Image Restoration and Atmospheric Correction

1
Image Restoration and Atmospheric Correction

• Lecture 3
• Prepared by R. Lathrop 10/99
• Revised 2/04

2
Analog-to-digital conversion process

• A-to-D conversion transforms continuous analog
  signal to discrete numerical (digital)
  representation by sampling that signal at a
  specified frequency

Continuous analog signal
Discrete sampled value
Radiance, L
dt
Adapted from Lillesand Kiefer
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Analog-to-digital conversion process

• Sampling rate - must be twice as high as the
  highest frequency in the signal if that highest
  frequency is to be resolved (Nyquist frequency)
• Example if highest frequency 4 cycles/sec then
  the sampling rate should be at least 8/sec

dt 1sec
Sweep across 4 line pairs in one second, need to
take signal measurement on both line and spacing
in between, thus 8 measures pr sec
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Signal-to-Noise Ratio (SNR)

• SNR measures the radiometric accuracy of the data
• Want high SNR
• Over low reflectance targets (I.e. dark pixels
  such as clear water) the noise may swamp the
  actual signal

True Signal
Observed Signal
Noise

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Noise Removal

• Noise extraneous unwanted signal response
• Noise removal techniques to restore image to as
  close an approximation of the original scene as
  possible
• Destriping correct defective sensor
• Line drop average lines above and below
• Bit errors random pixel to pixel variations,
  average neighborhood (e.g., 3x3) using a moving
  window (convolution kernel)

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Radiometric correction

• Radiometric correction to correct for varying
  factors such as scene illumination, atmospheric
  conditions, viewing geometry and instrument
  response
• Objective is to recover the true radiance
  and/or reflectance of the target of interest

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Units of EMR measurement

• Irradiance - radiant flux incident on a receiving
  surface from all directions, per unit
  surface area, W m-2
• Radiance - radiant flux emitted or scattered by a
  unit area of surface as measured through a solid
  angle, W m-2 sr-1
• Reflectance - fraction of the incident flux that
  is reflected by a medium

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For more info, go to http//ltpwww.gsfc.nasa.gov/
IAS/handbook/handbook_toc.html
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Radiometric response function

• Conversion from radiance (analog signal) to DN
  follows a calibrated radiometric response
  function that is unique for channel
• Inverse relationship permits user to convert from
  DN back to radiance. Useful in many quantitative
  applications where you want to know absolute
  rather than just relative amounts of signal
  radiance
• Calibration parameters available from published
  sources and image header

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Radiometric response function

• Radiance to DN conversion DN G x L
  B where G slope of response function
  (channel gain) L spectral radiance B
  intercept of response function (channel offset)
• DN to Radiance Conversion L (LMAX -
  LMIN)/255 x DN LMIN where LMAX
  radiance at which channel saturates LMIN
  minimum recordable radiance

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Radiometric response function
Spectral Radiance to DN
DN to Spectral Radiance
255
Lmax
Slope channel gain, G
DN
L
Slope (Lmax Lmin) / 255
Lmin
0
Lmin
L
Lmax
0
DN
255
Bias Y intercept
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Radiometric response functionExample Landsat 5
Band 1

• From sensor header, get Lmax Lmin
• Lmax 15.21 mW cm-2 sr-1 um-1
• Lmin -0.15200000 mW cm-2 sr-1 um-1
• L -0.15200000 ((15.21 - - 0.152)/255) DN
• L -0.15200000 (0.06024314) DN
• If DN 125, L 7.37839 mW cm-2 sr-1 um-1

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Radiometric response functionExample Landsat 7
Band 1

• Note that Landsat Header Record refers to gain
  and bias, but with different units (W m-2 sr-1
  um-1)
• L Bias (Gain DN)

• If DN 125, L ?

Landsat Science Data Users Handbook ltpwww.gsfc.n
asa.gov/IAS/handbook/handbook_htmls/chapter11
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DN-to-Radiance conversionExample Landsat ETM
Band Gain Bias
1 0.7756863 -6.1999969
2 0.7956862 -6.3999939
3 0.6192157 -5.0000000
4 0.6372549 -5.1000061
5 0.1257255 -0.9999981
6 0.0437255 -0.3500004

• Note that Landsat Header Record refers to gain
  and bias, but with different units (W m-2 sr-1
  um-1)

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Radiometric response functionExample Landsat 7
Band 1

• Note that Landsat Header Record refers to gain
  and bias, but with different units (W m-2 sr-1
  um-1)
• Gain 0.7756863 mW cm-2 sr-1 um-1
• Bias -6.1999969 mW cm-2 sr-1 um-1
• L -6.1999969 (0.7756863) DN

• If DN 125, L 90.76079 W m-2 sr-1 um-1
• Same 9.076079 mW cm-2 sr-1 um-1

Landsat Science Data Users Handbook ltpwww.gsfc.n
asa.gov/IAS/handbook/handbook_htmls/chapter11
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Radiometric response functionExample Landsat 5
Thermal IR

• Gain 0.005632 mW cm-2 sr-1 um-1
• Bias 0.1238 mW cm-2 sr-1 um-1
• L 0.1238 (0.005632) DN

To convert to at-satellite temperature (o K) T
1260.56 / loge (60.776/L) 1 Remember 0oC
273.1K
For more details see Markham Barker. 1986.
EOSAT Landsat Technical Notes v.1, pp.3-8.
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At-Satellite Reflectance

• To further correct for scene-to-scene differences
  in solar illumination, it is useful to convert to
  at-satellite reflectance. The term at-satellite
  refers to the fact that this conversion does not
  account for atmospheric influences.
• At-Satellite Reflectance, pl (p Ll d2 ) /
  (ESUNl cosq)
• Where
• Ll spectral radiance measured for the specific
  waveband
• q solar zenith angle
• ESUN mean solar exoatmospheric irradiance (W
  m-2 um-1), specific to the particular wavelength
  interval for each waveband, consult the sensor
  documentation
• d Earth-sun distance in astronomical units,
  ranges from approx. 0.9832 to 1.0167, consult an
  astronomical handbook for the earth-sun distance
  for the imagery acquisition date

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Solar Zenith angle
qo 0
qo 60
qo solar zenith angle qo 0 cosqo 1 As qo
cosqo
Solar elevation angle 90 - zenith angle
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At-Satellite Reflectance Example Landsat 7 Band
1

• If Acquisition Date Dec. 1, 2001
• At-Satellite Reflectance ?

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http//aa.usno.navy.mil/data/docs/AltAz.html
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Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units Table 11.4 Earth-Sun Distance in Astronomical Units
Julian Day Distance Julian Day Distance Julian Day Distance Julian Day Distance Julian Day Distance
1 .9832 74 .9945 152 1.0140 227 1.0128 305 .9925
15 .9836 91 .9993 166 1.0158 242 1.0092 319 .9892
32 .9853 106 1.0033 182 1.0167 258 1.0057 335 .9860
46 .9878 121 1.0076 196 1.0165 274 1.0011 349 .9843
60 .9909 135 1.0109 213 1.0149 288 .9972 365 .9833
Landsat Science Data Users Handbook ltpwww.gsfc.n
asa.gov/IAS/handbook/handbook_htmls/chapter11

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Solar Spectral Irradiances Landsat ETM
Watts m-2 um-1
Band 1 1969.0
Band 2 1840.0
Band 3 1551.0
Band 4 1044.0
Band 5 225.70
Band 7 82.07
Band 8 1368.0
Landsat Science Data Users Handbook ltpwww.gsfc.n
asa.gov/IAS/handbook/handbook_htmls/chapter11
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At-Satellite Reflectance Example Landsat 7 Band
1 pl (p Ll d2 ) / (ESUNl cosq)

• Dec. 1, 2001 ? Julian Day 335
• Earth-Sun d 0.986
• ESUNl 1969.0
• Cosq Cos(63.54) 0.44558
• Ll 90.76079 W m-2 sr-1 um-1
• pl (3.1415990.760790.9862)/(1969.00.44558)
• pl 277.20558/877.34702 0.31596

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Basic interactions between EMR and the atmosphere

• Scattering, S
• Absorption, A
• Transmission, T
• Incident E S A T
• Within atmosphere, determined by molecular
  constituents, aerosol particles, water vapor

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Satellite Received Radiance
Total radiance, Ls path radiance Lp target
radiance Lt Target radiance, Lt 1/p RTqu (E0
deltalTqo cosqo deltal Ed) Where R average
target reflectance qo solar zenith angle Qu
nadir view angle Tqo atmospheric transmittance
at angle q to zenith E0l spectral solar
irradiance at top of atmosphere Ed diffuse sky
irradiance (W m-2) Delta l band width, l2 l1
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Atmospheric correction

• Atmospheric correction procedures are designed to
  minimize scattering absorption effect due to
  the atmosphere
• Scattering increases brightness. Shorter
  wavelength visible region strongly influenced by
  scattering due to Rayleigh, Mie and nonselective
  scattering
• Absorption decreases brightness. Longer
  wavelength infrared region strongly influenced by
  water vapor absorption.

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Atmospheric correction techniques

• Absolute vs. relative correction
• Absolute removal of all atmospheric influences is
  difficult and requires a number of assumptions,
  additional ground and/or meteorological reference
  data and sophisticated software (beyond the
  scope of this introductory course)
• Relative correction takes one band and/or image
  as a baseline and transforms the other bands
  and/or images to match

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Atmospheric correction techniques Histogram
adjustment

• Histogram adjustment visible bands, esp. blue
  have a higher MIN brightness value. Band
  histograms are adjusted by subtracting the bias
  for each histogram, so that each histogram starts
  at zero.
• This method assumes that the darkest pixels
  should have zero reflectance and a BV 0.

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Atmospheric correction techniques Dark pixel
regression adjustment

• Select dark pixels, either deep clear water or
  shadowed areas where it is assumed that there is
  zero reflectance. Thus the observed BV in the
  VIS bands is assumed to be due to atmospheric
  scattering (skylight).
• Regress the NIR vs. the VIS. X-intercept
  represents the bias to be scattered from the VIS
  band.

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Atmospheric correction techniques Scene-to-scene
normalization

• Technique useful for multi-temporal data sets by
  normalizing (correcting) for scene-to-scene
  differences in solar illumination and atmospheric
  effects
• Select one date as a baseline. Select dark,
  medium and bright features that are relatively
  time-invariant (I.e., not vegetation). Measure DN
  for each date and regress. DB b1, t2 a b
  DN b1, t1

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Scene-to-Scene Normalization Example Landsat 5
vs Landsat 7Landsat 7 Sept 01 Landsat 5
Sept 95
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Scene-to-Scene NormalizationExample Landsat 5
vs Landsat 7Landsat 5 Sept 95 Landsat 7 Sept
99 01
99 R2 0.971 01 R2 0.968
99 R2 0.932 01 R2 0.963
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Terrain ShadowingUSGS DEM Landsat
ETM Dec 01
Solar elevation 26.46 Sun Azimuth 158.78
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Terrain correction

• To account for the seasonal position of the sun
  relative to the pixels position on the earth
  (I.e., slope and aspect)
• Normalizes to zenith (sun directly overhead)
• Lc Lo cos (Qo) / cos(i) where Lc
  slope-aspect corrected radiance Lo
  original uncorrected radiance
  cos (Qo) suns zenith angle cos(i)
  suns incidence angle in relation to the
  normal on a pixel (i Oo - slope)

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Cosine Terrain correction
Sensor
Qo
Sun
Lc Lo cos (Qo) / cos(i)
i
90o
Terrain assumed to be a Lambertian surface
Adapted from Jensen
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Terrain correction

• Terrain Correction algorithms arent just a black
  box as they dont always work well, may introduce
  artifacts to the image
• Example see results on right from ERDAS IMAGINE
  terrain correction function appears to
  overcorrect shadowed area