Method for iterative disk masking and automatic error repair for phase unwrapping

Disclosed is a new alternative method for the phase unwrapping of the interferogram of two SAR (Synthetic Aperture Radar) images of the same area. This new method uses an iterative approach to the phase unwrapping problem by applying local circular or elliptical masks centered on the phase residues. A phase unwrapping error is detected automatically during the unwrapping process by comparing each unwrapped value with neighboring unwrapped values. This new method for phase unwrapping significantly improves the quality of unwrapped phase maps. This will allow extraction of quantitative information such as height and deformation from interferometric SAR measurements. This is significant for the routine application of SAR interferometry in fields like digital elevation mapping and large scale deformation mapping.

The file of this patent contains at least one drawing executed in color. 
Copies of this patent with color drawing(s) will be provided by the Patent 
and Trademark Office upon request and payment of the necessary fee. 
The present invention relates to terrain mapping employing Synthetic 
Aperture Radar (SAR) and more particularly disk masking and automatic 
repair of phase unwrapping. 
BACKGROUND OF THE INVENTION 
There exists a need for inexpensive, accurate and quickly formed terrain 
maps. 
One method has been to use Synthetic Aperture Radar (SAR) which is operated 
on board of aircraft or spacecraft for mapping of the earth's surface with 
high resolution. Since the late 1980's, a new SAR technique, called SAR 
interferometry, has received much attention. In SAR interferometry, two 
SAR recordings of the same area are combined into a SAR interferogram. 
These two SAR data sets might be collected by two antennas on the same 
airborne or spaceborne platform. The most significant extra information in 
the interferogram is the phase difference between the two images. This 
phase difference for each pixel is directly related to the height of the 
local topography, and the height of that pixel can be calculated provided 
that we know, very accurately, the position of the recording platform(s) 
and the range and timing of the measurements. 
Alternatively, interferometric data might be collected by a single antenna 
system by repeating the data collection in a second pass over the same 
area. This is referred to as SAR repeat-pass interferometry. The phase 
difference between the images is, in this case, also dependent on very 
small motions or deformation of the earth's surface. If the interferogram 
and the geometry information are combined with an input DEM (Digital 
Elevation Model), this deformation information can be extracted. Typical 
accuracies are in the cm or mm range. Applications lie in the areas of 
mapping and monitoring deformation caused by earthquakes, volcanic 
eruptions, landslides and land subsidence. 
An example of an interferogram showing the phase difference between the 
images of two passes is given in FIG. 1. This is an image of a mountainous 
area in Japan collected by the JERS-1 (Japanese spaceborne SAR system). 
The image has dimensions of approximately 5.times.5 km and is filtered 
using an adaptive box filtering method. From this figure it becomes clear 
that there are two basic problems with repeat-pass interferometry: 
1. The phase is ambiguous. In this case, every cycle of phase corresponds 
with a height difference of approximately 100 m. The phase values do not 
directly relate to an absolute height. 
2. The phase is quite noisy (the phase coherence is low). 
Therefore, in order to extract absolute height information from the 
interferogram of FIG. 1, the interferogram has to be "phase unwrapped." 
For every pixel an integer number of cycles of phase should be added is a 
correct way without introducing phase unwrapping errors. 
Because of the low phase coherence and the occurrence of radar specific 
distortions in the image (e.g. layover of mountains), phase unwrapping is 
considered to be one of the most challenging problems in interferometric 
SAR processing and much research is devoted in the to develop robust phase 
unwrapping methods, particularly for repeat-pass interferometry, where the 
phase coherence is relatively low. 
A number of methods of phase unwrapping have been proposed in literature: 
1. Path dependent integration methods where areas of low power or low phase 
coherence are masked. This approach has been shown to work quite well for 
airborne interferometry (2 antennas on one platform) but does not work 
well for repeat-pass interferometry because of the lower phase coherence. 
This method is sometimes combined with phase residue connection methods 
(eg. Prati et al, "SAR interferometry: a 2-D phase unwrapping technique 
based on phase and absolute values information", Proceedings of the 
International Geoscience and Remote Sensing Symposium 1990, Washington, 
May 1990). 
2. The use of phase residues connection methods. These methods are often 
also path dependent. A phase residue map can be directly obtained from the 
interferogram. A phase residue represents a potential origin of phase 
unwrapping errors. If a single positive or negative residue is encircled 
during the unwrapping process, a global error will occur and might 
propagate, deteriorating the quality of the unwrapped phase maps 
significantly. Therefore, frequently pairs or multiples of related 
positive or negative residues are connected by so-called artificial ghost 
lines to prevent the integration path from crossing. The first publication 
using this method was written by Goldstein et al, "Satellite radar 
interferometry, Two-dimensional phase unwrapping", Radio Science, Vol 23, 
Nr 4, Pp 713-720, 1988. Since then, many investigators have tried to 
optimize this technique for repeat-pass interferometry (eg. Hartyl and Wu, 
"SAR interferometry: experiences with various phase unwrapping methods" 
Proceedings of the 2nd ERS-1 Symposium ESA SP-361, Hamburg, 1993). The 
basic strategy of many methods like these is to minimize the total residue 
connection length in some way. The problem is that it is not always 
possible to find the related positive and negative residues that should be 
connected. If a wrong connection is made, serious global unwrapping errors 
can occur, particularly in low coherence interferograms that are obtained 
by using ERS-1 (European ERS-1, 35 days repeat period), Japanese ERS-1 (42 
day repeat period) and RADARSAT (24 days repeat period). 
3. The use of path independent phase unwrapping methods. Some methods have 
been proposed that attempt to solve the phase unwrapping problem in a 
global way, by solving the Poisson equation. These methods are very 
experimental and have seemingly not yet yielded practical implementations 
that work satisfactorily on real data 
SUMMARY OF THE INVENTION 
Accordingly, it is an object of the invention to provide a new and improved 
alternative method for the phase unwrapping of the interferogram of two 
SAR (Synthetic Aperture Radar) images of the same area by employing 
iterative disk masking and automatic error repair which produces an image 
which is free from global unwrapping errors and prevents the propagation 
of local errors. 
It is another object of the invention to provide a new and improved method 
for phase unwrapping which significantly improves the quality of unwrapped 
phase maps. 
It is yet another object of the invention to provide a new and improved 
method for phase unwrapping which allows extraction of quantitative 
information such as height and deformation from interferometric SAR 
measurement which is significant for the routine application of SAR 
interferometry in fields like digital elevation mapping and large scale 
deformation mapping. 
It is a further object of this invention to provide a new and improved 
method for phase unwrapping whose execution is feasible, even for larger 
scenes. 
The invention and objects and features thereof will be more fully 
understood from the following detailed description and appended claims 
when taken with the drawings.

DETAILED DESCRIPTION OF THE INVENTION 
This new phase unwrapping method uses an iterative approach to the phase 
unwrapping problem by applying local circular or elliptical masks centered 
on the phase residues. A phase unwrapping error is detected automatically 
during the unwrapping process by comparing each unwrapped value with 
neighbouring unwrapped values. If the difference is larger than half a 
cycle of phase, it represents a phase unwrapping discontinuity (error). If 
a phase unwrapping error has been detected, the image is cleaned and a new 
mask is created with a larger local mask size. The phase unwrapping 
process is then restarted. If a phase unwrapping error is detected again, 
the image is cleaned again and the mask size is enlarged again. This 
process is repeated until no phase unwrapping error is detected. The image 
that has now been obtained is free from global unwrapping errors but still 
contains masked areas that have not been unwrapped. These remaining areas 
are unwrapped in a number of subsequent cycles, where the local mask size 
is reduced stepwise and the pixels that were released are unwrapped. 
During those subsequent cycles, the unwrapped values will not be checked 
for unwrapping errors. In principle, local errors might occur but they 
will not propagate. 
The method can be schematized as follows: 
start unwrapping, error detected 
clean phase image, enlarge masks 
restart unwrapping, error detected 
clean phase image, enlarge masks 
restart unwrapping, error detected 
restart unwrapping, successfully finished global unwrapping without errors 
replace masks with smaller masks 
continue unwrapping 
replace masks with smaller masks 
continue unwrapping 
remove remaining masks 
continue unwrapping, finished unwrapping process 
The occurrence and severity of local phase unwrapping errors can be reduced 
by using an additional low coherence mask during the iterative disk 
masking. Every pixel that is associated with low coherence will also 
create local circular of elliptical disk masks centered on that pixel. 
Execution of this method is even feasible for larger scenes. 
This phase unwrapping method is illustrated by showing intermediate results 
of the processing of the JERS-1 interferogram of FIG. 1. The image can be 
considered to be a difficult test case for unwrapping because the phase 
coherence is low and ranges between 0.2 and 0.5 in most of the land areas. 
The height in the scene varies between 0 and 500 meter. 
FIGS. 2a and 2b show the unwrapping mask and the unwrapped image after the 
first cycle of unwrapping with a circular disk mask with a radius of 10 
pixels. The residues are indicated in blue (positive) and red (negative), 
and the disk masks are displayed as dark grey disks centered on the 
residues. Black indicates areas that have not been unwrapped yet, light 
grey indicates that the pixel has been unwrapped. In the unwrapped image 
it is visible that only part of the image has been unwrapped, and that an 
error has occurred in the lower right of the image and the unwrapping 
process has stopped. 
FIGS. 3a and 3b show the unwrapping mask and unwrapped image after an 
unwrapping cycle with a circular disk mask with a radius after 15 pixels. 
The image has now been unwrapped successfully without unwrapping errors. 
FIGS. 4a and 4b show the image after a number of subsequent reductions of 
the disk size (the disk radius is equal to 10 pixels) and unwrapping of 
the "released" pixels. As can be seen from these figures, two lines of 
phase discontinuities appear between isolated phase residues of opposite 
signs. These discontinuity lines are related to layover (radar 
distortions) and were correctly identified by the unwrapping process. 
FIGS. 5a and 5b show the mask and unwrapped phase image when the disk size 
has been reduced to 5 pixels. No global unwrapping areas can be 
identified. 
FIG. 6 shows a final unwrapped image where the unwrapping disk mask size 
has been reduced to zero and coherence (noise) measurements are used to 
mask out ocean areas (and small local areas on the land) for presentation 
purposes. A satisfactory absolute phase map has been produced that can be 
directly converted to a DEM (digital elevation map). 
In accordance with one aspect of the present invention, there is provided a 
method of phase unwrapping of the interferogram of two synthetic radar 
images of the same area comprising: a) means for applying local circular 
or elliptical masks centered on the phase residues; b) means for 
automatically detecting phase unwrapping errors during the unwrapping 
process; c) means for stopping and restarting the phase unwrapping 
process; d) means for cleaning the image at any stage in the process; and 
e) means for increasing and decreasing the local mask size as required. 
The invention may be embodied in other specific forms without departing 
from the spirit or essential characteristics thereof. The present 
embodiments are therefore to be considered as illustrative and not 
restrictive, the scope of the invention being indicated by the appended 
claims rather than by the foregoing description, and all changes that come 
within the meaning and range of equivalency of the claims are therefore 
intended to be embraced therein.