scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

2021 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Linear Operator ◽  
Phase Retrieval ◽  
Space Dimension ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Two Dimensional ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem

<div>In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval, the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a two-dimensional extended domain in Fresnel zone.</div>

scholarly journals An SVD Approach for Estimating the Dimension of Phaseless Data on Multiple Arcs in Fresnel Zone

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 606
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Electric Current ◽  
Phase Retrieval ◽  
Fresnel Zone ◽  
Singular Values ◽  
Quadratic Model ◽  
Analytical Prediction ◽  
Data Space ◽  
Lifting Technique ◽  
Retrieval Problem ◽  
Lifting Operator

In this article, we tackle the question of evaluating the dimension of the data space in the phase retrieval problem. With the aim to achieve this task, we first exploit the lifting technique to recast the quadratic model as a linear one. After that, we evaluate analytically the singular values of the lifting operator, and we quantify the dimension of the data space by counting the number of “significant” singular values. In the last part of the article, we show some numerical results in order to corroborate our analytical prediction on the singular values’ behavior of the lifting operator and on the dimension of the data space. The analysis is performed for a 2D scalar geometry consisting of an electric current strip whose square magnitude of the radiated field is observed on multiple arcs of circumference in Fresnel zone.

scholarly journals On the Sampling of the Fresnel Field Intensity over a Full Angular Sector

Electronics ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 832
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Discrete Model ◽  
Fresnel Zone ◽  
Singular Values ◽  
Linear Representation ◽  
Continuous Model ◽  
Sampling Theorem ◽  
Theory Approach ◽  
Discretization Scheme ◽  
Lifting Technique ◽  
The Fourier Transform

In this article, the question of how to sample the square amplitude of the radiated field in the framework of phaseless antenna diagnostics is addressed. In particular, the goal of the article is to find a discretization scheme that exploits a non-redundant number of samples and returns a discrete model whose mathematical properties are similar to those of the continuous one. To this end, at first, the lifting technique is used to obtain a linear representation of the square amplitude of the radiated field. Later, a discretization scheme based on the Shannon sampling theorem is exploited to discretize the continuous model. More in detail, the kernel of the related eigenvalue problem is first recast as the Fourier transform of a window function, and after, it is evaluated. Finally, the sampling theory approach is applied to obtain a discrete model whose singular values approximate all the relevant singular values of the continuous linear model. The study refers to a strip source whose square magnitude of the radiated field is observed in the Fresnel zone over a 2D observation domain.

scholarly journals The Dimension of Phaseless Near-Field Data by Asymptotic Investigation of the Lifting Operator

Electronics ◽  
2021 ◽  
Vol 10 (14) ◽  
pp. 1658
Author(s):  
Rocco Pierri ◽  
Giovanni Leone ◽  
Raffaele Moretta
Keyword(s):  
Near Field ◽  
Singular Values ◽  
Quadratic Model ◽  
Magnetic Current ◽  
Data Space ◽  
Lifting Technique ◽  
Asymptotic Investigation ◽  
Analytical Estimation ◽  
Reactive Zone ◽  
Lifting Operator

In this paper, the question of evaluating the dimension of data space in an inverse source problem from near-field phaseless data is addressed. The study is developed for a 2D scalar geometry made up by a magnetic current strip whose square magnitude of the radiated field is observed in near non-reactive zone on multiple lines parallel to the source. With the aim of estimating the dimension of data space, at first, the lifting technique is exploited to recast the quadratic model as a linear one. After, the singular values decomposition of such linear operator is introduced. Finally, the dimension of data space is evaluated by quantifying the number of “relevant” singular values. In the last part of the article, some numerical simulations that corroborate the analytical estimation of data space dimension are shown.

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