EOS 740 Hyperspectral Imaging Systems

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EOS 740 - Hyperspectral Imaging Systems
Class Instructors Dr. Richard B.
Gomez rgomez_at_gmu.edu Dr. Ronald G.
Resmini ronald.g.resmini_at_boeing.com
LECTURE 9 (1 April 05)
George Mason University School of Computational
Sciences Spring Semester 2005 28 January 6 May
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Outline

• Finish algorithms
• Thermal infrared remote sensing
• Theory
• SEBASS
• Working with TIR in ENVI
• Seminar next week, 8 April
• Your semester project status

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Algorithms (continued)
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Constrained Energy Minimization (CEM)

• The description of CEM is similar to that of
  OSP/DSR (previous slides)
• Like OSP and DSR, CEM is an Orthogonal Subspace
  Projection (OSP)family algorithm
• CEM differs from OSP/DSR in the following,
  important ways
• CEM does not simply project away the first n
  eigenvectors
• The CEM operator is built using a weighted
  combination of theeigenvectors (all or a subset)
• Though an OSP algorithm, the structure of CEM is
  equally readily observed bya formal derivation
  using a Lagrange multiplier

• CEM is a commonly used statistical spectral
  matched filter
• CEM for spectral remote sensing has been
  published on for over 10 years
• CEM has a much longer history in the
  multi-dimensional/array signalprocessing
  literature
• Just about all HSI tools today contain CEM or a
  variant of CEM
• If an algorithm is using M-1d as the heart of its
  filter kernel (where M is thedata covariance
  matrix and d is the spectrum of the target of
  interest), thenthat algorithm is simply a CEM
  variant

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• The statistical spectral matched filter (SSMF)
• Derivation in detail
• Application of the filter
• Statistics
• Endmembers (FBA/MCEM)
• Interpretation of results
• Many algorithms are actually the basic SSMF
• Different ways to apply the filter/application
  strategies(i.e., in-scene spectra/library
  spectra)
• Matched filter in ENVI

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Derivation taken from
Stocker, A.D., Reed, I.S., and Yu, X., (1990).
Multi-dimensional signal processing for
electro-Optical target detection. In Signal
and Data Processing of Small Targets 1990,
Proceedingsof the SPIE, v. 1305, pp. 218-231.
J of Bands
Form the log-likelihood ratio test of Hº and H1
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Some algebra...
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A trick...recast as a univariable problem
After lots of simple algebra applied to the r.h.s
Now, go back to matrix-vector notation
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Take the natural log
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The vector QTx is a projection of the original
spectraldata onto the eigenvectors of the
covariance matrix, M, which corresponds to the
principal axes of clutterdistribution. Stocker
et al., 1990.
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Further SCR gain is obtained by forming the
optimumweighted combination of principal
components usingthe weight vector
Direct quote from Stocker et al., 1990.
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Constrained Energy Minimization (CEM)
(Harsanyi et al., 1994)
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Note...

• See also the Lagrange multiplier derivation
• Previous techniques exploit shape and albedo
• this can cause problems...
• Sub-classes of algorithms developed to mitigate
  this
• shape, only, operators
• MED, RSD of ASIT, Inc.
• MTMF of ENVI

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Last Class of Algorithms

• Spectral feature fitting/derivativespectroscopy
• Spectral parameterizations
• Wavelets
• Band depth/band depth mapping
• Application strategies (i.e., in-scenespectra/lib
  rary spectra)
• Mixed pixels...

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Another Note...

• Performance prediction/scoring/NP-Theory, etc...
• Hybrid techniques
• still some cream to be skimmed...
• Caveat emptor...
• lots of reproduction of work already accomplished
• who invented what? when?
• waste of resources
• please do your homework!read the lit.!

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Thermal Infrared (TIR) Remote Sensing...
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Reflective vs. Emissive
Reflective Band Emissive Band Physics
Reflected sunlight Direct thermal
emission Complex phenomena Simpler phenomena
Surface reflectivity Surface
temperature Illumination geometry Emissivity
Phenomena Familiar Familiar
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Properties of MWIR/LWIR

• Day and Night Operations
• Material Identification/Quantification
• Gas Identification/Quantification
• Fingerprint Spectral Region
• Better T measurements (ideally)
• Physics-Based Algorithms
• True for all band regions

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A Bit of Theory
The Planck or Blackbody Radiation Equation
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An Energy Balance
Good absorbers are good emitters
Kirchhoffs Law
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Stefan-Boltzmann Law
Two surfaces radiating at each other
What happens when T1 T2?
View Factor Algebra and Radiant Exchange...
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BTW...M for an HSI band is
BTW...(again)...are we in irradiance or radiance?
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Some More Interesting Stuff...
Wiens Displacement Law
A 2898 mm.K
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The radiant exitance of the sun is
The total flux from the surface of the sun is
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Some Values in the Previous Equations

• k Boltzmann Gas Constant 1.38 x 10-23 J/K
• s Stefan-Boltzmann Constant 5.67 x 10-8
  W/m2.K4
• c Speed of Light 2.9979 x 108 m/sec
• h Plancks Constant 6.6256 x 10-34 J.sec

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The Basic TIR RT Expression
Just about all papers on TIR HSI will start with
this basic RT expression. Its not the only one to
use what about other terms from the Big
Equation?
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Atmospheric Compensation
In-Scene Atmospheric Compensation (ISAC)
Young, S.J., Johnson, R.B., and Hackwell, J.A.,
(2002). An in-scene method for atmospheric
compensation of thermal hyperspectral data.
Journal of Geophysical Research, v. 107, no. D24,
4774, doi10.1029/2001JD001266, 20 p.
Start with
Let
Get
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Atmospheric Compensation (continued)

• Calculate a brightness temperature for each
  spectrum
• Calculate Planck function radiance for
  that temperature
• Plot Ll vs. Planck radiance
• Interested in blackbodies thus e 1

Get

• Fit a line to tops of clusters where LS is large
  as is e

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Atmospheric Compensation (continued)

• Note from linear equation that you get t and Lu
• Subtract Lu from original radiance spectra
• Divide by t
• Left with ground leaving radiance (GLR) spectra
• Must now apply temperature/emissivity
  separation(TES)
• Refer to Young et al., (2002) for more details

Other Theres also AAC and EELM
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Temperature/Emissivity Separation (TES)
The Normalized Emissivity Method (NEM)

• On a pixel-by-pixel basis
• Find the maximum radiance value
• Assume e 0.97 (or some such value)
• Find T by inverting the Planck function
• Divide original GLR spectrum but thePlanck
  function just calculated

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There are lots of TES routines.
See also
Kaiser, R. D. (1999), Quantitative comparison of
temperature / emissivity algorithm performance
using SEBASS data. SPIE Vol. 3717, pp. 47-57.
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Exploitation of TIR HSI

• Atmospheric compensation/TES
• Otherwise, apply algos. already discussed!
• TIR HSI are also points in n-D hyperspace
• Radiance, GLR, emissivity, temp.
• Which one? When? Why?
• How you conceive of/think of your data...
• ENVI spectral library is in reflectance
• Apply Kirchhoffs Law (e 1 r)

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The SEBASS TIR HSI Sensor...
SEBASS Radiance Units Are
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TIR Exploitation with ENVI...
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TIR HSI Applications

• Day/night remote sensing
• Gas phase remote sensing
• Solid material detection, identification, and
  quantification
• Precision thermometry T 0.01C
• Surveillance / security
• Geology / mineral mapping / volcanology
• Bowers and Resmini (2004)
• Others...many others!

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MWIR HSI

• Reflected plus emittedduring the day
• MWIR at night is analogous to LWIR
• Reflected plus emittedvery complicated
• Not much more will be said now
• See the following excellent, recently
  publishedreview article

Boyd, D., and Petitcolin, F., (2004). Remote
sensing of the terrestrial environment using
middle infrared radiation (3.0-5.0 mm).
International Journal of Remote Sensing, v. 25,
no. 17, September, pp. 3343-3368.
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• Your semester project status?
• Got data?