Information Content in Inverse Source With Symmetry and Support Priors

Solimene, Raffaele; Maisto, Maria Antonia; Pierri, Rocco

doi:10.2528/pierc17090903

Cited by 26 publications

(12 citation statements)

References 23 publications

(29 reference statements)

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“…The panels only zoom into a portion of the observation domain. In order to compare the capability to radiate the pattern provided by (21) along different maximum directions, we adopt as figures of merit both the half power beam width (HPBW), that is, the angular interval where the magnitude of the radiation pattern decreases by 50% (or −3 dB) from the peak, and the achieved directivity Table 1 reports the HPBW for the considered geometries. From the numerical results, it is clear that the main lobe widens by moving from the center of the observation domain to the extremal points, as expected from Figure 15, where the SC(θ) functions, generally, decrease toward θ = ±π/2.…”

Section: Pattern Synthesismentioning

confidence: 99%

“…Moreover, as discussed in [19,20], the NDF is also linked to the information content of the radiated field. In [21], its link with some symmetry priors about the source space is investigated. As far as concerns the inverse source problem we want to address, the NDF measures the rank deficiency of the operator and hence the level of ill-posedness of the inversion problem [22].…”

Section: Introductionmentioning

confidence: 99%

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Radiation Properties of Conformal Antennas: The Elliptical Source

2019

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The solution of inverse source problems by numerical procedures requires the investigation of the number of independent pieces of information that can be reconstructed stably. To this end, the mathematical properties of the relevant operators are to be examined in connection with the source shape. The aim of this work is to investigate the effect of the source shape on the eigendecomposition of the radiation operator in a 2D geometry, when the radiated field is observed over a semi-circumference in the far zone. We examine both the behavior of the eigenvalues and the effect of the choice of the representation variables on the point spread function (PSF). In particular, the effect of the choice of the representation variables is considered since operator properties may depend on it. We analyze different source shapes evolving from a line to a semi-ellipse and, finally, to a semi-circumference, in order to understand how the increase of the source aspect ratio affects the results. The main conclusions concern an estimate of the number of degrees of freedom in connection with the source geometry and the fact that the PSF exhibits the same variant behavior along the considered domain, independently of the observation variable. The practical relevance of the result is illustrated by two numerical examples. The first one deals with the conformal array diagnostics for the reliable reconstruction of the excitation of the array elements. The second one concerns the array synthesis problem, and a comparison between the radiating performances of the source geometries is presented.

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Section: Pattern Synthesismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Radiation Properties of Conformal Antennas: The Elliptical Source

2019

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“…This can be defined as the number of independent pieces of information necessary to represent the radiated field or, equivalently, the dimension of the subspace of the radiated field providing reliable solutions to the diagnostic problem. The NDF depends on the geometry of both the source and the field observation domain [11], but, unfortunately, cannot be evaluated in closed form for general source and observation domain geometries. Therefore, hereafter we suppose to know them by the numerical computation of the Singular Values (SVs) of the corresponding operator.…”

Section: Introductionmentioning

confidence: 99%

A PSF Approach to Far Field Discretization for Conformal Sources

Pierri¹,

Leone²,

Munno³

et al. 2022

Preprint

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In this paper we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

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“…In particular, the far-field Green function, i.e., the kernel of the scattering operator, behaves similarly to an entire function of exponential type. This results in an abrupt decay of the singular values beyond a certain critical index, the so-called number of degrees of freedom (NDF) [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ] of the scattered field. This singular value behavior, on one hand, is the result of the ill-posedness of the problem [ 31 , 32 ], which limits the achievable performance in the reconstructions.…”

Section: Introductionmentioning

confidence: 99%

Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration

Maisto

Masoodi

Leone

et al. 2021

Sensors

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This paper deals with an inverse scattering problem under a linearized scattering model for a multi-static/multi-frequency configuration. The focus is on the determination of a sampling strategy that allows the reduction of the number of measurement points and frequencies and at the same time keeping the same achievable performance in the reconstructions as for full data acquisition. For the sake of simplicity, a 2D scalar geometry is addressed, and the scattered far-field data are collected. The relevant scattering operator exhibits a singular value spectrum that abruptly decays (i.e., a step-like behavior) beyond a certain index, which identifies the so-called number of degrees of freedom (NDF) of the problem. Accordingly, the sampling strategy is derived by looking for a discrete finite set of data points for which the arising semi-discrete scattering operator approximation can reproduce the most significant part of the singular spectrum, i.e., the singular values preceding the abrupt decay. To this end, the observation variables are suitably transformed so that Fourier-based arguments can be used. The arising sampling grid returns several data that is close to the NDF. Unfortunately, the resulting data points (in the angle-frequency domain) leading to a complicated measurement configuration which requires collecting the data at different spatial positions for each different frequency. To simplify the measurement configuration, a suboptimal sampling strategy is then proposed which, by an iterative procedure, enforces the sampling points to belong to a rectangular grid in the angle-frequency domain. As a result of this procedure, the overall data points (i.e., the couples angle-frequency) actually increase but the number of different angles and frequencies reduce and lead to a measurement configuration that is more practical to implement. A few numerical examples are included to check the proposed sampling scheme.

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Information Content in Inverse Source With Symmetry and Support Priors

Cited by 26 publications

References 23 publications

Radiation Properties of Conformal Antennas: The Elliptical Source

Radiation Properties of Conformal Antennas: The Elliptical Source

A PSF Approach to Far Field Discretization for Conformal Sources

Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration

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