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The problem of reconstructing a strip electric current from its radiated field collected over a bounded finite rectilinear observation domain, orthogonal and centered with respect to the source, is dealt with. In particular, the study is developed for a two-dimensional, scalar geometry and focuses on the estimation of achievable performance in terms of the number of degrees of freedom (NDF) and depth resolution. This is a classical problem that we contributed to in the past by addressing a Fresnel zone configuration. Here, the plan is to expand those results by removing the geometrical limitations due to the Fresnel approximation. The main idea is to rewrite the involved radiation operator as a Fourier-type integral operator by introducing a suitable variable transformation. This allows applying simple Fourier-based reasoning to estimate the achievable point-spread function, which in turn is used to estimate the NDF and depth resolution. The obtained NDF and depth resolution estimations are compared to those returned by numerical computation of the relevant singular value decomposition, and very good agreement is found. Moreover, it is shown that the results obtained for the Fresnel zone are a particularization of the new findings when such an approximation holds true.

Planar near-field antenna measurement techniques are addressed with particular reference to the error in the radiation pattern estimation due to the finiteness of the observation aperture. The valid angle (VA) concept is a commonly used rule-of-thumb for predicting the region of validity of the calculated far-field pattern according to observation domain, the aperture antenna size and the distance between the two. However, it is based on simple asymptotic arguments which often lead to erroneous estimations. In this contribution, a new VA criterion and related radiation pattern representation are derived by exploiting the singular value decomposition of the radiation operator. Numerical examples show the goodness of the new VA criterion and the greatest stability of the proposed radiation pattern estimation compared to the classical Fourier transform.

In this paper, the problem on how to collect the radiated field in order to approximate the singular value decomposition of the continuous radiation operator is addressed.

In this paper, the problem of estimating the number of independent equations in phase retrieval via lifting is tackled. In particular, the impact of collecting the square amplitude field over multiple circular observation domains on the number of independent data is studied. The evaluation of such a number is given in terms of the number of observation domains.

In this paper it is studied how certain symmetry priors affect some metrics commonly used to evaluate the achievable performance in linear inverse problems such as the Number of Degrees of Freedom (NDF), the point-spread function (psf) and Kolmogorov entropy.

The Number of Degrees of Freedom (NDF), the point-spread function (psf) and Kolmogorov entropy representing metrics commonly used to evaluate the achievable performance in linear inverse problems are expressed in terms of the singular values decomposition of forward operator. The problem to establish a link between such figures is addressed.

In this paper the problem of studying the spectrum of the radiation operator in near reactive zone is addressed. This topic is of great importance because of its connection with the so-called Number of Degrees of Freedom concept which is a key parameter in inverse source problems. The case of a bounded rectilinear magnetic source with the radiated field observed over unbounded rectilinear domain parallel to the source is considered.

Through-wall imaging (TWI) requires dealing with targets embedded in a complex obscuring environment such as the walls of a building. This obscuring layout is often composed by many simple elements (possibly interacting) such as slabs, corners, and T-like structures. Most of the existing literature on TWI has focused on slab-like walls, which is reasonable when the targets are relatively far from corners. This paper instead concerns the TWI in the more challenging situation where the targets are in close proximity (inside and/or outside) of a building corner. The aim is to gain insight into how propagation through the corner impacts on the imaging problem. To keep the study simple, a preliminary analysis is presented for a 2-D geometry under the linearized Born approximation. First, the Green's function, as well as the kernel of the relevant scattering operator, is evaluated by using a high-frequency analytical approach based on the geometrical optics and the uniform theory of diffraction. This allows one to take into account the multipath propagation phenomena and provide thus an expression of the scattering operator more accurate than that viable under the assumption of a simple slab wall. Then, the imaging is achieved by solving the relevant linear inverse scattering problem with a regularizing truncated-singular-value-decomposition algorithm. The filtering introduced by the inversion procedure, which is dependent on the considered background scenario, is highlighted and linked to the achievable performance while imaging targets both internal and external with respect to the corner. Finally, reconstruction results obtained from synthetic data are reported to assess the approach.

The problem of detecting and localizing missing scatterers (faults) inside a known grid of small cross-sectional perfect-electric-conducting cylinders is dealt with. The case of a TM scalar 2-D geometry is considered, and the Multiple Signal Classification (MUSIC) spectral estimation technique is employed. Two different scattering models are employed and compared. The first one aims at localizing present objects within a free-space background medium. The second one aims at detecting the faults and exploits the Green's function of the full grid. The limitations of the first approach are pointed out and connected to the maximum dimension of the data space. Then, the second approach performs successfully when the fault number is lower than scattering objects.

We present a sparse tomographic inverse scattering approach for application in through-the-wall radar imaging, which enables reduction in data acquisition time and fast investigation of very large multi-targets domains, while maintaining a reasonable image quality. The imaging technique achieves fast 3-D scene reconstructions using a linear inverse scattering algorithm based on truncated singular value decomposition (SVD), combined with a 2-D sliced approach. The SVD of the integral equation relevant to the imaging system is used to guide the reduction in the number of data measurements. Performance of the proposed sparse scheme is evaluated using experimental data.

The role of multiple views and/or multiple frequencies on the achievable performance in linear inverse scattering problems is addressed. To this end, the impact of views and frequencies on the Kolmogorov entropy measure is studied. This way the metric information that can be conveyed back from data to the unknown can be estimated.For the sake of simplicity, the study deals with strip scatterers and the cases of discrete angles of incidence and/or frequencies.

A combined Migration-MUSIC approach is adopted to deal with the inverse problem of reconstructing the shape of strong scatterers composed of elementary shapes and embedded within an electrically large investigation domain from under-sampled backscattered field data. The scatterers are deployed over a metallic plane, which mimics the ground floor, as in SAR scenarios. In order to mitigate aliasing, migration images obtained by using disjoint available frequency bands are combined in an interferometric way. Next as each elementary shape is characterized by a small amount of parameters, a MUSIC algorithm is employed to reconstruct them separately.

In this paper the inverse source problem in presence of a reflecting plane is dealt with for a two-dimensional configuration and bounded rectilinear strip sources. The case of orthogonal (to a perfect electric conductor plane) source is considered. Analytical arguments are developed to estimate the singular value decomposition of the pertinent radiation operator. This allows to highlight the role played by the distance from the prefect electric conductor plane on the so-called number of degrees of freedom of the radiated field as well as on theachievable resolution while reconstructing the unknown sources.

A through-wall imaging problem for a 2-D scalar geometry is addressed. It is cast as an inverse scattering problem and tackled under the linear model of the electromagnetic scattering that is provided by the Born approximation. A truncated singular value decomposition inversion scheme is exploited, and the performances that are achievable by such an inversion scheme are assessed by exploiting synthetic data. The cases of weakly and strongly scattering objects are both considered. Finally, an example of reconstruction that is obtained by exploiting experimental data is presented.

In this paper, a 1-D inverse-scattering problem laying within the framework of through-wall imaging is addressed. In particular, the problem of localizing the interfaces of a slab hidden behind an obstacle, another slab whose electromagnetic features and thickness are known, is considered. To this end, an approximate linear mathematical relationship between the scattered field and the unknown slab-interface positions is stated. Such an approximate relationship arises from neglecting the multiple-reflections between the two unknown slab's interfaces and between the slab and the obstacle. The unknown locations of the slab's interfaces are represented as the support of Dirac-delta functions, and the problem is cast as the inversion of a linear integral operator whose inversion is achieved by means of the Truncated-Singular-Value-Decomposition (TSVD) inversion scheme. The effect of the parameters of the obstacle on the inversion algorithm and the performances achievable by the solution approach are assessed by exploiting synthetic data. Furthermore, a comparison with the reconstructions obtained under the Born approximation and with the time-backscattered field is achieved. Finally, results obtained by employing experimental data collected owing to a stepped-frequency ground-penetrating radar system are also presented.

In this paper an innovative procedure for the localization and reconstruction of objects composed of elementary shapes is described. Sparse backscattered multifrequency field data are assumed to be known. The strategy is based on two steps in order to decrease the computational costs and to allow the use of few measurement points (with respect of Number of Degrees of Freedom). At first an Interferometric-Migration (IM) strategy is introduced with the purpose of reducing the dimension of the solution space. The second step is founded on the assumption that the elementary shapes are known and their geometrical features can characterized by a small amount of parameters. Then an Interferometric-MUSIC (I-MUSIC) algorithm is applied by combining results at single frequency. The overall approach is numerically tested in a 2D geometry for electrically large objects and has been proved robust against uncertainties on data.

In this paper, we study the performance of multiple signal classification (MUSIC) in computational time-reversal (TR) applications. The analysis builds upon classical results on first-order perturbation of singular value decomposition. The closed form of mean-squared error (MSE) matrix of TR-MUSIC is derived for the single-frequency case in both multistatic co-located and non co-located scenarios. The proposed analysis is compared with Cramer–Rao lower-bound (CRLB), and it is exploited for comparison of TR-MUSIC when linear and (nonlinear) multiple-scattering is present. Finally, a numerical analysis is provided to confirm the theoretical findings.

We address the problem of reconstructing the shape of perfectly electric conducting cylinders for a two-dimensional scalar geometry when the physical optics (PO) model is exploited. We are interested in analyzing how the radiation pattern of the source providing the incident field affects the shape reconstruction problem. We find that, owing to the regularization necessary to deal with the ill-posedness of the problem, the more “weakly” illuminated objects are more “weakly” reconstructed. As a consequence, these objects can be mistaken for spurious artifacts appearing in the reconstruction and thus can be discarded when a threshold procedure is employed to curtail spurious artifacts. In order to overcome such a problem, we present a simple equalization strategy based on the knowledge of the incident field to compensate for the differences in amplitude of reconstructed image. Furthermore, we give a criterion which restricts the region over which we apply the procedure which enables us to perform the equalization in a stable way. The effectiveness of the equalization procedure is shown by reconstructions obtained with synthetic data and considering the unknown cylinders embedded in both a homogeneous and a half-space background medium, under single- and multi-view/multi-frequency measurement configuration.

In this paper, we address the problem of imaging "thin" metallic cylinders from the knowledge of the electric far-field scattered under the incidence of plane waves. A scattering model based on a multipole expansion accounting for the mutual scattering is introduced and then simplified under the single- and second-order scattering hypotheses. The locations of the unknown cylinders for the inverse problem are described in terms of support of /spl delta/-functions. The performances of a truncated singular value decomposition based linear inversion algorithm in the presence of model errors due to mutual scattering is investigated, by both analytical and numerical arguments, in three different measurement configurations: single-frequency/multiview, multifrequency/single-view, and multifrequency/multiview. The different effects of the angular and frequency diversities are pointed out.

In this paper a quadratic model for the reconstruction of objects embedded in a lossy half space from scattered field data is introduced in a two dimensional and scalar geometry. It is shown that the present approach allows to reconstruct permittivity profiles that are not retrievable within a simpler linear model. This is due to the non-linearity of the quadratic approach, that allows to take into account for multiple scattering phenomena neglected by a linear approach. To perform the inversion, the object to be retrieved is projected within a finite dimensional subspace depending on the geometry of the problem, the electromagnetic properties of the half space, the configuration of the source and of the measurements. This step allows to regularize suitably the inverse problem. Furthermore, an appropriate choice of such a subspace and the use of a two step minimization procedure, with different solution spaces with progressively enlarged number of unknowns, allows to counteract the problem of local minima and to perform a computationally viable inversion.

The problem of detecting and localizing “thin” metallic scatterers from electromagnetic scattered field measurements is addressed for a 2D scalar configuration and by the so-called distributional approach. The presence of a uniform grid of PEC (Perfect Electric Conductor) cylinders uniformly deployed around the scene under investigation is shown to enhance the achievabale resolution for aspect limited measurement configuration.

In this paper we study the performance of time-reversal multiple signal classification (TR-MUSIC) for computational TR applications. The analysis builds upon classical results on first-order perturbation of singular value decomposition. The closed form of mean-squared error (MSE) matrix of TR-MUSIC is derived for a narrowband multistatic co-located scenario and is compared with both numerical simulations and the Cramer-Rao lower bound.

The problem of detecting point-like sources whose frequency spectrum is unknown is addressed. Limitations of single- frequency approaches are identifled by analytical as well as numerical arguments. To overcome these limits, difierent multifrequency approaches which combine frequency data incoherently are compared. In particular, a novel multifrequency MUSIC-like algorithm based on interferometric concepts is proposed. Results show that the algorithm outperforms other methods under comparison.

The problem of retrieving the Fresnel reflection coefficients of a half-space medium starting from measurements collected under a reflection mode multistatic configuration is dealt with. According to our previous results, reflection coefficient estimation is cast as the inversion of linear operator. However, here, we take a step ahead towards more realistic scenarios as the role of antennas (both transmitting and receiving) is embodied in the estimation procedure. Numerical results are presented to show the effectiveness of the method for different types of half-space media.

A novel procedure for estimating the Fresnel re∞ection coe-cient of a transversally homogeneous half-space medium is introduced. GPR multistatic measurements are exploited as data whereas the Fresnel coe-cient (as a function of the incidence angle) is retrieved by inverting a linear integral equation. Having estimated the re∞ection coe-cient it can be exploited to determine the medium electromagnetic parameters. Numerical examples are used to show the procedure efiectiveness for difierent types of homogeneous half-space media within a two-dimensional scalar geometry. The case of a layered half-space is also discussed.

This work deals with the inverse source problem starting from the knowledge of the radiated fleld in the near fleld zone. The inverse problem is stated as the inversion of a linear integral equation and the Singular Value Decomposition (SVD) is exploited as an analysis and inversion tool. In particular, here, we deal with a 2D geometry and aim at comparing the features of the inverse problem in dependence on the nature of the source (electric or magnetic).

A through-wall-imaging problem where the scatterers are located beyond a 1-D nonhomogeneous unknown wall is considered. As is well known, as part of the propagation takes place within the wall, the knowledge of its electromagnetic properties is mandatory in order to obtain properly focused images. Accordingly, this paper's focus is on the wall estimation problem. To this end, a simple procedure to estimate the wall transmission coefficient is introduced and validated by synthetic data. The proposed estimation procedure works for a symmetric lossless wall and does not rely on optimization schemes but requires a multistatic configuration. As a proof of the principle, we address the problem for a 2-D scalar configuration. Moreover, the role of obscured scatterers on the estimation procedure is discussed, and a procedure for mitigating their effect is proposed as well. Finally, the procedure is also checked against a wall with losses.

The problem of imaging three-dimensional strong scatter- ers by means of a two-dimensional sliced tomographic reconstruction algorithm is dealt with. In particular, the focus of the paper is on the experimental validation of the involved inversion algorithm thanks to measurements collected in a controlled environment. A simple strategy exploiting reconstructions obtained at difierent time instants in order to detect slowly moving scatterers is also experimentally validated.

The problem of determining the shape of 3D perfect electric conducting (PEC) objects starting from the scattered far field under the incidence of plane waves with a fixed angle of incidence, varying frequency and two orthogonal polarizations is dealt with. Two strategies of reconstruction are presented and compared. In particular, in the first solution strategy the data acquired at the two polarizations are singularly exploited to achieve two different reconstructions and the object surface is then obtained as their “union”. In the second one, all the data (i.e., for both the adopted polarizations) are simultaneously exploited to obtain the reconstruction. In all the cases, by adopting a distributional formulation for the unknown of the problem and thanks to the exploitation of the Kirchhoff approximation, the problem is cast as a linear inverse one and the solution is made stable by adopting a regularization scheme based on the truncated singular value decomposition (TSVD). The reliability of the inversion approach is tested with synthetic data against model error and noise on data.

A through-wall imaging problem for a 3-D geometry is considered. Scatterers are located beyond a wall represented by a dielectric slab whose features are unknown or known with some degree of uncertainty. A two-step imaging procedure is presented. First, the thickness and the dielectric permittivity of the wall are estimated by a simple procedure which takes into account that actual measurements concern the total scattered field (i.e., the field reflected by the wall plus the one scattered by the obscured scatterers). Then, the problem is cast as a linear inverse scattering problem and solved by means of a truncated-singular value decomposition algorithm. In particular, a 2-D sliced approach is employed to obtain the 3-D scene. Numerical examples are shown to assess the effectiveness of the reconstruction procedure.

The problem of determining the number and the locations of "small" metallic spheres from scattered far-field measurements under plane waves incidence is considered. The problem is formulated by neglecting the mutual scattering between the spheres and by representing their locations as the support of delta-functions. This allows to cast the problem as the inversion of a linear integral operator we tackle by means of a Truncated Singular Value Decomposition. The performance of the inversion scheme are analyzed for both the cases of a multi- view/single-frequency and a single-view/multi-frequency configuration by exploiting synthetic exact data.

The information content of radiated fields and the achievable resolution limits in the reconstruction of a bounded current distribution are dealt with. The analysis refers to the scalar and one dimensional case of a rectilinear and bounded electric current distribution when data are collected over a segment location in the Fresnel or near zone, orthogonal and centered with respect to the source. In the Fresnel zone, the investigation is carried out by means of the analytical Singular Value Decomposition (SVD) of the radiation operator providing the unknown-data mapping. This has been made possible thanks to the introduction of suitable weighted scalar products both in the unknown and data spaces. In the near zone, a numerical approach based on the SVD of the radiation operator has been followed. The effect of the geometrical parameters of the measurement configuration on depth resolving power is also discussed.

The singular value decomposition of the far-zone scattering operator for weak strip-like scattering objects is studied under multiple view and/or multiple frequency illuminations. The aim is to highlight how such diversities impact the number of degrees of freedom (NDF) of the scattering problem. When the angles of incidence and/or frequencies vary within discrete finite sets, the singular values are analytically determined. It is shown that they exhibit a multistep behavior. For the continuous case, upper and lower bounds are found, which allows us to obtain estimations for the NDF dependending on the parameters of the configuration.

The problem of determining the number of degrees of freedom (NDF) of the field radiated by an electric current supported over a bounded rectilinear domain and observed over multiple bounded domains parallel to the source is addressed. The analysis is achieved by means of the singular value decomposition of the radiation operator so that the NDF is identified as the number of 'significant' singular values. The aim is to analyze whether the multidomain observation allows to increase the available NDF. By analytical arguments, we show that collecting data over multiple domains shapes the singular value behavior but it still presents a steep decay in correspondence to an index dictated by the observation domain that subtends the largest observation angular sector.

The problem of localizing small scatterers (in terms of wavelength) by Time Reversal-MUSIC (TR-MUSIC) algorithm is addressed. In particular, we focus on uniqueness problems that might arise for certain far zone conflgurations when noise corrupts data. These lead to reconstructions afiected by ghost targets from which it is di-cult to discern actual targets. In order to remedy such a drawback, data obtained at multiple frequencies are employed. In detail, a new multi-frequency version of TR-MUSIC is introduced. It consists in mixing reconstructions obtained at difierent frequencies. Numerical analysis shows that this method outperforms classical TR- MUSIC as well as its multi-frequency implementation already present in literature.