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Proceedings ArticleDOI

A complex spectrum based SAR image resampling method with restricted target sidelobes and statistics preservation

23 Jul 2017-pp 5358-5361

TL;DR: A resampling scheme for SAR images is presented that preserves spatial resolution and produces statistically accurate images at the same time and is completely faithful to the underlying signal.

AbstractThe aim of this work is to present a resampling scheme for SAR images that preserves spatial resolution and produces statistically accurate images at the same time. Indeed, SAR images are, for reasons due to their acquisition process, well sampled signals according to the Shannon sampling theory. In the presence of strong responses, that we will refer to as targets, a sinc-like function centered at the target is smeared over the entire image and is particularly visible in the range of tens of pixels surrounding the target. To mitigate this phenomenon, the usual solution is to apply an apodization window in the Fourier domain so as to change the cardinal sine impulse response into a much rapidly decaying one. This approach has two major drawbacks. It reduces the resolution of the image and introduces inaccurate statistical dependency between pixels. We propose to resample the image in an adaptive and robust way so that the target smear is canceled and the new sampled image is completely faithful to the underlying signal.

Topics: Image resolution (58%), Image scaling (55%), Pixel (53%), Impulse response (50%), Frequency domain (50%)

Summary (2 min read)

1. INTRODUCTION

  • SAR images are provided by complex signal processing being at the heart of the SAR technique (range compression, SAR synthesis).
  • The raw data received by the antenna before these operations are usually not provided by space agencies.
  • The provided Single Look Complex data (SLC) are affected by two important factors that can be seen in the complex Fourier spectrum of the image: over-sampling and weighting of the azimuth and range spectrum [1].
  • These factors can change depending on the data provider even for similar resolutions of the SLC images.
  • Section 2 introduces the notations and gives a method to cancel apodization when the weighting function is unknown.

2.1. Pseudo-raw image and pseudo-raw spectrum

  • Besides, it happens that the non-zero part of the Fourier spectrum is in fact apodized, which means that it resulted from a multiplication in the Fourier domain by a frequency attenuating function.
  • This function results from the weighting affecting the antenna pattern and the weighting applied to the data [1] which depends on the data provider.

2.2. Practical estimation of the pseudo-raw spectrum

  • Now, let us focus on the inversion of (2), that is, on the computation of the pseudo-raw spectrum û0.
  • When the subfrequency domain ω̂ and the frequency attenuating function γ are known (for instance provided by the spatial agency who generated the image) the relation (2) can be easily inverted and the authors get ∀(α, β) ∈ ω̂, û0(α, β) = û(α, β) γ(α, β) .

3.1. Model

  • An interpretation of this phenomenon is that the target is sufficiently narrow to be transformed, by the acquisition process, to the impulse response, yielding the cardinal sine function.
  • The obvious solution to this problem is to resample the image on a grid such that the coordinates of the target are integers, thus suppressing the side lobes contributions.
  • The authors see that, contrary to u0, the resampled signal v0 is not polluted anymore by the oscillations of the cardinal sine.
  • Since in practice, there may and will be numerous targets in a single image, a global translation will not be sufficient to accommodate all the targets of the image.
  • Indeed, contrary to [4, 5], the authors made the choice to not explicitly detect targets to keep the process as robust as possible.

3.2. Local displacement vector field

  • The idea is that, when sampled on the appropriate grid, the discrete total variation of a target-induced cardinal sine is minimal, whereas it is always higher for all non integer displacements of the grid (the red dashed curve in Fig. 3 is more oscillatory than the blue dotted curve and exhibits a higher discrete total variation).
  • Since their numerical expriments revealed that the third choice led to the most satisfying results, it was systematically used in all the experimental results displayed below.
  • The computation of the resampled image v0 defined by (9) from the pseudo-raw image u0 is summarized in Algorithm 1, and some experimental results are displayed and commented in Fig. 4 and Fig.

3.3. Statistical properties of the resampled image

  • The authors investigate the statistical properties of the resulting image and they show that, under a reasonable assumption, their sampling scheme produces a signal that is completely faithful to the underlying signal.
  • This means that the correlation between samples distant by an integer value is zero.
  • Thus, provided that their estimated tx equals to δ the final discrete result of their resampling will be, according to (8), U∗0 (k + δ) except at pixel k = k0 (the target appears here) which are integer distant samples from the underlying fully-developed speckle and hence i.i.d Gaussian variables.

4. REFERENCES

  • J. Tsao and B. Steinberg, “Reduction of Sidelobe and Speckle Artifacts in Microwave Imaging: the CLEAN technique,” IEEE Trans. on Antennas and Propagation, vol. 36, no. 4, 1988. [6].
  • C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, SciTech Publishing, 2004.

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A Complex Sprectrum Based SAR Image Resampling
Method With Restricted Target Sidelobes and Statistics
Preservation
Rémy Abergel, Saïd Ladjal, Florence Tupin, Jean-Marie Nicolas
To cite this version:
Rémy Abergel, Saïd Ladjal, Florence Tupin, Jean-Marie Nicolas. A Complex Sprectrum Based SAR
Image Resampling Method With Restricted Target Sidelobes and Statistics Preservation. 2017 IEEE
International Geoscience and Remote Sensing Symposium, Jul 2017, Fort Worth, United States.
�10.1109/IGARSS.2017.8128214�. �hal-01447608�

A COMPLEX SPECTRUM BASED SAR IMAGE RESAMPLING METHOD WITH
RESTRICTED TARGET SIDELOBES AND STATISTICS PRESERVATION
R
´
emy Abergel, Sa
¨
ıd Ladjal, Florence Tupin, and Jean-Marie Nicolas (first.last@telecom-paristech.fr)
LTCI, T
´
el
´
ecom ParisTech, Universit
´
e Paris Saclay, Paris, France
ABSTRACT
The aim of this work is to present a resampling scheme for SAR im-
ages that preserves spatial resolution and produces statistically accu-
rate images at the same time. Indeed, SAR images are, for reasons
due to their acquisition process, well sampled signals according to
the Shannon sampling theory. In the presence of strong responses,
that we will refer to as targets, a sinc-like function centered at the
target is smeared over the entire image and is particularly visible in
the range of tens of pixels surrounding the target. To mitigate this
phenomenon, the usual solution is to apply an apodization window
in the Fourier domain so as to change the cardinal sine impulse re-
sponse into a much rapidly decaying one. This approach has two
major drawbacks. It reduces the resolution of the image and intro-
duces inaccurate statistical dependency between pixels. We propose
to resample the image in an adaptive and robust way so that the target
smear is canceled and the new sampled image is completely faithful
to the underlying signal.
Index Terms Shannon interpolation, complex spectrum, total
variation, targets, subpixellic image processing
1. INTRODUCTION
SAR images are provided by complex signal processing being at
the heart of the SAR technique (range compression, SAR synthe-
sis). The raw data received by the antenna before these operations
are usually not provided by space agencies. The provided Single
Look Complex data (SLC) are affected by two important factors
that can be seen in the complex Fourier spectrum of the image:
over-sampling and weighting of the azimuth and range spectrum [1].
These factors can change depending on the data provider even for
similar resolutions of the SLC images. For instance, the weight-
ing functions of TerraSAR-X and CSK images are different. These
processing have a strong impact on the appearance of the images
(spreading of the strong targets) and induce a correlation between
neighboring pixels, which can affect further processing like physi-
cal parameter estimation [2]. In this paper we investigate how the
complex spectrum information can be taken into account to improve
SAR images by unweighting images while limiting sidelobes of the
impulse response of strong targets, and we show how to produce an
image suitable both for visualization and further processing. The pa-
per is organized as follows. Section 2 introduces the notations and
gives a method to cancel apodization when the weighting function is
unknown. Section 3 presents the proposed resampling scheme and
is concluded by a proof of statistical accuracy of the result under a
reasonable model.
This work is supported by the ANR through the MIRIAM project.
(a) amplitude image (b) Fourier spectrum
Fig. 1. Example of TerraSAR-X image data. We display in (a)
the modulus of a SAR image u : C, and in (b) the modulus
of bu over a single period
b
(high values are displayed in dark, low
values in bright, white meaning zero). The Fourier spectrum (b)
reveals the presence of zero-padding (bu is zero everywhere outside
of a rectangular sub-frequency domain bω (
b
delimited by the red
dashed line), showing that the image u was oversampled.
2. FROM THE SAR IMAGE DATA TO THE PSEUDO-RAW
SPECTRUM
2.1. Pseudo-raw image and pseudo-raw spectrum
Let u : C denote a complex-valued SAR image with domain
= I
M
× I
N
, where I
K
= {0, . . . , K 1} . We denote by bu the
discrete Fourier transform (DFT) of u, which is the two-dimensional
and (M, N)-periodic signal defined by
(α, β) Z
2
, bu(α, β) =
X
(k,l)
u(k, l) e
2
(
αk
M
+
βl
N
)
. (1)
We note
b
I
K
=
K
2
,
K
2
Z, then we set
b
=
b
I
M
×
b
I
N
, which
represents the cannonical frequency domain associated to and is
also a period of bu.
We display in Fig. 1 the modulus of a SLC TerraSAR-X image
u and the modulus of bu. We see on that particular example that bu is
non-zero on a rectangular sub-frequency domain bω =
b
I
m
×
b
I
n
b
(for some given integers m and n such as m M, n N), and zero
outside, showing that u was oversampled. Besides, it happens that
the non-zero part of the Fourier spectrum is in fact apodized, which
means that it resulted from a multiplication in the Fourier domain
by a frequency attenuating function. This function results from the
weighting affecting the antenna pattern and the weighting applied to
the data [1] which depends on the data provider.
In the following, we assume that for any (α, β)
b
, we have

bu(α, β) =
cu
0
(α, β) · γ(α, β) if(α, β) bω
0 otherwise,
(2)
where bω =
b
I
m
×
b
I
n
b
, γ : bω R
++
is a known frequency atten-
uating function and cu
0
: bω C is called the pseudo-raw spectrum.
We call pseudo-raw image the complex-valued image u
0
: ω C
with spatial domain ω = I
m
× I
n
obtained by taking the inverse
DFT of cu
0
. Since u
0
and u have different resolutions, the pseudo-
raw image will be compared to the image u
ω
: ω C obtained by
removing the zero-padding from bu, that is, the image defined in the
Fourier domain by cu
ω
(α, β) = bu(α, β) for all (α, β) bω.
2.2. Practical estimation of the pseudo-raw spectrum
Now, let us focus on the inversion of (2), that is, on the computation
of the pseudo-raw spectrum cu
0
. When the subfrequency domain bω
and the frequency attenuating function γ are known (for instance
provided by the spatial agency who generated the image) the rela-
tion (2) can be easily inverted and we get
(α, β) bω, cu
0
(α, β) =
bu(α, β)
γ(α, β)
. (3)
When those pieces of information are unavailable or lost, as we as-
sume in all the experiments that we propose in this document, they
must be estimated. We make the reasonable assumption that the sub-
frequency domain bω can be easily retrieved by looking at the Fourier
spectrum bu, as it is the case in Fig. 1. In the case γ is not explic-
itly known, we propose to consider the following separable estimate
given by
(α, β) bω, γ(α, β) = a
γ
· γ
1
(α) · γ
2
(β), (4)
where a
γ
R
++
is a normalization factor whose setting is dis-
cussed below, and γ
1
, γ
2
are the signals obtained by averaging |cu
ω
|
in both directions, that is, by setting for all (α, β) bω,
γ
1
(α) =
1
n
X
β
b
I
n
|cu
ω
(α, β)| , γ
2
(β) =
1
m
X
α
b
I
m
|cu
ω
(α, β)| ,
which yields two positively valued functions γ
1
:
b
I
m
R
++
and
γ
2
:
b
I
n
R
++
as soon as |cu
ω
| does not have a column or line
being identically-zero. The normalization factor a
γ
is computed in
order that |u
0
| and |u
ω
| assume the same maximum over ω, which
yields
a
γ
=
max
(k,l)ω
|u
0
0
(k, l)|
max
(k,l)ω
|u
ω
(k, l)|
, (5)
where u
0
0
is such that
c
u
0
0
(α, β) = cu
ω
(α, β)/(γ
1
(α) · γ
2
(β)) for all
(α, β) bω. Finally, u
0
can by computed using (3), (4) and (5).
In Fig. 2, we display a cropping of the amplitude images |u
ω
|
and |u
0
| computed from the image u of Fig. 1. As expected the
unweighted image is better localized (finer localization of the infor-
mation) at the price of a large spreading of strong targets in azimuth
and range directions.
3. ADAPTATIVE RESAMPLING SCHEME FOR THE
PSEUDO-RAW IMAGE
3.1. Model
We illustrate in Fig. 3 that the bright targets observed on the pseudo-
raw image can be very well approached by a two-dimensional cardi-
nal sine function defined by (as given by the SAR processing [1]):
(x, y) R
2
, sinc(x, y) =
sin(πx)
πx
·
sin(πy)
πy
, (6)
modulus of u
ω
modulus of u
0
(pseudo-raw)
Fig. 2. Comparison between apodized and pseudo-raw images.
Removing the apodization from u
ω
yields the pseudo-raw image u
0
,
we display here the modulus of a subpart of those two images. We
can see that the pseudo-raw image u
0
shows a better level of details
than u
ω
, as well as a more precise localization of the information.
However, in the presence of strong targets, the signal is polluted by
horizontal and vertical patterns.
with the continuity-preserving condition
sin(0)
0
= 1. An interpre-
tation of this phenomenon is that the target is sufficiently narrow to
be transformed, by the acquisition process, to the impulse response,
yielding the cardinal sine function. When the position of the tar-
get does not coincide with the sampling grid, an oscillatory pattern
peculiar to the sinc function pollutes the values of the pixels in the
vicinity of the target, yielding (we drop the double indexes for the
spatial coordinates in this section) an observed signal of the type
k ω, u
0
(k) = A sinc(k (k
0
+ δ)) + u
0
(k) , (7)
where A C denotes the target amplitude, k
0
+ δ (with k
0
ω,
δ [
1
2
,
1
2
]
2
) the subpixellic position of the target, and u
0
the signal
that would be acquired in the absence of the target.
The obvious solution to this problem is to resample the image
on a grid such that the coordinates of the target are integers, thus
suppressing the side lobes contributions. In order to do that, one has
to estimate the subpixellic position of the target and then perform
a translation of the image by the vector t = δ. Indeed, noting
U
0
: R
2
C the Shannon interpolate of u
0
which is computed
as U
0
= U
r
0
+ i · U
i
0
, where U
r
0
and U
i
0
denote the (real-valued)
Shannon interpolates of the real and imaginary parts of u
0
(see for
instance [3] for the explicit definition), the translated signal is v
0
:
k 7→ U
0
(k + δ) and satisfies
k ω, v
0
(k) = U
0
(k + δ) +
A if k = k
0
0 otherwise,
(8)
where U
0
denotes the Shannon interpolate of u
0
. We see that, con-
trary to u
0
, the resampled signal v
0
is not polluted anymore by the
oscillations of the cardinal sine.
Since in practice, there may and will be numerous targets in a
single image, a global translation will not be sufficient to accom-
modate all the targets of the image. For that reason, we propose to
devise a local scheme to compute, at each position in the image, the
translation that reduces the interference of the target-induced car-
dinal sine. Indeed, contrary to [4, 5], we made the choice to not
explicitly detect targets to keep the process as robust as possible.
3.2. Local displacement vector field
Our approach consists in computing from u
0
a dense field of dis-
placements T = (T
x
, T
y
) : ω [
1
2
,
1
2
] × [
1
2
,
1
2
], and resample

(a) pseudo-raw image (b) horizontal translation (c) 2-D translation
816 818 820 822 824 826 828
horizontal axis (x)
-5000
0
5000
10000
15000
real part of the complex signal
cardinal sine function
horizontal section of (a)
horizontal section of (b)
Fig. 3. Resampling targets at the subpixellic scale. We display
in (a) the modulus of the pseudo-raw image u
0
in the vinicity of a
strong target. We display in (b) and (c) the modulus of the image
u
0
resampled by means of a translation of vector t = (0.3, 0) and
t = (0.3, 0.1) respectively, yielding more localized signals. We
display in the second row a plot of the real part of an horizontal
section of u
0
, yielding the red dashed curve, and we do the same
for the resampled signal displayed in (b), yielding the blue dotted
curve. The green plain curve represents a pure cardinal sine, that
is a function of the type x 7→ A sinc(x) where A R. We see
that the samples of both red and blue signals match very well with
a sampling of the cardinal sine, the same observation holds for the
imaginary parts of the considered signals.
the image u
0
over the locally translated grid, which means to com-
pute the image v
0
: ω C defined by
(k, l) ω, v
0
(k, l) = U
0
(k T
x
(k, l), l T
y
(k, l)) . (9)
In practice, the two components T
x
and T
y
of T will be estimated
independently, we describe here the computation of T
x
, that of T
y
being totally similar.
Given a locality parameter K N (we took K = 25 in all
our experiments) and a position (k
0
, l
0
) ω, we associate to each
translation t
x
[
1
2
,
1
2
] the mono-dimensional signal v
t
x
C
2K+1
corresponding to the restriction of the horizontally translated signal
(x, y) 7→ U
0
(x t
x
, y) to the horizontal 2K + 1 neighborhood of
the pixel (k
0
, l
0
), that is,
p [K, K] Z, v
t
x
(p) = U
0
(k
0
p t
x
, l
0
) .
We propose to select among all candidate translations the one
that minimizes a particular cost function t
x
7→ J(v
t
x
) where
J : C
2K+1
R, yielding
T
x
(k
0
, l
0
) = argmin
1
2
t
x
<
1
2
J(v
t
x
) . (10)
We considered three different choices for J, denoted below as J
1
,
J
2
and J
3
.
(i) J
1
(v
t
x
) = max
p[K,K]
|v
t
x
(p)|. The idea underlying this
choice is that when a target exists in the vicinity of (k
0
, l
0
),
the appropriate translation is found by looking for the signal
v
t
x
having the highest maximal modulus (as it is for instance
the case for the blue dotted curve in Fig. 3).
(ii) J
2
(v
t
x
) = TV
d
(v
r
t
x
) + TV
d
(v
i
t
x
), noting v
r
t
x
and v
i
t
x
the
real and imaginary parts of v
t
x
, and TV
d
the discrete total
variation operator defined by
w R
2K+1
, TV
d
(w) =
X
Kp<K
|w(p + 1) w(p)| .
The idea is that, when sampled on the appropriate grid, the
discrete total variation of a target-induced cardinal sine is min-
imal, whereas it is always higher for all non integer displace-
ments of the grid (the red dashed curve in Fig. 3 is more oscil-
latory than the blue dotted curve and exhibits a higher discrete
total variation).
(iii) J
3
(v
t
x
) = TV
d
mask
(v
r
t
x
) + TV
d
mask
(v
i
t
x
), TV
d
mask
being de-
fined for any w R
2K+1
by
TV
d
mask
(w) =
X
Kp<K
p6∈{p
0
1,p
0
}
|w(p + 1) w(p)| ,
where p
0
denotes the position where |w| is maximal. Com-
pared to the previous criterion, we choose to mask the contri-
bution of the brightest pixel to the total variation so that the
TV
d
mask
of a pure cardinal sine function sampled on the ap-
propriate grid is zero.
Since our numerical expriments revealed that the third choice led
to the most satisfying results, it was systematically used in all the
experimental results displayed below. The computation of the re-
sampled image v
0
defined by (9) from the pseudo-raw image u
0
is
summarized in Algorithm 1, and some experimental results are dis-
played and commented in Fig. 4 and Fig. 5.
Algorithm 1: pseudo-raw image resampling
Input: a pseudo-raw image u
0
: ω C, a locality
parameter K, a discrete set of N
T
candidate translations
T =
1
2
+
1
N
T
· {0, . . . , N
T
1}, and a cost function J (in
all our experiments, we took K = 25, N
T
= 20 and J = J
3
defined in Section 3.2).
Output: a resampled pseudo-raw image v
0
: ω C, and a
translation map T : ω T × T.
Initialization: precompute the horizontally and vertically
translated signals v
x
t
= U
0
(ω (t, 0)), v
y
t
= U
0
(ω (0, t))
for all t T.
for (k, l) ω do
ω
x
(k + [K, K] Z) × {l}
ω
y
{k} × (l + [K, K] Z)
t
x
argmin
t
x
T
J(v
x
t
x
(∆ω
x
))
t
y
argmin
t
y
T
J(v
y
t
y
(∆ω
y
))
T (k, l) (t
x
, t
y
)
v
0
(k, l) U
0
(k t
x
, l t
y
)

(a) pseudo-raw image u
0
(b) resampled image v
0
close-up view of (a) close-up view of (b)
Fig. 4. Resampling the pseudo-raw image. We display in (a)
and (b) the modulus of the pseudo-raw image u
0
and the modulus of
the resampled image v
0
computed using Algorithm 1. In the second
row, we display some close-up views of the images (a) and (b). The
blue arrows indicate the values of the computed translation fields T
at each pixel location. One can see that the resampled image v
0
ex-
hibits a similar level of details than u
0
but is free of target induced
cardinal sine phenomenon.
3.3. Statistical properties of the resampled image
We investigate the statistical properties of the resulting image and we
show that, under a reasonable assumption, our sampling scheme pro-
duces a signal that is completely faithful to the underlying signal. We
make the assumption that the scene is the superposition of a signal
stemming from a bright target of amplitude A and a fully-developed
speckle. Under this model, the term u
0
(k) in (7) corresponds to the
sampling of a band-limited Gaussian white second-order stationary
process [6]. This means that the correlation between samples dis-
tant by an integer value is zero. The process being Gaussian, the
zero correlation implies independence. A consequence of the band-
limited property of the SAR-signal is that the original discrete image
allows one to recover the true values of U
0
(x) for real x by means
of Shannon interpolation of the available discrete signal. When ex-
amining the criteria J
1,2,3
proposed in Section 3.2, one can see that
for the entire line the optimal value of t
x
is the same for all pixels,
provided the computation window of the criterion is large enough.
Thus, provided that our estimated t
x
equals to δ the final discrete
result of our resampling will be, according to (8), U
0
(k + δ) except
at pixel k = k
0
(the target appears here) which are integer distant
samples from the underlying fully-developed speckle and hence i.i.d
Gaussian variables. We reduced the statistical accuracy of the result-
ing signal to the one of our estimator of t
x
. One can show that this
estimator is unbiased and has a variance depending on the ratio be-
tween the power of the u
0
process and A. In Fig. 6, we show how the
output image v
0
both respects the theoretical Gaussian distribution
of the samples and dramatically decreases the correlation between
neighboring pixels, supporting our claim of statistical accuracy of
the resampled image.
(a) apodized multi-look image (b) resampled multi-look image
Fig. 5. Multi-Look comparison between apodized data and re-
sampled pseudo-raw data. We display in (a) the multi-look real-
valued image u
ML
ω
= (
1
26
P
26
k=1
|u
k
ω
|
2
)
1/2
computed from a set of
26 views {u
k
ω
}
1k26
, and in (b) the multi-look image computed
from the corresponding set of resampled images {v
k
0
}
1k26
. The
image (b) exhibits a better level of details and a better localization
of the information than the image (a), as for instance in the areas
delimited by the colored rectangles, where the strong targets can be
more easily separated in (b) than in (a).
-300 -200 -100 0 100 200 300
0
1
2
3
4
5
6
7
8
×10
-3
empirical probability density function
Gaussian fitting (mean=1.8,std=64)
-300 -200 -100 0 100 200 300
0
1
2
3
4
5
6
7
8
×10
-3
empirical probability density function
Gaussian fitting (mean=0.25,std=64)
apodized image (corr = 0.49) resampled image (corr = 5 · 10
3
)
Fig. 6. First order statistics of a region with constant radiome-
try. We display here the empirical distribution of a 50 × 60 patch
of the real part of the apodized image u
ω
and the resampled image
v
0
where the signal corresponds to pure speckle. In both cases, the
empirical probability density function is very well approached by a
Gaussian function. Pixels of u
ω
are highly correlated (0.49) while
those of v
0
exhibit a one hundred times smaller correlation (we com-
puted corr(w) =
1
kwk
2
P
K
x
2
k=0
P
K
y
1
l=0
w(k +1, l)·
w(k, l), where
w : I
K
x
× I
K
y
C denotes the considered patch).
4. REFERENCES
[1] D. Massonnet and J. C. Souyris, Imaging with Synthetic Aper-
ture Radar, EPFL Press, 2008.
[2] Ch.-A. Deledalle, L. Denis, F. Tupin, A. Reigber, and M. J
¨
ager,
“NL-SAR: a unified Non-Local framework for resolution-
preserving (Pol)(In)SAR denoising, IEEE Trans. on Geo-
science and Remote Sensing, vol. 53, no. 4, 2015.
[3] R. Abergel and L. Moisan, “The Shannon Total Variation,
preprint MAP5, 2016.
[4] J. Li, “Implementation of the RELAX algorithm, Correspon-
dence in IEEE Trans. on Aerospace and Electronic Systems, vol.
24, no. 2, 1998.
[5] J. Tsao and B. Steinberg, “Reduction of Sidelobe and Speckle
Artifacts in Microwave Imaging: the CLEAN technique, IEEE
Trans. on Antennas and Propagation, vol. 36, no. 4, 1988.
[6] C. Oliver and S. Quegan, Understanding Synthetic Aperture
Radar Images, SciTech Publishing, 2004.
Figures (6)
Citations
More filters

Journal ArticleDOI
TL;DR: A deep learning algorithm with semi-supervision is proposed in this article: SAR2SAR, where Multitemporal time series are leveraged and the neural network learns to restore SAR images by only looking at noisy acquisitions.
Abstract: Speckle reduction is a key step in many remote sensing applications By strongly affecting synthetic aperture radar (SAR) images, it makes them difficult to analyze Due to the difficulty to model the spatial correlation of speckle, a deep learning algorithm with semi-supervision is proposed in this article: SAR2SAR Multitemporal time series are leveraged and the neural network learns to restore SAR images by only looking at noisy acquisitions To this purpose, the recently proposed noise2noise framework [1] has been employed The strategy to adapt it to SAR despeckling is presented, based on a compensation of temporal changes and a loss function adapted to the statistics of speckle A study with synthetic speckle noise is presented to compare the performances of the proposed method with other state-of-the-art filters Then, results on real images are discussed, to show the potential of the proposed algorithm The code is made available to allow testing and reproducible research in this field

17 citations


Cites background or methods from "A complex spectrum based SAR image ..."

  • ...Whitening the spectrum [17], [22], [23] or downsampling the image are possible strategies [18]....

    [...]

  • ...Algorithms developed using speckle generated under Goodmans fully developed speckle model generally assume an absence of spatial correlations [16], which is not the case in actual SAR images synthetized by space agencies [17], [21]....

    [...]

  • ...At a later stage, we feed the network with real acquisitions, allowing learning of the spatial correlation introduced by the SAR processing steps, namely spectral windowing and oversampling [17] [18]....

    [...]


Journal ArticleDOI
TL;DR: This paper describes strategies to cancel sidelobes around point-like targets while preserving the spatial resolution and the statistics of speckle-dominated areas in synthetic aperture radar images.
Abstract: Synthetic aperture radar (SAR) images display very high dynamic ranges. Man-made structures (like buildings or power towers) produce echoes that are several orders of magnitude stronger than echoes from diffusing areas (vegetated areas) or from smooth surfaces (e.g., roads). The impulse response of the SAR imaging system is, thus, clearly visible around the strongest targets: sidelobes spread over several pixels, masking the much weaker echoes from the background. To reduce the sidelobes of the impulse response, images are generally spectrally apodized, trading resolution for a reduction of the sidelobes. This apodization procedure (global or shift-variant) introduces spatial correlations in the speckle-dominated areas that complicates the design of estimation methods. This paper describes strategies to cancel sidelobes around point-like targets while preserving the spatial resolution and the statistics of speckle-dominated areas. An irregular sampling grid is built to compensate the subpixel shifts and turn cardinal sines into discrete Diracs. A statistically grounded approach for point-like target extraction is also introduced, thereby providing a decomposition of a single look complex image into two components: a speckle-dominated image and the point-like targets. This decomposition can be exploited to produce images with improved quality (full resolution and suppressed sidelobes) suitable both for visual inspection and further processing (multitemporal analysis, despeckling, interferometry).

15 citations


Cites background or methods from "A complex spectrum based SAR image ..."

  • ...We refer the reader to [3], [28] for more details about the computation of the pseudo-raw image u0 from u (in particular in the case when the frequency attenuating function γ is unknown)....

    [...]

  • ...In this section, we complete with more details and experimental results our previous work presented in [28], and we discuss the strengths and weaknesses of the proposed irregular resampling scheme....

    [...]

  • ...Contributions: this paper extends the recent conference paper [28] and introduces:...

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  • ...Algorithm 1: Irregular resampling scheme proposed in [28]...

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29 Mar 2021
TL;DR: A standard training strategy for deep learning of speckle correlations is proposed and the increased robustness brought by including a Total Variation term in the loss function is analyzed on Sentinel-1 images.
Abstract: Speckle noise strongly affects Synthetic Aperture Radar (SAR) images, causing strong intensity fluctuations that make them difficult to analyze. Although many speckle reduction algorithms have been proposed, how to effectively deal with the spatial correlations of speckle remains an open question, especially in the most recent deep learning approaches. This paper tries to address this problem. Existing approaches to tackle the speckle correlations are described. Then, a standard training strategy for deep learning is proposed. Two models are trained and the increased robustness brought by including a Total Variation (TV) term in the loss function is analyzed on Sentinel-1 images.

9 citations


Cites background from "A complex spectrum based SAR image ..."

  • ...As a downside, these operations introduce spatial correlations in the speckle [24]....

    [...]


Proceedings ArticleDOI
28 Jul 2019
TL;DR: To better preserve the spatial resolution, this work describes how to correctly resample SAR images and extract bright targets in order to process full-resolution images with speckle-reduction methods.
Abstract: Speckle reduction is a necessary step for many applications. Very effective methods have been developed in the recent years for single-image speckle reduction and multi-temporal speckle filtering. However, to reduce the presence of sidelobes around bright targets, SAR images are spectrally weighted and this processing impacts the speckle statistics by introducing spatial correlations. These correlations severely impact speckle reduction methods that require uncorrelated speckle as input. Thus, spatial down-sampling is typically applied to reduce the speckle spatial correlations prior to speckle filtering. To better preserve the spatial resolution, we describe how to correctly resample SAR images and extract bright targets in order to process full-resolution images with speckle-reduction methods.

4 citations


Cites methods from "A complex spectrum based SAR image ..."

  • ...As explained in [2, 3], computing the pseudo-raw image, such as that displayed in Fig....

    [...]

  • ...Besides, we explained in [2] how the apodization function γ could be estimated (if unknown), so that we can invert (6) and compute the pseudo-raw image u0....

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References
More filters

Book
01 Mar 1998
Abstract: Introduction. Principles of SAR Image Formation. Image Defects and their Correction. Fundamental Properties of SAR Images. Data Models. RCS Reconstruction Filters. RCS Classification and Segmentation. Texture Exploitation. Correlated Textures. Information in Multi-Channel SAR. Analysis Techniques for Multi-Dimensional Images. Target Information. Image Classification.

1,814 citations


Journal ArticleDOI
TL;DR: It is shown that targets much weaker than the sidelobe level can be detected and displayed without the hazard of artifacts and the target dynamic range and the image contrast can be increased by up to twice the signal-to-noise ratio per element.
Abstract: Large random thin arrays provide a high angular resolution microwave images but are plagued with artifacts (false targets and target breakup or speckle) caused by high sidelobe levels. The CLEAN algorithm for reducing the sidelobe-induced artifacts is extended to the coherent radiation field and the theory placed on a quantitative basis. The CLEAN technique decomposes the received echoes of a coherent multiple-target scene by iterative cancellation of the largest target found. At each step, cancellation information is used to create a target image. The image includes target intensities, phases, and directions. The process is designed for an imaging instrument consisting of a random thinned array. A condition is derived which, when satisfied, guarantees that all proper targets will be preserved in the cleaned image and all false targets discarded. An algorithm involving moving thresholds is derived to extract the target coordinates. It is shown that targets much weaker than the sidelobe level can be detected and displayed without the hazard of artifacts. The target dynamic range and the image contrast can be increased by up to twice the signal-to-noise ratio per element. >

407 citations


Additional excerpts

  • ...Indeed, contrary to [4, 5], we made the choice to not explicitly detect targets to keep the process as robust as possible....

    [...]


Journal ArticleDOI
TL;DR: A general method, i.e., NL-SAR, that builds extended nonlocal neighborhoods for denoising amplitude, polarimetric, and/or interferometric SAR images, and the best one is locally selected to form a single restored image with good preservation of radar structures and discontinuities is described.
Abstract: Speckle noise is an inherent problem in coherent imaging systems like synthetic aperture radar. It creates strong intensity fluctuations and hampers the analysis of images and the estimation of local radiometric, polarimetric or interferometric properties. SAR processing chains thus often include a multi-looking (i.e., averaging) filter for speckle reduction, at the expense of a strong resolution loss. Preservation of point-like and fine structures and textures requires to adapt locally the estimation. Non-local means successfully adapt smoothing by deriving data-driven weights from the similarity between small image patches. The generalization of non-local approaches offers a flexible framework for resolution-preserving speckle reduction. We describe a general method, NL-SAR, that builds extended non-local neighborhoods for denoising amplitude, polarimetric and/or interferometric SAR images. These neighborhoods are defined on the basis of pixel similarity as evaluated by multi-channel comparison of patches. Several non-local estimations are performed and the best one is locally selected to form a single restored image with good preservation of radar structures and discontinuities. The proposed method is fully automatic and handles single and multi-look images, with or without interferometric or polarimetric channels. Efficient speckle reduction with very good resolution preservation is demonstrated both on numerical experiments using simulated data, airborne and spaceborne radar images. The source code of a parallel implementation of NL-SAR is released with the paper.

316 citations


"A complex spectrum based SAR image ..." refers background in this paper

  • ...These processing have a strong impact on the appearance of the images (spreading of the strong targets) and induce a correlation between neighboring pixels, which can affect further processing like physical parameter estimation [2]....

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Book
01 May 2008
Abstract: Describing a field that has been transformed by the recent availability of data from a new generation of space and airborne systems, the authors offer a synthetic geometrical approach to the description of synthetic aperture radar, one that addresses physicists, radar specialists, as well as experts in image processing.

175 citations


"A complex spectrum based SAR image ..." refers background in this paper

  • ...This function results from the weighting affecting the antenna pattern and the weighting applied to the data [1] which depends on the data provider....

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  • ...The provided Single Look Complex data (SLC) are affected by two important factors that can be seen in the complex Fourier spectrum of the image: over-sampling and weighting of the azimuth and range spectrum [1]....

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  • ...3 that the bright targets observed on the pseudoraw image can be very well approached by a two-dimensional cardinal sine function defined by (as given by the SAR processing [1]):...

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Journal ArticleDOI
TL;DR: This correspondence presents a zoom-FFT based RELAX algorithm for estimating sinusoidal parameters in the presence of unknown colored noise and the estimation performance of the new algorithm is only slightly degraded as compared with the original one.
Abstract: This correspondence presents a zoom-FFT based RELAX algorithm for estimating sinusoidal parameters in the presence of unknown colored noise. The amount of computations required by this algorithm is much less than the original zero-padding FFT based RELAX. Yet the estimation performance of the new algorithm is only slightly degraded as compared with the original one.

41 citations


Additional excerpts

  • ...Indeed, contrary to [4, 5], we made the choice to not explicitly detect targets to keep the process as robust as possible....

    [...]


Frequently Asked Questions (1)
Q1. What have the authors contributed in "A complex sprectrum based sar image resampling method with restricted target sidelobes and statistics preservation" ?

The aim of this work is to present a resampling scheme for SAR images that preserves spatial resolution and produces statistically accurate images at the same time. It reduces the resolution of the image and introduces inaccurate statistical dependency between pixels. The authors propose to resample the image in an adaptive and robust way so that the target smear is canceled and the new sampled image is completely faithful to the underlying signal.