# US 9,519,054 B2 · Method and apparatus for reconstructing dielectric image using electromagnetic waves

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- Number: US 9,519,054 B2
- Document ID: US9519054B2
- Status: Granted
- Kind: B2
- Application number: 14/254,439
- Filed: 2014-04-16
- Published: 2015-02-12
- Granted: 2016-12-13
- Earliest claimed: 2013-08-09
- Assignees: Electronics and Telecommunications Research Institute
- Applicants: Electronics and Telecommunications Research Institute
- Inventors: Bo Ra Kim; Nikolai Simonov; Seong-Ho Son; Soon Ik Jeon; Hyuk Je Kim; Jong Moon Lee; Hyung Do Choi
- Web page: https://patentgrep.com/patent/US9519054B2

## CPC

- G01S 13/89: for mapping or imaging
- G01S 13/88: Radar or analogous systems specially adapted for specific applications (electromagnetic prospecting or detecting of objects, e.g. near-field detection, G01V3/00)
- G01S 13/887: {for detection of concealed objects, e.g. contraband or weapons}
- G01S 13/888: {through wall detection}
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES

## Abstract

A method for reconstructing a dielectric image using electromagnetic waves, comprising: acquiring a measurement value of the electromagnetic waves; generating a matching system matrixes between the meshes; generating a smoothed dyadic Green's function matrix; generating an electromagnetic wave calculation value; calculating a misfit error between the acquired electromagnetic wave measurement value and the generated electromagnetic wave calculation value, and checking whether a change of the calculated misfit error satisfies a predetermined optimization determination condition; updating dielectric parameters at the meshes; and outputting a reconstructed dielectric image in the image reconstruction region.

## Claims

### Claim 1

A method for reconstructing an image using electromagnetic waves, comprising:
acquiring a measurement value of the electromagnetic waves that are radiated by a transmitting antenna and propagate through an image reconstruction region;
setting a plurality of predetermined meshes in the image reconstruction region;
generating a matching system matrixes using basis functions related to the plurality of predetermined meshes;
generating a smoothed Green's function matrix using the generated matching system matrix;
generating an electromagnetic wave calculation value through performing of a forward electromagnetic analysis with respect to the image reconstruction region on the basis of the generated smoothed dyadic Green's function matrix;
calculating a misfit between the acquired electromagnetic wave measurement value and the generated electromagnetic wave calculation value, and checking whether a the calculated misfit error satisfies a predetermined optimization determination condition;
updating the dielectric parameters at the meshes if the predetermined optimization determination condition is not satisfied; and
outputting a reconstructed image in the image reconstruction region when the predetermined optimization determination condition is satisfied.

### Claim 2 (depends on 1)

The method of claim 1, wherein the plurality of meshes include a fine mesh, a coarse mesh having a relatively larger spacing than the fine mesh, and an image reconstruction mesh having a relatively larger spacing than the coarse mesh.

### Claim 3 (depends on 2)

The method of claim 2, wherein the plurality of meshes are in any one of rectangular grids, or hexagonal grids.

### Claim 4 (depends on 2)

The method of claim 2, wherein the basis function corresponding to the fine mesh and the coarse mesh and the basis function corresponding to the coarse mesh and the image reconstruction mesh are in a sinc-type function, spline function type or wavelet type.

### Claim 5 (depends on 2)

The method of claim 2, wherein the matrix Bc of matching system of the basis function, allocated at the fine mesh and centered at the coarse mesh nodes is generated as in an equation,
Bc=[bc,1,bc,2,bc,3, . . . ,bc,n, . . . ,bc,Nc]
where, bc,n denotes the vectors of basis function allocated to the fine mesh and centered at the n-th node of coarse mesh, and Nc denotes the total number of coarse mesh nodes.

### Claim 6 (depends on 5)

The method of claim 5, wherein the matching system matrix satisfies an equation,
Rc≡Bc·{tilde over (B)}cT=[rc,1,rc,2,rc,3, . . . ,rc,n, . . . ,rc,Nf]
where, Rc denotes a spatial resolution matrix, {tilde over (B)}cT: denotes a transpose matrix, which is dual to Bc, rc,n denotes a vector of a point spread function corresponding to the n-th fine mesh node, and Nf denotes the total number of fine mesh nodes.

### Claim 7 (depends on 6)

The method of claim 6, wherein Rc has property of a spatial filter for smoothing an image reconstruction value.

### Claim 8 (depends on 6)

The method of claim 6, wherein the matching system matrix simultaneously satisfies two conditions:
Condition 1: The effective width of the basis function is equal to or close to the grid spacing of the coarse mesh
Condition 2: All rows and columns of the spatial resolution matrix correspond to functions having the same shape and the same peak values but centered at different nodes of the fine mesh.

### Claim 9 (depends on 5)

The method of claim 5, wherein the matching system matrix Br of the basis functions allocated to the fine mesh and centered at the image reconstruction mesh nodes is generated as in an equation,
Br=[br,1,br,2,br,3, . . . ,br,n, . . . ,br,Nr]
where, br,n denotes the basis function allocated to the fine mesh and centered at the n-th node of image reconstruction mesh, and Nr denotes the total number of image reconstruction mesh nodes.

### Claim 10 (depends on 9)

The method of claim 9, wherein the generating the matching system matrix comprises generating a spatial resolution matrix using multiplication of the matching system matrix and a transpose matrix, which is dual to the matching system matrix.

### Claim 11 (depends on 2)

The method of claim 2, wherein the generating the smoothed Green's function matrix comprises generating the smoothed Green's function matrix by multiplying a Green's function matrix defined at the fine mesh by the matching system matrix and a transpose matrix, which is dual to the matching system matrix.

### Claim 12 (depends on 11)

The method of claim 11, wherein the generating the smoothed Green's function matrixes comprises:
calculating the dyadic Green's function matrix defined at all the fine mesh nodes in the image reconstruction; and
calculating the dyadic Green's function matrix for calculating scattered waves incident on receiving antennas.

### Claim 13 (depends on 2)

The method of claim 2, wherein the performing the forward electromagnetic analysis comprises analyzing electromagnetic wave scattering with respect to the coarse mesh and calculating the electromagnetic waves that can be acquired in positions of the receiving antennas.

### Claim 14 (depends on 1)

The method of claim 1, wherein the checking comprises determining that the predetermined optimization condition is satisfied if a difference value between a current misfit error and a previously calculated misfit error is smaller than a predetermined allowable difference value or exceeds a predetermined number of calculations.

### Claim 15 (depends on 2)

The method of claim 2, wherein the updating the dielectric parameters comprises:
generating a regularized Jacobian matrix using the generated matching system matrix with respect to the image reconstruction mesh, and the smoothed dyadic Green's function matrix; and
updating the dielectric parameters at the coarse mesh using the generated regularized Jacobian matrix.

### Claim 16 (depends on 15)

The method of claim 15, wherein the regularized Jacobian matrix Jr is generated as in an equation,
J
r
⁡
(
Tx
/
Rx
)
=
1
V
s
⁡
(
Tx
/
Rx
)
·
∑
i
=
1
3
⁢
(
G
signal
,
c
⁡
(
Rx
)
·
A
·
B
·
B
cr
)
X
i
where, Vs(Tx/Rx) denotes a voltage of signal of the wave for empty environment, transmitted by Tx antenna and received by Rx antenna, Gsignal,c(Rx) is a matrix of smoothed dyadic Green's function that denotes scattering electromagnetic waves with respect to the coarse mesh and receiving them with antennas Rx, A denotes a matrix by the relationship between contrast Cc with respect to the coarse mesh and smoothed dyadic Green's function Gc with respect to the coarse mesh, B denotes a diagonal matrix constructed with the total electric field distributed at the coarse mesh, and Bcr denotes a matrix that transforms images from the image reconstruction mesh to the coarse mesh.

### Claim 17 (depends on 15)

The method of claim 15, wherein the updating the dielectric parameters at the coarse mesh is expressed as in an equation,
∈k=∈k-1+αN−∈b·(JrT·Jr)−1JrT·Δγ
where, αN·∈b·(JrT·Jr)−JrT. Δγ denotes dielectric parameters update values, and in the update value term, αN denotes an increment coefficient, ∈b denotes a permittivity of a background material, Jr denotes a regularized Jacobian matrix, a superscript T denotes a transpose matrix, a superscript ‘−1’ denotes an inverse matrix, and Δγ denotes an misfit between the electromagnetic wave measurement value and the electromagnetic wave calculation value.

### Claim 18 (depends on 1)

The method of claim 1, wherein the outputting the reconstructed image comprises generating and outputting the reconstructed image as a visualization file that is visually identifiable or a data file.

### Claim 19

An apparatus for reconstructing an image using electromagnetic waves, comprising:
a measurement value acquisition block acquiring a measurement value of the electromagnetic waves that are radiated by a transmitting antenna and propagate through an image reconstruction region;
a mesh setting block setting a plurality of predetermined meshes in the image reconstruction region;
a matching system matrix generation block generating a matching system matrix using basis functions related to the plurality of predetermined meshes;
a Green's function matrix generation block generating a smoothed Green's function matrix using the generated matching system matrix;
an electromagnetic wave calculation block generating an electromagnetic wave calculation value through performing of a forward electromagnetic analysis with respect to the image reconstruction region on the basis of the generated smoothed Green's function matrix;
an optimization determination block calculating an misfit error between the acquired electromagnetic wave measurement value and the generated electromagnetic wave calculation value, and checking whether the calculated misfit error satisfies a predetermined optimization determination condition;
a parameter updating block generating a regularized Jacobian matrix using the matching system matrix, the image reconstruction mesh, and the smoothed Green's function matrix, and updating dielectric parameters at the coarse mesh using the generated regularized Jacobian matrix if the predetermined optimization determination condition is not satisfied; and
an image reconstruction value generation block generating a reconstructed image in the image reconstruction region as a visualization file that is visually identifiable or a data file when the predetermined optimization determination condition is satisfied.

### Claim 20 (depends on 19)

The apparatus of claim 19, wherein the mesh setting block sets a fine mesh, a coarse mesh having a relatively larger spacing than the fine mesh, and an image reconstruction mesh having a relatively larger spacing than the coarse mesh as the plurality of meshes.