To simulate an image of a new area, only the image file steps
(a) and (b) and the simulation steps (a) and (b) have to
be recomputed, provided the radar-processor combination re-
mains. The texture of simulated image speckle is related to
the resolution of the radar. It is represented mathematically
by the autocorrelation function of the speckle. The intensity
distribution of the speckle is related to the number and in-
dependence of the looks. The authors proved with a number
of test speckle data sets that the parameters of the speckle
(autocorrelation shape and intensity distribution) vary with,
and only with the appropriate parameters.
This approach, which requires exact sensor specifications,
is very accurate in considering the spatial characteristics of
speckle noise. Multiple looks as well as the difference between
pixel size and resolution cell are taken into account.
More recently, the implementation of speckle in a raw sig-
nal simulator is described by [Franceschetti, 1992]. In the
Synthetic Aperture Radar Advanced Simulator (SARAS) pre-
sented, the statistical features are implemented on the phys-
ical model and not on the final image. The height profile
of the scene is approximated by square plane facets, large
in terms of the incident wavelength, but small when com-
pared to the resolution cell. Each facet is characterized by
the coordinates of its vertices and by the electro-magnetic
parameters (permittivity and conductivity) of the underlying
material. The computation of individual facet backscatter-
ing takes into account local incidence angle, polarization of
the incident wave, the facet's roughness and any shadowing
effect, if present. The small scale statistics are considered
by a large number of uncorrelated scatterers per facet, so
that the facets' return is characterized by a uniform phase
and Rayleigh amplitude distribution. The correct large scale
statistical simulation due to irregularities of the macroscopic
terrain profile is modeled by associating with each facet a
random displacement of three of its four vertices. The small
and large scale characterization of the electro- magnetic scat-
tering results in the inclusion of the appropriate statistics of
the speckle on the raw signal and, after computation, on the
image. The simulator output, which is the SAR raw signal,
is the appropriate superposition of returns from each facet.
The efficient summation of all returns is accomplished via
two-dimensional FFT code and an asymptotic evaluation of
the system transfer function.
This simulator is based on a physical model which takes into
account the elevation profile together with shadows and lay-
over, terrain electromagnetic properties together with fre-
quency and polarization dependence, and small as well as
large scale statistics. With exact specifications, various dif-
ferent sensor types can be handled by this simulator.
[Wiles, 1993] deals with a particular data set, namely Mag-
ellan images of planet Venus. Simulated imagery is used to
test a correlation algorithm developed for the automated de-
tection of volcanos on Venus. A control experiment is carried
out to calibrate the ability both of humans and the machine
to identify small 'pit like' features in the presence of speckle
noise. To achieve this, it was necessary to produce simulated
radar images of synthetic terrain, designed to resemble Mag-
ellan imagery as closely as possible. This procedure involved
several stages:
1. Production of artificial terrain: A Digital Elevation
Model (DEM) was produced which would closely re-
semble the morphology of volcanic pits on Venus.
22
2. Radar image simulation: A radar image simulation de-
scribed in [Leberl, 1990] was employed, the effect of
speckle was modeled separately and added to the final
image (see below).
3. Scene generation: Artificial scenes were generated for
a whole range of pit diameters from 2 - 16 pixels. The
pits were at a random location within the scene.
4. Addition of speckle: The effects of speckle were sim-
ulated by using a Rayleigh random number generator
to produce a speckle image of the same size as the
simulated image, with a mean value of 1.0. To incor-
porate multiple looks, several such images were gener-
ated using different random number seeds. For simu-
lated Magellan images, five of the speckle images were
averaged together. Finally, since speckle noise is mul-
tiplicative, the artificial scene was multiplied by the
five-average speckle image pixel by pixel.
5. Resolution degradation: The last stage of the data
simulation was to emulate the resampling of Magellan
images. Therefore a 3x3 local neighborhood blurring
was employed. The blurring kernel was chosen so as
to mimic the resampling of typical Magellan resolution
cells of 150m x 110m into 75m x 75m pixels.
With the so generated synthetic data, [Wiles, 1993] showed
that their correlation algorithm performed at least as good as
human observers. The speckle simulation model used takes
both multiple looks and the difference between pixel size and
resolution cell into consideration.
3 IMPLEMENTATION AND RESULTS
Starting point of our implementation was an already exist-
ing SAR image simulator which uses a DEM and knowledge
about the sensor flight path to generate a simulated noise-free
image. Therefore, we only deal with the generation of SAR
speckle at the image level, by modeling its statistical proper-
ties, as opposed to the more basic incorporation of speckle at
the signal level. Due to the multiplicative nature of speckle,
the simulated noise-free image is then multiplied by a sepa-
rately generated speckle file. The simulation program used
to produce the noise-free image is part of the RSG software
package of JOANNEUM RESEARCH [JR, 1993]. The al-
gorithms were implemented in [IDL, 1994] (Interactive Data
Language). Performance evaluation was carried out by visual
comparison with real SAR images.
Figure 1 shows a section of a real ERS-1 image of the Ötztal
test site, a highly mountainous terrain in Tyrol, Austria. This
image was processed using 3 independent looks. The size of
a resolution cell on the ground is 25m x 25m, and the final
pixel size is 12.5m x 12.5m. A simulated image of the same
scene, but without speckle noise, can be seen from Figure 2.
The goal is now to reduce the differences between the two
images by including simulated speckle noise.
Since the statistical properties of speckle noise can be de-
scribed by a Rayleigh probability distribution, our first ap-
proach was to multiply the simulated image pixel by pixel
with a speckle file of the same size with Rayleigh distributed
random numbers. A Rayleigh distributed random numbers Z
can be generated from a uniformly distributed random num-
ber u, as provided in IDL, by using
Z — 4 —2c? In (1 — v) (5)
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
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