IEEE Geoscience and Remote Sensing Magazine - June 2017 - 38

High-Resolution HS Image
Denoising
Blurring and
Downsampling

Spectral Response

Add Noise

Add Noise

Observed HS Image

Observed MS Image

HS-MS Fusion
Estimated High-Resolution
HS Image
Denoising

Quality Measures

FIGURE 5. A flow diagram of the evaluation methodology, including
the standard simulation procedure (used, e.g., in [56]).

simulation, spatial simulation, and noise simulation and
2) an end-to-end simulation that takes into account the entire image acquisition and processing chain, starting from
raw data. The first strategy is used for data sets 1-7, and the
second strategy is used for data set 8.
standard simULation
The flow diagram of the evaluation methodology with the
standard simulation is shown in Figure 5. Here, spectral
simulation is performed to generate the MS image by degrading the reference image in the spectral domain using MS SRFs as filters. For the diversity of MS sensors,
the SRFs of four MS imagers
were used for spectral simulation, i.e., WV-2 for data set 5;
TO IMPROVE THE
WV-3 for data sets 1 and 2;
RELIABILITY OF
QuickBird for data sets 3, 4,
QUANTITATIVE EVALUATION,
and 6; and Sentinel-2 VNIR
A DENOISING METHOD
bands at a 10-m GSD for data
set 7 (see Table 2).
IS APPLIED TO THE
Figure 6 shows overlaps
ORIGINAL IMAGES TO
of
SRFs
between the HS-MS
INCREASE THE SNRs OF THE
imagers for all data sets. For
REFERENCE IMAGES.
data sets 1, 2, 5, and 6, the MS
SRFs evenly cover most of the
spectral range of the HS imager. In contrast, there is no high-resolution MS image in
the SWIR for data sets 3, 4, and 8. The latter case is more
challenging and was included in the experiment to investigate the impact of the SRF overlap between HS and MS imagers on the quality of fused data. Spatial simulation was
performed to generate the low-resolution HS image using
an isotropic Gaussian PSF with an FWHM of the Gaussian
38

function equal to the resolution ratio between the GSDs
of both input images. Five different GSD ratios, i.e., 3, 4,
5, 6, and 8, were included for spatial simulation in the
standard simulation (see Table 2) to simulate multiple realistic combinations of spaceborne HS-MS sensors, shown
in Figure 2. After spectral and spatial simulations, banddependent Gaussian noise was added to the simulated HS-
MS images. For realistic noise conditions, an SNR of 35 dB
was simulated in all bands.
end-to-end simULation
On the basis of data set 8, the EnMAP and Sentinel-2 L2a
(orthorectified surface reflectance data) products were simulated using the sensor end-to-end simulation tools EnMAP
end-to-end simulation [71] and Sentinel-2 end-to-end simulation [72]. These tools comprise forward and backward
simulators that simulate the data-acquisition procedure and
the calibration and preprocessing chain, respectively, from
spatially and spectrally oversampled data to the final EnMAP and Sentinel-2 products [75]. The forward simulator
consists of four independent atmospheric, spatial, spectral,
and radiometric modules. The spatial and spectral modules
include resampling an image in the spatial and spectral domains using the sensor-specific PSFs and SRFs, respectively. The radiometric module transformed the at-sensor radiance to a digital number (DN) by simulating instrumental
noise and calibration coefficients.
The backward simulator consists of calibration modules
such as nonlinearity, dark current, and absolute radiometric calibration and preprocessing modules such as radiometric calibration and atmospheric correction. Compared
to the standard simulation, the end-to-end simulation can
generate more realistic data sets that include errors such
as sensor-specific noise and residual errors of atmospheric
correction. Sentinel-2 VNIR images with a GSD of 10 m
(bands 2, 3, 4, and 8) were used as the MS data only, even
though the 20-m GSD SWIR images could potentially be
used in addition for enhancing the EnMAP image, which
is of a 30-m GSD.
QUALITY MEASURES
We use the following four complementary and widely
used quality measures for the quantitative fusion assessment: 1)  peak SNR (PSNR), 2) spectral angle mapper (SAM), 3)  erreur relative globale adimensionnelle de
synthèse (ERGAS), and 4) Q2 n. Let X ! R B # P denote the
reference HS image with B spectral bands and P pixels.
X = [x 1, ..., x B] T = [x 1, ..., x P], where x i ! R P # 1 is the ith band
( i = 1, ..., B ) and x j ! R B # 1 is the spectral signature of the
jth pixel ( j = 1, ..., P ). W
X denotes the estimated HS image.
Psnr
The PSNR is used to evaluate the spatial reconstruction
quality of each band. It is the ratio between the maximum
power of a signal and the power of residual errors. The
PSNR of the ith band is defined as
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