HIGH RESOLUTION NEAR-FIELD MULTIPLE TARGET DETECTION AND LOCALIZATION USING SUPPORT VECTOR MACHINES

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1 ICONIC 2007 St. Louis, O, USA June 27-29, 2007 HIGH RESOLUTION NEAR-FIELD ULTIPLE TARGET DETECTION AND LOCALIZATION USING SUPPORT VECTOR ACHINES A. Randazzo,. A. Abou-Khousa 2,.Pastorino, and R. Zoughi 2 Departent of Biophysical and Electronic Engineering University of Genova Via Opera Pia A, I-645 Genova, Italy Tel.: +39 (00) , Fax: +39 (00) e-ail: {randazzo, pastorino}@dibe.unige.it 2 Applied icrowave Nondestructive Testing Laboratory (antl) Electrical and Coputer Engineering Departent University of issouri-rolla Rolla, O Tel: + (573) , Fax: + (573) e-ail: {aac2, zoughir}@ur.edu Abstract. In near-field icrowave nondestructive testing, iages of concealed targets are typically captured using scanning probes with sall footprint, e.g., open-ended waveguides. Using such iaging probes, it is of great interest to detect and resolve closely-spaced targets, i.e., targets that are less than half of a footprint apart. This paper is focused on applying a Support Vector achines-based approach to detect and localize closely-spaced targets. It will be shown that the proposed ethod is capable of providing high-resolution estiates of targets positions. Keywords: icrowave nondestructive testing, target localization, support vector achines. INTRODUCTION Near-field icrowave nondestructive testing and iaging techniques have shown great potential in a wide range of applications. In particular, open-ended waveguide-based near-field iaging systes are appealing for any inspection scenarios []. Basically, the waveguide is used to transit the icrowave signal and receive the signal backscattered fro the scene of interest (possibly, a dielectric ediu with ebedded flaws). The near-field iages are then obtained by scanning the waveguide probe in a certain iaging plane and recording the easureents at each scan point. In the near-field, the spatial resolution obtained using open-ended waveguide iaging probes is inversely proportional to the footprint of probe at the target s location. The footprint size is a function of the waveguide s aperture size as well as the dielectric properties of the inspected ediu [2]. It is well-established that if the coherent scan easureents are to be processed using passive correlation techniques, e.g., atched filtering, synthetic aperture focusing, etc, the resolution is lower bounded by half the probe s aperture size. In other words, resolving targets that are less than half-footprint apart is rather challenging. In this paper we propose utilizing an approach based on support vector achines (SV) to detect and localize closely spaced targets illuinated by near-field icrowave signals. SVbased eitting source localization has shown great efficacy for angle-of-arrival estiation purposes, i.e., far-field setup [3,4]. Here, we investigate the perforance of the SV approach in 26

2 A. Randazzo,. A. Abou-Khousa,.Pastorino, and R. Zoughi the near-field of an iaging probe by considering the one-diensional iaging proble, i.e., line scans. 2 PROBLE SETUP For the D proble, the iaging probe traverses a line while illuinating the structure under inspection. The easureents of the backscattered field, Γ, are taken at N discrete points along a line with a sapling interval of d s. Since a single antenna is used to intercept the backscattered signal, the D scanning process is conceived as a unifor linear array (ULA) of N perfectly decoupled eleents spaced by d, as shown in Fig.. s 0 d s ULA d ( N ) d s 2 s ˆx y = D δ x Target Target 2 ŷ Figure : D near-field iaging proble setup. For sake of siplicity, the case of two targets in free-space is considered in this paper. The scattering centers are located along the line y = D and spaced by δ x as shown in Fig.. The distance D is saller than the far-field liit of a single array eleent. After easuring the backscattered signal at the output of each eleent, the objective is to deterine the location of the targets scattering centers along the line y = D even if the inter-target separation δ x is less than half the linear diension (x-diension) of the iaging probe s aperture. To this end, an approach based on the SV theory is ipleented. 3 OUTLINE OF THE SV-BASED LOCALIZATION APPROACH The developed localization approach is based on the use of a support vector regression algorith [5]. In the proposed ethod, the unknown function that relates the values of the backscattered field at the N easureent points, Γ n, n =,,N, to the positions of the centers of the two targets, x and x 2, is approxiated as: x ( ) t ( ) ( x ) =< w, Φ( x) > b g ~ + () where = Γ,,, Φ x is a nonlinear transforation which aps the input values Γn, n = Γ N,, N, into a Hilbert space H with inner product,, w and b are paraeters chosen such that 262

3 ICONIC 2007 St. Louis, O, USA June 27-29, 2007 the function in () approxiates as faithfully as possible the transfored values using the iniu w possible. The paraeters of the approxiating function g ~ are estiated starting by a set of training saples, each one coposed by the N backscattered field values and by the corresponding actual positions of the targets. According to the SV theory, the paraeters w and b can be found by solving the following quadratic optiization proble with respect to the Lagrange ultipliers α and α, =,,, [6]: ax 2 ε = = n= subject to the following constraints of: oreover, the optiization results in [6]: and, ( α α )( α α ) Φ( x ), Φ( x ) ( α + α ) + g ( α α ) w = = = n ( α α ) α, α [ 0, C] n = 0 ( α ) Φ( l = α x ) n (2) (3) (4) L ~ = α x + (5) g( x) ( α ) Φ( x ), Φ( ) b It is worth noting that the nonlinear transforation ( x) l= Φ is always present only inside the inner product. Therefore, the need for explicit calculation of the nonlinear transforation is κ x x = Φ x, Φ x. In the present work, the avoided by defining a kernel function ( ) ( ) ( ) following Gaussian kernel is used: ( x, x), 2 γ x x = e κ (6) where γ is a constant chosen by the user and controls the accuracy of the approxiation. In this work, the functional (2) is efficiently axiized using a SO type decoposition algorith [5]. 263

4 A. Randazzo,. A. Abou-Khousa,.Pastorino, and R. Zoughi 4 SIULATION RESULTS The SV localization approach was validated via siulation by considering two thin identical etallic circular cylinders as targets. The values of the backscattered field used for training the SVs were nuerically obtained using a code based on the ethod of oents [7] with T illuination conditions. In particular, the operating frequency was set to 0 GHz and cylinders of radius were considered. The cylinders were positioned at D =5 with their axes parallel to z axis. N = 25 easureent points with d = 7.5 ( λ / 4) were used to s o produce the line scan. The training saples were generated using 600 values of scatterers centers, whose x-coordinates are uniforly distributed in the range [0, 80]. The values of the backscattered fields have been obtained using a configuration siilar to the one used for the generation of the training saples. A white Gaussian noise with zero ean value was added to the coputed field values. oreover, the siulations were repeated 200 ties for every case. Figure 2 shows the behavior of the ean relative error versus the signal-tonoise ratio (SNR) in db for the case in which the actual positions of the two scatterers are x = 50 and x 2 = 70 (i.e., δx = 20.) As can be seen, when SNR > 25 db, the proposed approach is able to localize the scatterers with an error less than %. oreover, Table shows the position estiation results (ean values) for the case in which SNR = 30 db and for different values of the inter-target separation δ x in the range [5, 20] st target 2 nd target Relative error SNR [db] Figure 2: ean relative errors on the estiation of the centers of the two scatterers versus the signal-to-noise ratio, δx = 20. Actual position () Estiated position () Absolute error () Target Target2 Target Target2 Target Target Table : SV-based approach position estiation results. Synthetic data, SNR = 30 db. 264

5 ICONIC 2007 St. Louis, O, USA June 27-29, EXPERIENTAL RESULTS To further illustrate the efficacy of the developed approach, the localization of test targets was perfored experientally in laboratory environent. An X-band open-ended rectangular waveguide ( a = 22.86, b = 0.6 ) operating at 0 GHz was used to produce line scans of two identical etallic cylinders of radius. Referring to Figure, the waveguide was scanned along the x -axis with its broad diension ( a ) along the x -axis (its aperture laying in the xz -plane). The length of each cylinder was sufficiently larger than b. The two-target coposition was centered on x = 90. Two cases of inter-target separation were considered, naely; δ x = 40, andδ x = 0. Figure 3 shows the easured agnitude and phase responses of the two cylinders withδ x = 40 andδ x = 0. As shown in the figure, both targets were detected and accurately localized when δ x = 40. On the other hand, when δ x = 0, the obtained response resebles the response of a single target located at x = 90. Consequently, it is not possible to localize both targets in this case directly fro the easureents (notice that δ x = 0 < a / 2 ). Figure 3: agnitude and phase responses of the two cylindrical targets with δ x = 40 and δ x = 0. The SV-based approach was applied to the easured data set in order to estiate the location of the centers of the cylinders. The SV estiation results along with the absolute estiation errors are provided in Table 2. As suggested by these results, the SV was successfully capable of localizing the targets for both cases of inter-separation. Actual position () Estiated position () Absolute error () Target Target2 Target Target2 Target Target Table 2: SV-based approach position estiation experiental results. 265

6 A. Randazzo,. A. Abou-Khousa,.Pastorino, and R. Zoughi 6 CONCLUSIONS In this paper, a support vector regression approach based on near-field icrowave interrogation has been developed for the localization of closely spaced targets. The proposed approach has been validated using both siulations and experients. The obtained results confir that the support vector achine-based approach is successfully capable of localizing the targets even when they are spaced less than half-footprint apart. REFERENCES. R. Zoughi, icrowave Non-Destructive Testing and Evaluation, Kluwer Acadeic Publishers, the Netherlands, N. N. Qaddoui,. Abou-Khousa, and W.. Saleh, Near-field icrowave iaging utilizing tapered rectangular waveguides, IEEE Trans. Instr. and easr., vol. 55, no. 5, pp , Oct Pasttorino and A. Randazzo, A sart antenna syste for direction of arrival estiation based on a support vector regression, IEEE Trans. Antennas Propag., vol. 53, no. 7, pp , July A. Abou-Khousa, A. Randazzo,. Pastorino, and R. Zoughi, An SV-based approach for AOA estiation: nuerical and experiental coparison with the USIC algorith, Proc. editerranean icrowave Syposiu, S 2006, Genova, Italy, Sept. 9-2, 2006, pp A. J. Sola and B. Schölkopf, A tutorial on support vector regression, Statistics and Coputing, vol. 4, no. 3, pp , Aug V. Vapnik, Statistical Learning Theory. New York: Wiley, J. H. Richond, "Scattering by a dielectric cylinder of arbitrary cross-section shape," IEEE Trans. Antennas Propagat., vol. AP-3, pp ,