fferent
d, and
nd the
bution
tischen
ieben
nd von
vie der
square
se mit
image
zimuth
to sta-
]. The
ayleigh
ibuted,
ive ex-
N non-
ion for
m. As
stribu-
inguish
ors. In
sensor
an ap-
image.
> phys-
1g into
a high
üins in-
image
ing ge-
image
peckle
its sta-
'adows
iniques
we de-
d algo-
g SAR
image simulator. The results obtained from application to
ERS-1 images are presented and evaluated by visual compar-
ison with the corresponding real image.
2 SPECKLE SIMULATION METHODS
Whereas a considerable body of literature deals with SAR
speckle filtering, the topic of SAR speckle simulation can
only be found in a limited number of publications.
An early work suited to the analog representation of radar
images on film was published by [Holtzman, 1978]. In 1978,
when this paper was published, the intensity of the video sig-
nal exiting the receiver was recorded on film, and this process
is modeled by the simulator. The starting point for the radar
simulation imaging model (gray tone equation) is the pre-
diction of the power reflected from each resolvable ground
element (resolution cell). It is assumed that the ground can
be modeled as a collection of homogeneous regions, each at
least the size of a resolution cell.
After the ground truth data base (terrain feature model) of
the described site has been specified, the reflectivity data for
the various categories included in the data base have been
obtained, and the complex geometry relating the radar plat-
form to the scene has been determined, the imaging model is
used to calculate the power reflected from the ground back
to the radar for each pixel in the image. The return power
from a single resolution cell is given by the radar equation
242 O0
= P:G‘X\‘0 A (1)
(4x)* R^
where the average transmitted power is represented by P, the
two way gain of the transmitting/receiving antenna is given
by G?, and the transmitted wavelength is given by A; the re-
flectivity model, which is a function of wavelength and local
incidence angle, among others, is o°; the area of the resolu-
tion cell on the ground being sensed is A; and the distance
from the antenna to the resolution cell being sensed is R.
Speckle statistics, depending on the number of independent
looks, are considered at this level:
PPS
Pr = (=) (Y (2)
where Pr is the expected value of the return power from a
resolution cell, Ÿ is a random number with a standard chi-
square distribution having 2N degrees of freedom, and N
is the number of independent looks. When the number of
independent samples being averaged is large, (2) becomes
=Pr(1+ 5) (3)
where z is a Gaussian random variable with zero mean and
unit variance. This return power calculated for each resolu-
tion cell is coded into one pixel in the simulated image using
the gray tone equation:
n—1
2
Gr = Gre +
(718 Pr +y1g M 1g K —lg[c)" Kc])
(4)
where 2"^! denotes the number of possible gray values, x
is the base 10 logarithm of the dynamic range of the radar
signal being mapped into the linear range portion of the film
TI
dynamic range, and M is the transfer function of the radar re-
ceiver; K is a constant depending upon the exposure time and
the film processing and development, and y is a positive con-
stant representing the slope of the linear portion of the film
curve of density versus logarithm of exposure; Ic, Kc, Gre
are calibration parameters.
The graytone equation (4) represents the conversion of the
signal returned from each resolution element into the appro-
priate gray value for each image pixel after the elevation pro-
file, dielectric categories, and spatial relationships of the var-
ious cells have been properly considered. Multiple looks are
also taken into account.
The approach to simulation of SAR image products described
by [Rainey, 1988] departs from most other simulation algo-
rithms in the method of speckle generation. Speckle is pre-
pared corresponding to the frequency, weightings and look av-
eraging strategy of the radar-processor combination desired,
and then multiplied by the source scene data preconditioned
by the desired resolution. The method allows output pixel
spacings to be specified independent of more fundamental
system parameters. This accounts for the fact that, when
dealing with SAR, pixel and resolution are two quite different
concepts and quantities. Fundamental SAR spatial behavior
occurs at the resolution cell level, whereas digital image rep-
resentation is at pixel level. So, the authors argue that it is
not sufficient to simulate speckle simply by imposing a ran-
dom distribution on each pixel, and treating adjacent pixels
as statistically independent. Their approach is as follows:
1. Image File
(a) From a source file of ideal imagery, the reflectivity
map, create one unspeckled image by convolving
the source against the (desired) two-dimensional
impulse response function.
(b) If additive noise is to be included, add a constant
to the resulting intermediate image.
2. Speckle File
(a) Prepare N files each of which is a complex Gaus-
sian pseudo-random field, essentially a "white
noise’ source. Adjacent samples should be sta-
tistically independent.
(b) Bandpass filter each file with the two-dimensional
frequency spectra corresponding to the radar and
processor to be simulated. Each filter should be
weighted and overlapped as per the described
system.
(c) Square law detect the filter outputs, and sum,
again using any weighting representative of the
system. Normalize.
(d) Store the resulting real variates as a "speckle file’.
This file, of course, is also in two dimensions.
3. Simulation
(a) Subsample the image file and the speckle file to
match the desired pixel spacing.
(b) Pixel by pixel, multiply the two files together to
create the final speckled image files.
For a given radar-processor combination the computationally
expensive creation of the speckle file is computed only once.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
