IEEE Geoscience and Remote Sensing Magazine - September 2013 - 23

time there are no parameters to estimate on segments, as
for GG. Thus, a classified approach consists of switching
among different estimators, e.g., MAP-LG and LMMSE,
depending on the degree of texture of each segment. In
Fig. 10-(c) and 10-(d), the results of MAP-GG and MAP-LG
estimators, the former with segmentation (GG-MAP-S),
the latter with classification (LG-MAP-C), on the image
in Fig. 10-(a) are shown.
A segmentation based approach seems also a natural
solution to changes in the speckle model occurring as
the spatial resolution of single-look products increases.
This happens for very high resolution (VHR) new generation SAR systems, especially with Spotlight products. As
the size of the elementary resolution cell decreases, the
assumption of distributed scatterers is less and less verified. In substance, what is homogeneous at 10 m scale
may no longer be so at 1 m. So, we expect that VHR SAR
images are more textured and contain more persistent
scatterers, and less homogeneous regions, than earlier
products. A viable solution with segmented processing in
UDWT domain is introducing corrective factors for under
smoothing in textured segments, depending on the class
of texture energy measured in the UDWT domain, analogously to what proposed in [78].
VI. NON-LOCAL MEAN FILTERING
The NL mean (NLM) filter proposed by Buades et al. in
[110] is based on the simple idea of estimating the noise
free image as a weighted average of noisy pixels

tf (n) = / m w (n, m) g (m) ,

/ m w (n, m)

(33)

(a)

where the weights w ^n, m h take into account the "similarity" between pixels g ^n h and g ^m h . The key idea of
the NLM filter is that the weights w ^n, m h are based on
the Euclidean distance between local patches centered at
g ^n h and g ^m h, according to
1
w (n, m) = exp c - h / a k g (n + k) - g (m + k) 2 m ,

(34)

k

where a k 's define a Gaussian window and h controls the
decay of the exponential function.
The NLM filter obtains a very good performance in the
presence of additive white Gaussian noise, since the Euclidean distance is a natural similarity measure for this kind of
model. However, in the case of SAR images, the weights have
to be generalized to the case of multiplicative and non-Gaussian speckle. It is also interesting to combine the effectiveness
of the NL principle with the benefits of the sparse representation offered by the wavelet transform. In the following, we
will review two SAR despeckling filters based on the NL principle in the spatial [108] and in the wavelet domain [109].
A. ProbAbilistic PAtch-bAsed Filter
The probabilistic patch-based (PPB) filter, proposed by
Deledalle et al. in [108], extends the NLM filter to the
domain of SAR images by exploiting its connections to
the weighted maximum likelihood extimator (WMLE).
Namely, under the WMLE principle the noise-free image
can be estimated as the value maximizing a weighted likelihood function of the observed data

tf (n) = arg max / w (n, m) log p (g (m)
f

f ).

(35)

m

(b)

FIGuRE 11. Examples of the application of (a) PPB filter and (b) SAR-BM3D filter to the 4-look COSMO-SkyMed image in Fig. 10-(a).
September 2013

ieee Geoscience and remote sensing magazine

23



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