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For the retrieval of the surface reflectance, the LUTs were
adjusted only for the pixel location in the swath and water
vapour content using a bi- linear interpolation routine (Press et
al, 1992) since single values for the other LUT parameters
were used for the entire cube. For this purpose, the water
vapour content was estimated for each pixel in the scene with
an iterative curve fitting technique (Staenz et al., 1997). The
surface reflectance was then computed for each pixel as
described in Staenz and Williams (1997).
The next processing step performs an empirical correction for
irregularities in the reflectance data (band-to-band errors) that
may have originated in the sensor, or that may have resulted
from the approximation made in atmospheric modelling and the
selection of RT code input parameters. These band-to-band
errors were removed by calculating correction gains and offsets
using spectrally flat targets (Staenz et al., 1999). The removal
of these errors is referred to as post-processing.
3.3 Endmember Selection and Spectral Unmixing
Endmembers, required for the spectral unmixing, were selected
from the data cubes themselves using an automated method, the
Iterative Error Analysis (IEA: Szeredi et al., 2002). In a first
step, the average spectrum of the scene is used to unmix the
data set. When a data set is unmixed, a residual error image is
produced. These errors, which are also a measure of the
distance in n-dimensional space (n = number of bands) between
the average spectrum and all the spectra of the data set, are
calculated using a least-square estimate between the average
spectrum and the spectrum of each pixel. The next step is to
find the pixel or pixels that encompass the largest errors, i.e.,
that are furthest away from the average spectrum. The user
selects the number of pixels forming these endmembers. This
first endmember is then used to unmix the image cube, and the
average spectrum is discarded. The errors will again be used to
, find the furthest pixels from the first endmember and will create
the second endmember. This process is repeated until the
number of endmembers predetermined by the user is reached.
In this case, 15 endmembers have been selected.
Once all the endmembers were fourtd, the image cube was
unmixed using a constrained linear technique (Shimabukuru
and Smith, 1991; Boardman, 1995). Spectral unmixing uses a
linear combination of a set of endmember spectra to unmix the
composite spectrum into endmember fractions (between O0 and
1) for each pixel of the scene. The reduced (428 nm — 2458 nm)
AVIRIS wavelength range was utilised for the endmember
selection and spectral unmixing.
4.0 FIDELITY ASSESSMENT
The assessment of the fidelity between original and de-
compressed data was carried out at different data processing
levels. The Root Mean Square Error (RMSE) was calculated
between original and de- compressed 16-bit digital numbers
(scaled radiance) data cubes as follows:
RAINE - I 2x YEN Say DAN (xp. — ib
Ho HH. umi E j '
it,
where DN, is the digital number of the de-compressed cube,
DNo is the digital number of the original cube, nx is total
number of pixels in the cube, ny is the number of lines in the
cube, nb is total number of bands in the cube, x and y are the
pixel and line position, respectively and b is the band number.
IAPRS & SIS, Vol.34, Part 7, “Resource and Environmental Monitoring”, Hyderabad, India,2002
In addition, the percent relative absolute difference (PRAD)
was used as a fidelity measure for spectral variations on a pixe:
basis between original and de- compressed data. PRAD is
defined as follows:
MA x y dh Lux, v Ww
PRAD z 100 2 (21
{ :
where Lo is the radiance of the original spectrum and rp is the
radiance in the de-compressed spectrum. Similarly, PRAD was
also calculated for selected bands for all pixels in the scene to
show the spatial variability of the data compression of the
radiance data.
The assessment of the endmember spectra was carried out using
the Average PRAD (APRAD) and Spectral Angle Mapper
SAM; Kruse et al., 1993) as a fidelity measure. These measures
can be written as:
I. ] 4.
APRAD- — M PRAD(US) i3)
Hn Fr
and
1 X
2 i
V em, (n em, (in i
NAA — cos” - i : [4
b | en, np 3 Y ; hs] à
hd FA * { i
i
where emO(b) is the endmember reflectance in band b of the
original cube and emD(b) is the endmember reflectance in band
b of the de-compressed cube. SAM varies between O and 1
where 0 indicates a perfect match between original and de-
compressed endmember spectra. While APRAD provides a
measure of the overall difference between original and de-
compressed endmember spectra, SAM, which is insensitive to
gain factors, gives a good indication about the preservation of
absorption features in the de-compressed data.
The fraction maps for each of the 15 endmembers were
compared using the RMSE.
5.0 RESULTS
5.1 Radiance Data
The RMSE, calculated with equation (1) between original and
de-compressed radiance cubes, increases with increasing data
compression ratio (Tablé 2). A similar trend can be observed
for the spatial within-band differences between original and de-
compressed data expressed via PRAD. As an example, Figure 2
shows the frequency distribution of PRAD, calculated for each
pixel of bands 69 (1011 nm) and 205 (2319 nm), for data
compression ratios of 10:1, 20:1, and 40:1. Both graphs show
the same trend, although larger errors occur in band 205 for all
compression ratios. Most pixels; 99.8 % at compression ratios
of 10:1 and 99.3 % at 20:1, lie within 2.5 % error for band 69
compared to 69.1 % and 65.3 %, respectively, for band 205.
| Compression Matin 11:1 2411 41
RMSE 34d SR 7
ng
CAN
l'able 2 RMSE of the original {average DN, = 4961) and de-
compressed data cubes for different compression ratios. DN,
and RMSE are in DN (scaled radiance).
