Reconstructing Dispersive Scatterers With Minimal Frequency Data

Kalepu, Yaswanth; Sanghvi, Yash; Khankhoje, Uday K.

doi:10.1109/lgrs.2020.2968256

Cited by 6 publications

(18 citation statements)

References 20 publications

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“…The main ideas of the improvement are as follows: The original direct reconstruction of the electrical parameter differences (frequency‐dependent) is changed into the indirect inversion of the Debye model parameters (frequency‐independent). Three two‐dimensional (2D) computational examples are examined by methods from this work, 4,10 respectively, and the comparisons of the simulation results preliminarily confirm their performance. This modification is expected to enrich the theory of electromagnetic inverse scattering, or to provide a reference for microwave imaging systems and/or technology.…”

Section: Introductionmentioning

confidence: 75%

“…In the 2D TM case, the frequency‐domain complex‐valued incident electric field component E inc and scattered electric field component E sct satisfy the ST state equation: 8,9

χ (boldr) E^{inc} (boldr) = J (boldr) - χ (boldr) G_{scriptD} (J), r \in D,

and the ST data equation: 8,9

E^{sct} (boldr) = G_{normalℳ} (J), r \in M,

respectively, where J = χE tot indicates the normalized contrast source (CS) component, (the subscript z shared by the fields and source components is omitted for brevity), r represents the position vector, operators

G_{scriptD}

(·) and G ℳ (·) are defined to be:

{normalγ}_{normalb}^{2} \int_{scriptD} ℊ (r, {boldr}^{'}) J (r^{'}) d {boldr}^{'} ∶ = \{\begin{matrix} G_{scriptD} (J), r \in D \\ G_{scriptM} (J), r \in M \end{matrix}

where

γ_{normalb}

is the propagation coefficient of the background medium, and

ℊ

is the 2D scalar Green's function 8 . The symbol χ in (1) denotes the contrast of the complex relative permittivity between the scatterers and the background medium, which is, based on a single‐pole Debye model, defined as: 10

χ =

…”

Section: Theory and Methodsmentioning

confidence: 99%

“…Therefore, we assume that

τ

is known a priori . Thus, similar to, 4,10 only three kinds of Debye parameters

ε_{\infty}

∆ ε

σ_{normals}

, namely

p = \{ε_{\infty}, ∆ ε, σ_{s}\}

, is to be estimated. Conventionally, we describe it as the following minimization problem:

p = \underset{p}{\arg \min} [F (p, J)],

where the cost functional

F

is given by:

F (p, J) = {scriptF}^{LS} (p, J) ∙ {scriptF}^{MR} (boldp),

in which a least‐squares (LS) residual term

{scriptF}^{LS}

is defined as:

{scriptF}^{LS} (p, J) = \sum_{k} [η_{scriptM}^{k} \sum_{m} {(‖‖, δ_{M}^{m, k} ((), J))}_{scriptM}^{2}] / K +

\sum_{k} [η_{scriptD}^{k} (boldp) \sum_{m} (‖‖, δ_{})]

…”

Section: Theory and Methodsmentioning

confidence: 99%

“…First,

{boldJ}^{m, k, 0}

is obtained by the back‐propagation (BP) method, 8–10,12–15 and then the initial guess of Debye model parameters

{boldε}_{\infty}^{k, 0}

∆ {boldε}^{k, 0}

, and

{boldσ}_{normals}^{k, 0}

are determined. It is worth noting that these vector symbols represent the discretized form of their corresponding continuous variables.…”

Section: Theory and Methodsmentioning

confidence: 99%

“…Methodologically, these inverse problems can be solved in the time domain, such as the forward‐backward time‐stepping (FBTS) approach, 3 and the time‐domain inverse scattering (TDIS) technique, 4 or solved in the frequency domain, such as the Born‐type iterative methods, 5,6 the Gauss‐Newton inversion (GNI) technique, 7 the contrast source inversion (CSI) approach, 8 and the subspace‐based optimization method (SOM) 9 . According to the adopted operating frequency range, the aforementioned frequency‐domain methods may be classified as the single frequency (SF) 5–9 multi frequency (MF), and frequency hopping (FH) versions 10 . Also, in terms of the form of equations to be treated, they could be separated into the field‐type (FT) 5–7 and source‐type (ST) methods 8,9 .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A modified contrast source inversion method for microwave tomographic imaging of Debye dispersive media

Liu

Zhang

2022

Int J Imaging Syst Tech

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The Debye empirical formulas are often used for the description of the dispersion characteristics of common media, such as biological tissues, water, and soil. In order to reconstruct their frequency-related electrical properties, a multi-frequency contrast source inversion (CSI) method is modified from the direct estimation of the contrast between Debye scatterers and background medium, into the reconstruction of three kinds of Debye model parameters, namely, the optical relative permittivity, relative permittivity difference, and static conductivity. Through three two-dimensional (2D) benchmark numerical experiments, detailed comparisons between the results by the improved CSI method, and those by the frequency hopping (FH) technique, single frequency subspace-based optimization method (SOM) with deep learning (DL), multi frequency (MF) dispersive SOM, and time-domain inverse scattering (TDIS) approach, show preliminarily that the modified CSI (M-CSI) method is feasible and robust, and that it exhibits acceptable compromise performance by the comprehensive consideration of convergence characteristics, positioning accuracy, reconstruction errors, and computational efficiency. Also, the M-CSI method has been successfully applied to quantitatively reconstruct the internal breast composition in a 2D cancerous phantom extracted from a realistic numerical breast, dielectrically and anatomically.

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Section: Introductionmentioning

confidence: 75%

“…In the 2D TM case, the frequency‐domain complex‐valued incident electric field component E inc and scattered electric field component E sct satisfy the ST state equation: 8,9