IEEE Geoscience and Remote Sensing Magazine - June 2021 - 32

0 dB, which is much smaller than the typical SNRs observed
for optical images. Needless to say, such strong noise can
be highly disruptive to the extraction of useful information,
altogether masking precious fine details of the imaged
scene. Hence, removing or at least reducing speckle is of paramount
importance for the success of SAR image processing
applications.
A primary way to reduce speckle intensity is multilooking,
which involves the incoherent averaging of multiple independent
observations of the same stochastic signal. The
multilooked signal keeps obeying the multiplicative noise
model of (1), with the same signal component as before,
but the noise term is now gamma-distributed with a pdf,
pn
() () () (),
exp
=-C
-
L 1
L
L nLnnu
L
[] ,
(4)
where L 12 represents the number of looks and ()$C is
the gamma function. In particular, due to the averaging,
the noise mean remains unitary,
reduces linearly with the number of looks, Va [] /nL1r =
En 1= but its variance
,
thus providing much cleaner images. Unfortunately, both
frequency and spatial multilooking, which are easily implemented,
cause a loss of spatial resolution, itself proportional
to L, which significantly impairs the value of SAR
images for the most advanced and demanding applications.
Temporal multilooking, on the contrary, preserves spatial
resolution but relies on hypotheses of signal ergodicity that
are rarely met. For these reasons, in the following, we mostly
focus on single-look images, L = 1, which are the most
valuable for applications, due to their high resolution, and
represent the most scientifically interesting condition.
Dealing with multiplicative noise may be challenging,
but there is a vast literature on the removal of additive
(signal-independent) noise, with a wealth of ideas, methods,
and algorithms that are definitely worth considering.
For these reasons, a common despeckling technique, called
the homomorphic approach, takes the log of the signal so as to
convert the problem into an additive one, perform additive
noise removal, and then take the exponent of the result to go
back to the original domain. Taking the log of (1), we obtain
a plain additive noise model,
yx ,n=+
uu u
(5)
where the log domain noise, ,nu follows a Fisher-Tippett distribution
[30],
pn
() () () (),
exp
u =-C
uu
L
L e
Le
with mean [] () ()log
} (, ),L1 where ()$} and (), L$}
En LL}=-u
Lnn
u n
L
(6)
and variance Va []nr =u
are the digamma function
and the polygamma function of order L, respectively. As
desired, neither the mean nor the variance depends on the
signal. However, the mean is nonzero and will not be removed
by any denoising algorithm, contributing a bias that
must be compensated for explicitly before going back to the
original domain.
The desire to exploit methods developed for the popular
additive white Gaussian noise (AWGN) case motivates
some researchers to approximate nu
as nonzero mean
Gaussian noise. Figure 2 compares Fisher-Tippet distributions
with Gaussian distributions that have the same mean
and variance. While for the case L 4= a reasonably good
match can be seen, this is certainly not true for the most
interesting condition of
L ,1=
for which the Gaussian approximation
is definitely unsuitable. Moreover, it should
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Fisher-Tippet
FIGURE 2. A comparison of Fisher-Tippet and Gaussian pdfs. (a) L = 1. (b) L = 4.
32
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE JUNE 2021
Mean -0.577
Variance 1.645
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-6 -4 -2 02 46 -6 -4 -2 02 46
(a)
(b)
Gaussian
Mean -0.13
Variance 0.284
IEEE Geoscience and Remote Sensing Magazine - June 2021

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