Imaging spectroscopy

Some spectral images contain only a few image planes of a spectral data cube, while others are better thought of as full spectra at every location in the image. For example, solar physicists use the spectroheliograph to make 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 resolution of over 100,000 (${\displaystyle \lambda /\Delta \lambda }$) and be used to measure local motion (via the

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

With ${\displaystyle x}$ satisfying the two constraints: 1. Abundance Nonnegativity 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.

There are many algorithms to unmix hyperspectral 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 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.
• N-FINDR ^[2]
• Gift Wrapping Algorithm
• Independent Component Analysis Endmember Extraction Algorithm - works by assuming that pure pixels occur independently than mixed pixels. Assumes pure pixels are present.
• Vertex Component Analysis - works on the fact that the affine transformation of a simplex is another simplex which helps to find hidden (folded) vertices of the simplex. Assumes pure pixels are present.
• Principal component analysis - could also be used to determine endmembers, projection on principal axes could permit endmember selection [Smith, Johnson et Adams (1985), Bateson et Curtiss (1996)]
• Multi endmembers spatial mixture analysis based on the SMA algorithm
• Spectral phasor analysis based on Fourier transformation of spectra and plotting them on a 2D plot.

Non-linear unmixing algorithms also exist: support vector machines or analytical neural network.

Probabilistic methods have also been attempted to unmix pixel through Monte Carlo unmixing algorithm.

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

Planned

• EnMAP

Current and Past

• AVIRIS
  — airborne
• MODIS — on board EOS Terra and Aqua
  platforms
• MERIS — on board Envisat
• Hyperion — on board Earth Observing-1
• Several commercial manufacturers for laboratory, ground-based, aerial, or industrial imaging spectrographs

See also

• Remote sensing
• Hyperspectral imaging
• Full Spectral Imaging
• List of Earth observation satellites
• Chemical Imaging
• Imaging spectrometer
• Infrared Microscopy
• Phasor approach to fluorescence lifetime and spectral imaging
• Video spectroscopy

References