Angelo Liseno

In-depth resolution for a strip source in the Fresnel zone.

The problem of determining the achievable resolution limits in the reconstruction of a current distribution is considered. The analysis refers to the one-dimensional, scalar case of a rectilinear, bounded electric current distribution when data are collected by measurement of the radiated field over a finite rectilinear observation domain located in the Fresnel zone, orthogonal and centered with respect to the source. The investigation is carried out by means of analytical singular-value decomposition of the radiation operator connecting data and unknown, which is made possible by the introduction of suitable scalar products in both the unknown and data spaces. This strategy permits the use of the results concerning prolate spheroidal wave functions described by B. R. Frieden [Progress in Optics Vol. IX, E. Wolf, ed. (North-Holland, Amsterdam 1971), p. 311.] For values of the space-bandwidth product much larger than 1, the steplike behavior of the singular values reveals that the inverse problem is severely ill posed. This, in turn, makes it mandatory to use regularization to obtain a stable solution and suggests a regularization scheme based on a truncated singular-value decomposition. The task of determining the depth-resolving power is accomplished with resort to Rayleighs criterion, and the effect of the geometrical parameters of the measurement configuration is also discussed.

Improving a Shape Reconstruction Algorithm with Thresholds and Multi-View Data

Abstract This paper deals with the reconstruction of the shape of unknown perfectly conducting objects from the knowledge of the scattered electric far field in axa0two-dimensional geometry. By adopting the Kirchhoff approximation, the problem is cast as axa0linear inverse one and is solved by resorting to the Singular Value Decomposition (SVD) approach. The finiteness of the available data along with the presence of the noise make undesired features on the reconstructed image arise. We here give some criteria for the choice of axa0threshold to cut them out from the reconstructions. Furthermore, we illustrate the processing of multi-view data.

Shape reconstruction of 2-D buried objects under a Kirchhoff approximation

The problem of reconstructing the shape of buried metallic objects for multifrequency plane wave incidence in a two-dimensional geometry is dealt with under the Kirchhoff approximation and solved by means of the singular value decomposition approach. Numerical results show the effectiveness of the solution method and outline the role of the parameters of the measurement configuration and of the properties of the ground on the features of the reconstruction.

Imaging of voids by means of a physical-optics-based shape-reconstruction algorithm

We analyze the performance of a shape-reconstruction algorithm for the retrieval of voids starting from the electromagnetic scattered field. Such an algorithm exploits the physical optics (PO) approximation to obtain a linear unknown-data relationship and performs inversions by means of the singular-value-decomposition approach. In the case of voids, in addition to a geometrical optics reflection, the presence of the lateral wave phenomenon must be considered. We analyze the effect of the presence of lateral waves on the reconstructions. For the sake of shape reconstruction, we can regard the PO algorithm as one of assuming the electric and magnetic field on the illuminated side as constant in amplitude and linear in phase, as far as the dependence on the frequency is concerned. Therefore we analyze how much the lateral wave phenomenon impairs such an assumption, and we show inversions for both one single and two circular voids, for different values of the background permittivity.

Shape identification by physical optics: the two-dimensional TE case

A method is provided for reconstruction of the shape of perfectly conducting objects in a homogeneous space starting from knowledge of the scattered far field under the incidence of TE-polarized plane waves. The Kirchhoff model of scattering permits linearization of the inverse problem, which is further simplified by adopting an asymptotic approximation. Thus the problem is tackled with an approach based on singular-value decomposition already developed for the TM case.

Resolution Limits in the Fresnel Zone: Roles of Aperture and Frequency

The reconstruction of the dielectric permittivity profile from scattered field measurements in two dimensions is addressed in free space under the Born approximation. Canonical geometries suitable for future extensions to subsurface sensing configurations are dealt with. In particular, a rectilinear measurement aperture located in the Fresnel zone and rectilinear investigation domains parallel or orthogonal to the measurement line are considered for the scalar e.m. case. Firstly, the dependence of both transversal and longitudinal resolution on the geometrical parameters of the sensing configuration is analytically worked out in only aspect diversity. Then, the effect of frequency diversity on depth-resolution is also pointed out.

Depth Resolving Power in Near Zone: Numerical Results for a Strip Source

Summary The problem of determining an unknown rectilinear source from the knowledge of its radiated field over a rectilinear bounded observation domain located in the near zone, orthogonal and centered with respect to the source is dealt with. In particular, we firstly analyze the information content of data by means of the Singular Value Decomposition of the radiation operator. Secondly, the resolution limits achievable in the reconstruction are discussed by examining the effect of the key geometrical parameters of the measurement configuration.

Linear distribution-based retrieval of underground voids

This paper deals with the problem of determining the shape of unknown scattering voids embedded in a homogeneous half-space from the measurements of the magnetic scattered field over a measurement domain parallel to the air-soil interface. The formulation accommodates the distributional nature of the induced surface equivalent current densities. Thus, as unknown, a single layer distribution whose support accounts for the boundary of the scatterers is chosen and is reconstructed by a singular value decomposition based algorithm. Numerical examples resulting from the application of such algorithm are presented.

GPR-based shape reconstruction of metallic objects

The problem of determining the shape of buried objects for multifrequency plane wave incidence in a 2D geometry is dealt with. The problem is tackled by searching for the support of the currents induced on the contour of the objects, is formulated as the inversion of the linear operator arising from the application of the Kirchhoff approximation and is solved by means of the Singular Value Decomposition approach. The presented numerical results show the effectiveness of the proposed inversion algorithm.

Parameter inversion of "reduced" SAR flight-tracks: first results over forest

In this paper, inversion of synthetic aperture radar data is dealt with and, in particular, the problem of reconstructing forest height is addressed. The forest is modelled as a random volume of particles over a rough ground. Under this model, the forest height turns out to be related to the bandwidth of the scattered field. The inversion is cast as an optimization one. Preliminary results using DLR-ESAR experimental SAR data are shown