IEEE Geoscience and Remote Sensing Magazine - June 2020 - 88

TABLE 2. THE MULTILAYER STRATEGY COMPARED WITH THE
CELL-BY-CELL STRATEGY.
MULTILAYER
ADVANTAGES Efficient
Simple and feasible
LIMITATIONS

CELL BY CELL
Accurate
Suitable for a variety of
forest scenes

Can calculate scenes only
Difficult to deal with
with similar horizontal distri- huge-volume scatterers,
bution, such as forests of the such as trunks
same specification

volume (volumetric density) of the scatterers, and k 0 is the
propagation constant in free space.
Vegetation in the forest scene is unevenly distributed, so
a single M pq cannot be used for the entire scene. There are
two common strategies for solving this problem. The first is
to divide the vegetation into multiple layers [41]; here, vertical distribution is considered the dominant nonuniform
factor. To account for vertical inhomogeneity, the forest scene
can be viewed as an M-layered, random media construction
above the rough surface. The final transmission matrices can
be written as
T (L) = T1(L 1) T2(L 2) f TM(L M),

(8)

where Tm(L m) can be obtained by (6).
Another technique is the cell-by-cell [46] strategy, which
divides the scene into a number of small cells, with the scatterers in each cell sharing the same attenuation coefficient
[42]. Electromagnetic waves may pass through multiple
cells as they encounter each
scatterer, and the transmisTREES GENERATED BY
sion matrix of each cell can
be calculated by (6). After
L-SYSTEMS ARE QUITE
multiplying
each transmisREALISTIC IN APPEARANCE.
sion matrix along the path,
the final transmission matrix
is obtained and is the same as the calculation method in
(8). The differences between these two strategies are given
in Table 2.
The process of coherent scattering calculation for PolInSAR simulation is summarized as follows:
1) The forest scene is generated based on Monte Carlo
simulation.
2) The tree scene is divided into several layers or many
cells, depending on the characteristics of the forest.
3) The ray-based scattering contribution for each scatterer
is calculated.
4) Coherent summing is performed of the scattered fields
from all scatterers.
For this article, we simulated a forest scene covered
by the same species poplar, so we adopted the multilayer strategy in step 2. We chose this coherent scattering
model because it accounts for the effects of different scattering mechanisms, which makes the simulated image
more realistic.
88

IMAGING SIMULATION
High-quality SAR imaging simulation could be very useful for parameter inversion and system parameter analysis.
As a result, a variety of imaging simulation methods for
vegetation have been proposed. Currently, the approach
frequently used for SAR simulation of forest canopies can
be roughly divided into three categories, according to the
complexity-of-imaging principle.
1) The simplest strategy combines the scattering coefficients
with the projection geometry of SAR systems to directly
generate the scattering-coefficient images [42], [59], [63].
2) Using the ideal impulse response function (IRF) of a
point target, an SAR image can be easily obtained by
convoluting the scattering map with the IRF [64].
3) Some new approaches incorporating a raw-signalgeneration process can simulate more realistic SAR
images [58].
The significant advantage of the imaging technique
described in category  1 is its efficiency, and representative works include the following. Xu and Jin presented
a fast algorithm, the mapping and projection algorithm
(MPA) [63], [65], developed to compute single and multiple scattering, attenuation, and shadowing of volumetric and surface scatterers in a partitioned, multigrid scene
and thus yield a polarimetric scattering map. The SAR
raw data and coherent speckle are generated on the basis
of a simulated polarimetric scattering map. The MPA approach is based on VRT theory for incoherent scattering
power and, thus, is not able to simulate InSAR data. Liu
[42] and Qiao [59] proposed an image-processing algorithm based on radar coherent scattering. To simulate a
forest region, the scene is divided into a number of pixels.
The radar system transmits a signal from fstart to fstop at
N k discrete frequency points, and the scene's number of
spatial sampling points is N x . The scattering field of pixel
r0 can be obtained by [66]
Nk

Nx

1
s
E total
(r0) = N N / / E ^k m, x n h E 0(k m))
k
x
m=1 n=1
# exp(2ik m R(x n) - r0 ),

(9)

where R(x n) and r0 denote the positions of radar and pixel
in a global coordinate system, and E 0(k m) is the reference
signal. The received signal E(k m, x n) is the coherent sum of
the scattered fields from all of the scatterers and the ground
in the observation region at azimuthal position x and
wavenumber k m, which has the same expression as (1).
Using the IRF described in category 2, the fidelity of the
simulated SAR image can be improved while ensuring efficiency. Varekamp and Hoekman applied the idealized
radar IRF [67] to the SAR image simulation [64]. The IRF is
assumed to be
d x d r sina

W (x, r) =

##

rx
rr
k sina k
dr
dx
xr
,
rx
rr
d x d r sina
k sina k
dx
dr
dxdr
xr

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

(10)

JUNE 2020
IEEE Geoscience and Remote Sensing Magazine - June 2020

Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - June 2020
