Vittorio Picco

Measurements to Validate the UTD Triple Diffraction Coefficient

Measurement results to validate the UTD triple diffraction coefficient are presented. The experimental setup consists of multiple metallic objects, with triangular and rectangular profiles, located inside an anechoic chamber and illuminated by a sector antenna to reproduce a spherical wavefront with a transverse electromagnetic (TEM) incident field. Another sector antenna is moved vertically to collect electromagnetic fields across the second order UTD Incident Shadow Boundaries and in the triple diffraction transition region. The measured and theoretical fields are compared using a free space normalization. Such comparison is also validated by calculating the mean error, the standard deviation, and root mean square error that occur between the theoretical model and the measured field. The results show excellent agreement between the theoretical third order UTD solution, employing the novel triple diffraction coefficient, and the experimental results.

RF Tomography in Free Space: Experimental Validation of the Forward Model and an Inversion Algorithm Based on the Algebraic Reconstruction Technique

Radio-frequency tomography was originally proposed to image underground cavities. Its flexible forward model can be used in free-space by choosing an appropriate dyadic Greens function and can be translated in the microwave domain. Experimental data are used to validate a novel inversion scheme, based on the algebraic reconstruction technique. The proposed method is improved by introducing physical bounds on the solution returned. As a result, the images of the dielectric permittivity profiles obtained are superior in quality to the ones obtained using classical regularization approaches such as the truncated singular value decomposition. The results from three experimental case studies are presented and discussed.

Experimental Validation of the Quadratic Forward Model for RF Tomography

An effective way to solve the inverse scattering from dielectric objects relies on the Born approximation, which allows to linearize the problem and retrieve a qualitative reconstruction of the targets in terms of location and extent. The limits of the validity of the linear model can be extended by considering a quadratic approximation of the operator relating the scattered field data to the unknown object function. The use of the quadratic operator allows on the one hand to recover additional spatial variations of the object profile and on the other hand to mitigate the local minima (false solution) problem typically affecting nonlinear inversion methods. In this letter, we present an experimental validation of the quadratic inverse model for dielectric objects in free space. The data processing confirms that the tomographic images based on the quadratic model are better resolved compared to the ones provided by the inversion of the linear Born model.

RF tomography under the quadratic approximation

In this work, we discuss imaging results obtained by applying a quadratic approximation to RF Tomography.

RF tomography in free space: Experimental validation of the forward model and of a Conjugate Gradient inversion algorithm

Experimental data are used to validate a novel inversion scheme, based on a Conjugate Gradient algorithm. The proposed inversion provides actionable reconstruction results at a fraction of the computational effort needed by classical regularization techniques. Additionally, Conjugate Gradient allows us to introduce physical bounds on the solution returned, if a re-orthogonalization technique is also applied. Experimental case studies are presented and discussed.

A quadratic RF Tomography inverse model for reflection configuration

Radio Frequency (RF) tomography (L. Lo Monte, D. Erricolo, F. Soldovieri, M.C. Wicks, “Radio Frequency Tomography for Tunnel Detection,” IEEE Trans. Geoscience and Remote Sensing, Vol. 48, No. 3, Mar. 2010, pp. 1128–1137) aims at imaging targets in a scene starting from the measurements of the scattered field under the illumination of known incident fields. Therefore, such an imaging method shares the classical issues of inverse scattering problems such as ill-posedness and non-linearity. These mathematical questions, if not properly addressed, have a detrimental effect on the reliability and accuracy of the solution by impairing the outcomes of the overall imaging procedure.

The use of the Algebraic Reconstruction Technique (ART) for imaging of dielectric targets in Radio Frequency Tomography

In this paper, we investigated the used of the Algebraic Reconstruction Technique to obtain images of dielectric targets. A standard implementation of ART has been modified so as to impose physical bounds on the image obtained. Our results show images that in general outperform reconstruction obtained with TSVD (or CG). Images are less noisy, more sharp, and the reconstructed shapes are in better agreement with the dimensions of the actual objects. However, ART is unable to reconstruct correctly a large object when it is not empty, showing an incorrect shape in the measurement data and simply not converging in the simulated data. This unexpected behavior is currently under investigation.

A quadratic inverse model for RF tomography

The linear model provided by the Born approximation is frequently exploited in inverse scattering problems. Anyway, the limits of validity of the Born model can be extended by a quadratic approximation of the non-linear operator relating the scattered field data to the unknown object function. The aim of this contribution is to present a quadratic approach and describe its experimental validation regarding laboratory tests carried out in the case of dielectric objects. The results of the quadratic inverse approach are compared to the ones of the linear Born model; such a comparison highlights that the quadratic model yields superior reconstruction performance in terms of image focusing and artifact mitigation.

Quadratic forward model for RF tomography: Preliminary results

Summary form only given. We propose a novel forward model for Radio Frequency (RF) Tomography. RF Tomography is formulated around a scattered electric field integral equation, which represents its forward model. Such equation is inherently non-linear, because the unknown scattered electric field can be calculated only from the knowledge of the total field, which includes the unknown scattered field as well. To overcome this problem, the Born approximation is usually employed. The approximation allows to linearize the forward model, by assuming that the scattering field is very small compared to the total field: hence, the total field can be approximated with the incident field, and a linear model is obtained. This is equivalent to considering the Neumann series expansion of the forward model and dropping all but the first term of it. This approach shows important limitations, such as the assumption that the difference between the dielectric permittivity of the target and the one of the medium where the target is located be small. Even in this scenario, the removal of non-linear effects has detrimental consequences on the quality of the reconstructed image. It can be shown that the Born approximation operates as a spatial low-pass filter on the forward model integral operator. This translates into an overall loss of resolution and sharpness in the target reconstruction. We propose to overcome these limitations by introducing a forward model based on a quadratic operator. The approach is equivalent to keeping an additional term in the Neumann series expansion of the non-linear integral operator. The advantage of this method is to create a much better model of the forward problem, which translates in turn into a superior image reconstruction. The cost of this approach is mainly computational, since it requires the calculation of both a linear operator (equivalent to the one obtained with the Born approximation) and a quadratic one.

Dyadic contrast function for RF tomography: Preliminary results

A dyadic contrast function for Radio Frequency Tomography is developed. The goal of such contrast function is to allow the reconstruction of the orientation in a three-dimensional space of thin-elongated metallic scatterers. This is accomplished by modeling the scatterer with a dyadic matrix. An intuitive visual representation of the target is obtained performing the eigen-decomposition of such dyadic matrix. Numerical results to validate the approach are presented.