Tài liệu Digital Signal Processing Handbook P33 docx

Clay Stewart. “Synthetic Aperture Radar Algorithms.”
2000 CRC Press LLC. <>.
SyntheticApertureRadar
Algorithms
ClayStewart
ScienceApplicationsInternational
Corporation
VicLarson
ScienceApplicationsInternational
Corporation
33.1Introduction
33.2ImageFormation
Side-LookingAirborneRadar(SLAR)
•
UnfocusedSynthetic
ApertureRadar
•
FocusedSyntheticApertureRadar
33.3SARImageEnhancement
33.4AutomaticObjectDetectionandClassificationinSAR
Imagery
References
FurtherReadingandOpenResearchIssues
33.1 Introduction
Asyntheticapertureradar(SAR)isaradarsensorthatprovidesazimuthresolutionsuperiortothat
achievablewithitsrealbeambysynthesizingalongapertureusingplatformmotion.Thegeometryfor
theproductionoftheSARimageisshowninFig.33.1.TheSARisusedtogenerateanelectromagnetic
mapofthesurfaceoftheearthfromanairborneorspaceborneplatform.Thiselectromagneticmap
ofthesurfacecontainsinformationthatcanbeusedtodistinguishdifferenttypesofobjectsthatmake
upthesurface.Thesensoriscalledasyntheticapertureradarbecauseasyntheticapertureisusedto
achievethenarrowbeamwidthnecessarytogetahighcross-rangeresolution.InSARimagerythe

twodimensionsarerange(perpendiculartothesensor)andcross-range(paralleltothesensor).The
rangeresolutionisachievedusingahighbandwidthpulsedwaveform.Thecross-rangeresolution
isachievedbymakinguseoftheforwardmotionoftheradarplatformtosynthesizealongaperture
givinganarrowbeamwidthandhighcross-rangeresolution.Thepulsereturnscollectedalongthis
syntheticaperturearecoherentlycombinedtocreatethehighcross-rangeresolutionimage.ASAR
sensorisadvantageouscomparedtoanopticalsensorbecauseitcanoperatedayandnightthrough
clouds,fog,andrain,aswellasatverylongranges.Atverylownominaloperatingfrequencies,less
than1GHz,theradarevenpenetratesfoliageandcanimageobjectsbelowthetreecanopy.The
resolutionofaSARgroundmapisalsonotfundamentallylimitedbytherangefromthesensorto
theground.Ifagivenresolutionisdesiredatalongerrange,thesyntheticaperturecansimplybe
madelongertoachievethedesiredcross-rangeresolution.
ASARimagemaycontain“speckle”orcoherentnoisebecauseitresultsfromcoherentprocessingof
thedata.ThisspecklenoiseisacommoncharacteristicofhighfrequencySARimageryandreducing
speckle,orbuildingalgorithmsthatminimizespeckle,isamajorpartofprocessingSARimagery
beyondtheimageformationstage.Traditionaltechniquesaveragedtheintensityofadjacentpixels,
resultinginasmootherbutlowerresolutionimage.AdvancedSARsensorscancollectmultiple
polarimetricand/orfrequencychannelswhereeachchannelcontainsuniqueinformationaboutthe
c

1999byCRCPressLLC
FIGURE 33.1: SAR imaging geometry.
surface. Recent systems have also used elevation angle diversity to produce 3-D SAR images using
interferometric techniques. In all of these techniques, some sort of averaging is employed to reduce
the speckle.
The largestconsumersof SARsensors andproducts are thedefense andintelligencecommunities.
These communities use SAR to locate and target relocatable and fixed objects. Manmade objects,
especially ones with sharp corners, have very bright signals in SAR imagery, making these objects
particularlyeasytolocatewithaSARsensor. AtechnologysimilartoSARisinversesyntheticaperture
radar (ISAR) which employs motion of the platform to image the target in cross-range. The ISAR
data can be collected from a fixed radar platform since the target motion creates the viewing angle

diversitynecessaryto achieve a given cross-range resolution. ISAR systems have been used to image
ships, aircraft, and ground vehicles.
InadditiontothedefenseandintelligenceapplicationsofSAR,thereareseveralcommercialremote
sensing applications. Because aSARsensor can operate day and night and in all weather, it provides
the ability to collect data atregular intervals uninterrupted by natural influences. This stable source
of ground mapping information is invaluable in tracking agriculture and other natural resources.
SAR sensors have also been used to track oil spills (oil-coated water has a different backscatter than
natural water), image underground rock formations (at some frequencies the radar will penetrate
some soils), track ice conditions in the Arctic, and collect digital terrain elevation data.
RadarisanabbreviationforRAdio DetectionAndRanging. Radarwasdevelopedinthe1930s and
1940s to detect and track ships and aircraft. These surveillance and tracking radars were designed
so that a target was contained in a single resolution cell. The size of the resolution cell was a critical
design parameter. Smaller resolution cells allowed one to determine the location of a target more
accurately and increased the target-to-clutter ratio, improving the ability to detect a target. In the
c

1999 by CRC Press LLC
1950s it was observed that one could map the ground (an extended target that takes up more than
oneresolution cell) by mountingthe radaron thesideof anaircraft andbuildinga surface mapfrom
the radar returns. High range resolution was achieved by using a short pulse or high bandwidth
waveform. The cross-range resolution was limited by the size of the antenna, with the cross-range
resolution roughly proportional to R/L
a
where R is the range from the sensor to the ground and
L
a
is the length of the antenna. The physical length of the antenna was constrained, limiting the
resolution. In 1951,CarlWileyof theGoodyearAircraftCorporation noted thatthereflections from
twofixedtargetsin theantennabeam, butatdifferentangular positionsrelative tothevelocityvector
of the platform, could be resolved by frequency analysis of the along track (or cross-range) signal

spectrum. Wiley simplyobservedthateachtarget haddifferentDopplercharacteristics becauseofits
relative positionto ther adarplatformand that onecouldexploit theDoppler tosepar ate thetargets.
The Doppler effect is, of course, the change in frequency of a signal transmitted or received from a
moving platform discovered by Christian J. Doppler in 1853:
f
d
= ν/λ
where f
d
is the Doppler shift, ν is the radial velocity between the radar and target, and λ is the
radar wavelength. While the Doppler effect had been used in radar processing before the 1950s to
separate moving targets from stationary ground clutter, Wiley’s contribution was to discover that
with aside lookingairborne radar(SLAR), Dopplercould beusedto improvethe cross-range spatial
resolution of the radar. Other early work onSAR was done independentlyof Wiley at the University
ofIllinoisandthe UniversityofMichiganduringthe1950s. ThefirstdemonstrationofSARmapping
was done in 1953 by the University of Illinois by performing frequency analysis of data collected by
a radar operating at a 3-cm wavelength from a C-46 aircraft. Much work has been accomplished
perfecting SAR hardware and processing algorithms since the first demonstration. For a much
more detailed description of the history of SAR including the development of focused SAR, phase
compensation techniques, calibration techniques, and autofocus, see the recent book by Curlander
and McDonough[1].
Before offering a brief description of some processing approaches for forming, enhancing, and
interpreting SARimagery,we give twoexamples of existing SAR systems andtheir applications. The
firstsystemistheShuttleImagingRadar(SIR)developedbytheNASAJetPropulsionLaboratory(JPL)
and flown on several space shuttle missions. This system was designed for non-military collection
of geographic data. The second example is the Advanced Detection Technology Sensor (ADTS)
built by the Loral Corporation for the MIT Lincoln Laboratory. The ADTS sensor was designed to
demonstrate the capability of a SAR to detect and classify military targets. Table 33.1 contains the
basicparameters fortheADTSand SIRSARsystems alongwithdetailsonseveralother SARsystems.
Figure33.2showsanexampleimageformedfromdatacollectedbytheSIRSAR.TheJPLengineers

describe this image as follows:
ThisisaradarimageofMountRainierinWashingtonstate Thisimagewasacquired
by the Spaceborne Imaging Radar-C and X-band Synthetic Aperture Radar (SIR-C/X-
SAR) aboard the space shuttle Endeavor on its 20th orbit on October 1, 1994. The area
shown in the image is approximately 59 kilometers by 60 kilometers (36.5 miles by 37
miles). North is toward the top left of the image, which was composed by assigning red
and green colors to the L-band, horizontally transmitted and vertically received, and
the L-band, horizontallytransmitted and vertically received. Blueindicates theC-band,
horizontallytransmittedandverticallyreceived. Inadditiontohighlightingtopographic
slopes facingthe space shuttle, SIR-C recordsruggedareasas brighter andsmooth areas
as darker. The scene was illuminated by the shuttle’s radar from the northwest so that
northwest-facing slopes are brighter and southeast-facing slopes are dark. Forested
regions are pale green in color; clear cuts and bare ground are bluish or purple; ice is
c

1999 by CRC Press LLC
TABLE 33.1 Example SARSystems
Resolution Swath
Platform Bands polarization (m) width Interferometry
JPL AIRSAR C, L, P–Full 4 10–18 km Cross track L,C
Along track L,C
SIR-C/X-SAR C, L–Full,X-VV 30
× 30 15–90 Multi-pass
ERIM IFSARE X–HH 2.5
× 0.8 10km Cross track
ERIM DCS X–Full
< 1 1 km Cross track
MIT LL ADTS Ka (33 GHz)–Full 0.33 400 m Multi-pass
NORDEN G11 Ku–VV 1,3 5 km 3 Along track
3 Crosstrack

Phase centers
SRI UWB 100–300 MHz, 1
× 1 400–600 m None
FOLPEN 2 200–400 MHz,
300–500 MHz,
HH
LORAL UHF 500–800MHz, 0.6
× 0.6 280m None
MSAR Full
NAWC P-3 C, L, X–Full 1.5
× 0.7 5km Along track X,C
NAWC P-3 600 MHz–Full 0.33
× 0.66 930 km None
UWB Upgrade tunable over 200–
900 MHz
Tier II+ UAV X 1 and 0.3 10 km None
SAR
dark green and white. The round cone at the center of the image is the 14,435-foot
(4,399-meter) active volcano, Mount Rainier. On the lower slopes is a zone of rock
ridges and rubble (purple to reddish) above coniferous forests (in yellow/green). The
westernboundaryofMountRainierNationalParkisseenasatransitionfromprotected,
old-growth forest to heavily logged private land, a mosaic of recent clear cuts (bright
purple/blue) and partiallyregrown timber plantations (pale blue).
Figure 33.3 is an example image collected by the ADTS system. The ADTS system operates at a
nominal frequency of 33 GHz and collects fully polarimetric, 1-ft resolution data. This image was
formed using the polarimetric whitening filter (PWF) combination of three polar imetric channels
toreduce thespeckle noise. Theoutput of thePWF isanestimateof radar backscatter intensity. The
image displayed in Fig. 33.3is basedon a falsecolormapwhich mapslowintensity toblack followed
by green, yellow, and finally white. The color map simply gives the non-color radar sensor output
falsecolorsthatmakethelowintensityshadowslookblack,thegrasslookgreen,thetreeslookyellow,

and bright objects look white. This sample image was collected near Stockbridge, New York, and is
of ahouse with an above groundswimmingpool andseveral junkedcars in thebackyard. The radar
is at the top of the image looking down at a 20
◦
depression angle. The scene contains large areas of
grass or crops and some foliage. Note the bright returns from the manmade objects, including the
circular above-ground swimming pool, and strong corner reflector scatteringfrom some of the cars
in thebackyard. Also note the relatively strong return from the foliagecanopy. At thisfrequency the
radar does not penetrate the foliage canopy. Note the shadows behind the trees where there is no
radar illumination.
In this chapter on SAR algorithms, we give a brief introduction to the image formation process
in Section 33.2. We review a few simple algorithms for reducing speckle noise in SAR imagery
and automatic detection of manmade objects in Section 33.3. We rev iew a few simple automatic
objectclassification algorithmsfor SARimagery inSection33.4. This briefintroductionto SARonly
contains a few example algor ithms. In the Section “Further Reading”, we recommend some starting
c

1999 by CRC Press LLC
FIGURE 33.2: SAR image of Mt. Rainier in Washington State taken from shuttle imagingra dar.
pointsfor further reading onSARalgorithms,and discussseveralopen issuesundercurrentresearch
in the SAR community.
33.2 Image Formation
In this section, we discuss some basic principles of SAR image formation. For more detailed infor-
mation about SAR image formation, the reader is directed to the references given at the end of this
chapter. One fundamental scenario under which SAR data is collected is shown in Fig. 33.1.An
aircraft flies in a straight path at a constant velocity and collects radar data at a boresight of 90
◦
.In
practice it is impossible foranaircraft to fly in a perfectly straight line at a constant velocity (at least
within a wavelength), so motion (phase) compensation of the received radar signal is needed to ac-

countfor aircraftperturbations. The radaron theaircraft transmitsa short pulsedwaveform oruses
frequency modulation to achieve highrangeresolution imaging of the surface. The pulses collected
fromseveralpositionsalongthetrajectoryoftheaircraftarecoherentlycombinedtosynthesizealong
synthetic aperture in order to achieve a high cross-range resolution on the surface. In this section,
we first discuss SLAR where only range processing is performed. Next, we discuss unfocused SAR
where both range and cross-range processing are executed. Finally, we discuss focused SAR where
“focusing” is performed inaddition to rangeandcross-range processing to achieve the highestreso-
lution and best image quality. At the end of this section we briefly mention several other important
c

1999 by CRC Press LLC
FIGURE 33.3: SAR image near Stockbridge, New York, collected by the ADTS.
SARimageformationtopicssuchasphase compensation, clutter-lock,autofocus,spotlightSAR,and
ISAR. The details of these topics can be found in [1]–[3].
33.2.1 Side-Looking Airborne Radar (SLAR)
SLAR is the earliest ra dar system for remote surveillance of a surface. These radar systems could
only perform range processing to form the 2-D reflectivity map of the surface, so the cross-range
resolution is limited by the real antenna beamwidth. TheseSLAR systems typicallyoperated at high
frequencies(microwaveormillimeter-wave)tomaximizethecross-rangeresolution. WecoverSLAR
systems because SLAR performs the same range processing as SAR, and the limitations of a SLAR
motivate the need for SAR processing.
The resolution of a SLAR system is limited by the radarpulse width in the range dimension, and
the beamwidth and slant range in the cross-range dimension:
δ
r
= cT /2 cos η
δ
cr
= Rλ/L
a

wherewe representtheapproximate3-dB beamwidth ofthe antennabyλ/L
a
,δ
r
is therange resolu-
tion, δ
cr
is the cross-range resolution, c is the speed of wave propagation, T is the compressed pulse
width, η is the angle between the radar beam and the surface, R is the slant range to the surface, λ is
the wavelength, and L
a
is the length of the antenna.
Thegoalistodesign theSLARwithanarrowbeamwidth,shortslantrange,andashort pulsewidth
toachievehigh resolution. Inpractice, thepulsewidth oftheradar islimitedbyhardwareconstraints
and theamountof“energy ontarget” requiredto getsufficient signal-to-noiseratio to obtaina good
c

1999 by CRC Press LLC
image. To achieve a high rangeresolution without a short pulse, frequency modulation can be used
to synthesize an effectively short pulse. This process of generating a narrow synthetic pulsewidth is
called pulse compression. The approach is to introduce a modulation on the transmitted pulse,and
then pass the received signal through a filter matched to the transmit signal modulation. The most
common transmit waveforms usedfor pulse compression are linearFM (or chirp) andphase coded.
Some radars use a digital version of linear FM called a stepped frequency waveform.
Weillustrate pulsecompressionwiththe idealapplication of thelinear FM waveform. Thesquare
pulse is modulated by a linear FM signal, and the resulting transmit signal is
s(t) =




cos

ω
0
†
−
1
2
µ†
2

|
†|≤T/2
0 |
†| >T/2
where the bandwidth (frequency deviation) introduced by the linear FM is
f = Tµ/2π
Ifthistransmitpulseisperfectly reflectedfromastationarypointtarget, rangelossesareignored,and
weshiftintimetoremovethetwo-waydelay;thereceivedsignalisexactlythesameasthetransmitted
signal. The matched filter response for the transmitted signal is
h(t) =

2µ
π

1/2
cos

ω
0

†
+
1
2
µ
†
2

The output of the received signal applied to the matched filter is:
(
†) =

µT
2
2π

1/2
sin
(
µT †/2
)
(
µT
†/2
)
Re

e
j


ω
0
†+
1
2
µ†
2
+π/4


This output has a mainlobe that has a 4-dB beamwidth of 1/f . The resulting compressed pulse
can besignificantlynarrower than thewidthof thetransmitted pulse with apulse compression ratio
of Tf. The range resolution of the radar has been increased by this pulse compression factor and
is now given by:
δ
r
≈ c/2f cos η
Note that the range resolution in the ideal case is now completely independent of the physical width
of thetransmitted pulse. Performing range compression against real radar targets thatDoppler shift
the frequency of the receive signal introduces ambiguities resulting in additional signal processing
issues thatmust be addressed. Thereis a trade-offbetween the abilityof a radarwaveform to resolve
a target in range and frequency. The performance of a waveform in range-frequency space is given
by its ambiguity. The ambiguityfunction is the output of the matched filter for the signal for which
it is matched and for frequency shifted versions of that signal. The references contain a much more
detailed description of ambiguity functions and radar waveform design.
Using pulse compression, a SLAR system can achieve a very high range resolution on the order
of 1 ft or less, but the cross-range resolution of the SLAR is limited by the physical beamwidth of
the antenna, the operating frequency, and the slant range. This cross-range resolution limitation of
SLAR motivates the use of a synthetic array antenna to increase the cross-range resolution.
33.2.2 Unfocused Synthetic Aperture Radar

Figure 33.1 provides a good geometric description of SAR. As with SLAR, the radar platform moves
alongastraightlinecollectingradardatafromthesurface. TheSARsystemgoesonestepfurtherthan
c

1999 by CRC Press LLC
SLAR by coherently combining pulses collected along the flight path to synthesize a long synthetic
array. Thebeamwidthofthissyntheticapertureissignificantlynarrowerthanthephysicalbeamwidth
(real beam) of the real antenna. The ideal synthetic beamwidth of this synthetic aperture is
θ
B
= λ/2L
θ
The factor of two results from the two-way propagation from the movingplatform. The unfocused
SARcanbeimplementedbyperformingFFTprocessinginthecross-rangedimensionforthesamples
in each range bin. Thisissimply the conventional beamformer for an array antenna. The difference
between SAR and real beam radar is that the aperture samples that comprise the SAR are collected
at different times by a moving platform. There are several design constraints on a SAR system,
including:
• Thespeed of the platform and pulserepetition rate (PRF) oftheradarmust be mutually
selected so that thesample points of the synthetic array are separated by less than λ/2 to
avoid gratinglobes.
• ThePRF must be selected so that the swath width is unambiguously sampled.
• Apointonthegroundmustbevisibletotheradarrealbeamacrosstheentirelengthofthe
synthetic array. This limitsthe sizeof thereal beamantenna. This constraint leadsto the
observation that with SAR, the smaller the real-beam antenna, the better the resolution,
whereas with SLAR the larger the real-beam antenna, the better the resolution.
• TheSARassumes that a ground target has an isotropic signalacross the collection angle
of the radar platform as it flies along the synthetic array.
TheresolutionoftheunfocusedSARislimitedbecausetheslantrangetoascattereratafixedlocation
on the surface changes along the synthetic aperture. If we limit the synthetic aperture to a length so

that the range from every array point in the aperture to a fixed surface location differs by less than
λ/8, then the cross-rangeresolution of the unfocused SAR is limited to:
δ
cr
=

Rλ/2
33.2.3 Focused Synthetic Aperture Radar
The cross-range limitation of an unfocused SAR can be removed by focusing the data, as in optics.
The focusing procedure for the SAR involves adjusting the phase of the received signal for every
range sample in the image so that all of the points processed in cross-range through the synthetic
beamformer appear to be at the same range. The phase error at each range sample used to form the
SAR image is
φ =
2π
λ

d
2
n
R

radiar
where d
n
is the cross-range distance from the beam center, R is the slant range to the point on the
ground from the beam center, and λ is the wavelength. The range samples can be focused before
cross-rangeprocessingbyremovingthisphaseerrorfromthephasehistorydata. Notethat each data
point hasa different phasecorrection basedon thealong-t rack positionof thesensor and thepoint’s
range from the sensor.

When focusingis performed, theresulting SARimage resolution isindependent ofthe slantrange
between the sensor and ground. This can be shown as follows:
δ
cr
= Rθ
s
c

1999 by CRC Press LLC
where,
θ
s
≈
λ
2L
e
and L
e
≈
Rλ
L
a
therefore,
δ
cr
≈ L
a
/2
The effective beamwidthof thesynthetic apertureis approximately λ/2L
e

wherethe factoroftwo
comes from the two-way propagation of the energy (the exact effective beamwidth depends on the
synthetic array taper used to control sidelobes). The length of the effective aperture (L
e
) is limited
by the fact that a given scatterer on the surface must be in the mainbeam of the real radar beam for
every position along the synthetic aperture. The result is that the resolution of the SAR when the
data is focused is approximately L
a
/2.
SAR processing can also be developed by considering the Doppler of the radar signal from the
surface as first done by Wiley in 1951. When the real beamwidth of the SAR is small, a point on
the surface has an approximately linearly decreasing Doppler frequency as it passes through the
main beam of the real SAR beamwidth. This time varying Doppler frequency has been shown to be
approximately:
f
d
(t) =
2ν
2
|t −t
0
|
λR
where ν is the velocity of the platform and t
0
is the time that the point scatterer is in the center
of the main beam. The change in Doppler frequency as the point passes through the main beam is
2ν
2

T
d
/λR,andT
d
isthetimethatthepointisinthemainbeam. AswithlinearFMpulsecompression,
covered in Section 33.2.1, this Doppler signal can be processed through a filter to produce a higher
cross-rangeresolutionsignalwhich islimitedbythe size of therealaperturejustaswith thesynthetic
antenna interpretation (δ
cr
= L
a
/2). In a modern SAR system, typically both pulse compression
(syntheticrangeprocessing)andasyntheticaperture(syntheticcross-rangeprocessing)areemployed.
In most cases, these transformations are separable where the range processing is referred to as “fast
time” processing and the cross-range processing is referred to as “slow-time” processing.
A modern SAR system requires several additional signal processing algorithms to achieve high
resolution imagery. In practice, the platform does not fly a straight and level path, so the phase
of the raw receive signal must be adjusted to account for aircraft perturbations, a procedure called
motion compensation. In addition, since it is difficult to exactly estimate the platform parameters
necessarytofocustheSARimage,anautofocusalgorithmisused. Thisalgorithmderivestheplatform
parameters from the raw SAR data to focus the imagery. There is also an interpolation algorithm
that converts from polar to rectangular formats for the imagerydisplay. Most modern SAR systems
form imagery digitallyusing either an FFTor a bankof matched filters. Typically, aSAR will operate
in either a stripmap or spotlight mode. In the stripmap mode, the SAR antenna is t ypically pointed
perpendicular to the flight path (althoughit may be squinted slightly to one side). A stripmap SAR
keeps its antenna position fixe d and collects SAR imageryalong a swath to one side of the platform.
A spotlight SAR can move its antenna to point at a position on the ground for a longer period of
time(thusactuallyachievingcross-rangeresolutionsevengreaterthantheaperturelengthover two).
Many SAR systems support both stripmap and spotlight modes, using the stripmap mode to cover
large areas of the surface in a slightly lower resolution mode, and spotlight modes to p erform very

high resolution imaging of areas of high interest.
33.3 SAR Image Enhancement
In thissection we review a few techniques forremoving speckle noisefrom SAR imagery. Removing
the speckle can make it easier to extract information from SAR imagery and improves the visual
quality.
c

1999 by CRC Press LLC
Coherentnoiseorspecklecanbeamajordistortioninhighresolution,highfrequencySARimagery.
The speckle is caused when the intensity of a resolution cell results from the coherent combination
ofmany wavefrontsresulting from randomlyoriented clutter surfaces within aresolutioncell. These
wavefronts can combine constructively or destructively resulting in intensity variations across the
image. When the number of wavefronts approaches infinity(i.e., large resolution cell collected by a
high frequency radar)theRayleigh clutter modelcanbe usedtorepresentthe speckleunderthe right
statistical assumptions. When the number of wavefrontsis less thaninfinity,the K-distribution and
other product models do a better job of theoretically and empirically modeling the clutter.
When the combination of the radar system design and clutter properties results in images that
containlargeamountsofspeckle,itisdesirabletoperformadditionalprocessingtoreducethespeckle.
One approach for speckle reduction is to noncoherently spatially average adjacent resolution cells,
sacrificing resolution for the speckle reduction. This spatial averaging can be performed as a part
of the image formation analogous to the Bartlett method of spectral estimation. Another approach
for reducing speckle is to average across polarimetricchannels if multiple polarimetric channels are
available.
The polarimetric whitening filter (PWF) reduces the speckle content while preserving the image
resolution. The PWF was derived by Novak et al. [5] as a quadratic filter that minimizes a specific
speckle metric (defined as the ratio of the clutter standard deviation to its mean). The PWF first
whitens the polarimetric data withrespect to the clutter’s polarimetric covariance, and then nonco-
herently averages across the polarimetric channels. This whitening filter essentially diagonalizes the
covariance matrix of the complex backscatter vector [HH,HV,VV]
T

, such that the resulting new
linear polarization basis [HH

,HV

,VV

]
T
has equal power in each component, where:


HH

HV

VV



=




HH
HV
√
ε
VV−ρ

∗
√
γHH
√
γ
(
1−|ρ|
2
)




(33.1)
where
ε =
E

|HV|
2

E

|HH|
2

,γ =
E

|W |

2

E

|HH|
2

,ρ =
E
(
HH · W
∗
)

E

|HH|
2

· E

|W |
2

(33.2)
The polarization scattering matrix (using a linear-polarization basis) can then be expressed as

= σ
HH
 10ρ

√
γ 
| 0 ε 0 |
 ρ
∗
√
γ 0 γ 
(33.3)
The pixel intensity(power) is then derived through non-coherent averaging of the power in each of
the new polarization components,
Y =|HH|
2
+




HV
√
ε




2
+







W − ρ
∗
√
γHH

γ

1 −|p|
2







2
(33.4)
yielding a minimal speckle image at the or iginalimage resolution. Novak et al. [5] have shown that
on the ADTS SAR data, the PWF reduces the clutter standard deviation by 2.0 to 2.7 dB compared
with the standard de viation of single-polarimetric-channel data. The PWF has a dramatic effect on
the visual quality of the SAR imagery and the performance of automatic detection and classification
c

1999 by CRC Press LLC
algorithms applied to SAR images. The PWF does not take into account the effect of the speckle
reduction operation on target signals. It only minimizes the clutter. There has been recent work on
polarimetricspeckle reduction filters thatbothreduce theclutter speckle whilepreservingthe target

signal. Fig. 33.4 shows the three polarimetric channels and the resulting PWF image for an ADTS
SAR chip of a target-like object.
FIGURE 33.4: Polarimetricprocessing of SAR data to reduce speckle.
33.4 Automatic Object Detection and Classification in
SAR Imagery
SARalgorithmic tasksofhighinteresttothedefenseandintelligencecommunitiesincludeautomatic
target detection and recognition (ATD/R). Since SAR imagery has very different target and clutter
characteristics as compared with visual and infrared imagery, uniquely designed ATD/R algorithms
are required for SAR data. In this section, we describe a few basic ATD/R algorithms that have been
developed for high resolution, high frequency SAR imagery(10 GHz or above) [6, 7, 8].
Performing target detection and classification against remote sensing imagery and, in particular,
SAR imagery is verydifferentfrom the classicalpattern recognitionproblem. In the classicalpattern
recognition problem, we have models defining N classes, and the goal is to design a classifier to
separate sensor data into one of the N classes. In SAR target classification, the imagery contains
regions of diffuse clutter which can be represented to some degree by models, but the imagery also
contains a possibly uncountable set of target-like discrete unknown and unmodelable objects. The
goal is to reject both the diffuse clutter and the unknown discrete objects and to classify the target
c

1999 by CRC Press LLC
objects. This need to handle the unknown object means that the classifier must have the unknown
class as a possibleoutcome of the classifier. Since the unknown class cannot be modeled, most SAR
ATR systems solve the problem by employ ing a distance metric to compare the sensor data with
models foreachtargetof interest, andif thedistanceis too great, thedata isclassified as anunknow n
object.
Anotherdesignissue foraSARATD/Rsystemistheneedtoprocesshundredsofsquarekilometers
of data in near real-time to be of practical benefit. One widely used approach for solving this
computational problem is to use a simple focus-of-attention or pre-detection algorithm to reject
most of the diffuse clutter and pass only regions of interest (ROI), including allof the targets. These
ROIs are thenprocessed throughasetof computationally more complicatedclassifierswhichclassify

objects in the ROIs as one of the targets or as an unknown object.
In high frequency SAR imagery most target signatures have extremely bright peaks caused by
physicalcorners on thetarget. One effective pre-detectiontechnique involves applying a single pixel
detector to find the bright pixels caused by corner reflectors on the targets. Since the background
clutterpowerisunknownandvariesacross theimage,wecannotsimplyuseathresholdingoperation
to find these bright pixels. One approach for handling the unknown clutter power is to estimate it
from clutter samples surrounding a test pixel. This approach for target detection is referred to as a
constant false alarm rate (CFAR) detector because with the proper clutter and target models, it can
be shown that the output of the detector has a constant false alarm rate in the presence of unknown
clutter parameters. Fig. 33.5 depicts one design for a CFAR template. The clutter parameters are
estimated using the auxiliary samples along a box with a test sample in the center. This test sample
may or may not be on a target. The size of the box containing the auxiliar y samples is sized so that
the auxiliary samples do not overlap a target when the test sample is on the target. We also need to
keep the size of the box containing the auxiliary samples as small as possible, so that we get a good
local estimate of the clutter parameters. With these design constraints, a good choice for the CFAR
template is just over twice the maximum dimension of the targets of interest.
FIGURE 33.5: CFAR template.
Oneofthese CFARalgorithms, firstdevelopedbyGoldstein[9],is referredtoasthetwoparameter
CFAR or the log-t test:
log x −
1
N

N
i=1
log y
i

1
N−1


N
i=1

log y
i
−
1
N

N
i=1
log y
i

2
H
1
>
<
H
0
t
where x is the test sample, and y
1
, ,y
N
are the auxiliary samples. This test is performed for
c


1999 by CRC Press LLC
every pixel in the SAR scene and the output is thresholded with the threshold t. When N is large,
the test statistic is approximately Gaussian if the SAR data is log normally distributed. In this case,
Gaussian statistics can be used to determine the threshold for a given probability of false alarm. In
practice, it is much more accurate to determine the threshold with a set of training data. This is
primarily a corner reflector detector, and the output will almost always get more than one detection
per target. In practice, a simple clustering algorithm can be used based on the size of the targets
and the expected spacing of targets to get one detection per target and reduce the number of false
alarms which are usually also clustered. The two-parameter CFAR test is one example of a simple
SAR target detector. Researchers have also developed more sophisticated ordered statistic detectors,
multi-polarimetric channel detectors, and feature-based discriminators to get improved SAR target
detector performance [6, 7, 8].
This simple pre-detector gets a large number of false alarms (hundreds per square kilometer in
single polarimetric channel, one foot resolution imagery) [5]. In order to further reduce the false
alarm rate and classify the targets, further processing is necessaryon the output of the pre-detector.
One widely used approach for performing thisclassification operation is to apply a linearfilter bank
classifier to the ROIs identified by the pre-detector. Researchers have developed a large number
of approaches for designing these linear filter bank classifiers including spatial matched filters [7],
synthetic discriminant functions [7], and vector quantization/learning vectorquantization[8]. The
simplest approach is to build the spatial matched filters by breaking the target into angle subclasses,
and averaging thetrainingsignaturesin a given anglesubclasstorepresent thatsubclass. Inpractice,
thetemplatesmustbenormalizedbecausetheabsoluteenergyofagiventargetsignatureisunknown.
The exact location of a target in the ROI is also unknown, so the matched filter must be applied for
every possible spatial position of the target. This is performed more efficiently in the frequency
domain as follows:
ρ
ij
= max

FFT

−1

FFT

t
ij

· FFT(x)
∗


where x is a ROI and t
ij
is the spatial matched filter representing the ith target and the j th angle
subclassofthattarget. Theρ
ij
iscomputedforeveryanglesubclassofeverytarget,andthemaximum
represents the estimate of the correct target and angle subclass. The output can be thresholded to
reject false alarms. In practice the level of the threshold is determined by testing on both target and
false alarm data.
In this section, we have reviewed a few basic concepts in SAR ATD/R. For a much more detailed
treatment of this topic, consult the references and the recommended further reading given below.
References
[1] Curlander, J.C. and McDonough, R.N., Synthetic Aperture Radar: Systems and Signal Pro-
cessing,
John Wiley & Sons, New York, 1991.
[2] Wehner, D.R.,
High Resolution Radar, 2nd ed., Artech House, Boston, MA, 1995.
[3] Stimson,G.W.,
Introduction to Airborne Radar, Hughes Aircraft Company, 1983.

[4] Skolnik, M.,
Introduction to Radar Systems, 2nd ed., McGraw-Hill, New York, 1980.
[5] Novak, L., Burl, M., and Irving, B., Optimal polarimetric processing for enhanced target
detection,
IEEE Trans. AES, 29(1),234-244, Jan. 1993.
[6] Stewart, C., Moghaddam, B., Hintz, K., and Novak, L., Fractional brownian motion for syn-
thetic aperture radar imagery scene segmentation,
Proc. IEEE, 81(10), 1511-1522, Oct. 1993.
[7] Novak, L., Owirka, G., and Netishen, C., Radar target identification using spatial matched
filters,
Pattern Recognition, 27(4), 607-617, Apr. 1994.
[8] Stewart, C., Lu, Y C., and Larson, V., A neural clustering approach for high resolution radar
target classification,
Pattern Recognition, 27(4), 503-513, Apr. 1994.
c

1999 by CRC Press LLC
[9] Goldstein, G., False-alarm regulation in log-normal and Weibull clutter, IEEE Trans. AES, 9,
84-92, 1972.
Further Reading and Open Research Issues
AverybriefoverviewofSARwithafewexamplealgorithmsisgivenhere.Theitemsinthereferencelist
giveamoredetailedtreatmentofthetopicscoveredinthischapter.SARisaveryactiveresearchtopic.
Articles on SAR algorithms are regularly published in many journals and conferences, including:
Journals
IEEE Transactions on Aerospace and Electronic Syste ms, IEEE Transactions on Geoscience and
Remote Sensing, IEEE Transactions on Antennas and Propagation, IEEE Transactions on Signal
Processing,
and IEEE Transactions on Image Processing.
Conferences
IEEE National Radar Conference, IEEE International Radar Conference, and the International

Society for Optical Engineering (SPIE) has se veral SAR Conferences.
There are numerous open areas of research on SAR signal processing algorithms including:
• Still developing an understanding of the utility and applications of multi-polarimetric,
multi-frequency, and 3-D SAR.
• Performance/robustness of model-based image formation not completely understood.
• Performance/robustness of different detection, discrimination, and classification algo-
rithms given radar, clutter, and target parameters not completely understood.
• No fundamentaltheoretical understandingof performance limitationsgiven radar, clut-
ter, and target parameters (i.e., no Shannon theory).
c

1999 by CRC Press LLC