Holographic Reconstruction Is Usually A Poor Solution To The Inverse Scattering Problem: A Comparison Between The Bojarski Exact Inverse Scattering Theory And Holography As Applied To The Holographic Radio Camera

1980 ◽  
Author(s):  
W. Ross Stone
Keyword(s):  
Inverse Scattering ◽  
Scattering Theory ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Inverse Scattering Theory ◽  
Holographic Reconstruction

scholarly journals Inverse scattering problem in turbulent magnetic fluctuations

2016 ◽  
Vol 34 (8) ◽  
pp. 673-689 ◽  
Author(s):  
Rudolf A. Treumann ◽  
Wolfgang Baumjohann ◽  
Yasuhito Narita
Keyword(s):  
Response Function ◽  
Inverse Scattering ◽  
Scattering Theory ◽  
Spatial Information ◽  
Scattering Problem ◽  
Low Frequency ◽  
Spectral Lines ◽  
Inverse Theory ◽  
Magnetic Fluctuations ◽  
Inverse Scattering Theory

Abstract. We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gelfand–Levitan–Marchenko equation of quantum mechanical scattering theory. The last of these applies to transmission and reflection in an active medium. The theory of turbulent magnetic fluctuations does not refer to such quantities. It requires a somewhat different formulation. We reduce the theory to the measurement of the low-frequency electromagnetic fluctuation spectrum, which is not the turbulent spectral energy density. The inverse theory in this form enables obtaining information about the turbulent response function of the medium. The dynamic causes of the electromagnetic fluctuations are implicit to it. Thus, it is of vital interest in low-frequency magnetic turbulence. The theory is developed until presentation of the equations in applicable form to observations of turbulent electromagnetic fluctuations as input from measurements. Solution of the final integral equation should be done by standard numerical methods based on iteration. We point to the possibility of treating power law fluctuation spectra as an example. Formulation of the problem to include observations of spectral power densities in turbulence is not attempted. This leads to severe mathematical problems and requires a reformulation of inverse scattering theory. One particular aspect of the present inverse theory of turbulent fluctuations is that its structure naturally leads to spatial information which is obtained from the temporal information that is inherent to the observation of time series. The Taylor assumption is not needed here. This is a consequence of Maxwell's equations, which couple space and time evolution. The inversion procedure takes advantage of a particular mapping from time to space domains. Though the theory is developed for homogeneous stationary non-flowing media, its extension to include flows, anisotropy, non-stationarity, and the presence of spectral lines, i.e. plasma eigenmodes like those present in the foreshock or the magnetosheath, is obvious.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

Reconstruction of inclusions in electrical conductors

2020 ◽  
Author(s):  
Michele Di Cristo ◽  
Giacomo Milan
Keyword(s):  
Electrical Impedance Tomography ◽  
Inverse Scattering ◽  
Scattering Theory ◽  
Electrical Impedance ◽  
Functional Method ◽  
Impedance Tomography ◽  
Numerical Examples ◽  
Electrical Conductors ◽  
Inverse Scattering Theory

Abstract We investigate the reciprocity gap functional method, which has been developed in the inverse scattering theory, in the context of electrical impedance tomography. In particular, we aim to reconstruct an inclusion contained in a body, whose conductivity is different from the conductivity of the surrounding material. Numerical examples are given, showing the performance of our algorithm.

scholarly journals Evaluating Performance of Microwave Image Reconstruction Algorithms: Extracting Tissue Types with Segmentation Using Machine Learning

2021 ◽  
Vol 7 (1) ◽  
pp. 5
Author(s):  
Douglas Kurrant ◽  
Muhammad Omer ◽  
Nasim Abdollahi ◽  
Pedram Mojabi ◽  
Elise Fear ◽  
...  
Keyword(s):  
Machine Learning ◽  
Dielectric Properties ◽  
Image Quality ◽  
Inverse Scattering ◽  
Quantitative Assessment ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Malignant Tissue ◽  
Segmentation Technique ◽  
Specific Tissue

Evaluating the quality of reconstructed images requires consistent approaches to extracting information and applying metrics. Partitioning medical images into tissue types permits the quantitative assessment of regions that contain a specific tissue. The assessment facilitates the evaluation of an imaging algorithm in terms of its ability to reconstruct the properties of various tissue types and identify anomalies. Microwave tomography is an imaging modality that is model-based and reconstructs an approximation of the actual internal spatial distribution of the dielectric properties of a breast over a reconstruction model consisting of discrete elements. The breast tissue types are characterized by their dielectric properties, so the complex permittivity profile that is reconstructed may be used to distinguish different tissue types. This manuscript presents a robust and flexible medical image segmentation technique to partition microwave breast images into tissue types in order to facilitate the evaluation of image quality. The approach combines an unsupervised machine learning method with statistical techniques. The key advantage for using the algorithm over other approaches, such as a threshold-based segmentation method, is that it supports this quantitative analysis without prior assumptions such as knowledge of the expected dielectric property values that characterize each tissue type. Moreover, it can be used for scenarios where there is a scarcity of data available for supervised learning. Microwave images are formed by solving an inverse scattering problem that is severely ill-posed, which has a significant impact on image quality. A number of strategies have been developed to alleviate the ill-posedness of the inverse scattering problem. The degree of success of each strategy varies, leading to reconstructions that have a wide range of image quality. A requirement for the segmentation technique is the ability to partition tissue types over a range of image qualities, which is demonstrated in the first part of the paper. The segmentation of images into regions of interest corresponding to various tissue types leads to the decomposition of the breast interior into disjoint tissue masks. An array of region and distance-based metrics are applied to compare masks extracted from reconstructed images and ground truth models. The quantitative results reveal the accuracy with which the geometric and dielectric properties are reconstructed. The incorporation of the segmentation that results in a framework that effectively furnishes the quantitative assessment of regions that contain a specific tissue is also demonstrated. The algorithm is applied to reconstructed microwave images derived from breasts with various densities and tissue distributions to demonstrate the flexibility of the algorithm and that it is not data-specific. The potential for using the algorithm to assist in diagnosis is exhibited with a tumor tracking example. This example also establishes the usefulness of the approach in evaluating the performance of the reconstruction algorithm in terms of its sensitivity and specificity to malignant tissue and its ability to accurately reconstruct malignant tissue.

scholarly journals Adaptive B -spline scheme for solving an inverse scattering problem

2004 ◽  
Vol 20 (2) ◽  
pp. 347-365 ◽  
Author(s):  
Alexandre Baussard ◽  
Eric L Miller ◽  
Denis Prémel
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
B Spline
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