Scattering tomography device and scattering tomography method
A scattering tomography device includes: a transmitting antenna that transmits radio waves into an interior of an object; a receiving antenna that receives, outside the object, scattered waves of the radio waves; and an information processing circuit that obtains measurement results over a plurality of days and generates a reconstructed image showing a persistent element inside the object based on the measurement results. The information processing circuit calculates a scattering field function for each of the measurement results, calculates a visualization function for each of the measurement results, generates intermediate images for the measurement results, and generates a reconstructed image by calculating a minimum value of an image intensity at each position in the intermediate images using a logical conjunction.
1 . A scattering tomography device comprising:
a transmitting antenna that transmits radio waves into an interior of an object from outside the object;
a receiving antenna that receives, outside the object, scattered waves of the radio waves transmitted into the interior of the object by the transmitting antenna; and
an information processing circuit that obtains a measurement result of the scattered waves on each of a plurality of days to obtain measurement results over a plurality of days, and generates a reconstructed image showing a persistent element inside the object based on the measurement results,
wherein the information processing circuit:
calculates, for each of the measurement results and using the measurement result as a boundary condition, a scattering field function that takes a transmission position of the radio waves and a reception position of the scattered waves as inputs and outputs an amount of the scattered waves at the reception position;
calculates, for each of the measurement results, a visualization function that takes a location to be visualized as an input and outputs an image intensity at the location to be visualized, and is defined based on the amount output from the scattering field function in response to inputting the location to be visualized into the scattering field function as the transmission position and the reception position;
generates an intermediate image for each of the measurement results based on the visualization function to generate intermediate images for the measurement results; and
generates the reconstructed image by calculating a minimum value of the image intensity at each position in the intermediate images using a logical conjunction.
2 . The scattering tomography device according to claim 1 ,
wherein the information processing circuit generates the reconstructed image using P N (r)=b 1 (r)∧ . . . ∧b N (r) ∧ . . . ∧ b N (r), where P N (r) is the reconstructed image, r is a position, N is a total number of the intermediate images, b i is the visualization function where i is 1 to N, and ∧ is the logical conjunction.
3 . The scattering tomography device according to claim 1 ,
wherein the information processing circuit:
generates the intermediate image based on the visualization function and a diffusion coefficient; and
when generating the intermediate image, increases a spatial scope of diffusion of the image intensity at the location to be visualized in the intermediate image as the diffusion coefficient increases.
4 . The scattering tomography device according to claim 3 ,
wherein the information processing circuit generates the reconstructed image using P N (r)=e vΔ b 1 (r)∧ e vΔ b 2 (r) ∧ . . . ∧ e vΔ b N (r), where P N (r) is the reconstructed image, r is a position, N is a total number of the intermediate images, b i is the visualization function where i is 1 to N, e vΔ b i (r) is the intermediate image where i is 1 to N, v is the diffusion coefficient, Δ is a two-dimensional Laplace operator corresponding to two directions in which a shift occurs in the measurement of the scattered waves, and ∧ is the logical conjunction.
5 . The scattering tomography device according to claim 4 ,
wherein the information processing circuit calculates e vΔ b i (r) by calculating a Fourier transform of b i (r), multiplying a result of the Fourier transform by exp(−v(k x 2 +k y 2 )), and calculating an inverse Fourier transform of a result of the multiplication of exp (−v(k x 2 +k y 2 )), where k x and k y in exp (−v(k x 2 +k y 2 )) are two wavenumbers corresponding to the two directions of b i .
6 . The scattering tomography device according to claim 3 ,
wherein the diffusion coefficient is defined as a value proportional to a mean squared error of measurement positions of the scattered waves.
7 . The scattering tomography device according to claim 3 ,
wherein the diffusion coefficient is defined as a value equal to a mean squared error of measurement positions of the scattered waves.
8 . The scattering tomography device according to claim 3 ,
wherein the diffusion coefficient is defined as zero.
9 . The scattering tomography device according to claim 3 ,
wherein the diffusion coefficient is defined as a value greater than zero.
10 . The scattering tomography device according to claim 1 ,
wherein in a three-dimensional space of X coordinates, Y coordinates, and Z coordinates, an X coordinate and a Z coordinate of a position of the transmitting antenna are identical to an X coordinate and a Z coordinate of a position of the receiving antenna, respectively,
the scattering field function is defined as:
[
Math
.
1
]
φ
(
x
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k
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z
d
k
x
d
k
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1
d
k
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2
where x is an X coordinate of the transmission position and the reception position, y 1 is a Y coordinate of the transmission position, y 2 is a Y coordinate of the reception position, z is a Z coordinate of the transmission position and the reception position, k is a wavenumber of the radio waves, and k x , k y1 , and k y2 in the scattering field function are wavenumbers related to x, y 1 , and y 2 in the scattering field function, respectively,
a (k x , k y1 , k y2 ) is defined as:
[
Math
.
2
]
a
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k
x
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=
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k
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I
e
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{
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k
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}
z
I
Φ
~
(
x
I
,
k
y
1
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k
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k
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where I is an index of the transmission position and the reception position at which the transmitting antenna and the receiving antenna are present, x I is an X coordinate of the transmission position and the reception position at which the transmitting antenna and the receiving antenna are present, and z I is a Z coordinate of the transmission position and the reception position at which the transmitting antenna and the receiving antenna are present,
{tilde over (Φ)}(x, k y 1 , k y 2 , k) [Math. 3]
expresses a Fourier transform image related to y 1 , y 2 , and t in Φ(x, y 1 , y 2 , t) expressing a measurement result at x, y 1 , y 2 , and t, and
the visualization function is defined as:
[
Math
.
4
]
ρ
(
r
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=
ρ
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x
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=
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z
dk
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dk
where x, y, and z in the visualization function are an X coordinate, a Y coordinate, and a Z coordinate of the location to be visualized, respectively.
11 . A scattering tomography method comprising:
transmitting, by a transmitting antenna, radio waves into an interior of an object from outside the object;
receiving outside the object, by a receiving antenna, scattered waves of the radio waves transmitted into the interior of the object by the transmitting antenna; and
obtaining a measurement result of the scattered waves on each of a plurality of days to obtain measurement results over a plurality of days, and generating a reconstructed image showing a persistent element inside the object based on the measurement results,
wherein the obtaining of measurement results and generating of a reconstructed image includes:
calculating, for each of the measurement results and using the measurement result as a boundary condition, a scattering field function that takes a transmission position of the radio waves and a reception position of the scattered waves as inputs and outputs an amount of the scattered waves at the reception position;
calculating, for each of the measurement results, a visualization function that takes a location to be visualized as an input and outputs an image intensity at the location to be visualized, and is defined based on the amount output from the scattering field function in response to inputting the location to be visualized into the scattering field function as the transmission position and the reception position;
generating an intermediate image for each of the measurement results based on the visualization function to generate intermediate images for the measurement results; and
generating the reconstructed image by calculating a minimum value of the image intensity at each position in the intermediate images using a logical conjunction.