High-Definition Vector Imaging (Radar) [Jnl Article] -

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


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



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



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,



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



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)



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.



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



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^



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



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-



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



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



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


nge (m)5 10 35

45

+30 dB30 dB

5565

30

20

10

dB

010


nge (m)5 10 35

4555

65

30

20

10

010


nge (m)5 10 35

45

+30 dB30 dB

5565



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



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



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



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



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



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



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



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.



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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.

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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.

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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.

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