Shape reconstruction methods are particularly well suited for imaging of concealed targets. Yet, these methods are rarely employed in real nondestructive testing applications, since they generally require the electrical parameters of outer object as a priori knowledge. In this regard, we propose an approach to relieve two well known shape reconstruction algorithms, which are the linear sampling and the factorization methods, from the requirement of the a priori knowledge on electrical parameters of the surrounding medium. The idea behind this paper is that if a measurement of the reference medium (a medium which can approximate the material, except the inclusion) can be supplied to these methods, reconstructions with very high qualities can be obtained even when there is no information about the electrical parameters of the surrounding medium. Taking the advantage of this idea, we consider that it is possible to use shape reconstruction methods in buried object detection. To this end, we perform several experiments inside an anechoic chamber to verify the approach against real measurements. Accuracy and stability of the obtained results show that both the linear sampling and the factorization methods can be quite useful for various buried obstacle imaging problems.

Imaging of concealed targets is an important problem, which can have different applications ranging from medical imaging [

There are already several studies to remedy the a priori information problems of qualitative imaging methods [

This paper introduces a practical solution procedure for two famous qualitative inversion schemes, which are the linear sampling method (LSM) [

In the following section, we briefly revise the LSM and FM, and then, in the subsequent part, we give the formulations of the modified LSM and FM for concealed target detection. Consequently, in the experimental verification section, we will present the results for two different inclusions buried inside dry soil. Throughout the paper, time convention is assumed

Consider the scenario in Figure

Configuration of the problem (

The general objective of the shape reconstruction methods is to recover an estimate of the support of the inclusion

Linear sampling method (LSM) is a common example of such support identification methods [

Another famous support identification algorithm is the factorization method (FM), which is developed as an alternative to LSM [

Although the above procedures are simple to implement and stable in nature, they are rarely employed in experimental concealed target detection. This is basically due to the fact that they require some a priori information, which cannot be available in most of the practical problems. Those requirements in the above scenarios can be stated as follows.

Far field equation in (

Furthermore, to be able to construct the equation system in (

Similarly, the main equation of FM can be changed as

In the light of the theoretical evaluations, this section includes the discussions of what kind of results can be obtained for different scatterers and for what applications the approach that we have proposed can be useful. To illustrate the applicability of the methodologies, we prepare the measurement setup shown in Figure

Measurement setup.

Measured (red squares) and simulated (blue circles) electric fields for canonical target at 4 GHz: (a) normalized absolute values (b) phase.

The first material, for which the measurements are performed, is shown in Figure

(a) Measured material, (b) LSM reconstruction with the proposed formulation, (c) FM reconstruction with the proposed formulation, (d) LSM reconstruction with the exact Green’s function, and (e) FM reconstruction with the exact Green’s function, for the scatterer filled with water.

(a) Measured material, (b) LSM reconstruction, and (c) FM reconstruction for the scatterer filled with air.

After demonstrating the applicability of the proposed approach, we investigate how the information of the exact Green’s function affects the quality of the results. For this aim, the dyadic Green’s function of the reference medium is computed with a 3D Method of Moments solver, utilized from biconjugate gradient fast Fourier transform method [

Next, we continue with a second example to further illustrate the performance when the scatterer is weak (i.e., the electrical properties of the buried material is low.) and the electrical contrast between the inclusion and the surrounding medium is low. (Note that the electrical properties of the water is

Up to now, we show the feasibility of the presented method when the measurements are taken on a full aperture. However, the common measurement schemes for concealed target detection problems consist of a limited incidence-observation angles. Thus, to be able to give a merit to the presented formulations, they must be analyzed when such a measurement configuration is employed. For this aim, certain parts of the obtained scattering matrix are cut and the inversions are applied by using only these measurements. The imaging results when the scatterer is water filled balloon are given in Figure

Reconstructions obtained for the water filled scatterer by using (a) LSM, (b) FM when the transmitting and receiving antennas are located on

Finally, the same measurement configurations can be applied to the air filled scatterer. The obtained results, when the transmitting and receiving antennas are located on the same arc, are given in Figures

Reconstructions obtained for the air filled scatterer by using (a) LSM, (b) FM when the transmitting and receiving antennas are located on

In this paper, we propose an experimental technique to move around the a priori information requirements of the qualitative methods. The proposed approach works for the situations where an extra measurement for the reference medium is feasible. In particular, we modified the formulations of two well known qualitative methods, the linear sampling method (LSM) and the factorization method (FM). The accuracy of the modified formulations is tested against realistic measurements. Besides showing the accuracy of the presented formulations, the obtained results imply the feasibility of proposed approach, especially for subsurface imaging, where the targets are buried into soil.

Lastly, we want to emphasize that the proposed formulations are important from the aspect that it can make the usage of qualitative methods possible in many real world problems. Future research will be devoted to application of these methods in more realistic environments.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by the Scientific and Research Council of Turkey (TUBITAK) under the Project no. 113E977.