) trade-off between spectral and spatial resolution. We have developed a technique, called CRISP, that combines
low-resolution hyperspectral data and high-resolution multispectral data to produce high quality, high-resolution
hyperspectral data. This technique shows good quantitative performance when applied to realistic applications such as
land cover estimation and anomaly detection. As a test of this technique, we have performed an experiment using
HyMap hyperspectral data and multispectral instruments over the coast waters of Oahu, Hawaii. The accuracy of the
CRISP sharpening approach when used for coastal applications such as depth mapping is assessed.

Resolution enhancement of hyperspectral data using multispectral imagery

Observations of accelerating seismic activity prior to large earthquakes in natural fault systems have raised hopes for intermediate-term eartquake forecasting. If this phenomena does exist, then what causes it to occur? Recent theoretical work suggests that the accelerating seismic release sequence is a symptom of increasing long-wavelength stress correlation in the fault region. A more traditional explanation, based on Reid's elastic rebound theory, argues that an accelerating sequence of seismic energy release could be a consequence of increasing stress in a fault system whose stress moment release is dominated by large events. Both of these theories are examined using two discrete models of seismicity: a Burridge-Knopoff block-slider model and an elastic continuum based model. Both models display an accelerating release of seismic energy prior to large simulated earthquakes. In both models there is a correlation between the rate of seismic energy release with the total root-mean-squared stress and the level of long-wavelength stress correlation. Furthermore, both models exhibit a systematic increase in the number of large events at high stress and high long-wavelength stress correlation levels. These results suggest that either explanation is plausible for the accelerating moment release in the models examined. A statistical model based on the Burridge-Knopoff block-slider is constructed which indicates that stress alone is sufficient to produce accelerating release of seismic energy with time prior to a large earthquake.

The Plausibility of Long-wavelength Stress Correlation or Stress Magnitude as a Mechanism for Precursory Seismicity: Results from Two Simple Elastic Models

Michael E. Winter

Papers

N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data

Autonomous hyperspectral end-member determination methods

Hyperspectral processing in graphical processing units

Resolution enhancement of hyperspectral data using multispectral imagery

The Plausibility of Long-wavelength Stress Correlation or Stress Magnitude as a Mechanism for Precursory Seismicity: Results from Two Simple Elastic Models