Retrieval of Environmental and Geophysical Parameters Through Bayesian Fusion of ERS and RADARSAT Data
|Edmond Nezry, Francis Yakam-Simen, Iwan Supit, Francis Zagolski
||PRIVATEERS NV, Great Bay Marina, P.O. Box 190, Philipsburg, Sint Maarten, Netherlands Antilles
Two new Bayesian vector speckle filters have been developed for multi-channel SAR images.
This filters incorporate first and second order statistical descriptions of the scene and
of the speckle in multi-channel SAR images. Since these new filters present the structure
of data fusion control systems, speckle filtering should be regarded as the first step of
application oriented control systems to exploit the synergy between SAR sensors. Such a
control system allowing the retrieval of soil roughness and soil moisture as well as the
identification of snow covered areas from ERS and Radarsat images through Bayesian data
fusion is presented. Results show that: 1) the new speckle filters present convincing
performances for speckle reduction as well as for texture preservation and for small scene
objects detection, 2) the retrieval of soil roughness and soil moisture as well as the
identification of snow covered areas through Bayesian data fusion of ERS and Radarsat data
provide valuable results.
Keywords: environmental monitoring, ERS/RADARSAT synergy, soil moisture, soil
roughness, snow cover, control systems
Important issues of interest in the field of multi-channel SAR images processing remain still
open. Among them, the introduction of A Priori knowledge (or guess) in the processing of multi-
SAR's images and multi-date SAR images. In the case of mono-channel SAR images, a Bayesian method,
the Maximum A Posteriori (MAP) filtering method has already proved to be particularly suited for
the restoration of both the radar reflectivity and the textural properties of natural scenes .
In the case of multi-channel detected SAR images, as described in [1,2], the i-th component Ri
(channel i) of the radar reflectivity vector R is obtained when:
where I is the speckled intensity vector available in the actual SAR data.
P(I/R) is the joint probability density function (pdf) of the speckle.
P(R) is the joint pdf of the radar reflectivity, introduced as statistical A Priori
information in the restoration process. The first term of Eq. 1, (Maximum Likelihood) accounts for
the effects of the compound imaging system. The second term (Maximum A Priori) represents the prior
statistical knowledge of the imaged scene. In the Bayesian inference process, induction is
influenced by the prior expectations allowed by the prior knowledge of P(R). Also the
non-linear system and scene effects are taken into account by the restoration process. Therefore
MAP speckle filtering can be considered as a controlled restoration of R, where A Priori
knowledge controls the inference process, allowing an accurate estimation of the radar
backscattering coefficients i.
At this point, additional Bayesian processes can be designed to retrieve important environmental and
geo-physical parameters, in a cascade of control processes.
2. Multi-channel scene model
It is now well established that a Gamma pdf would be the most suitable representation of the first
order statistical properties of a natural scene. However, to describe these properties as viewed by
diverse SAR sensors (different scene physics) or at different dates (scene evolution), there is no
analytic multivariate Gamma pdf available. Therefore, we will use in the following a multivariate
Gaussian pdf as analytic multi-channel (i.e. coupled) scene statistical model. This statistical
model is convenient to preserve the mathematical tractability of the problem. In addition, the Gaussian
model is still commonly used to describe the statistical properties of natural scenes.
3. Speckle models and MAP filters
Let first consider the case of very different SAR sensors (very different wavelengths, for instance).
In this case, it is justified to consider that the speckle is independent between the N image channels.
Under this assumption, P(I/R) can be modelled as a set of N independent Gamma
distributions. Under this assumption, the Gamma-Gaussian MAP filter for multi-channel detected
SAR images (N channels) comes down to the resolution of a set of N scalar equations :
where Cr is the covariance matrix of the scene, (1i ) is a vector where all components but the ith
are equal to zero, and the Li are the Equivalent Numbers of Looks (ENL) of the individual SAR images.
Replacing the speckle noise model by the convenient optical noise model in the concerned image channels,
this filter adapts easily to the case of multi-channel optical and SAR images. Thus, the introduction
of coupling between the scene statistical representations is already a data fusion process.
On the other hand, in the case of multi-date images acquired on repeat-pass by the same SAR sensor, or
of a set of images acquired by diverse SAR’s with similar properties (similar orbit, track, frequency
and resolution, with only different polarisation configuration, or small differences in incidence angle,
for example), the correlation of the speckle between SAR image channels should be taken into account to
deal optimally with system effects in the series. In theory, P(I/R) should be a
multivariate Gamma pdf. Nevertheless, since there is no analytic multivariate Gamma pdf available,
another reasonable choice for P(I/R) must be done for the sake of mathematical
tractability: Lee  has shown that, in the case of multilook SAR images (more than 3-looks),
P(I/R) can be reasonably approximated by a Gaussian distribution. Under this assumption,
the Gaussian-Gaussian MAP filter for multi-channel detected multilook SAR images is the set of
where Cs is the covariance matrix of the speckle.
4. MAP filters and control systems
These filters offer numerous advantages, which are described in : non linear image restoration,
preservation of high-resolution through the correction of the effects of the compound multi-sensor
imaging system, improvement of the probability of detection of thin scene structures due to both the
diversity and redundancy aspects of information in all the channels.
Nevertheless, the most remarkable feature is that they present the structure of control systems. Both
Eqs. (2) and (3) can be rewritten as Riccati’s algebraic equations:
Equation (4) represents the optimal state controlled reconstruction at constant gain of linear invariant
processes (R and textures of the channels) perturbed by white noises (speckle, pixel spatial
mismatch between channels). It can easily be shown that the scene A Priori model acts as a command, and
that the covariance matrices act as multipoles or controls.
5. Filtering of ERS / RADARSAT data set
This new filtering technique is evaluated on a couple of Radarsat (C-HH) and ERS-1 (C-VV) SAR images,
acquired along descending passes within 4 hours on Feb. 13, 1996. Figure 1 (left column) shows a detail of
the Radarsat (up) and ERS-1 (bottom) images, around the Schipol-Amsterdam airport in the Netherlands.
Figure 1: Upper images: original ERS-1 PRI image (13 Feb. 1996, @ESA/Eurimage 1996) and its
filtered version. Bottom images: original Radarsat Standard Beam image (13 Feb. 1996, @Radarsat
International 1996) and its filtered version (Gaussian-Gaussian MAP filter for multi-channel detected
SAR images, 9x9 basic window size).
The Radarsat and ERS SAR’s operate at the same frequency from a very similar orbit (similar altitude
and inclination angle). In this case, the angles of incidence are also very similar and image
superimposition is possible without geometrical corrections over wide areas. The two sensors differ
only in polarisation configuration, so that they are sensitive to similar physical properties of extended
land areas, even if these properties do not contribute in the same amount to the backscattered signal.
However, their different sensitivity to structural scene elements is of major interest for the
identification of these particular targets. In this context, it is appropriate to use the new
Gaussian-Gaussian MAP filter. The filtered images are shown in Figure 1 (right images). Thin details such
as roads, runways, airport terminals, planes, point targets in the built-up areas, are very well denoised
and preserved, as it is also the case for field edges. On the other hand, speckle noise is strongly
filtered within the surrounding homogeneous agricultural fields (ENL=120 for Radarsat, ENL=100 for ERS-1).
For both images, the filtered images were found superior in quality to the images filtered using the
mono-channel Gamma-Gamma MAP filter  using the same structure detection algorithm .
6. Bayesian retrieval of soil parameters
Haddad & Dubois  have developed a Bayesian estimation method of soil roughness and soil moisture.
Although their method present some built-in limitations (the imaginary part of the dielectric constant
is not taken into account, no dependence on the surface correlation,
cf. ), it is based on the same principle as our new filtering method and present common
Since our data are accurately filtered and calibrated, instead of the model presented in , we can use
directly the soil backscattering empirical model of Dubois et al. :
where is the wave incidence angle,
is the radar wavelength, is the soil dielectric constant, and h is
the r.m.s. height (soil roughness).
Using Bayes’ theorem, the unnormalised version of the conditional joint probability of
(,h) verifies :
The optimum unbiased estimator for that has minimum variance is
the conditional mean :
Finally, the dielectric constant is converted to volumetric soil moisture through a set of empirical
With our data accurately filtered and calibrated, the nature of the randomness present in (m,n) can only
be due to relief. Since our Netherlands area present negligible relief, P(M1,M2) is reasonably assumed a
Dirac distribution. This results in a straightforward estimation of
P(,h|m,n), i.e. a drastic simplification of the process
and potentially more accurate results.
Results of this method, applied over the Netherlands (area size 73x63 km), are shown in Figure 2. Note
that at this period of the year (February), the low or non-existent vegetation layer does not affect
significantly the retrieval of soil parameters over agricultural areas (crops/pasture).
Figure 2: The Netherlands on February 13, 1996. Area size: 73x63 km. Red: soil roughness map.
Green: soil moisture map. Blue: snow cover map.
Maps produced using ERS-1 and Radarsat SAR imagery.
As shown in this figure, snow covered areas (thin snow layer of a few centimeters), difficult to identify
in the original SAR images, can be identified by simple classification of the soil moisture and roughness
The interest of the quantitative results (especially soil moisture) for the initialisation of
agro-meteorological and growth models has already been widely expressed. In addition, since soil roughness
(in red) allows also the identification of cultivated areas, such a result can be a useful as a
photo-interpretation tool, to support other agriculture applications such as crop surfaces estimation ,
or to monitor special environmental conditions (snow cover, frozen lakes, etc.).
Two new Bayesian speckle filters have been developed for multi-channel SAR images, with very convincing
results. The Gaussian-Gaussian MAP filter SAR images is suitable to process series of images from the
same SAR system operating in repeat-pass mode or from diverse SAR’s systems with relatively close
properties. The Gamma-Gaussian MAP filter is suitable to process series of images originating from
different SAR systems (different frequencies, incidence angles, or spatial resolution, but same
spatial sampling). Combined with the two-points statistics based algorithm presented in , these
filtering techniques are able to produce filtered images without loss in spatial resolution. Within
homogeneous areas, speckle noise is strongly filtered, allowing the accurate estimation of
required by most of the remote sensing SAR applications such as
the retrieval of soil parameters (roughness and moisture).
The major interest of this technique is that we apply pure control systems. This offers wide
possibilities for the choice and the design of additional commands (statistical or physical models)
for further data exploitation. In this view, speckle filtering should be regarded as the first step
of integrated application oriented control systems rather than of processing chains.
The ERS-1 and Radarsat images have been provided by the European Space Agency (Project PE-FRNE2) and
the Canadian Space Agency (Project ADRO#581).
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