On the Singular Spectrum of the Radiation Operator for Multiple and Extended Observation Domains

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

doi:10.1155/2013/585238

Cited by 26 publications

(22 citation statements)

References 28 publications

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“…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%

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%

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

Leone¹,

Maisto²,

Pierri³

2018

PIER M

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“…In particular, the maximum on the left side can be easily evaluated from (10) and when inserted in (20) yields…”

Section: Sampling Schemementioning

confidence: 99%

“…However, they usually employ a fine sampling grid (i.e., large N ) and an a priori fixed size, L, of the data to be retained. The latter matter is of course connected to the Number of Degrees of Freedom of the scattered field which can be used to estimate L [9], [10] and can also provide insight for sampling the field data [11].…”

Section: Introductionmentioning

confidence: 99%

Spatial Sampling in Monostatic Subsurface Radar Imaging

Maisto¹,

Pierri²,

Solimene³

2020

Preprint

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<div>This paper deals with microwave subsurface imaging obtained by a migration-like inversion scheme, for a 2D monostatic scalar configuration and a two-layered background medium. The focus is on the determination of a data sampling strategy which allows to reduce the number of required measurements and at the same time keep the same performance in the reconstructions. To this end, the measurement points are determined in order to approximate the point-spread function corresponding to the ideal continuous case (i.e., the case in which the data space is not sampled at all). Basically, thanks to suitable variable transformations the point-spread functions is recast as a Fourier-like operator and this provides insight to devise the sampling scheme. It is shown that resulting measurement spatial positions are non-uniformly arranged across the measurement domain and their number can be much lower than the one provided by some literature standard sampling criteria. The study also contains a comparison with the free space case so as to highlight the role played by the half-space that schematized the subsurface scattering scenario on the number and the locations of the measurement points. Numerical examples are also included to check the theoretical arguments.</div>

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“…Posing x + y = a is equivalent to choosing the intermediate frequency of modulation [31]. Accordingly, this term translates the frequency band Ω m of a k m z a factor.…”

Section: Frequency Diversitymentioning

confidence: 99%

The Role of Diversity on Linear Scattering Operator: The Case of Strip Scatterers Observed under the Fresnel Approximation

Maisto

Munno

2019

Electronics

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The aim of this paper is to investigate the role of multiple views and multiple frequencies in linear inverse scattering problems. The study was performed assuming the Fresnel-zone approximation on the scattering operator. Due to the crucial role played by singular values into analysing the linear inverse scattering problems, the impact of view and frequency diversities on singular values behaviour was established. In fact, the singular values were related to the most common metrics used to quantify the achievable performances in inverse scattering problems, such as the number of degrees of freedom (NDF), the information content and the resolution.

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On the Singular Spectrum of the Radiation Operator for Multiple and Extended Observation Domains

Cited by 26 publications

References 28 publications

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

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

Spatial Sampling in Monostatic Subsurface Radar Imaging

The Role of Diversity on Linear Scattering Operator: The Case of Strip Scatterers Observed under the Fresnel Approximation

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