Feature Enhancement of Robust Adaptive Target Detection...

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Feature Enhancement of Robust Adaptive Target Detection with the Y-configured Multisensor Imaging Radar Y. Shkvarko and V. Espadas Department of Electrical Engineering. CINVESTAV Unidad Guadalajara Av. Del Bosque 1145 Col. El Bajío, Zapopan, Jalisco, México E-mail: [email protected] AbstractA new Descriptive Experiment Design Regulari- zation-based Robust Adaptive Beamforming (DEDR-RAB) approach is presented for high resolution array radar imaging of multiple targets with the Y-configured Multi- sensor Imaging Radar (MIR). Our approach is based on the advanced minimum risk inspired DEDR framework for enhanced radar imaging and optimization of the MIR resolu- tion performances. We adopt the celebrated GeoSTAR sensor array configuration that provides a desirable low side lobes shape of the point spread function (PSF) attained employing the conventional matched spatial filtering (MSF) technique for radar image formation. The effectiveness (signal to inter- ference plus noise ratio, SINR) of the new aggregated DEDR- RAB radar imaging method is corroborated via extended simulations of different DEDR-related imaging techniques. The results are indicative of the superior operational effi- ciency of high resolution localization of the multiple closely spaced targets with the new DEDR-RAB methodology. Keywords: descriptive experiment design regularization, target detection, beamforming, multi-sensor imaging radar 1. Introduction Beamforming is a pervading task in remote sensing (RS) imaging applications. The adaptive beamformers (ABF) se- lect a weight vector as a function of the data to optimize the performance subject to various constraints, these ABF can have better resolution and much better interference rejection capability than the data-independent beamformers. However the ABF are much more sensitive to errors, such as steering vector errors caused by imprecise sensor calibration than the data-independent beamformers [1]. The latter has spurred development of various ABFs and devise RABs for enhancing the RS images, and many sophisticated techniques are now available (see, for example [1], [2] and the refer- ences therein). Crucial still unresolved ABFs issues relate to robust enhanced imaging in harsh operational scenarios characterized by possible imperfect array calibration, partial sensor failure and/or uncertain noise statistics [3]. We address a new DEDR-RAB approach for attain- ing virtual high-resolution performances of radar imag- ing with differently configured mm-band array radars. Our new aggregated DEDR-RAB approach is a robust adap- tive beamforming-oriented generalization of the conven- tional MSF method for radar image formation [4] based on the advanced descriptive experiment design regularization framework for radar imagery enhancement [5], [6]. At an initial stage, we optimize the sensor array configuration employing the celebrated GeoSTAR geometry [7] to attain the desired shape of the MSF system PSF, that is, we secure lowest possible side-lobes level ba-lanced over the minimum effective width of the main PSF beam by optimizing the antenna inter-element spacing. At a reconstructive stage, the low resolution MSF image is next enhanced via performing the new aggregated DEDR-RAB post-processing aimed at attaining the overall super-high resolution remote sensing (RS) performances. The effectiveness of the new aggre- gated DEDR-RAB radar imaging method is corroborated via extended simulations of the multiple target localization experiment of different DEDR-related imaging techniques using the specialized elaborated software that we refer to as ’Virtual Remote Sensing Laboratory’ (VRSL) [8]. The latter are indicative of the superior operational efficiency of the imaging radar system that employs the new DEDR- RAB method adapted to the DEDR-optimized GeoSTAR configuration over other tested competing techniques [1] - [9]. In this study, the robustness of the ABF is performed by aggregating it with the DEDR-based minimum variance distortionless response (MVDR) digital beamforming ap- proach that exploits structural information on the desired image map sparsity over the RS scene [10]. The developed aggregated DEDR-RAB technique is implemented in an implicit iterative form to enhance the overall imaging and target localization performances. 2. MIR concept The MIR-Y antenna array is shown in Fig. 1a and corresponding uv samples (Fig. 1b), in this case, u and v specify the normalized (so-called visibility domain) coor- dinate representation format, u = x/λ o , and v = y/λ o . This MIR array (GeoSTAR, Geo Synthesized Thinned Array Radiometer) is composed of 24 (M = 24) antenna ele- ments as in [7], where it is addressed in as a concept to provide high resolution imaging of distributed RS scenes in

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Feature Enhancement of Robust Adaptive Target Detection withthe Y-configured Multisensor Imaging Radar

Y. Shkvarko and V. EspadasDepartment of Electrical Engineering. CINVESTAV Unidad Guadalajara

Av. Del Bosque 1145 Col. El Bajío, Zapopan, Jalisco, México

E-mail: [email protected]

Abstract— A new Descriptive Experiment Design Regulari-zation-based Robust Adaptive Beamforming (DEDR-RAB)approach is presented for high resolution array radarimaging of multiple targets with the Y-configured Multi-sensor Imaging Radar (MIR). Our approach is based onthe advanced minimum risk inspired DEDR framework forenhanced radar imaging and optimization of the MIR resolu-tion performances. We adopt the celebrated GeoSTAR sensorarray configuration that provides a desirable low side lobesshape of the point spread function (PSF) attained employingthe conventional matched spatial filtering (MSF) techniquefor radar image formation. The effectiveness (signal to inter-ference plus noise ratio, SINR) of the new aggregated DEDR-RAB radar imaging method is corroborated via extendedsimulations of different DEDR-related imaging techniques.The results are indicative of the superior operational effi-ciency of high resolution localization of the multiple closelyspaced targets with the new DEDR-RAB methodology.

Keywords: descriptive experiment design regularization, target

detection, beamforming, multi-sensor imaging radar

1. IntroductionBeamforming is a pervading task in remote sensing (RS)

imaging applications. The adaptive beamformers (ABF) se-

lect a weight vector as a function of the data to optimize

the performance subject to various constraints, these ABF

can have better resolution and much better interference

rejection capability than the data-independent beamformers.

However the ABF are much more sensitive to errors, such as

steering vector errors caused by imprecise sensor calibration

than the data-independent beamformers [1]. The latter has

spurred development of various ABFs and devise RABs for

enhancing the RS images, and many sophisticated techniques

are now available (see, for example [1], [2] and the refer-

ences therein). Crucial still unresolved ABFs issues relate

to robust enhanced imaging in harsh operational scenarios

characterized by possible imperfect array calibration, partial

sensor failure and/or uncertain noise statistics [3].

We address a new DEDR-RAB approach for attain-

ing virtual high-resolution performances of radar imag-

ing with differently configured mm-band array radars. Our

new aggregated DEDR-RAB approach is a robust adap-

tive beamforming-oriented generalization of the conven-

tional MSF method for radar image formation [4] based on

the advanced descriptive experiment design regularization

framework for radar imagery enhancement [5], [6]. At an

initial stage, we optimize the sensor array configuration

employing the celebrated GeoSTAR geometry [7] to attain

the desired shape of the MSF system PSF, that is, we secure

lowest possible side-lobes level ba-lanced over the minimum

effective width of the main PSF beam by optimizing the

antenna inter-element spacing. At a reconstructive stage, the

low resolution MSF image is next enhanced via performing

the new aggregated DEDR-RAB post-processing aimed at

attaining the overall super-high resolution remote sensing

(RS) performances. The effectiveness of the new aggre-

gated DEDR-RAB radar imaging method is corroborated

via extended simulations of the multiple target localization

experiment of different DEDR-related imaging techniques

using the specialized elaborated software that we refer to

as ’Virtual Remote Sensing Laboratory’ (VRSL) [8]. The

latter are indicative of the superior operational efficiency

of the imaging radar system that employs the new DEDR-

RAB method adapted to the DEDR-optimized GeoSTAR

configuration over other tested competing techniques [1] -

[9]. In this study, the robustness of the ABF is performed

by aggregating it with the DEDR-based minimum variance

distortionless response (MVDR) digital beamforming ap-

proach that exploits structural information on the desired

image map sparsity over the RS scene [10]. The developed

aggregated DEDR-RAB technique is implemented in an

implicit iterative form to enhance the overall imaging and

target localization performances.

2. MIR conceptThe MIR-Y antenna array is shown in Fig. 1a and

corresponding uv samples (Fig. 1b), in this case, u and vspecify the normalized (so-called visibility domain) coor-

dinate representation format, u = x/λo, and v = y/λo.

This MIR array (GeoSTAR, Geo Synthesized Thinned Array

Radiometer) is composed of 24 (M = 24) antenna ele-

ments as in [7], where it is addressed in as a concept to

provide high resolution imaging of distributed RS scenes in

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Fig. 1: (a) Antenna array layout with sensor numbering (M = 24) for Y-shaped GeoSTAR configuration, (b) corresponding

uv samples fot inter-element spacing dA(1) = 0.5λo; carrier frequency fo=24GHz

microwave and mm wavebands. In this work, the particular

system under consideration is operated at two separate yet

concurrent frequencies of 24 GHz and 36 GHz with dual

polarization (Vertical V and Horizontal H). At one instant,

radio frequency (RF) pulses of a specified pulse width (PW)

are transmitted concurrently at 24 and 36 GHZ in either V

polarization or H polarization. These pulses are “calibrated"

to maintain coherency so that their amplitudes and phases

are constant for different pulses. The transmitting antenna

is switched between V and H polarizations; i.e., V and H

transmitted pulses are delayed by a certain time. For each

frequency (24 or 36 GHZ), transmitted V polarized and H

polarized RF pulses are separated by a half of the fixed pulse

repetition time (PRT/2). The V polarized RF pulses and H

polarized RF pulses are repeated after every PRT.

Each antenna element receives signals of V and H polar-

izations. It follows that, we can send V pulses and receive

the same polarization mode (VV) or receive H polarization

(VH); similarly, we have HH and HV modes. The operation

range of the MIR system is in the order of 1 m to 100 m,

with a range resolution cell of 0.3 m, so we have 165 range

gates for processing. The sensors provide two measurements

for each data snapshot, In-phase (I) and Quadrature (Q).

The crucial issue relates to the formation of the empirical

estimate (Yr) sensor data cross-correlation matrix (Yr) for

each range gate r = 1, . . . , Rr = 165. To form the full rank

cross-correlation matrix (Yr) we need to perform averaging

over a great number J of independent recorded sensor array

data realizations. These independent realizations are to be

recorded using J transmitted pulses for each range gate

r = 1, . . . , Rr = 165

To form the full-rank sensor data covariance matrix (Yr),the minimal number of independent recordings J should be

not less than the number of sensors (M = 24), thus for each

range gate J > M , (i.e. J > 24) independent realizations are

to be recorded for each range gate r = 1, . . . , Rr = 165.

In the case of J < 24, the data covariance matrix is rank-

deficient; this means that if we apply the robust beamforming

processing for sensor focusing, we inevitably will face the

problem of huge artifacts (so called ghosts on the speckle

corrupted scene images). In the radar terminology [2], these

artifacts (speckle and ghost targets) will inevitably increase

the false alarm rate.

3. Low Resolution StageThe general mathematical formalism of the problem at

hand and the DEDR framework that we employ in this

section is similar in notations and structure to those in the

previous studies [4], [5], [6], and some crucial elements are

repeated for convenience of the reader.

3.1 Problem FormalismThe mathematical model of the power spectrum distribu-

tion (the so-called spatial spectrum pattern, SSP) restoration

problem is stated as follows. Consider the unknown con-

tinuous spatial distribution of the extended radiating source

within the given spatial domain (interval of analysis) Θ � θdefined by the instantaneous complex amplitudes e(t, θ) of

the source. In a convenient discrete-form representation,

we consider the discretized interval of spatial analysis Θwith a set of K prescribed spatial directions {θk; k =1, 2, ...,K} ∈ Θ. The vector

e(t) = vec{ek(t) = e(t, θk); k = 1, ...,K} (1)

composed with the complex amplitudes of the source signals

from all K spatial directions is referred to as the vector of

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random unknown instantaneous source complex amplitudes.

For the Y- configured MIR at hand, the phase at the mth

antenna element as a result of the kth source is ωkym where

ωk = 2π sin(θk) and ym = is the location of the elemental

phase center with respect to the midpoint of the array

in wavelengths (λ). We assume the statistically uncertain

scenario where tth time sampled signal at the mth element

of the array for a fixed range gate r is

um(t) =

K∑

k=1

ek(t)gm(θk)exp(iωkym) + nm(t) (2)

where gm(θk) is the pattern response of the mth array

element in the direction θk and nm(t) is the tth sample

of the adopted Gaussian noise from the mth array element.

This noise component is modeled as a random variable

independent of both time index t and the element index m.

The previous equation of observation (2) can be put in the

following vectorial form:

u(t) = Se(t) + n(t); t = 1, ..., T (3)

where n(t) represents the observation noise and S is the

signal formation matrix (SFO) defined as

S = matrix{Smk = gm(θk)exp(iωkym)} (4)

where m = 1, ...,M ; k = 1, ...,K. In (3), u(t), e(t) y n(t)represent zero-mean complex vectors composed of the sam-

ple coefficients {ek(t), nm(t), um(t); k = 1, . . . ,K;m =1, . . . ,M}. These vectors are characterized by the correla-

tion matrices [4]

Ru =< SReS+ > +Rn (5)

where

Re = D(b) (6)

is the diagonal matrix with the vector-form SSP b at its

principal diagonal {bk = b(θk) = < ek(t)ek(t)∗ > = <

|ek(t)|2 >; k = 1, . . . ,K} and Rn = N0I, respectively,

where I defines the identity matrix, N0 is the observation

white noise power, superscript + stands for Hermitian con-

jugate and < · > defines averaging.

3.2 DEDR-MSF MethodThe low resolution RS imaging problem is stated generally

as follows: to form the image of the tag b̂(θk) as a function

of the spatial scene coordinates applying the MSF method

[4], i.e.

b̂(θk) = s(θk)+Yrs(θk); k = 1, ..., K (7)

in which the image is formed as an MSF estimate of the SSP

distribution over the remotely sensed scene at a particular

rth range gate. In the pursued here non-parametric problem

treatment, the resolution quality is assessed by the shape of

the resulting system PSF associated with the MSF image (7)

of a single point-type target located at the scene origin at the

corresponding range gate r ∈ R. In particular, the desired

system PSF is associated with the shape that provides the

lowest possible side lobes (and grating lobes) level balanced

over the minimum achievable effective width of the PSF

main beam [2].

In (7), s(θk) is the kth array steering vector composed of

the corresponding kth row (k = 1, ...,K) of the regular SFO

matrix S and the estimate Yr (M -by-M ) of the array spatial

correlation matrix is computed via performing averaging

over the J snapshots as:

Yr = {R̂u} =1

J

J∑

j=1

uju+j . (8)

Based on (7), let us next analyse the PSF of the MIR

imaging system attainable with the employment of the con-

ventional GeoSTAR-configured Y-shaped array. In Fig. 2, we

present the PSF related to the MSF-based single target (TAG)

imaging procedure (7) employing the GeoSTAR-configured

Y-shaped sensor array radar. The PSF cross-section in the x-

y imaging scene provide explicit information on the spatial

resolution cells achievable with such configured imaging

sensor array that employ the conventional 2-D MSF method

(7) for RS image formation. The PSF in Fig. 2 is presented

with an inter-element spacing dA = 2λo, i.e., equal to

the double of the carrier wavelength. Note that the most

important characteristics of this PSF is the width of the

main beam and the maximum level of the secondary lobes

(including the suppressed grating lobes).

The next feature enhanced RS imaging problem at hand

is to develop the framework (in this study, the DEDR-RAB

method) and the related technique(s) for high-resolution

estimation (feature-enhanced reconstruction) of the SSP b,

we tackle this situation in the next section.

4. DEDR-RAB TechniqueThe clasical robust adaptive MVDR method [10] adapted

for the high-resolution spatial spectrum pattern estimation as

a solution to the problem b̂ = estMVDR{b|u} results in the

non-linear solution dependent strategy [10]:

b̂(θk) =1

s+(θk)R−1u s(θk)

; k = 1, ...,K (9)

optimal (in the MVDR sense) for the theoretical model-

dependent covariance matrix inverse R−1u . In the practical

RS target imaging scenarios, the unknown exact (model)

covariance matrix is substituted by its J-sample maximum

likelihood estimate (8) that results in the corresponding

MVDR estimation algorithm [1], [10]

b̂(θk) =1

s+(θk)Y−1r s(θk)

; k = 1, ...,K (10)

feasible for the full rank Yr only. From Bayes Minimum

Risk Estimation Strategy [5], [6] and from simple algebra,

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Fig. 2: Point Spread function (PSF) for 24 element

Y-shaped configured multisensor imaging radar with

dA = 2λo inter-element spacing for 30m range gate.

it is easy to corroborate that the theoretical model-based

strategy (10) is algorithmically equivalent to the solution

with respect to b of the non-linear equation

D(b̂) = {W(b̂) YrW+(b̂)}diag (11)

with the solution operator (SO)

W(b̂) = K(b̂)S+R−1n . (12)

Since Rn = N0I, the last SO becomes:

W(b̂) = K(b̂)S+ (13)

where K(b̂) = (Ψ+N0R−1e )−1 and Ψ = S+S represents the

matrix-form PSF of the MSF low-resolution image formation

system [2].The DEDR framework [5], [6] suggests the worst case

statistical performances optimization approach to the prob-

lem of b̂ = estMVDR{b|u} with the model uncertain-

ties regarding the statistics of the SFO perturbations that

yields the robust (13). The RAB modification of the DEDR

(DEDR-RAB) is constructed by replacing in (13) N0 by

the composite (loaded) NΣ = N0 + β. The latter is the

observation noise power N0 augmented by factor β ≥ 0adjusted to the regular SFO Loewner ordering factor and the

statistical uncertainty bound for the for the SFO perturbation

(see [5] for details). Finally, we can define the new DEDR-

RAB as:

D(b̂) = {(S+S+NΣR−1e )−1S+YrS(S+S+NΣR−1

e )−1}diag(14)

Fig. 3: Point Spread function (PSF) for 24 element

Y-shaped configured multisensor imaging radar with

dA = 2λo inter-element spacing for 30m range gate.

In Fig. 3, we present the PSF related to the DEDR-

RAB single target (TAG) imaging procedure (14) employing

the GeoSTAR-configured Y-shaped sensor array radar. The

PSF cross-section in the x-y imaging scene provide explicit

information on the spatial resolution cells achievable with

such configured imaging sensor array that employ (14) for

RS image formation. As in Fig.2, the PSF in Fig. 3 is

presented with an inter-element spacing dA = 2λo. Note the

difference between the two PSFs at hand, that is, the width

of the main beam and the maximum level of the secondary

lobes (including the suppressed grating lobes).

Fig. 4: Nominal multiple TAGs scene

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Fig. 5: Simulations protocols for the Y-configured MIR: (a)-(c) Low resolution scene image formed using the conventional

DEDR-MSF technique (7), SNR = 10 dB, for a range gate of r = 10m, 30m and 100m respectively; (d)-(f) Feature

enhanced image reconstructed employing the new aggregated DEDR-RAB method (14), SNR = 10 dB, for a range gate of

r = 10m, 30m and 100m respectively.

5. Target Localization ProtocolsWe corroborated the effectiveness of the new DEDR-

RAB technique (14) via simulation studies performed with

the ela-borated VRSL software. Three typical simulation

protocols of radar imaging of a scene composed of five

closely spaced targets (TAGs) in the range gates r = 10m,

30m and 100m (respectively, in columns) are presented in

Fig. 5 for the Y-configured MIR. In Fig. 4 we present the

nominal multiple TAGs scene. Figures 5a trough 5c show

the low resolution images of that scene formed using the

conventional DEDR-MSF technique (7) for the 10 dB signal-

to-noise ratio (SNR) typical for radar imaging scenarios [2]

with a signal interference (INR) of 20 dB. Similarly, figures

5d trough 5f present the feature enhanced (high-resolution)

images of the same scene reconstructed with the proposed

aggregated DEDR-RAB technique (14). The reported target

localization protocols are indicative of the drastically supe-

rior operational efficiency provided with method (14) that

employs the DEDR-optimized GeoSTAR-configured array

over other competing tested imaging array radar geometries

[3].

To maintain consistency with the adaptive beamforming

literature, we adopt the SINR as a measure of the effec-

tiveness of our new aggregated DEDR-RAB method. The

DEDR-MSF performs poorly against the new DEDR-RAB

method as the latter presents an impressive average SINR

of 30 dB compared to 12 dB for the DEDR-MSF when

the signal of interest SNR=10 dB and exists a signal of

interference of 20 dB. This is shown in Figures 6 and 7.

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Fig. 6: Comparison of the DEDR-MSF and DEDR-RAB

methods. Average SINR (dB) for a SNR=0 dB and

INR=20 dB.

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Fig. 7: Comparison of the DEDR-MSF and DEDR-RAB

methods. Average SINR (dB) for a SNR=10 dB and

INR=20 dB.

6. ConclusionWe have addressed the new robust DEDR-RAB approach

for enhanced imaging of multiple target scenes in harsh

operational environments directly adapted to MIR imag-

ing systems, in this work particularly with Y-configured

GeoSTAR MIR. The presented high-resolution target local-

ization protocols are indicative of the superior operational ef-

ficiency of the Y-configured multimode imaging MIR system

with the adopted GeoSTAR array geometry. The reported

PSFs provide explicit information on the spatial resolution

achievable with such MIR system that employs the proposed

DEDR-RAB image formation technique. We demonstrated

via the analysis of behavior of SINR quality metric that

method (14) yields the best imaging performances. In future

studies, we intend to focus on the HW-SW co-design aimed

at the resolution enhancement of the DEDR imagery and

approaching the super-resolution imaging performances with

MAR systems.

This will push forward our capabilities in the hardware-

software codesign-based optimization of the RS and multi-

sensor radar systems paving a way toward adaptive superres-

olution sensing with the mm-waveband array radar systems.

References[1] J. Li and P. Stoica, Robust Adaptive Beamforming. John Wiley &

Sons Ltd, 2006.[2] F. M. Henderson and A. J. Lewis, Eds., Principles & Applications of

Imaging Radar, Manual of Remote Sensing, 3rd ed. John Wiley &Sons Ltd, 1998, vol. 2.

[3] V. Espadas and Y. Shkvarko, “Descriptive experiment design frame-work for high resolution imaging with multimode array radar sys-tems,” Applied Radio Electronics, vol. 12, no. 1, pp. 157–165.

[4] Y. Shkvarko, “From matched spatial filtering towardsthe fused statistical descriptive regularization method forenhanced radar imaging,” EURASIP J. Appl. Signal Process.,vol. 2006, pp. 16–16, Jan. 2006. [Online]. Available:http://dx.doi.org/10.1155/ASP/2006/39657

[5] Y. V. Shkvarko, “Unifying experiment design and convex regu-larization techniques for enhanced imaging with uncertain remotesensing data, part i: Theory,” Geoscience and Remote Sensing, IEEETransactions on, vol. 48, no. 1, pp. 82–95, Jan 2010.

[6] ——, “Unifying regularization and bayesian estimation methods forenhanced imaging with remotely sensed data-part ii: implementationand performance issues,” Geoscience and Remote Sensing, IEEETransactions on, vol. 42, no. 5, pp. 932–940, May 2004.

[7] A. Tanner, W. Wilson, B. Lambrigsten, S. Dinardo, S. Brown, P. Kan-gaslahti, T. Gaier, C. Ruf, S. Gross, B. Lim, S. Musko, S. Rogacki,and J. Piepmeier, “Initial results of the geostationary synthetic thinnedarray radiometer (geostar) demonstrator instrument,” Geoscience andRemote Sensing, IEEE Transactions on, vol. 45, no. 7, pp. 1947–1957,July 2007.

[8] Y. Shkvarko and V. Espadas, “Experiment design framework for super-high resolution imaging with the geostar configured sensor array data,”in Physics and Engineering of Microwaves, Millimeter and Submil-limeter Waves (MSMW), 2010 International Kharkov Symposium on,June 2010, pp. 1–3.

[9] Y. V. Shkvarko, “Estimation of wavefield power distribution in theremotely sensed environment: Bayesian maximum entropy approach,”Signal Processing, IEEE Transactions on, vol. 50, no. 9, pp. 2333–2346, Sep 2002.

[10] Y. Shkvarko, J. Tuxpan, and S. Santos, “Dynamic experiment designregularization approach to adaptive imaging with array radar/sarsensor systems,” Sensors, vol. 11, no. 5, pp. 4483–4511, 2011.[Online]. Available: http://www.mdpi.com/1424-8220/11/5/4483