-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 147
High-Definition Vector ImagingGerald R. Benitz
n High-definition vector imaging (HDVI) is a data-adaptive
approach tosynthetic-aperture radar (SAR) image reconstruction
based on superresolutiontechniques originally developed for passive
sensor arrays. The goals are toproduce more informative,
higher-resolution imagery for improving targetrecognition with UHF
and millimeter-wave SAR and to aid the image analyst inidentifying
targets in radar imagery. Algorithms presented here include
two-dimensional minimum-variance techniques based on the
maximum-likelihoodmethod (Capon) algorithm and a two-dimensional
version of the MUSICalgorithm. We use simulations to compare
processing techniques, and wepresent results of wideband Rail SAR
measurements of reflectors in foliage,demonstrating resolution
improvement and clutter rejection. Results withairborne
millimeter-wave SAR data demonstrate improved resolution andspeckle
reduction. We also discuss the vector aspect of HDVI, i.e., the
incor-poration of non-pointlike scattering models to enable feature
detection. Anexample of a vector image is presented for data from
an airborne UHF radar,using the broadside flash model to reveal
greater information in the data.
H igh-definition vector imaging (HDVI)is the application of
superresolution digitalsignal processing techniques to radar
imag-ing. HDVI is built on the expertise developed in re-search on
the passive array processing problem, whichprovides resolution
beyond the limits of conventionaldigital signal processing methods,
and provides theability to cancel unwanted interference. The
benefitsof HDVI to radar imaging are subpixel resolution,and
sidelobe and clutter cancellation. Additional ben-efits come from
exploiting the richness of informa-tion in the radar data, which
provides analysts andtarget-recognition systems with the ability to
catego-rize scattering mechanisms. Thus HDVI replaces con-ventional
processing by providing us with a more ac-curate and
higher-resolution image, and allowing usto extract additional
information about the composi-tion of radar backscatter.
The goal of HDVI is twofold, namely, to improvethe automated
recognition of targets, and to aid theimage analyst in identifying
targets in radar imagery.It is well known that resolution is the
single most im-portant factor in the ability to recognize targets
viaradar. Radar resolution is limited by bandwidth and
integration time, two expensive commodities in a sys-tem
architecture. Image resolution, however, can beimproved in a less
expensive manner via digital signalprocessing, due to continuing
advances in computers.This is the approach of HDVI.
The most promising aspect of HDVI is the abilityto distinguish
scatterers according to their scatteringmechanisms. While a
conventional image provides asingle value for each pixeli.e., the
radar cross sec-tion (RCS)HDVI can provide multiple values.This is
the vector aspect of HDVI. Elements of theHDVI vector can include
RCS, trihedral likeness, di-hedral likeness, plate likeness,
height, and polariza-tion. HDVI accomplishes this vector
decompositionby incorporating models of the scattering mecha-nisms
in the image-formation process. In contrast,conventional radar
imaging employs only a point-scatterer model. Furthermore, the
adaptive algo-rithms of HDVI attenuate scatterers that deviatefrom
the model, thus providing discrimination ofscattering types.
HDVI is an entirely new approach to image for-mation. It employs
both amplitude and phase infor-mation; it is not a post-processing
technique applied
-
BENITZHigh-Definition Vector Imaging
148 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
Image: A Beamforming Approach, describes SARimage formation and
shows how classical superreso-lution processing techniques such as
Capons adaptivebeamformer have been modified to function withSAR
data. This section describes the formation of thecovariance matrix
and the robustness constraints forCapons technique, as well as
assumptions and modelssuch as the point-scatterer model and the
extensionsto this model. This section also shows how HDVI
isefficiently applied to an image. Later sections showresults of
HDVI processing for airborne UHF SARradar and the Ka-band Advanced
Detection Technol-ogy Sensor (ADTS) radar. Articles in this issue
byK.W. Forsythe [7] and L.M. Novak [8] provide de-scriptions of the
superresolution algorithms and theimprovements in automatic target
recognition due toHDVI.
Creating a SAR Image: A Beamforming Approach
This section provides a detailed summary of HDVI.We begin with
an overview of adaptive-beamformingconcepts and then we describe
the application ofthese concepts to SAR data. We also present the
de-tails of two-dimensional MLM and two-dimensionalMUSIC, and we
compare two-dimensional MLMwith the technique of bandwidth
extrapolation. Thepoint-scatterer model and flash model are also
dis-cussed, along with how they are incorporated into
thealgorithms.
Beamforming Concepts
We begin a presentation of HDVI by comparing itwith conventional
SAR imaging techniques. Becausethe output of SAR processing is
usually an image, it isbest to consider the version of HDVI that
replaces theconventional SAR image. Since this version is an
in-tensity-only image, it is sometimes referred to as ascalar image
rather than a vector image.
Beamforming is the process of integrating separatedata samples
to estimate the amplitude of a desiredsignal. The term arises from
the application to adap-tive arrays where we can view the beam, or
antennapattern, that arises from the combination of
antennaelements. A simple beamformer is the steered array,generally
accomplished via the Fourier transform inthe case of a uniform
linear antenna array. In this
to intensity-only images. HDVI recasts image forma-tion as a
spectrum-estimation problem, treating indi-vidual pixels as
beamformer outputs. It employs algo-rithms such as Capons
maximum-likelihood method(MLM), which is an adaptive-beamforming
algo-rithm, and multiple signal classification (MUSIC), apowerful
direction-finding algorithm. HDVI is afully two-dimensional
approach, not a successive ap-plication of one-dimensional
algorithms that sepa-rately resolve an image in range and
cross-range.
Previous attempts at applying superresolution pro-cessing
techniques to radar images had varying de-grees of success.
Bandwidth extrapolation, a linear-prediction technique, provided
superresolution inimages with high signal-to-noise ratios and high
tar-get-to-clutter ratios [1]. Bandwidth extrapolation is
aone-dimensional approach providing superresolutionin range, and
can be repeated in the cross-range, orDoppler, dimension. It is
less than optimal because itis a one-dimensional approach, and
because the lin-ear-prediction model does not fit the data very
well. Atotal least-squares approach (maximum likelihood inthe case
of white Gaussian noise) by S.R. DeGraaf ex-hibits good results,
but is too computationally inten-sive [2], and suffers from model
mismatch.
Adaptive-beamforming techniques include spa-tially variant
apodization [3], adaptive sidelobe reduc-tion [4], and an
adaptive-filtering approach by J. Liand P. Stoica [5]. Both
spatially variant apodizationand adaptive sidelobe reduction
attempt to performsidelobe nulling without first computing a
covariancematrix, resulting in cancellation of weak scatterers.
Liand Stoicas adaptive-filtering approach preservesweak scatterers
but provides wider main lobes, i.e.,lower resolution. Also, J.W.
Odendaal et al. [6] haveimplemented fully two-dimensional MUSIC in
amanner similar to HDVI, but with inherently lowerresolution due to
a less effective covariance formationmethod. In contrast to all the
methods listed above,HDVI is fully two-dimensional, does not
require ahigh signal-to-noise ratio or target-to-clutter
ratio,preserves gain on weak scatterers, and provides a
moreeffective trade-off between robustness and resolution.
This article provides a detailed description ofHDVI as applied
to synthetic-aperture radar (SAR)data. The following section,
entitled Creating a SAR
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 149
case, the varying time delays are simply removed toprovide
maximum integration gain for the directionof interest.
The limitation of the conventional beamformer isits
susceptibility to interference. Because an antennapattern exhibits
gain in directions other than the di-rection of interest, undesired
signals are not alwaysrejected. Interference from a signal widely
separatedfrom the direction of interest is called sidelobe
inter-ference. Conventional beamforming addresses side-lobe
interference by a priori shaping of the beamthrough the use of a
windowed fast Fourier transform(FFT). Interference from a direction
near the direc-tion of interest is called main-lobe interference.
Theconventional beamformer is ineffective against main-lobe
interference because the main-lobe width, whichis also called the
beamwidth, or resolution of the ar-ray, is a function of the
antenna aperture and cannotbe reduced. The sidelobes and the main
lobe can bothbe adaptively controlled by processing techniquesthat
are based on the environment, e.g., CaponsMLM technique, which is a
processing method ofHDVI. Examples with SAR data are given
below.
Conventional SAR Image Formation
The conventional SAR data-collection and image-formation process
is a simple beamformer withsidelobe control, as illustrated in
Figure 1. Radar re-flection coefficients over a band of frequencies
arecollected for various viewing angles of the targets. Theantenna
positions that provide these viewing anglesconstitute the synthetic
aperture, which is a viewingaperture synthesized over time.
Information aboutthe target location is encoded in the phase of the
datasamples {zmn}. The range of the target results in a cer-tain
phase delay versus frequency, and the azimuth ofthe target results
in a certain phase delay versus an-tenna position. The phase and
amplitude characteris-tics of the target are encoded in the
reflection coeffi-cient r , illustrated in Figure 1(b) for a tank,
a cornerreflector, and environmental clutter, as a function
offrequency f and look angle a . Image formation is theprocess of
undoing these delays, integrating the data,and forming the RCS at
the desired location. Returnsfrom the desired pixel add coherently,
while returnsfrom other pixels add incoherently.
FIGURE 1. Synthetic-aperture radar (SAR) data collection and
image formation. (a) The radar collects backscatter coefficientsZ =
{zmn} over a band of frequencies at each of several antenna
positions. (b) The backscatter contains a superposition of
re-flection coefficients r (which depend on the radar frequency f
and look angle a ), but shifted in phase because of the target
loca-tion (x, y). Image formation, which is a beamforming process,
is accomplished through a weighted integration of the data
{zmn}with unique weighting coefficients for each pixel location in
the image (for example, a windowed fast Fourier transform, or
FFT,provides sidelobe control). The squared magnitude of r ^
provides an estimate of the radar cross section, or RCS, of the
target.
SARantenna
z11
w1w2w3
wmn
z13 z1n
z21 z22 z23 z2n
z31 z32 z33 z3n
zm3 zmn
Estimated radar cross sectionat desired location
(x, y)
Weighting coefficients (a) (b)
Clutter
^ 2S
Frequency
z12
zm1 zm2Ant
enna
pos
ition (x1, y1), 1(f, 1)
Corner reflector
(x2, y2), 2(f, 2)r
r
r
Target
(x3, y3), 3(f, 3)r a
a
a
Z
-
BENITZHigh-Definition Vector Imaging
150 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
The various methods of SAR image formation em-ployed in
operational systems are computationally af-fordable approximations
to the simple beamformer il-lustrated in Figure 1. The book by W.J.
Carrara et al.provides abundant details [9]. The operational
image-formation process usually employs some data re-sampling, such
as polar-to-rectangular conversion, tomake the phase linear and
enable the use of a two-dimensional FFT. In other words, raw SAR
data havepoint responses with second-order and higher-orderphase
components that must be removed if an FFT isto be used to compute
the RCS. Operational SARimage formation also employs an automatic
focusingroutine, called autofocus, to remove residual phase er-rors
caused by uncompensated platform motion.
The Point-Scatterer Model
The underlying assumption in SAR image formationis that the data
consist of a superposition of discretepoint scatterers in
stationary noise. The ideal pointscatterer exhibits no variation in
reflection coefficientwith look angle or frequency. The ideal SAR
responsethat results from an ideal point scatterer is a
constantamplitude with a phase delay determined solely bygeometry
(the delay due to distance) and frequency.This phase delay is 4p r
f radians for an object at ranger and frequency f (the factor of 4p
occurs because ofthe radar signals round trip).
Application of Adaptive Beamforming to SAR Data
Adaptive beamforming applied to SAR data entailsthe derivation
of a unique set of weighting coeffi-cients, or weights, to estimate
the RCS at each pixel inthe output image. These weights replace the
FFTused in conventional image formation. (For an illus-tration of
the differences between conventional imageformation and the
adaptive beamforming accom-plished with HDVI, see the sidebar
entitled Com-parison of Conventional Image Formation
withHigh-Definition Vector Imaging.) A critical step inthe
derivation of weights in adaptive beamforming isthe estimation of
an autocorrelation matrix, alsocalled the covariance matrix. Given
a covariance ma-trix R, the weights w are determined from the
Caponalgorithm as w R v - 1 [7, 10], where v is the
desiredscatterer response, or steering vector.
The sections below describe the generation of thecovariance
matrix and the associated steering vectors.Details about Capons MLM
algorithm are describedlater in the article in the section entitled
CaponsTechnique.
Generation of the Sample Covariance Matrix
The purpose of adaptive beamforming is to providean accurate
estimate of the cross section and locationof a scatterer in the
presence of neighboring scatterersthat cause interference. The
sample covariance ma-trix, which is necessary for this estimation
task, is asecond-order statistic that provides information onhow to
adapt the nulling pattern to minimize the in-fluence of the
interfering scatterers. The covariancematrix arises naturally in
minimum-variance adap-tive-filtering problems, such as the Capon
algorithm.
In a communications application, the sample cova-riance matrix
is computed as a time average of pair-wise correlations of antenna
outputs. To determinethe covariance matrix from SAR data, where
time av-eraging is not an option, another computationalmethod must
be used in place of time averaging. SARdata collection doesnt
provide multiple renditions ofthe scene, or looks, as is customary
in the communica-tions application, in which samples are
continuallyarriving over time. SAR data collection provides onlya
single two-dimensional sample of the two-dimen-sional scene. To get
looks for SAR that are analogousto looks in the communications
application, wewould have to retrace the SAR flight path exactly,
andwe would have to change reflection coefficients toemulate
modulation. This is clearly impossible.
One way to generate looks from SAR data is toform images from
subsets of the given data. For ex-ample, two images could be formed
by sectioning thesynthetic aperture into halves, and computing an
im-age with each half. An analogous sectioning could bedone in
frequency. This sectioning would providefour looks, but each of
these looks would possess onlyhalf the original resolution.
A better way to form looks is to section the SARdata into
overlapping subsets that do not sacrifice somuch resolution, such
as subsets using 80% of thesynthetic aperture. For example, if the
full set of SARdata in Figure 1 is represented by 100 100
samples,
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 151
every 80 80 contiguous subset will provide a uniqueimage of the
scene. Though not independent, suchlooks are sufficient to define a
covariance matrix andsupport adaptive beamforming.
A drawback of using looks that contain more than50% of the
synthetic aperture and 50% of the fre-quency band is that there are
fewer looks than dimen-sions in the covariance matrix. Having an
insufficientnumber of looks results in a rank-deficient matrixthat
is not invertible. There are two advantages, how-ever, of employing
such higher-resolution looks. Theyrelieve the burden on the
algorithm to make up forthe loss in resolution that occurs with
lower-resolu-tion looks, and they maintain a higher
target-to-clut-ter ratio, which is critical in the imaging of
groundtargets.
In practice, HDVI begins with polar-formatteddata in the
frequency, or pre-image, domain. That is,the data have been
resampled and refocused so thatthe point-response function has
linear phase, whichallows image formation via FFTs. This linear
phaseresponse of a point scatterer is then
f w wm n x yxm yn, ,= + (1)
where (m, n) is the SAR data index, (x, y) is the
point-scatterer location, and w x and w y are constants. Notethat
if the SAR data are sectioned into equally sizedsubsets, each
subset will exhibit this same phase func-tion, but with a unique
overall phase offset. That is,the phase response of a point
scatterer is preserved inthe formation of looks. Hence an adaptive
beam-former will exhibit identical gain patterns to each ofthe
looks. The problem is now analogous to that ofapplying adaptive
beamforming to a two-dimensionalphased-array antenna.
Let us examine the process of generating theHDVI covariance
matrix in more detail. HDVI be-gins with the complex-valued SAR
image, transformsit to the frequency domain via a
two-dimensionalFFT (the reverse of the conventional image
forma-tion), removes any sidelobe control (for example, theHamming
weighting applied in conventional imageformation), and decimates
the data into 12 12 datasets. This decimation is accomplished by a
conven-tional filter bank that effectively sections the SAR im-age
into overlapping tiles. Looks are formed as 10
10 contiguous subsets of the 12 12 data, thus pro-viding a total
of nine distinct looks. Another ninelooks are obtained via
forward-backward averaging, aprocess that exploits the symmetry of
the point-scat-terer phase response. In Equation 1, note that
phaseconjugation is equivalent to a negation of the data in-dex (m,
n). Hence a backward look (i.e., reversing thedata indices and
taking the conjugate) preserves thepoint-scatterer phase response
(within a phase con-stant). The advantage of using the backward
looks isimproved noise averaging and scatterer decorrelation,and
thus a more accurate covariance matrix. (Note:backward looks are
applicable for point-scattereranalysis but not for azimuthal
variations such asbroadside flash.) The resultant covariance matrix
hasdimension 100 (from the 10 10 look), but has rankof only 18
(from the eighteen subset looks).
In more detailed notation, let zi denote a look vec-tor, i.e., a
100 1 vector containing the samples of a10 10 subset. Then the 100
100 covariance ma-trix is determined to be
.R z z==
118
1
18
i iH
i(2)
This form of R reveals that its elements contain thepair-wise
correlations of the elements of zi, which isexactly the information
required to implement adap-tive beamforming. In practice, R is not
explicitlyformed; rather, its eigendecomposition is
computeddirectly from the looks. The information is the samebut the
number of computations is significantly re-duced by using the
decomposition.
Generation of the Steering Vector
The next step in the adaptive-beamforming algo-rithm is
computing the response function of the de-sired scatterer; this
response function is called thesteering vector (the name derives
from its use in elec-tronically steered directional arrays). It
contains boththe location of the scatterer and the model of the
de-sired scattering. Furthermore, the steering vector en-ables HDVI
to superresolve a scatterer in location anddiscriminate according
to scattering type (an essentialand important result of vector
imaging).
The simplest steering vector is the point-scatterer
-
BENITZHigh-Definition Vector Imaging
152 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
FIGURE A. Comparison of three image-reconstruction techniques.
Two point scatterers separated by 1.5 pixels at highsignal-to-noise
ratio are imaged via (1) two-dimensional fast Fourier transform
(FFT), (2) Taylor-weighted FFT (conven-tional image), and (3)
HDVI.
FIGURE B. Spatial leakage patterns for the integration
coefficients used to image the center of the patch (at the +
sign):(1) two-dimensional FFT, (2) Taylor-weighted FFT, and (3)
HDVI. The circles show the locations of the scatterers. HDVIshifts
the null pattern (dark areas) onto the scatterers, thus cancelling
their contribution (i.e., cancelling the sidelobes).
C O M P A R I S O N O F C O N V E N T I O N A L I M A G EF O R M
A T I O N W I T H H I G H D E F I N I T I O N
V E C T O R I M A G I N G
the figures in this sidebar illus-trate the image
improvementsproduced by high-definition vec-tor imaging (HDVI) in
main-lobereduction and sidelobe cancella-tion, along with how
HDVI
adapts the beamforming coeffi-cients to produce these
improve-ments. The simulated targets aretwo point scatterers
separated by1.5 pixels, each with high signal-to-noise ratio.
Figure A shows im-
ages of the two point scatterers, asproduced by the
two-dimensionalfast Fourier transform (FFT), theTaylor-weighted
FFT, and thequadratically constrained Caponstechnique used in HDVI.
The
Cross-range Cross-range Cross-range
Ran
ge
(1) (2) (3)
Ran
ge
Cross-range
Ran
ge
Cross-range
Ran
geCross-range(1) (2) (3)
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 153
response shown in Equation 1. This steering vectoremulates a
point scatterer in that the amplitude isconstant, both in azimuth
and in frequency, and thephase is linear. The location of the
scatterer (x, y) isencoded in the steering vector as the phase
changefrom sample to sample. A steering vector is computedfor each
pixel in the desired output image by recom-puting Equation 1 for
each pixel location (x, y ). Steer-ing vectors can be generated
explicitly as in Equation1, or they can be generated implicitly via
a two-di-mensional FFT in special cases.
For non-pointlike scattering, an amplitude andphase function are
superimposed on the point-scat-terer model. A simple model of
non-pointlike scatter-ing is the azimuthal flash, which we discuss
in moredetail in a later section. Steering vectors for thismodel
are computed as for point scatterers, but withan amplitude profile
applied in the dimension corre-sponding to azimuth.
Description of HDVI Algorithms
This section presents the particulars of the applica-tion of the
techniques of adaptive processing to SARdata. The enabling
stepsgeneration of the covari-
ance matrix and the corresponding steering vectorsare computed
as described in the preceding section,and are used in conjunction
with the techniques de-scribed below.
Capons Technique
Capons technique is a well-known approach to theproblem of
adaptive beamforming for the purpose ofestimating a power spectrum
[10]. In the applicationof this technique to radar, the power being
estimatedis the RCS of the scatterer, and the power spectrum isthe
image. In other words, Capons technique pro-vides RCS estimates for
each pixel location (x, y); theestimates are then displayed as the
brightness of eachpixel, hence forming an image. Capons technique
isalso known as the maximum-likelihood method(MLM), which was
Capons original name for thetechnique; minimum-variance
distortionless response(MVDR); and reduced-variance distortionless
re-sponse (RVDR) [11]. Capons technique produces aSAR image that
appears similar to the conventionalimage, but with improved
resolution. The classicalform of this technique is not applicable
here, how-ever, because the covariance matrix is rank
deficient.
two-dimensional FFT imageshows separation of the scatterersbut
exhibits high sidelobes, andthe Taylor-weighted FFT sacri-fices
resolution of the scatterers toachieve a reduction in sidelobes.In
contrast, HDVI provides dra-matic sidelobe cancellation alongwith
significantly improved scat-terer resolution (i.e., narrowermain
lobes).
The improvements in HDVIare accomplished by adaptivebeamforming.
As Figure 1 in themain text shows, an image isformed from a
weighted integra-tion of synthetic-aperture radardata. In FFT
processing, these co-efficients are chosen to provide
maximum gain at the location ofinterest, namely, the location
ofthe pixel in the output image. Be-cause of the physical
limitationsof finite aperture and bandwidth,the beamforming
coefficients al-low some of the energy fromneighboring pixels to
leak into theintegrated output, resulting in thephenomenon of
sidelobes. Thegoal of adaptive beamforming isto minimize this
leakage.
Figure B shows the spatial leak-age patterns for the three
process-ing techniques shown in Figure A.The location of interest
is the cen-ter of the patch, indicated by theplus sign. In Figure
B(1), the leak-age pattern in the traditional two-
dimensional FFT technique al-lows energy from both
scatterers,indicated by the circles, to bias theestimate of the
radar cross section.In Figure B(2), the Taylor-weighted FFT
decreases the leak-age from the distant scatterer butincreases the
leakage from thenearby scatterer. In Figure B(3),however, HDVI
simultaneouslyreduces the leakage from bothscatterers while
maintaining unitgain at the patch center. Hence thecorresponding
image in FigureA(3) evidences no sidelobes at thepatch center. By
repeating theadaptive beamforming at everypixel, HDVI produces an
imagewithout sidelobes.
-
BENITZHigh-Definition Vector Imaging
154 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
The modified form of Capons technique is presentedbelow.
The fundamental idea in Capons technique is todetermine
beamforming coefficients that minimizethe detected energy of
interferers while simulta-neously keeping unit gain on the location
of interest(x, y). That is,
RCS( , ) min x y H=w
w Rw
such that
w vH x y( , ) ,= 1
where v( , )x y is the steering vector for a point scat-terer at
location (x, y), and ||v || = 1. If the covariancematrix R were
full rank (in other words, invertible),the solution would be the
classical form of Caponstechnique given by
RCS( , ) ( ) .x y H= - -v R v1 1
In the case of SAR data, R is not full rank, andCapons technique
is not applicable, as stated above.The solution to this difficulty
is to constrain the al-lowable set of weighting coefficients w. We
considertwo constraints on w: a norm constraint and a sub-space
constraint. The norm constraint, or quadraticconstraint, limits the
ability to resolve closely spacedscatters, effectively limiting the
amount of adaptivity,that is, the amount of deviation of the
adaptivebeamformer from the conventional. The subspaceconstraint
has the additional benefit of retaining theclutter background in
the resultant image.
Quadratically Constrained Coefficients. The qua-dratic
constraint [12] restricts the amount of adap-tivity; this
constraint is achieved by limiting the normof the weights w,
where
w w w= H .
Figure 2 visualizes this concept and illustrates the be-havior
of w in Capons technique. Observe the unit-norm steering vector, v(
, )x y = vmodel, and the locusof vectors w such that wHv = 1
(Capons gain con-straint), shown by the dashed line. The
conventionalbeamformer is simply w = vmodel. Adaptivity is
illus-trated as deviations of w from vmodel.
The goal of Capons technique is to find the w onthe dashed line
such that this w minimizes output en-ergy. Suppose the vector vtrue
in Figure 2 is the re-sponse of a scatterer at a subpixel
separation fromvmodel. With no constraint, Capons techniquechooses
wfree orthogonal to vtrue, thus nulling thisscatterer. In practice,
it may be undesirable to allow anull to fall so close to v,
especially when we need to al-low for modeling errors. It is then
desirable to restrictthe angular separation between w and vmodel,
which iseffectively accomplished by restricting the norm
ofwconstrained (shown in green).
One method of constraining the norm of w is toadd the norm,
multiplied by a weighting factor a ,into the minimized quantity;
i.e.,
min ,w
w Rw w wH H+ a
for which the minimizing w is
w R I v + -( ) .a 1
In this expression, a is added to the diagonal elementsof R.
This method is referred to as diagonal loading ofthe covariance
matrix, and is the method of H. Coxand R. Zeskind [11]. Diagonal
loading is a soft con-
FIGURE 2. Illustration of the quadratically
constrainedbeamformer. The unconstrained Capon beamformer
wfreepreserves gain on vmodel while nulling vtrue . The
quadraticconstraint prevents the nulling of vtrue by restricting
wfree tobe within angle q of vmodel. The table lists the
equivalencebetween the norm of w and the angle q , and the
effectiveangle for Taylor and Hamming weights.
vtrue
q
vmodel
wconstrainedwfree
wHv = 1
w dB q
0.5 201.0 273.0 45
Hamming 31Taylor 24
( v = 1)
w dB q
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 155
straint because the norm of w can still become large.It is not
often employed as a technique for HDVI,however, because there is no
reliable means of choos-ing a .
The constraint generally used in HDVI is a hardconstraint on the
norm of w; i.e.,
RCS( , ) min ,x y H=w
w Rw
such that
w wH b ,
where b is the length of the vector wconstrained. Thisinequality
is called a quadratic constraint because thequantity w wH is of
quadratic (second order) form.The form of wconstrained is
w R R v I vconstrained +-[ ( , , ) ]a b 1
for some value of a . Though this solution has theform of
diagonal loading, now the loading is opti-mized by the algorithm on
a pixel-by-pixel basis.
Subspace Constraints. The subspace constraint wasdevised to
preserve the background, or clutter, re-gions of the image. The
quadratic constraint alone isnot sufficient to prevent loss of
background informa-tion, because it allows the null solution RCS(x,
y) = 0.In Figure 2 this null solution can be seen whenwconstrained
and wfree coincide, which occurs, for ex-ample, if vtrue is further
separated from vmodel. Thenwconstrained will be orthogonal to vtrue
so that
w vconstrained trueH
= 0 .
The resultant pixel will be black, signifying RCS = 0.In
practice, this null solution generally occurs in clut-ter regions
of the image and is not representative ofthe actual RCS. The null
solution is an artifact thatcan be disturbing to the image analyst,
however, andneeds to be mitigated.
Figure 3 visualizes the problem of the null solutionin a more
general fashion, and visualizes the subspace-constraint solution.
The null solution occurs whenthe quadratically constrained weight
vector wq(shown in red) becomes orthogonal to the columns ofthe
covariance matrix, denoted by span( R). The no-tation span( R)
denotes the subspace spanned by thecolumns of R (see Equation 2),
which is also called
the signal subspace. The goal of the subspace con-straint is to
prevent w from becoming orthogonal tospan( R) by constraining the
allowable directions inwhich w can lie with respect to v.
We can understand this concept by viewing theadaptive beamformer
as a perturbation of the conven-tional beamformer. The conventional
beamformer as-signs w = v ; that is, w is not adapted to the data.
Theadaptive beamformer allows modification of w suchthat
w vH = 1,
which is shown as the dashed line in Figure 2. Theweight vector
w can be viewed as a perturbed versionof v, such that the
perturbation is orthogonal to v.Mathematically, w = v + e such that
e is orthogonal tov. The length of the perturbation vector e is an
indica-tor of the amount of adaptivity; that is, a smaller e
in-dicates little adaptivity and a larger e indicates more.In
addition to the length of e , there is also a directionto e . The
direction of e is the subject of the subspaceconstraint.
Returning to Figure 3, we consider constrainingthe direction of
e such that it must be derived fromspan( R) while also being
orthogonal to v. This set ofallowable vectors in span( R) is
illustrated by the topedge of the dashed parallelogram. (The bottom
edgeof the parallelogram lies in span( R) and is orthogonalto the
projection of v into span( R), denoted projR v,
FIGURE 3. Illustration of the subspace-constrained beam-former.
The subspace constraint on the weighting coeffi-cients prevents the
null solution wq (in red). The plane de-notes the space spanned by
the covariance matrix, orspan(R^ ). The constrained weights ws (in
green) result fromperturbing v by a vector e derived from span(R^
).
v e
ws
wq
ws = v + e
Constraint:
Hx = 0wqi
span(R)^
e v and e span(R)^
projR v^
-
BENITZHigh-Definition Vector Imaging
156 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
to satisfy the orthogonality constraint.) In this case, eis
prohibited from pointing away from span( R), andtherefore w is
prevented from approaching wq . Thesubspace-constrained solution
will then be ws = v + e(shown in green) and will not be orthogonal
tospan( R). Thus the subspace constraint on e effec-tively prevents
the null solution.
The subspace-constrained and quadratically con-strained version
of Capons technique is given by
RCS( , ) min ,x y H=w
w Rw
such that
w v
v
R
w
= +
^
e
e
e span{ }
.2
b
This subspace-constrained technique (sometimes re-ferred to as
the confined-weight technique) is em-ployed in HDVI at higher
frequencies, i.e., X-bandand above. It has the property of
preserving the back-ground information and reducing the speckle,
whichis a by-product of the averaging inherent in the for-mation of
the covariance matrix.
Coherent versus Incoherent Summing of Looks. TheCapon technique
produces an RCS estimate that iscomputed as the incoherent sum of
the individuallooks averaged in the covariance matrix. This
inco-herent sum is
w Rw w zH H ii
L
L ,=
=
1 2
1
where the zi denote the looks and L is the number oflooks (e.g.,
L = 18 in Equation 2). Incoherent averag-ing is necessary if the
relative phasing of the desiredsignal is unknown from look to look.
With SAR data,however, the relative phasing is known because
thelooks were created from one coherent set of collecteddata. This
knowledge of the relative phasing can beexploited to provide an
image of the target with en-hanced sidelobe and clutter
rejection.
Coherent summing exploits the known relative
phase of the looks. It was originally proposed by L.L.Horowitz
as a means of estimating scatterer phase inaddition to RCS. Let ui
be the L 1 vector of thephase progression of the looks, where u is
a functionof v( , )x y . The coherent sum of looks can then be
ex-pressed as
z x yL
uH i ii
L
( , ) ,*==
1
1
w z
where z(x, y) is the complex output, and w is derivedas in the
incoherent case. Note that the above sum-mation is computed only
over the forward looks; i.e.,backward looks must be excluded.
Computational Load. Current implementations ofCapons technique
for the point-scatterer model re-quire approximately two thousand
operations peroutput sample, where an operation is one
real-valuedmultiplication or addition. This operation require-ment
is not dependent on the size of the image. Forcomparison, a
conventional image requires one thou-sand to two thousand
operations per pixel, includingpolar formatting and autofocus.
The MUSIC Algorithm
The MUSIC algorithm is a powerful direction-find-ing algorithm
that exploits properties of the signalsubspace of the covariance
matrix [13]. It does notproduce an estimate of the RCS, but rather
an esti-mate of how closely the data match the scatteringmodel. If
the point-scatterer model is employed, aMUSIC image shows how
pointlike the scattering is.
Let {ei} be a set of orthonormal vectors that spanthe column
space of R. These vectors can be derivedfrom an eigendecomposition
of R as the eigenvectorsthat correspond to the nonzero eigenvalues.
TheMUSIC output is then
MUSIC( , ) log ( , ) .x y x yiH
i
L
= - -
=
10 1102
1
e v
We can recognize the summation as the norm of theprojection of
v( , )x y into the span of the eigenvec-tors. If the norm of the
projection of v( , )x y is large(near one), then the MUSIC output
is large. Al-though MUSIC usually employs an estimate of the
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 157
number of signals, HDVI simply uses the rank of thecovariance
matrix as an estimate of the number of sig-nals because there are
so few looks.
Other Related Techniques
While investigations in HDVI have employed MLM(Capons technique)
and MUSIC, there are a varietyof modern spectrum-estimation
techniques that maybe applied to the problem, such as maximum
likeli-hood, linear prediction (so-called bandwidth
extrapo-lation), adaptive event processing [7], ESPRIT [14],and a
sinusoid estimation technique adapted to imag-ing by Li [5]. Two of
these techniques are addressedfurther.
The maximum-likelihood algorithm attempts ajoint estimation of
scatterer locations, amplitudes,and phases by assuming that the
data are a sum ofideal scatterers in noise [2]. This algorithm has
notbeen employed in practice because of its computa-tional burden
and its sensitivity to model mismatch.
Bandwidth extrapolation is an application of linearprediction to
SAR data [1]. It derives a prediction fil-ter to estimate
out-of-band data samples, which effec-tively increases resolution,
and it employs the point-
FIGURE 4. A comparison between bandwidth extrapolation (left)
and Capons maxi-mum-likelihood method (MLM) using the soft
quadratic constraint (right). The simu-lated target is four point
scatterers within one resolution cell, and the area imaged is1.5 1
resolution cells. Capons technique clearly provides resolution of
the fourscatterers.
dB
05
101520253040
scatterer model to extend the dominant sinusoidalcomponents in
the data. Also, it is an inherently one-dimensional technique that
is applied successively inrange and cross-range to produce the
effect of two-di-mensional superresolution.
Figure 4 shows a comparison of bandwidth ex-trapolation with the
MLM technique employing thesoft constraint (defined earlier in the
section on qua-dratically constrained coefficients). The
simulatedtarget consists of four scatterers in one resolution
cell(pixel), which is a difficult superresolution example.The
result is that MLM does a better job than band-width extrapolation
in resolving the scatterers becauseMLM is a fully two-dimensional
technique that isgenerally better suited to SAR data.
Vector Imaging
Vector imaging refers to the incorporation of multiplescatterer
models into the image-formation process.The goal of vector imaging
is to categorize and clas-sify radar backscatter according to the
phenomenonthat caused the reflection. Figure 5 shows a
notionalvector image, where each element of the vector is aseparate
high-definition image formed by using a dif-
-
BENITZHigh-Definition Vector Imaging
158 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
ferent scattering model. Vector imaging requires theuser to
define the scattering models that are most rep-resentative and
useful, which unfortunately is not asimple task. Some notional
vector images include thepoint-scatterer and flash phenomena,
discussed inthis article, as well as other scattering phenomenasuch
as scatterer height (an extension of interferomet-ric SAR) or
polarization.
Figure 6 illustrates the computation of a vector im-age. The
vector capability is achieved in the selectionof the steering
vector v( , )x y because the steering vec-tor incorporates the
model of the desired scattering.Also, some changes may be required
in the generationof the covariance matrix; these changes are
describedbelow, along with a description of the flash model andthe
polarimetric model.
The Azimuthal-Flash Model
Azimuthal flash is a scattering phenomenon causedby a flat
reflecting surface several wavelengths long.Though this phenomenon
can occur at any frequency
FIGURE 6. The processing flow in HDVI. The image is processed in
small image chips, and a covariance matrix isformed for each chip.
The adaptive-filtering technique (e.g., Capons technique) employs
the covariance matrix and thedesired scattering model to produce
the high-definition vector image.
FIGURE 5. Illustration of a vector image, where a
separateelemental high-definition image is produced for each
scat-tering model. Each pixel in the vector image contains a
vec-tor of parameters that analyzes the received backscatter
ac-cording to its similarity to the scattering model. This
vectorstructure provides a more comprehensive understanding ofthe
target.
Elementalhigh-definition
image
High-definition vector image Scattering model
Point
Flash
Height
Even bounce
Select grid point to be processed (range, cross-range)*
Center and reduce dataconceptual picture
Region
Grid point(range, cross-range)
Imagechip
Compute covariance matrix
Scattering models
Point scatterer
Azimuthal flash
Polarizations
* Region is overlaid with a high-resolution grid(Centered and
reduced
amplitude and phasehistories)
High-definition vector image
1
2 3
Apply adaptive two-dimensionalmatched filters
4
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 159
with many types of target, a common example is ob-served at UHF
when a vehicle is illuminated frombroadside. This broadside flash
occurs when the en-tire side of a vehicle acts as a reflector,
causing theRCS to be dependent on the look angle, with thebrightest
return occurring when the radar is normalto the side of the
vehicle.
The model for the azimuthal flash used in HDVIwas generated
heuristically as a coherent sum of pointscatterers in adjacent
resolution cells. This form of themodel results in a sum-of-cosines
amplitude profileacross the rows (the azimuthal observations) of
thedata matrix (i.e., the flash was approximated by aFourier
series). Broad flashes require low-order co-sines, while narrow
flashes require higher-order co-sines. The underlying phase of the
azimuthal-flashmodel is identical to that of the linear-phase
pointscatterer defined in Equation 1.
The azimuthal-flash model does not exhibit theshift-invariance
property of the point-scatterer modelassumed in the generation of
the covariance matrix.For azimuthal-flash processing, looks must be
limitedin the amount of azimuthal shifting allowed, and
for-ward-backward averaging cannot be used.
The processing requirements for image formationare increased
because it is now necessary to search forthe location of the
azimuthal flash within the syn-thetic aperture. The benefit of this
search, however, isthat we gain an estimate of the orientation of
the re-flecting object.
Polarimetric Models
Both the point-scatterer model and the azimuthal-flash model are
easily extended to include polariza-tions [15]. Polarimetric data
can be viewed as an ex-tension of the two-dimensional SAR data
discussedabove, wherein each data sample is replaced with
athree-element vector containing the HH, HV, andVV polarization
information. The looks and covari-ance matrix are formed in the
usual fashion, exceptthat forward-only looks are employed. The
resultantcovariance matrix has a dimension three times that ofthe
covariance matrix for a single polarization. Wecan choose the
steering vectors to model a desired re-sponse, e.g., trihedral or
dihedral. The importance ofthis vector processing is that nulls can
be generated in
polarization space as well as in range and azimuth. Afew
preliminary results have been achieved and de-scribed elsewhere
[15].
Rail SAR Results
The early results of HDVI were achieved with theLincoln
Laboratory ultra-wideband Rail SAR. Shown
FIGURE 7. (a) The ultra-wideband Rail SARconsisting ofa movable
antenna mounted on a railprovides in situ mea-surements of small
areas over a wide band of frequencies.(b) Multiple antennas allow
SAR coverage over a range offrequency bands from 100 MHz to 18
GHz.
(a)
(b)
Antenna
Rail
-
BENITZHigh-Definition Vector Imaging
160 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
in Figure 7, the Rail SAR is an instrumentation-qual-ity radar
designed for in situ measurements of singletargets, thus avoiding
the errors introduced by plat-form motion and waveform limitations.
For the re-sults that follow, the Rail SAR measured the
complexreflection coefficients of a target from 500 MHz to2.0 GHz
in 801 frequency steps, and traversed a 4.5-m synthetic aperture in
31 steps.
Clutter Rejection Examples
This example shows the ability of the Capon algo-rithm to
discriminate reflectors from foliage. Four re-flectorsthree
eight-foot trihedral reflectors and onefour-foot dihedral
reflectorwere placed at variouslocations in foliage, with the
farthest reflector placedat a range of sixty meters, and thirty
meters deep in
FIGURE 8. Comparison of conventional image processing (left) and
HDVI (right) at L-band frequen-cies for four reflectors in foliage.
The quadratically constrained MLM algorithm used to produce theHDVI
image reveals the reflectors and suppresses the foliage.
FIGURE 9. Comparison of conventional image processing (left) and
HDVI (right) at UHF frequenciesfor four reflectors in foliage. The
quadratically constrained MLM algorithm used to produce the
HDVIimage reveals the reflectors and suppresses the foliage, except
for two tree trunks that appear as scat-terers (which are seen in
this HDVI image but not in the HDVI image in Figure 8).
30
20
10
dB
010
50Cross-range (m) Ra
nge (m)5 10 35
4555
65
30
20
10
010
50Cross-range (m) Ra
nge (m)5 10 35
45
+30 dB30 dB
5565
30
20
10
dB
010
50Cross-range (m) Ra
nge (m)5 10 35
4555
65
30
20
10
010
50Cross-range (m) Ra
nge (m)5 10 35
45
+30 dB30 dB
5565
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 161
foliage. We compare conventional image processing(without
azimuthal sidelobe control) and quadrati-cally constrained MLM
processing without the sub-space constraint. A three-dimensional
display revealsthe shape of the sidelobes.
Figure 8 shows the result of this discrimination testat L-band,
1.0-to-1.44-GHz, VV polarization. Thenominal range resolution is
0.34 m, and cross-rangeresolution is 1.1 m at a range of forty
meters. Thefour reflectors are easily discerned in the HDVI im-age;
the weakest discrimination is the four-foot dihe-dral. The reduced
gain on the reflector at a range ofsixty meters in the HDVI image
is due to the degra-dation of its response because of the foliage.
MLM isdesigned to preserve gain on ideal point scatterers,and
reduces gain on non-pointlike scatterers such astrees and corrupted
reflectors.
Figure 9 shows the result of this discrimination testat UHF,
500-to-720-MHz, VV polarization. Thenominal range resolution is now
0.68 m, and cross-range resolution is 2.1 m at a range of forty
meters.Reflector RCS is smaller at this lower frequency, andthe
lower resolution allows more clutter per resolu-tion cell. Because
of the lower target-to-clutter ratio,the MLM constraint had to be
relaxed, resulting inthe appearance of two clutter returns (tree
trunks),which are not visible in the HDVI image in Figure 8.
FIGURE 10. Superresolution of target features for VV (vertical)
polarization (left) and HH (horizontal)polarization (right) at
half-beamwidth separation. The two-dimensional MUSIC algorithm
resolvestwo scattering centers within one pixel. The target is a
circular disk that exhibits a single scatteringcenter when
illuminated with VV polarization but two resolvable scattering
centers when illuminatedwith HH polarization.
The improvement over the conventional image, how-ever, is
readily apparent.
Superresolution Example
This example demonstrates the ability of the MUSICalgorithm to
resolve the edges of a circular disk,which appears as two
scattering centers separated by adistance of half a resolution
cell. The SAR data werecollected for a disk illuminated at
near-normal inci-dence. Electromagnetic theory predicts that a
circulardisk, when illuminated with linear polarization,
willexhibit flux concentrations at its physical extremes,namely, in
the vertical direction for vertical polariza-tion and in azimuth
for horizontal polarization. Be-cause the Rail SAR has a horizontal
aperture, we canexpect to resolve scatterers exhibiting horizontal
sepa-ration but not scatterers exhibiting only vertical
sepa-ration. Hence we can expect to resolve the circulardisk into
two scatterers when HH polarization is em-ployed but not when VV
polarization is employed.Figure 10 shows the results of the MUSIC
algorithmfor VV polarization and HH polarization, at 1.2 to1.5 GHz.
Note that the VV polarization reveals onepeak while the HH
polarization reveals two, as ex-pected. The separation of the
scattering centers in thefigure is approximately equal to the
diameter of thedisk.
5
dB
00
2Cross-range (m) Range (
m)4 4142
43
21
00
2Cross-range (m) Range (
m)4 4142
21 dB0 dB
43
-
BENITZHigh-Definition Vector Imaging
162 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
Airborne UHF SAR Results
Lincoln Laboratory has done extensive studies on thedetection of
targets in foliage. Foliage renders micro-wave radar useless,
forcing the radar to employ lowerfrequencies where resolution is
limited. One promis-ing approach to penetrating foliage has been to
em-ploy a wide-bandwidth UHF radar and to integratethe data over a
wide synthetic aperture. The resultantradar signatures, however,
present a unique detectionproblem for which HDVI may provide a
solution.
The results presented here employ data from a se-
FIGURE 12. Aerial photo (top) and SAR image (bottom) of the
Cedar Swamp, Maine, deployment. The radar lineof flight in the SAR
image was across the top of the photo. The vehicles in the center
were not visible from thepoint of view of the radar because of the
thick foliage.
ries of SAR data collections that were performed inCedar Swamp,
Maine, using the SRI International ul-tra-wideband UHF SAR, shown
in Figure 11. The ra-dar waveform is a 200-MHz-bandwidth impulse
witha carrier frequency of 300 MHz, and the polarizationis HH (see
Table 1). The synthetic aperture is a 30intercept with respect to
the region of interest, result-ing in an image with 1-m 1-m nominal
resolution.This resolution is sufficient to spatially separate
ve-hicles from tree-trunk returns (the dominant cluttersource), but
the resultant target-to-clutter levels arenot high enough to
provide reliable detection.
The goal of HDVI is to employ models that moreclosely resemble
the backscatter from man-made ob-
FIGURE 11. SRI International ultra-wideband UHF SAR. Theantenna
is mounted under the wing of the aircraft. The SARparameters are
listed in Table 1.
Table 1. Ultra-Wideband SAR Parameters
Waveform Impulse
Bands 200400 MHz, 100300 MHz
Resolution 1 m 1 m
Polarization HH
Power 50-kW peak, 0.1-W average
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 163
FIGURE 13. Overview of the Cedar Swamp deploymentshown in Figure
12. The nine vehicles in this illustration aredescribed in Table
2.
Table 2. Cedar Swamp Vehicle Descriptions
Vehicle Label Vehicle Type Length (m)
V1 Logging truck, loaded 24
V2 Logging truck, empty 18
V3 Five-ton truck 8.4
V4 Lincoln Laboratory test target 15
V5 Logging truck, loaded 24
V6 Logging truck, empty 18
V7 Two-ton truck 6.7
V8 HEMTT (truck) 10
V9 Five-ton truck 8.4
Eight-foot reflector
Radar line of sight
V1V2
V3 V4 V5 V6 V7V8 V9
Scrub
Trees
jects, rather than backscatter from trees, thus provid-ing a way
of discriminating the man-made objects.The models employed are the
point-scatterer modeland the azimuthal-flash model, both of which
weredescribed earlier. Point-scatterer responses are regu-larly
observed with man-made objects. Azimuthal-flash responses are the
result of the interaction of thebroadside of the vehicle and the
ground, forming adihedral-type reflection. The extent of this
dihedral isseveral wavelengths; e.g., a vehicle ten meters inlength
is ten wavelengths at 300 MHz, which is vis-ible only over a narrow
range of angles. Trees, on theother hand, are neither pointlike nor
flashlike at thesefrequencies. Though closer to point scatterers,
treesexhibit random amplitude and phase variations,which tends to
separate them from ideal point signa-tures. HDVI is thus able to
reject more of the tree re-sponses through the use of these
models.
Point-Scatterer Results
Figure 12 shows an aerial photograph of the SARdata-collection
site in Cedar Swamp, Maine. The ra-dar path was parallel to the top
of the photo, at arange of about six hundred meters, and at a 45
eleva-tion with respect to the vehicles along the road. Ve-hicles
in the middle to right part of the photo areparked next to tall
pine trees, and are thus concealedfrom the view of the radar.
Figure 13 shows a diagram
of the locations of the nine vehicles at Cedar Swamp,and Table 2
lists their types and lengths.
Figure 14 presents a comparison of the conven-tional image and
the HDVI image using the point-scatterer model. A dynamic range of
30 dB is dis-played with a rainbow color scale, and peaks above
athreshold are displayed three-dimensionally. Thethresholds are
chosen for each image such that eightof the nine vehicles exceed
it; i.e., the probability ofdetection is 0.89 in each image. HDVI
has reducedthe number of false detections by a factor of
four,making it much easier to identify the returns from thevehicles
along the top edge of the roadway. The larg-est return in the
center is from an eight-foot trihedralcorner reflector, also
concealed in trees.
We employed the MUSIC algorithm here to pro-vide a measure of
point likeness, that is, the similaritybetween the measured data
and a true point-scattererresponse. The output of MUSIC was
compared to athreshold, and a matched-filter radar-cross-section
es-timate was inserted for the display. A false back-ground was
added to provide a visual reference for theroadway.
Vector-Imaging Results
We processed the same data by using two sizes of
theazimuthal-flash model, a 10 flash and a 3 flash. Re-call that
the synthetic aperture is a 30 intercept with
-
BENITZHigh-Definition Vector Imaging
164 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
respect to the targets. Figure 15 shows the HDVIresults for the
azimuthal-flash models, using theMUSIC algorithm as a detector. At
each pixel, theMUSIC output was computed for several shifted
po-sitions of the azimuthal flash within the synthetic ap-erture,
to allow for the unknown orientation of thevehicle. The largest
value was reported and comparedto a detection threshold. Positive
detections are dis-played with a radar-cross-section estimate
computedwith a flash-matched filter.
The point-scatterer and two flash-scatterer imagesconstitute a
three-level vector image, which is signifi-cantly more useful than
a conventional image in ananalysis of the received backscatter. The
vector imagealso provides improved clutter rejection beyond thatof
the point-scatterer image alone, especially for the3 flash, where
all bright returns are targets. Figure 16shows an overlay of the
MUSIC outputs with vehiclereturns outlined and clutter excised.
Note how flashsize corresponds to the inverse of vehicle length.
Sev-eral vehicles exhibit multiple signatures. For example,
the two logging trucks on the left exhibit a 3 flashfrom the
entire body and a point return from the cabend. Not shown is the
orientation estimate derivedfrom the flash timing; i.e., the peak
of the flash occurswhen the radar is broadside to the vehicle.
The vector image clearly provides information thatconventional
radar image processing did not reveal.The next step is to discover
a method to jointly ex-ploit the multiple levels of the vector
image for targetdetection and recognition.
Advanced Detection Technology Sensor Results
To achieve better than 1-m 1-m resolution withSAR data, we must
operate at microwave frequencies.The Advanced Detection Technology
Sensor (ADTS)Ka-band radar operated by Lincoln Laboratory pro-vides
1-ft 1-ft resolution and fully polarimetric out-put [16]. It has
been used to collect more than twohundred square kilometers of data
to support LincolnLaboratorys automatic target-recognition
studies.
An important issue in target recognition is the
FIGURE 14. Comparison of conventional image processing (top)
with HDVI (bottom). HDVI em-ploys the point-scatterer model, which
reduces clutter false alarms in the image by a factor offour. A
smaller number of false alarms reduces the burden on subsequent
automatic-target-recognition algorithms because fewer detections
need to be reviewed. Both images are normal-ized to detect eight of
the nine vehicles, with detections displayed in three-dimensional
relief.
0 dB 30 dB
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 165
resolution required for reliable performance. ADTSstudies
demonstrate that a resolution of one foot issufficient for reliable
target recognition. Operationalradars, however, often provide
coarser resolution and,correspondingly, markedly reduced
recognition per-formance. For example, the resolution of the
SAR
mounted on the TIER II+ unmanned air vehicle isone meter in
wide-area (stripmap) mode. One of themotivations, then, for HDVI
was to improve theresolution of a one-meter radar with the hope of
im-proving target recognition. This goal has beenachieved [12].
FIGURE 15. Vector image of the Cedar Swamp deployment. By
employing 10 and 3 flashmodels, HDVI further reduces clutter false
alarms. The flash models reject the corner reflec-tor, which is the
large return in the center of the point-scatterer image.
FIGURE 16. Vector-image signature analysis. The vehicles exhibit
multiple signatures, and ve-hicle length is inversely proportional
to flash size. Hence the vector image reveals more infor-mation
about the targets than the conventional image shown in Figure
14.
Point scatterer (30) 10 Flash 3 Flash
24 18 8.4 15 24 18 6.7 8.410
Known length of target (m)
Point scatterer (30 aperture)
10 flash model
3 flash model
-
BENITZHigh-Definition Vector Imaging
166 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
FIGURE 18. Comparison of imaging techniques at one-meter and
one-foot resolution, showing the rightmost vehicle in Figure17.
HDVI at one-foot resolution clearly improves on the conventional
image at one-foot resolution. HDVI, using one-meter data,approaches
the one-foot conventional image in appearance, but with lower
sidelobes.
FIGURE 17. Comparison of conventional imaging (left) and HDVI
(right) of two vehicles at Ka-band. HDVI provides
improvedresolution, reduced sidelobes, and reduced speckle. The
HDVI algorithm employed here is Capons technique with both
thesubspace and quadratic constraints.
Conventional image at one-meter resolution
Conventional image at one-foot resolution
HDVI at one-meter resolution
HDVI at one-foot resolution
Conventional image HDVI
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 167
FIGURE 19. Comparison of imaging techniques at one-meter
resolution: (a) conventional, (b) incoherent-look
two-dimensionalMLM, and (c) coherent-look two-dimensional MLM. The
vehicles, from top to bottom, are a Howitzer, a personnel carrier,
and atank. Quantitative measurements showing improvement in the
lobe widths, target-to-clutter ratio, and speckle appear in Table
3.
The first result with the ADTS radar was for twotargets of
opportunity at Westover Air Reserve Base,Massachusetts, as shown in
Figure 17. This figurecompares conventional imaging using
Hammingweighting with HDVI employing Capons techniquewith norm and
subspace constraints, and with an in-coherent combination of looks.
(The sidelobes rundiagonally because north is toward the top of
theimage and the radar is at about two oclock.) Thiscomparison
demonstrates resolution improvement,
sidelobe reduction, and speckle reduction. Speckle re-duction
results from the incoherent combination oflooks in Capons
technique.
Figure 18 provides a close-up of the rightmost ve-hicle shown in
Figure 17. This figure compares con-ventional imaging with HDVI
(coherent look) atresolutions of one foot and one meter. The
one-meterdata were extracted from the one-foot data through
acoherent spoiling process. While one-meter data pro-cessed with
HDVI clearly do not achieve the same re-
Conventional image Incoherent MLM Coherent MLM
Table 3. Statistics for Images in Figure 19
Lobe Width Target-to-Clutter Ratio Speckle*
Conventional 1.04 m 31.8 dB 5.8 dB
Incoherent MLM 0.59 m 31.9 dB 3.8 dB
Coherent MLM 0.58 m 33.5 dB 5.8 dB
* Standard deviation
-
BENITZHigh-Definition Vector Imaging
168 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
sult as one-foot data processed conventionally, thegeneral
appearance of results from the two techniquesis the same, and the
sidelobes in HDVI are lower.
Figure 19 shows results for military vehicles at one-meter
resolution, and provides a comparison of thecoherent-look and
incoherent-look versions of HDVI(Capons technique with norm and
subspace con-straints). The vehicles, from top to bottom, are
aHowitzer, a personnel carrier, and a tank. The im-provement in
resolution is indicated by the 3-dB lobewidth, which decreases from
1.04 m to 0.58 m (seeTable 3). Target-to-clutter ratios are
calculated as theratio of the brightest return to the average of
the sur-rounding clutter; these ratios show a slight improve-ment
with coherent-look HDVI. Speckle reduction isindicated by the
standard deviation of the dB-valuedimages evaluated over a patch of
clutter: the conven-tional image shows 5.8 dB and
incoherent-lookHDVI shows 3.8 dBa marked reduction.
The two versions of HDVI are visibly and statisti-cally
different, with the coherent-look technique pro-viding slightly
higher target-to-clutter ratio andhigher speckle. It is worth
noting that the incoherent-look technique provides the best
performance with atemplate-matching classifier, while the
coherent-looktechnique provides the sharper image preferred byimage
analysts.
Conclusion
High-definition vector imaging is a new approach toprocessing
SAR data. It employs modern spectrum-estimation techniques to
derive more informationfrom SAR data. Benefits include improved
resolution,reduced sidelobes, reduced speckle, reduced clutter,and
better discrimination based on scattering phe-nomenology. HDVI
provides improved images forexploitation by image analysts and more
informationfor automatic target recognition.
We describe and demonstrate several HDVI tech-niques. Versions
of Capons adaptive-beamformingtechnique have demonstrated improved
resolution,and reduced sidelobes, speckle, and clutter. A versionof
the MUSIC algorithm proved useful in discrimi-nating targets from
clutter for UHF SAR data. Wealso discuss modifications of the
techniques, the ap-plication of these modified techniques to SAR
data,
and the trade-offs between algorithm robustness
andresolution.
The implication of HDVI technology is that radarperformance can
be significantly improved via digitalsignal processing. Existing
systems can achieve im-proved performance, and new system designs
couldbe less expensive. Further extensions of HDVI couldprove
beneficial to more advanced problems such aschange detection,
moving-target exploitation, and in-terference cancellation.
Continual advances in com-puter design make HDVI a practical and
affordableoption.
Acknowledgments
I would like to acknowledge the assistance of DennisBlejer in
providing me with Rail SAR data, and theassistance of the
Surveillance Systems group at Lin-coln Laboratory for providing me
with ADTS andFOPEN data.
-
BENITZHigh-Definition Vector Imaging
VOLUME 10, NUMBER 2, 1997 LINCOLN LABORATORY JOURNAL 169
R E F E R E N C E S1. S.L. Borison, S.B. Bowling, and K.M.
Cuomo, Super-Reso-
lution Methods for Wideband Radar, Linc. Lab. J. 5 (3),1992, pp.
441462.
2. S.R. DeGraaf, Parametric Estimation of Complex 2-D
Sinu-soids, 4th Annual Workshop on Spectrum Estimation and
Mod-eling, Minneapolis, 35 Aug. 1988, pp. 391396.
3. H.C. Stankwitz, R.J. Daillaire, and J.R. Fienup,
NonlinearApodization for Sidelobe Control in SAR Imagery,
IEEETrans. Aerosp. Electron. Syst. 31 (1), 1995, pp. 267279.
4. S.R. DeGraaf, Sidelobe Reduction via Adaptive FIR Filteringin
SAR Imagery, IEEE Trans. Image Proc. 3 (3), 1994, pp.292301.
5. J. Li and P. Stoica, An Adaptive Filtering Approach to
SpectralEstimation and SAR Imaging, IEEE Trans. Signal Process.
44(6), 1996, pp. 14691484.
6. J.W. Odendaal, E. Bernard, and C.W.I. Pistorius,
TwoDimensional Superresolution Radar Imaging Using theMUSIC
Algorithms, IEEE Trans. Antennas Propag. 42 (10),1994, pp.
13861391.
7. K.W. Forsythe, Utilizing Waveform Features for
AdaptiveBeamforming and Direction Finding with Narrowband Sig-nals,
Linc. Lab. J. 10 (2), 1997, in this issue.
8. L.M. Novak, G.J. Owirka, W.S. Brower, and A.L.
Weaver,Automatic Target Recognition with Enhanced PolarimetricSAR
Data, Linc. Lab J., in this issue.
9. W.J. Carrara, R.S. Goodman, and R.M. Majewski,
SpotlightSynthetic Aperture Radar: Signal Processing Algorithms
(ArtechHouse, Boston, 1995).
10. J. Capon, High-Resolution Frequency-Wavenumber Spec-trum
Analysis, Proc. IEEE 57 (8), 1969, pp. 14081419.
11. H. Cox and R. Zeskind, Reduced Variance
DistortionlessResponse (RVDR) Performance with Signal Mismatch,
25thAsilomar Conf. on Signals, Systems & Computers 2, Pacific
Grove,Calif., 46 Nov. 1992, pp. 825829.
12. B. Van Veen, Minimum Variance Beamforming, chap. 4
inAdaptive Radar Detection and Estimation, S. Haykin and
A.Steinhardt, eds. (Wiley, New York, 1992), pp. 161236.
13. R. Schmidt, Multiple Emitter Location and Signal
ParameterEstimation, Proc. RADC Spectrum Estimation Workshop,Rome,
N.Y., 1979, 35 Oct. 1979, pp. 243258.
14. S. Barbarossa, L. Marsili, and G. Mungari, SAR
Super-Reso-lution Imaging by Signal Subspace Projection
Techniques,AE Int. J. Electron. Commun. 50 (2), 1996, pp.
133138.
15. D.F. DeLong and G.R. Benitz, Extensions of High
DefinitionImaging, SPIE 2487, 1995, pp. 165180.
16. L.M. Novak, M.C. Burl, R.D. Chaney, and G.J. Owirka,Optimal
Processing of Polarimetric SAR Automatic TargetRecognition System,
Linc. Lab J. 3 (2), 1990, pp. 273290.
-
BENITZHigh-Definition Vector Imaging
170 LINCOLN LABORATORY JOURNAL VOLUME 10, NUMBER 2, 1997
gerald r. benitzis a staff member in the Ad-vanced Techniques
group. Hereceived a B.S. degree inelectrical engineering fromPurdue
University, and anM.S. degree in electrical engi-neering, an M.A.
degree inmathematics, and a Ph.D.degree in electrical engineer-ing,
all from the University ofWisconsin, Madison. Histhesis work was an
investiga-tion of the asymptotic theoryof optimal quantization
anddetection. His areas of researchat Lincoln Laboratory
haveincluded analysis, develop-ment, and testing of algo-rithms for
direction findingand waveform estimation withadaptive antenna
arrays. Hiscurrent research includesapplications of adaptive
tech-niques to image processing.He is a member of the Infor-mation
Theory Society of theIEEE.