IEEE Geoscience and Remote Sensing Magazine - June 2020 - 73
performance in dealing with high topographies and heterogeneities (such as isolated scenes). For clarity, the NL-filter
processing flowchart is presented as Figure 10.
in a local region, overcoming the neighbor-connection
limitation. The NL-filter concept can be traced to Lee's pioneering work [79]; Buades's seminal contributions [80], [81]
developed the patch-based filter framework. NL filters were
incorporated into InSAR by establishing a new technology
known as NL-InSAR [21], which is one of the most typical
and effective phase-denoising methods. NL filters employ
the patch-wise method to measure the patch similarity in
the interferogram domain, and the weighted average is applied to estimate the filtered interferogram and phase denoising. With this framework, the most relevant samples
can be reliably selected, and phase denoising is achieved
by distinguishing the contributions among different samples. NL filters have the advantage of preserving the phase
fringe/texture by effectively capturing the phase structure
and extracting the phase redundancy in the patch space.
Compared with traditional local filters, NL filters are more
powerful and possess unique superiorities, such as better
Goldstein Filter
3
2
1
uI ux =
/ ~ u,t $ I zt
t
/ ~ u,t , ~ u = /t ~ u,t,
(23)
t
where ~ u, t is the weighted coefficient derived by considering the contribution from the pixel at site t. The key idea
behind the NL filter is that the weight, ~ u, t, is measured
from the similarity between patches C u (centered at site u)
3
2
1
0
0
-1
Wavelet Filter
CONCEPT OF NONLOCAL FILTERS
Buades [80], [81] established the NL-filter framework
through the patch-based method and weighted-average
strategy. To estimate the noise-free interferogram at site u,
the generalized formulation of the NL filter is expressed as
0.8
0.6
0.4
-1
-2
-2
0.2
-3
-3
0
3
2
1
3
2
1
0
0
-1
0.8
0.6
-1
0.4
-2
-2
0.2
-3
-3
(a)
(b)
(c)
(d)
0
FIGURE 9. The filtered phase images obtained using transformed-domain filters. The (a) filtered phase, (b) phase difference, (c) residues,
and (d) coherence of the filtered images. The first and second rows show the Goldstein [62] and wavelet filters [29], respectively.
Patch-Similarity Modeling
in the Image Space
Patch Space
Stacking
and
Grouping
Average or
Collaborative
Filtering
Noise-Reduced Images
(Phase and Intensity)
Reprojection
Parameter
Estimation
FIGURE 10. A processing flowchart for NL filters.
JUNE 2020
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
73
IEEE Geoscience and Remote Sensing Magazine - June 2020
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