![Fig. 3: Speckle plus target decomposition of Sentinel-1 images. We display in (a) the modulus of a pseudo-raw image u0, in (c) the modulus of its speckle component w0 and in (d) the modulus of its target component S0(C ). The set of targets C extracted from u0 was computed using the decomposition algorithm proposed in [3]. By construction, we have u0 = w0 + S0(C ). Replacing the linear combination of cardinal sines S0(C ) by a linear combination of discrete Diracs Dω(C ) in this additive decomposition yields the image Rω(u0), whose modulus is displayed in (b): this image is free of sidelobe effects.](/figures/fig-3-speckle-plus-target-decomposition-of-sentinel-1-images-1u12zzoh.webp)
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Resolution-Preserving Speckle Reduction of SAR
Images: the Benets of Speckle Decorrelation and
Targets Extraction
Rémy Abergel, Loïc Denis, Florence Tupin, Saïd Ladjal, Charles-Alban
Deledalle, Andrés Almansa
To cite this version:
Rémy Abergel, Loïc Denis, Florence Tupin, Saïd Ladjal, Charles-Alban Deledalle, et al.. Resolution-
Preserving Speckle Reduction of SAR Images: the Benets of Speckle Decorrelation and Targets Ex-
traction. 2019 IEEE International Geoscience and Remote Sensing Symposium, Jul 2019, Yokohama,
Japan. �10.1109/IGARSS.2019.8900036�. �hal-02148907�
RESOLUTION-PRESERVING SPECKLE REDUCTION OF SAR IMAGES:
THE BENEFITS OF SPECKLE DECORRELATION AND TARGETS EXTRACTION
R
´
emy Abergel
1
, Lo
¨
ıc Denis
2
, Florence Tupin
3
, Sa
¨
ıd Ladjal
3
, Charles-Alban Deledalle
4
, Andr
´
es Almansa
1
1
Laboratoire MAP5 (CNRS UMR 8145), Universit
´
e Paris Descartes, Sorbonne Paris Cit
´
e, France
2
Univ Lyon, UJM-Saint-Etienne, Institut d’Optique Graduate School, Laboratoire Hubert Curien CNRS UMR 5516, Saint-Etienne, France
3
LTCI, T
´
el
´
ecom ParisTech, Universit
´
e Paris Saclay, Paris, France
4
IMB, CNRS, Univ. Bordeaux, Bordeaux INP, F-33405 Talence, France
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. How-
ever, 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 correla-
tions severely impact speckle reduction methods that require uncor-
related 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.
Index Terms— Sentinel-1, deramping, sub-pixel target detec-
tion, sidelobe reduction, despeckling.
1. INTRODUCTION
The analysis of SAR images requires a speckle reduction step. While
this step was for a long time performed by local averaging (spatial
multi-looking), with the recent progress accomplished in speckle fil-
tering the use of more evolved methods cannot be overlooked. The
goal of speckle reduction methods is to suppress as much as possible
the speckle fluctuations while preserving at best the spatial resolu-
tion (i.e., without introducing notable blurring). To achieve this goal,
the methods combine observed SAR intensities based on transforms
(e.g., wavelets transforms), image models (e.g., total variation min-
imization, sparse coding), selection approaches (e.g., the sigma fil-
ter, patch comparisons) or learned transforms (e.g., deep neural net-
works). In order to separate the speckle fluctuations from the under-
lying SAR refectivity, a statistical modeling of speckle is necessary.
In the overwhelming majority of cases, the speckle model assumes
spatial independence from a pixel to the next. This assumption is
valid only if the SAR image is sampled at the Shannon-Nyquist crit-
ical rate and no spectral apodization is applied. This is generally not
the case of SAR images provided by spatial agencies. If only the
intensity information is available, the spatial correlation of speckle
can be reduced by sub-sampling the image. This however decreases
the spatial resolution of the image. When the single-look complex
(SLC) image is available, it is possible to decorrelate the speckle by
carefully undoing the spectral apodization, the zero-padding and, in
the case of Sentinel-1 TOPS acquisition mode, deramping and de-
modulating the images. Without spectral apodization, strong targets
This work was partially supported by the ANR MIRIAM project ANR-
14-CE27-0019.
produce the typical extended cardinal sine signature. These targets
can be extracted to improve the processing. In this paper, we show
how speckle decorrelation and strong targets extraction can improve
the performance of speckle reduction methods.
2. DERAMPING, DEMODULATION AND COMPUTATION
OF THE PSEUDO-RAW SENTINEL-1 IMAGES
2.1. Deramping and demodulation of a Sentinel-1 SLC image
As explained in [1], the TOPS SLC products undergo a linear fre-
quency modulation which is due to the steering of the antenna in az-
imuth during the acquisition process. Inverting this linear frequency
modulation is necessary for performing subpixel operations such as
interpolation and resampling. This operation is called deramping.
In addition to deramping, it is also useful to perform a so-called de-
modulation, which consists in centering the support of the complex
spectrum on 0Hz. This operation roughly consists in the estimation
of the Doppler centroid frequency, followed by a global translation
of the complex spectrum.
Let v : Ω → C be a TOPS SLC image of size M × N and
discrete domain Ω = I
M
× I
N
, noting I
K
= {0, . . . , K − 1}.
Applying deramping and demodulation to v boils done to computing
the image u : Ω → C such that, for any pixel location (x, y), we
have
u(x, y) = v(x, y) · Φ(τ (x), η(y)) · Ψ(τ(x), η(y)) , (1)
where Φ and Ψ are called the deramping and demodulation functions
respectively, τ(x) corresponds to the range time of the pixels located
in the x-th column of the image, and η(y) corresponds to the azimuth
time of the pixels located in the y-th row of the image.
The computation of the deramping and demodulation functions
relies on the metadata attached on the TOPS SLC product, follow-
ing the procedure described in [1]. For the sake of completness, we
describe the main steps of this procedure. For all (τ, η) ∈ R
2
, func-
tions Φ and Ψ are defined by:
Φ(τ, η) = exp
−iπ
k
a
(τ) k
s
k
a
(τ) − k
s
· (η − η
ref
(τ))
2
, (2)
Ψ(τ, η) = exp (−2iπf
ηc
(τ) · (η − η
ref
(τ))) , (3)
where k
s
= 2
V
s
c
f
c
k
ψ
and η
ref
(τ) =
f
ηc
(0)
k
a
(0)
−
f
ηc
(τ)
k
a
(τ)
.
In the definition of k
s
above, c denotes the speed of light (in m/s),
V
s
the spacecraft velocity (m/s), f
c
the radar frequency (Hz) and k
ψ
the antenna steering angle (rad/s). Both values of f
c
and k
ψ
can be
(a) modulus of a TOPS SLC image v
(b) Fourier spectrum of v
(bright = low values, dark = high values)
(c) Fourier spectrum after deramping
(d) Fourier spectrum after
deramping and demodulation
Fig. 1: Deramping and demodulation of a TOPS Sentinel-1 SLC
image. A TOPS SLC image v whose modulus is displayed in (a)
undergoes a linear frequency modulation which results in a spread-
ing of the spectrum along the vertical direction (b). A pointwise
multiplication in the spatial domain between v and Φ leads to the
deramped image whose spectrum has a rectangular support, as dis-
played in (c). Demodulation is done by multiplying the deramped
image by Ψ, which centers the rectangular spectrum support on the
zero-frequency, as displayed in (d). It is interesting to notice that
deramping and demodulation operations do not change the modulus
of the signal, but ony the phase information.
found explicitely in the metadata of the TOPS SLC product. There-
fore, only V
s
, k
a
(τ) and f
ηc
(τ) need to be computed. The three
components (in cartesian coordinates) of the spacecraft velocity can
be found in the metadata for several azimuth times. Interpolating
those values at the given azimuth time η (e.g. using bilinear interpo-
lation), we can estimate the spacecraft velocity. In the equations (2)
and (3), the dependency of V
s
and k
s
on the variable η is not made
explicit by the notation, following the same convention as in [1]. The
computation of k
a
(τ) is performed based on the model
k
a
(τ) = c
0
+ c
1
(τ − τ
0
) + c
2
(τ − τ
0
)
2
, (4)
where τ
0
and the polynomial coefficients c
0
, c
1
and c
2
are measured
(and made available in the metadata) at several azimuth times. Like
k
a
, these coefficients are time dependent. For a given range time
τ, we can compute k
a
(τ) at each tabulated azimuth time, and in-
terpolate the resulting signal at the desired azimuth time η. Exactly
the same approach is used to compute f
ηc
(τ) which also relies on a
sequence of second order polynomials.
2.2. Computation of a pseudo-raw Sentinel-1 image
Let us consider from now the deramped and demodulated image u
defined in (1). Let bu denote the discrete Fourier transform (DFT) of
u, defined by
∀(α, β) ∈ Z
2
, bu(α, β) =
X
(k,`)∈Ω
u(k, `) e
−2iπ
(
αk
M
+
β`
N
)
. (5)
As can be seen in Fig. 1 (d), the Fourier spectrum bu has a rectangular
support bω (
b
Ω (delimited by the red dashed-rectangle in Fig. 1 (d)),
showing that the image u has been sampled above the Shannon-
Nyquist critical rate (oversampling). Besides, the spectrum bu also
underwent some attenuation, more precisely, for all (α, β) ∈
b
Ω, we
have
bu(α, β) =
cu
0
(α, β) · γ(α, β) if (α, β) ∈ bω
0 otherwise ,
(6)
where γ : bω → R
++
denotes the spectral weighting function (or
apodization), and u
0
is called hereafter the pseudo-raw image. The
pseudo-raw image corresponds to the image that would have been
acquired at the Shannon-Nyquist critical sampling rate without any
spectral weighting. The dimensions m × n of the frequency support
bω =
b
I
m
×
b
I
n
, noting
b
I
K
= [−K/2, K/2) ∩ Z, can be obtained
based on the bandwidth and sampling frequencies,
m =
B
r
f
r
· M
, n =
B
az
f
az
· N
, (7)
where b·e denotes the rounding function, f
r
and f
az
the sampling
frequency in range and azimuth directions, and B
r
and B
az
the band-
width in the corresponding directions, all available through the meta-
data of the TOPS SLC product. Thanks to the centering of the spec-
trum provided by the demodulation, we can automatically find the
position of the frequency support bω. 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 u
0
. An ex-
ample of a pseudo-raw image u
0
computed from a TOPS SLC image
v is displayed in Fig. 2. Since the TOPS SLC image v undergoes an
important phase modulation due to the phase-ramping, this image
cannot be directly interpolated using the standard Shannon interpo-
lation. This is particularly visible in the left-hand side of Fig. 2 (c),
where we display the Shannon interpolate of the image v in the vicin-
ity of a bright target, leading to unrealistic high frequency patterns
in the azimuth direction. After deramping, we get an image which is
compatible with Shannon interpolation and that can be easily manip-
ulated at the subpixellic scale. As explained in [2, 3], computing the
pseudo-raw image, such as that displayed in Fig. 2 (b), is particularly
interesting from a statistical viewpoint, since the speckle in homoge-
neous regions exhibits almost no spatial correlation in contrast to the
spatially correlated original image. Correlations in the original im-
ages are due to the oversampling and the spectral apodization. The
pseudo-raw images also exhibit very strong sidelobes around bright
targets (especially in urban areas) which is due to the cardinal sine
response of those targets, as illustrated in the right side of Fig. 2 (c).
In what follows, we illustrate how those targets can be efficiently
handled via the subpixellic methods that we recently proposed in [3].
3. BRIGHT TARGETS EXTRACTION AND
RELOCALIZATION IN PSEUDO-RAW IMAGES
The range and azimuth profiles of isolated bright targets in the
pseudo-raw images match very well cardinal sine functions, as illus-
trated in the right side of Fig. 2 (c). Therefore, the contribution of a
bright target to the pseudo-raw image can be modeled by
∀(k, `) ∈ ω , u
0
(k, `) = A sinc(k − x, ` − y) + u
∗
0
(k, `) , (8)
where A ∈ C denotes the complex amplitude of the bright tar-
get, (x, y) ∈ [0, m) × [0, n) the subpixellic position of its center,
(c) Shannon interpolation of bright targets
(a) TOPS SLC image
(b) pseudo-raw image
Fig. 2: Pseudo-raw Sentinel-1 images. We display in (a) the mod-
ulus of a TOPS SLC image v, and in (b) the modulus of the pseudo-
raw image u
0
computed from v. Both images exhibit different pixel
sizes because of the resampling involved in the computation of u
0
to
remove the zero-padding.
sinc(s, t) = sin (πs)/(πs) · sin (πt)/(πt) the 2D-separable prod-
uct of cardinal sine functions, and u
∗
0
the pseudo-raw image that
we would have observed in the absence of the target. We recently
proposed in [3] an algorithm for the detection and the extraction
of bright targets with cardinal sine profile such as in (8). We ap-
ply in this paper the algorithm to Sentinel-1 pseudo-raw images u
0
.
In practice, the algorithm returns a set C = {(x
j
, y
j
, A
j
)}
1≤j≤T
where T represents the number of meaningful targets (automatically
derived by the algorithm thanks to an a contrario criterion), and
such that the j-th target is characterized by its subpixellic position
(x
j
, y
j
) ∈ [0, m) × [0, n) and its complex amplitude A
j
∈ C. After
detection of the targets, we can form a decomposition of the image
u
0
into the sum of a target component, noted S
0
(C ), which is the
linear combination of cardinal sine functions defined by
∀(k, `) ∈ ω , S
0
(C )(k, `) =
T
X
j=1
A
j
sinc(k − x
j
, ` − y
j
) , (9)
and a speckle component w
0
= u
0
− S
0
(C ), which represents the
image that would have been acquired in the absence of the targets
of C . An example of such decomposition of a Sentinel-1 pseudo-
raw image is displayed in Fig. 3. As suggested in [3], an inter-
esting way to suppress the sidelobes consists in recombining the
extracted targets as a linear combination of discrete Diracs, which
corresponds to computing the image R
ω
(u
0
) = w
0
+ D
ω
(C ), not-
ing D
ω
(C ) =
P
T
j=1
A
j
δ
bx
j
e,by
j
e
, and δ
(k,`)
the discrete Dirac
centered at (k, `) (taking the value 0 everywhere except at position
(k, `) where it takes the value 1). An example of such recombined
image is displayed in Fig. 3 (b). Beyond the interesting sidelobes
suppression offered by this approach, we illustrate in the next sec-
tion how such a decomposition can improve the quality of speckle
reduction methods.
4. IMPACT OF RESAMPLING AND TARGET
EXTRACTION ON SPECKLE FILTERING
With the short revisit time of TerraSAR-X and Sentinel-1 satellite
constellations, long time series can be obtained. These SAR im-
ages can then be combined in order to produce images with strongly
suppressed speckle while preserving the spatial resolution. The re-
cent RABASAR framework [4] offers a simple yet surprisingly ef-
ficient way to exploit the temporal information: a so-called super-
image is produced by combining temporal multi-looking and an ad-
(a) pseudo-raw image u
0
(b) recombined image R
ω
(u
0
)
(c) speckle component w
0
(d) target component S
0
(C )
Fig. 3: Speckle plus target decomposition of Sentinel-1 images.
We display in (a) the modulus of a pseudo-raw image u
0
, in (c) the
modulus of its speckle component w
0
and in (d) the modulus of its
target component S
0
(C ). The set of targets C extracted from u
0
was computed using the decomposition algorithm proposed in [3].
By construction, we have u
0
= w
0
+ S
0
(C ). Replacing the linear
combination of cardinal sines S
0
(C ) by a linear combination of dis-
crete Diracs D
ω
(C ) in this additive decomposition yields the image
R
ω
(u
0
), whose modulus is displayed in (b): this image is free of
sidelobe effects.
(a) stack of SLC images (b) super-image
(c) stack of (subsampled) ratios (d) stack of denoised images
Fig. 4: Principle of multi-temporal speckle reduction with
RABASAR. Temporal multi-looking of a stack of SLC images (a)
and an additional speckle-reduction step produce a high signal-to-
noise ratio image called the super-image (b). Dividing the stack (a)
by the super-image (b) gives a stack of ratio images (c). Time-
specific changes are visible in these ratio images. After speckle re-
duction of the ratio images and recombination with the super-image,
the final stack of restored images is obtained (d). One can notice that
the stack of denoised images (d) is more faithful to the stack of SLC
images (a) than the super-image (b). However, in this framework,
subsampling of the ratio images (c) is necessary to avoid restoration
artifacts caused by strong speckle correlations.
ditional spatial speckle-reduction step designed to remove the resid-
ual speckle fluctuations. This super-image contains most of the spa-
tial structures that are present in an image at any given date t (roads,
field boundaries, buildings, forests), but at a much improved signal-
(a) SLC image (b) RABASAR denoising of (a)
without subsampling
(c) RABASAR denoising of (a) (d) RABASAR denoising of R
ω
(u
0
)
using subsampling of factor 2
Fig. 5: Denoising a stack of TerraSAR-X SLC images. We used
RABASAR to denoise a stack of 20 SLC images. We display in (a)
one of the images of this stack. On the one hand, denoising (a) with-
out subsampling the intermediate ratio image yields the image (b)
with artifacts in homogeneous areas, due to the spatial correlations
of the speckle. One the other hand, using subsampling reduces those
artifacts but affects the image quality: we observe in (c) a loss of
details and some aliasing artifacts. Besides, in both situations (b)
and (c), we can observe that targets that were not present in the initial
image appear in the denoised image (e.g. in the yellow rectangle).
Noting u
0
the pseudo-raw image associated to (a), we display in (d)
the denoising of R
ω
(u
0
) obtained using the super-image computed
from the speckle-components w
0
of the whole stack. Image (d) is
free of the artifacts observed in (b) and (c).
to-noise ratio, as illustrated in Fig. 4 (b). However, the reflectivity of
the scene varies from one date to another and some abrupt changes
may occur. In order to produce a despeckled image that is faithful
to the content of the image at date t, the ratio image between the
observation at date t and the super-image is formed. This ratio is fil-
tered using a single-image speckle reduction algorithm. Should the
super-image perfectly match the reflectivity of the scene at date t,
the ratio image will contain pure (stationary) speckle noise. On the
converse, areas where the reflectivity at date t differs from the super-
image will appear in the ratio image as a speckle with a mean value
that differs from 1. After despeckling this ratio image, the filtered
image at date t is obtained by multiplication with the super-image,
as illustrated in Fig. 4 (d). See [4] for more details on the method.
In RABASAR framework, two speckle-reduction steps are per-
formed: one to obtain the super-image, the other to filter the ratio
image. In each of these two steps, spatial correlation of the speckle
is an issue. In practice, images are down-sampled to reduce speckle
correlation, which causes a resolution loss. This is illustrated in
Fig. 5 (TerraSAR-X) and Fig. 6 (Sentinel-1), where we can see that,
without subsampling prior to despeckling, the denoised image (b)
exhibits some strong artefacts in homogeneous areas, while, when
subsampling is used, the artefacts are attenuated at the cost of a
severe loss of resolution in the denoised image (c) and even alias-
ing artifacts (visible in Fig. 5). Another issue in the multi-temporal
filtering by RABASAR is that some bright targets, present in the
super-image but not in a given SLC image at time t, may appear
when multiplying the denoised ratio by the super-image, at the end
(a) SLC image (b) RABASAR denoising of (a)
without subsampling
(c) RABASAR denoising of (a) (d) RABASAR denoising of R
ω
(u
0
)
using subsampling of factor 2
Fig. 6: Denoising a stack of Sentinel-1 images. We performed the
same experiment as in Fig. 5 on a stack of Sentinel-1 SLC images.
The restoration (b) displays the same artifacts in homogeneous areas
as observed in Fig. 5. Those artefacts are avoided in (c), thanks
to subsampling before despeckling, but also in (d), thanks to the
speckle plus target decomposition. Restoration (d) has a slightly im-
proved resolution compared to (b) and also avoids phantom targets
such as that observed in the yellow rectangle. However, the differ-
ences between those two restoration is more modest than in the case
of the TerraSAR-X images of Fig. 5. It seems to be harder, at the
spatial resolution of Sentinel-1, to preserve fine details during the
MuLoG denoising step involved in RABASAR.
of the process. This is illustrated in Fig. 5 and Fig. 6, where we indi-
cate with a yellow rectangle, the presence of a phantom target that is
present (b) and (c), but absent in the initial SLC image (a). Thanks
to the speckle plus target decomposition described in Section 3, we
are able to replace each pseudo-raw SLC image u
0
of the stack by a
SLC image R
ω
(u
0
) = w
0
+ D
ω
(C ), where the speckle component
w
0
has no spatial speckle correlations in homogeneous areas and
D
ω
(C ) is a linear combination of discrete Diracs. Besides, com-
puting the super-image only using the stack of speckle components
w
0
yields an image without bright targets. Therefore, applying the
RABASAR framework to denoise a SLC image R
ω
(u
0
) using such
target-free super-image prevents the aforementioned phantom target
phenomenon. Besides, the ratio between R
ω
(u
0
) and the super-
image being uncorrelated, it can be efficiently denoised, as we show
in Fig. 5 (d) and Fig. 6 (d).
5. REFERENCES
[1] N. Miranda, “Definition of the TOPS SLC deramping function
for products generated by the S-1 IPF,” Tech. Rep., ESA, 2014.
[2] R. Abergel, S. Ladjal, F. Tupin, and J. Nicolas, “A complex
spectrum based SAR image resampling method with restricted
target sidelobes and statistics preservation,” in IGARSS, 2017.
[3] R. Abergel, L. Denis, S. Ladjal, and F. Tupin, “Subpixellic
methods for sidelobes suppression and strong targets extraction
in single look complex SAR images,” IEEE JSTARS, 2018.
[4] W. Zhao, C. Deledalle, L. Denis, H. Ma
ˆ
ıtre, J. Nicolas, and
F. Tupin, “RABASAR: A fast ratio based multi-temporal SAR
despeckling,” in IGARSS, 2018.