IEEE Geoscience and Remote Sensing Magazine - June 2020 - 71

its refined versions [63]-[74]. The basic idea ties into the
fact that the interferometric phase is locally stationary and
homogeneous, and most of the useful components of the
local phase are typically limited to a narrow band, while
the noise is distributed through the entire frequency band.
The Goldstein filter transfers the interferometric phase image into the frequency domain and weights the phase spectrum for noise reduction. The generalized formulation of
the Goldstein filter is expressed as

Mean Filter

Filtered Phase

Su x(k, l) = IFFT2(SM (; Yzwin^p, q h;)a $ Yzwin(p, q)),

where Yzwin is the Fourier spectrum of the interferometric-phase image in a local window centered at site (k, l),
IFFT2($) is the 2D inverse Fourier transform, SM($) represents the smoothing operation, and a is the filtered
parameter. The proper selection of a is very important.
The  Goldstein filter's performance is significantly affected
by the patch size of the local window and filter parameter a.

Phase Difference
3
2
1
0
-1
-2
-3

Residue
3
2
1
0
-1
-2
-3

Median Filter

(a)
3
2
1
0
-1
-2
-3

3
2
1
0
-1
-2
-3

Local Frequency Estimator
of the ML Method

Lee Filter

(b)

Region-Growing

(19)

3
2
1
0
-1
-2

3
2
1
0
-1
-2

-3

-3
(c)

3
2
1
0
-1
-2

3
2
1
0
-1
-2

-3

-3
(d)

3
2
1
0
-1
-2

3
2
1
0
-1
-2

-3

-3
(e)

Coherence
0.8
0.6
0.4
0.2
0

0.8
0.6
0.4
0.2
0
0.8
0.6
0.4
0.2
0
0.8
0.6
0.4
0.2
0

0.8
0.6
0.4
0.2
0

FIGURE 7. The filtered phase images obtained using local filters. (a) The pivoting mean filter [19] (residue number: 2,831). (b) The pivoting

median filter [39] (residue number: 2,826). (c) The Lee filter [13] (residue number: 6,161). (d) The local frequency estimator derived through
the ML method [42] (residue number: 2,409). (e) The region-growing method [60] (residue number: 2,189).
JUNE 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

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IEEE Geoscience and Remote Sensing Magazine - June 2020

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