IEEE Geoscience and Remote Sensing Magazine - June 2020 - 68

that there has been no significant growth in the number
of publications since 2002, indicating the relatively mature
status of the research. The NL filter can be treated as a new
generation of phase-denoising technology. Figure 4 displays
the publication statistics for NL filters and shows that there
has been significant research growth since 2009. Considering one typical advanced technique, publication statistics for

REVIEW OF LOCAL FILTERS
As a mature research field, local-filter methods have a long
history, and the multilook filter [11], [30]-[32] can be treated as one of the very earliest. The basic principle of these
methods employs a local window with pixels connected to
select stationary and homogenous samples for phase estimation. In this section, the introduction of local filters is
divided into four groups. For clarity, a processing flowchart
is shown in Figure 6.

Total Number of Publications

25
20
15
10
5

sparse methods are given in Figure 5. As a very new technology, the sparse techniques methods have had limited study
and need more attention to evaluate their potential. In the
following, a nonexhaustive review is attempted to classify
the existing methods, analyzing the strengths and limitations of different technologies.

FIGURE 3. The number of publications concerning local- and
transformed-domain filters.

MEDIAN/MEAN FILTERS
These methods utilize the mathematical morphologies of
mean [19], [33]-[36] and median [16]-[18], [37]-[39] functions to estimate the phase, assuming that the local phase in a
small window is statistically stationary and homogenous so
that it follows the IID assumption. The purpose of a pivoting
mean/median filter is to obtain optimal filtered results from
local statistics. The formulation of the pivoting mean filter is
expressed as

Total Number of Publications

zu xmean (k, l) =

d k, l =

15
10
5

09
20

FIGURE 4. The number of publications covering NL filters.

4
Total Number of Publications

^ kl , llh ! win^ k, l h

S z ^kl , llh
mm + + ^d k, l h
d k, l

S z ^kl , llh,

(12)

where win(k, l) is a filter window centered at site (k, l),
zu mean
(k, l) is the estimated phase of pixel (k, l), and mean ^ $ h
x
is an average operator. Meanwhile, the formulation of the
median filter is given by

3
2

19
95
19
97
19
99
20
01
20
03
20
05
20
07
20
09
20
11
20
13
20
15
20
17

FIGURE 5. The number of publications about sparse methods.

mean c + c

^ kl , llh ! win^ k, l h

S z ^kl , llh
mm + + ^d k, l h,
zu xmedian (k, l) = median c + c d
^ kl , llh ! win^ k, l h

k, l

(13)

where median ^ $ h is a median operator. The preconditions
for both filters depend significantly on the local phase's
stationary and homogenous property: the topography
fluctuation in the local region is slow for the sampling
rate, and the adjacent pixels have a high correlation. When
the noise is additive Gaussian noise, the pivoting mean
filter is statistically optimal from the view of ML estimation. However, the stationary and homogenous assumption conflicts with fast topography variations. Similar to
the multilook filter, the mean filter has an oversmoothing effect and cannot deal well with the phase details of
rapid topography variations. Compared with the mean
filter, the pivoting median form has a better preservation
of the phase fringe, but the power of its noise suppression
reduces to some degree. Besides, one major limitation is
that this group of methods is nonadaptive, regardless of
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

JUNE 2020

IEEE Geoscience and Remote Sensing Magazine - June 2020

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