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Imaging spectroscopy

Imaging spectroscopy (also spectral imaging or chemical imaging) is similar to color photography, but each pixel acquires many bands of light intensity data from the spectrum, instead of just the three bands of the RGB color model. More precisely, it is the simultaneous acquisition of spatially coregistered images in many spectrally contiguous bands.

Some spectral images contain only a few image planes of spectral data, while others are better thought of as full spectra at every location in the image. For example, solar physicists use spectroheliograms, images of the Sun built up by scanning the slit of a spectrograph, to study the behavior of surface features on the Sun; such a spectroheliogram may have a spectral sensitivity of over 100,000 ( $λ / Δλ$ ) and be used to measure local motion (via the Doppler shift) and even the magnetic field (via the Zeeman splitting or Hanle effect) at each location in the image plane. The hyperspectral images collected by the Opportunity rover, in contrast, have only four wavelength bands and hence are only a little more than 3-color images.

To be scientifically useful, such measurement should be done using an internationally recognized system of units.

One example application is geophysical spectral imaging, which allows quantitative and qualitative characterization of both, the surface and the atmosphere, using geometrically coherent spectrodirectional radiometric measurements. These measurements can then be used for the unambiguous direct and indirect identification of surface materials and atmospheric trace gases, the measurement of their relative concentrations, subsequently the assignment of the proportional contribution of mixed pixel signals (e.g., the spectral unmixing problem), the derivation of their spatial distribution (mapping problem), and finally their study over time (multi-temporal analysis).

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Background

About 300 years ago, in 1704, Sir Isaac Newton published in his ‘Treatise of Light’ (Newton, 1704) the concept of dispersion of light. He demonstrated that white light could be split up into component colours by means of a prism, and found that each pure colour is characterized by a specific refrangibility. The corpuscular theory by Newton was gradually succeeded over time by the wave theory. Consequently, the substantial summary of past experiences performed by Maxwell (1873), resulted in his equations of electromagnetic waves. But it was not until the 19th century that the quantitative measurement of dispersed light was recognized and standardized.

A major contribution was Fraunhofer's discovery of the dark lines in the solar spectrum (Fraunhofer, 1817); and their interpretation as absorption lines on the basis of experiments by Bunsen and Kirchhoff (1863). The term spectroscopy was first used in the late 19th century and provides the empirical foundations for atomic and molecular physics (Born & Wolf, 1999). Significant achievements in imaging spectroscopy are attributed to airborne instruments, particularly arising in the early 1980s and 1990s (Goetz et al., 1985; Vane et al., 1984). However, it was not until 1999 that the first imaging spectrometer was launched in space (the NASA Moderate-resolution Imaging Spectroradiometer, or MODIS).

Also scientific terminology and definitions evolve over time. Presently an imaging spectrometer is usually not any longer defined by a total minimum number of spectral bands (earlier, >10 spectral bands was a justification to use the term imaging spectrometer), rather than by a contiguous (or redundancy) statement of spectral bands.

The term hyperspectral imaging is sometimes used interchangeably with imaging spectroscopy. Due to its heavy use in military related applications, the civil world has established a slight preference for using the term imaging spectroscopy.

Unmixing

Hyperspectral data is often used to determine what materials are present in a scene. Materials of interest could include roadways, vegetation, and specific targets (i.e. pollutants, hazardous materials, etc). Trivially, each pixel of a hyperpsectral image could be compared to a material database to determine the type of material making up the pixel. However, many hyerspectral imaging platforms have low resolution (>5m per pixel) causing each pixel to be a mixture of several materials. The process of unmixing one of these 'mixed' pixels is called hyperspectral image unmixing or simply hyperspectral unmixing.

Models

A solution to hyperspectral unmixing is to reverse the mixing process. Generally, two models of mixing are assumed: linear and nonlinear. Linear mixing models the ground as being flat and incident sunlight on the ground causes the materials to radiate some amount of the incident energy back to the sensor. Each pixel then, is modeled as a linear sum of all the radiated energy curves of materials making up the pixel. Therefore, each material contributes to the sensor's observation in a positive linear fashion. Additionally, a conservation of energy constraint is often observed thereby forcing the weights of the linear mixture to sum to one in addition to being positive. The model can be described mathematically as follows:

$p = A*x\,$

where $p$ represent a pixels observed by the sensor, $A$ is a matrix of material reflectance signatures (each signature is a column of the matrix), and $x$ is the proportion of material present in the observed pixel. This type of model is also referred to as a simplex.

With $x$ satisfying the two constraints: 1. Abundance Nonnegativty Constraint (ANC) - each element of x is positive. 2. Abundance Sum-to-one Constraint (ASC) - the elements of x must sum to one.

Non-linear mixing results from multiple scattering often due to non-flat surface such as buildings and vegetation.

Unmixing (Endmember Detection) Algorithms

There are many algorithms to unmix hyperspecectral data each with their own strengths and weaknesses. Many algorithms assume that pure pixels (pixels which contain only one materials) are present in a scene. Some algorithms to perform unmixing are listed below:

Pixel Purity Index (PPI) - Works by projecting each pixel onto one vector from a set of random vectors spanning the reflectance space. A pixel receives a score when it represent an extremum of all the projections. Pixels with the highest scores are deemed to be spectrally pure.
NFINDR
Gift Wrapping Algorithm
Independent Component Analysis Endmember Extraction Algorithm (ICA-EEA) - Works by assuming that pure pixels occur independently than mixed pixels. Assumes pure pixels are present.
Vertex Component Analysis (VCA) - Works on the fact that the affine transformation of a simplex is another simplex which helps to find hidden (folded) verticies of the simplex. Assumes pure pixels are present.

Abundance Maps

Once the fundamental materials of a scene are determined, it is often useful to construct an abundance map of each material which displays the fractional amount of material present at each pixel. Often linear programming is done to observed ANC and ASC.

Sensors

AVIRIS - aircraft, (224 bands)
MODIS
HyDice
Hyperion - on board the Earth Observing 1 satellite

References

Born, M. & Wolf, E. (1999) Principles of Optics, 7 edn. Cambridge University Press, Cambridge.
Bunsen, R. & Kirchhoff, G. (1863) Untersuchungen über das Sonnenspektrum und die Spektren der Chemischen Elemente. Abh. kgl. Akad. Wiss., 1861.
Fraunhofer, J. (1817) Bestimmung des Brechungs- und Farbenzerstreuungs-Vermögens verschiedener Glasarten, in Bezug auf die Vervollkommnung achromatischer Fernrohre, Vol. 56, pp. 264-313. Gilberts Annalen der Physik.
Goetz, A.F.H., Vane, G., Solomon, J.E., & Rock, B.N. (1985) Imaging spectrometry for earth remote sensing. Science, 228, 1147.
Maxwell, J.C. (1873) A Treatise on Electricity and Magnetism Clarendon Press, Oxford.
Newton, I. (1704) Opticks: Or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light Sam Smith and Benj. Walford, London.
Schaepman, M. (2005) Spectrodirectional Imaging: From Pixels to Processes. Inaugural address, Wageningen University, Wageningen (NL).
Vane, G., Chrisp, M., Enmark, H., Macenka, S., & Solomon, J. (1984) Airborne Visible Infrared Imaging Spec-trometer (AVIRIS): An Advanced Tool for Earth Remote Sensing. European Space Agency, (Special Publication) ESA SP, 2, 751.