Resolution limits in inverse source problem for strip currents not in Fresnel zone

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

doi:10.1364/josaa.36.000826

Cited by 38 publications

(59 citation statements)

References 22 publications

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“…We are not able, herein, to work out the relevant singular system. Hence, in order to obtain the point-spread function, we follow the same approach developed in [20,21] where a weighted adjoint method is exploited. This procedure permits to directly approximate the point-spread function so that Eq.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…(30) should be solved for Δx. However, unlike the case of homogeneous medium [20], this does not appear as an easy task. Nonetheless, that equation links, even if implicitly (i.e., as an implicit function), the configuration parameters and Δx.…”

Section: Resolution and Ndf Estimationmentioning

confidence: 99%

“…At this juncture, in order to appreciate the role of the half-space scenario, it is interesting to compare the obtained resolution with the one of the homogeneous medium, Δx h , (whose analytical expression has been derived in [20]). This comparison is shown in Fig.…”

Section: Resolution and Ndf Estimationmentioning

confidence: 99%

“…As a result, for the aspect limited configuration, the estimated transverse resolution is incorrect and fails to capture the spatially varying behaviour that characterises the resolution for the near-zone configuration [14]. The estimation of the resolution for near-field configuration is also addressed in [17,18,20,21]. However, those papers consider a homogeneous background medium.…”

Section: Introductionmentioning

confidence: 99%

“…However, for the problem at hand, the SVD of the scattering operator is not known in closed form, and hence, by this method, resolution cannot be estimated analytically. Therefore, in order to analytically estimate the achievable transverse resolution, we follow the approach developed in [20,21]. Basically, the regularised inverse is approximated by the adjoint of the scattering operator once the scattered field has properly been filtered through a suitable weighting function.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Transverse Resolution in Microwave Imaging for Strip Objects Buried in a Half-Space Medium

Maisto¹,

Solimene²,

Pierri³

2020

PIER M

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In this paper we are concerned with a microwave imaging problem for a non-magnetic two-layered background medium, where objects are buried in the lower half-space, and the scattered field is collected in the upper one according to a multi-monostatic configuration. In particular, we are interested in estimating the achievable transverse resolution. As well known, range resolution mainly depends on the working frequency band whereas transverse resolution depends on the geometrical parameters of the configuration and is usually computed in correspondence to the highest (or even the average) adopted frequency. Determining transverse resolution is much more difficult, and closed form estimations have been actually found only for the case of unbounded observation domain. However, in real scattering scenarios, measurements have to be necessarily collected under an aspect limited setup. Therefore, in order to fill such a theoretical gap, here the focus is on the estimation of transverse resolution for bounded observation domains. To this end, we consider a single-frequency 2D scalar prototype configuration where the buried scattering object domain is represented by a strip parallel to the half-space interface. More in detail, we succeed in finding an analytical estimation of the transverse resolution which highlights the role of the configuration parameters as well as the dielectric permittivity of the lower half-space.

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Section: Problem Descriptionmentioning

confidence: 99%

Section: Resolution and Ndf Estimationmentioning

confidence: 99%

Section: Resolution and Ndf Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Transverse Resolution in Microwave Imaging for Strip Objects Buried in a Half-Space Medium

Maisto¹,

Solimene²,

Pierri³

2020

PIER M

Self Cite

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NDF of the Near-Zone Field on a Line Perpendicular to the Source

Pierri

Moretta

2021

IEEE Access

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In this paper, the problem of computing the number of degrees of freedom (NDF) of the field radiated by a strip current along all the possible lines orthogonal to the source is addressed. As well known, the NDF is equal to the number of singular values of the radiation operator that are before a critical index at which they abrupt decay. Unfortunately, in the considered case, the solution of the associate eigenvalue problem is not known in closed-form, and this prevents us from directly evaluating the singular values of the radiation operator. To overcome this drawback, a weighted adjoint operator is exploited. The latter allows obtaining an eigenvalue problem whose solution is known in closed-form but, at the same time, it modifies the behavior of the singular values. However, since the change affects only the dynamics of the singular values but not the critical index at which they abrupt decay, the NDF of the radiated field can be analytically estimated by resorting to the weighted adjoint operator.INDEX TERMS dimension of data, eigenvalue problem, inverse source problem, integral equation, radiation operator, singular values, NDF.

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