Inverse source in the presence of a reflecting plane for the strip case

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

doi:10.1364/josaa.31.002814

Cited by 26 publications

(22 citation statements)

References 20 publications

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“…It is defined as the reconstruction of an impulsive source and the width of its main lobe provides a measure of the resolution. It can be proved that the PSF can be expressed in terms of the NDF and the singular functions [8]. The behavior of the SVs plays an important role in achieving a stable solution to any inverse problem, when the simplest regularization scheme, the truncated singular value decomposition (TSVD), is adopted [7].…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by [8][9][10][11][12][13], the aim of this paper is to investigate the role of some 2D scalar source geometries in the SVD of the relevant far zone radiation operator. Since it is not always known in closed form, sometimes, information about the SVD can be gained by considering different representations of the pertinent singular functions, such as the Fourier series.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Inverse Source of Circumference Geometries: SVD Investigation Based on Fourier Analysis

Leone¹,

Maisto²,

Pierri³

2018

PIER M

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The role of the source geometry is investigated within the realm of inverse source problems. In order to examine the properties of the far zone radiation operator of some 2D curved sources its Singular Value Decomposition (SVD) is studied, either analytically, when possible, or numerically. This allows to evaluate the number of independent pieces of information, i.e., the number of degrees of freedom (NDF), of the source and to point out the set of far zone fields corresponding to stable solutions of the inverse problem. In particular, upper bounds for the NDF are obtained by exploiting Fourier series representations of the singular functions. Both curved (i.e., circumference and arc of circumference) and rectilinear geometries are considered, pointing out the role of limited angular observation domains. Moreover, in order to obtain some clues about the resolution achievable in the inverse source problem, a point-spread function analysis is performed. The latter reveals a spatially variant resolution for limited angular observation domains. The practical relevance of these results is highlighted with numerical examples of array diagnostics.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inverse Source of Circumference Geometries: SVD Investigation Based on Fourier Analysis

Leone¹,

Maisto²,

Pierri³

2018

PIER M

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“…This is because results concerning the prolate spheroidal spectrum can again be exploited fruitfully. This is immediate, for example, in the case that the source is above a reflecting mirror [21] or for scattering problems under the Born approximation [22].…”

Section: Possible Extensionsmentioning

confidence: 99%

“…The eigenspectrum of Eq. (28) has been studied in a number of recent papers (see for example [16] and [21]). It has been shown that, if the spatial-bandwidth product c s l = m(Ω)Δ xl /2 associated with each domain is sufficiently greater than one (indeed c s l > 4 is enough [16] …”

Section: Support Priorsmentioning

confidence: 99%

Information Content in Inverse Source With Symmetry and Support Priors

Solimene¹,

Maisto²,

Pierri³

2018

PIER C

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Abstract-This paper illustrates how inverse source problems are affected by certain symmetry and support priors concerning the source space. The study is developed for a prototype configuration where the field radiated by square integrable strip sources is observed in far-zone. Three symmetry priors are considered: the source is a priori known to be a real or Hermitian or even (resp. odd) function. Instead, as spatial priors we assume that the source support consists of a single or multiple disjoint domains. The role of the aforementioned priors is assessed against some metrics commonly used to characterise inverse source problems such as the number of degrees of freedom, the point-spread function and the "information content" measured through the Kolmogorov entropy.

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“…The effect of a single point-like in-homogeneity located between the sensors and the scene to be diagnosed is studied in [3], whereas the role of a reflecting plane in [4], for inverse source problem, and in [5], for inverse scattering under linearised scattering operators. Under the same assumption, the impact of a reflecting plane located at the bottom of the scattering scene is addressed in the framework of single and multi-frequency case in [6] and [7], respectively.…”

Section: Introductionmentioning

confidence: 99%

Inverse Scattering in a Multipath Environment

Cuccaro

Solimene

2016

AEM

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In this contribution an inverse scattering problem is addressed in a multipath environment. In particular, multipath is created by known "extra" point-like scatterers (passive elements) expressely deployed between the scene under investigation and the source/measurement domains. Through a back-projection imaging scheme, the role of the passive elements on the achievable performance is shown and compared to the free-space case.

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Inverse source in the presence of a reflecting plane for the strip case

Cited by 26 publications

References 20 publications

Inverse Source of Circumference Geometries: SVD Investigation Based on Fourier Analysis

Inverse Source of Circumference Geometries: SVD Investigation Based on Fourier Analysis

Information Content in Inverse Source With Symmetry and Support Priors

Inverse Scattering in a Multipath Environment

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