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Image reconstruction device, image reconstruction method, image reconstruction program, and CT apparatus

Foreign code F120007020
Posted date Nov 19, 2012
Country United States of America
Application number 51457907
Gazette No. 20090279768
Gazette No. 8090182
Date of filing Nov 13, 2007
Gazette Date Nov 12, 2009
Gazette Date Jan 3, 2012
International application number JP2007072339
International publication number WO2008059982
Date of international filing Nov 13, 2007
Date of international publication May 22, 2008
Priority data
  • P2006-307058 (Nov 13, 2006) JP
  • 2007WO-JP72339 (Nov 13, 2007) WO
Title Image reconstruction device, image reconstruction method, image reconstruction program, and CT apparatus
Abstract (US8090182)
A computerized tomography apparatus and program for obtaining a cross-sectional image corresponding to projections are provided in which, for a temporary cross-sectional image f(x, y) obtained in some manner, an evaluation function E is defined which includes differences between projections calculated from f(x, y) and measured projections, and f(x, y) is changed in a manner which substantially decreases E.
The computerized tomography apparatus and program are characterized in which a back projection operation, which is required by conventional computerized tomography, is not essentially required.
The computerized tomography apparatus and program are particularly effective in removal or reduction of metal artifacts, aliasing artifacts and the like.
Scope of claims [claim1]
1. An image reconstructing device for obtaining a cross-sectional image of an object from projections (hereinafter referred to as "radiographic projections") obtained by irradiating the object with a beam of radiation, comprising: means (a) for obtaining an evaluation function (hereinafter referred to as an "energy") (E0) including differences between projections calculated from a current estimated cross-sectional image of the object and the radiographic projections;
means (b) for modifying a portion of the current estimated cross-sectional image;
means (c) for obtaining an energy (E1) including differences between projections calculated from the modified estimated cross-sectional image and the radiographic projections;
means (d) for obtaining a differential (DELTA E) between the energy (E0) and the energy (E1);
means (e) for determining whether or not the modification is to be accepted, based on an acceptance function using the differential (DELTA E) and a temperature parameter (T) for controlling an acceptance probability, and reflecting a result of the determination on the current estimated cross-sectional image; and
means (f) for changing a value of the temperature parameter (T) every time the number of iterations of a series of processes of the means (a) to (e) reaches a predetermined value.
[claim2]
2. The image reconstructing device of claim 1, wherein the means (a) calculates an energy (E0) including a sum of differences between projections calculated from the current estimated cross-sectional image and the radiographic projections, and a standard deviation of a local region of the current estimated cross-sectional image, and
the means (c) calculates an energy (E1) including a sum of differences between projections calculated from the modified estimated cross-sectional image and the radiographic projections, and a standard deviation of a local region of the modified estimated cross-sectional image.
[claim3]
3. The image reconstructing device of claim 1, wherein the means (a) calculates an energy (E0) including a sum of differences between projections calculated from the current estimated cross-sectional image and the radiographic projections, and an entropy of a local region of the current estimated cross-sectional image, and
the means (c) calculates an energy (E1) including a sum of differences between projections calculated from the modified estimated cross-sectional image and the radiographic projections, and an entropy of a local region of the modified estimated cross-sectional image.
[claim4]
4. The image reconstructing device of claim 1, wherein the means (a) calculates an energy (E0) including a sum of differences between projections calculated from the current estimated cross-sectional image and the radiographic projections, a standard deviation of a local region of the current estimated cross-sectional image, and an entropy of the local region of the current estimated cross-sectional image, and
the means (c) calculates an energy (E1) including a sum of differences between projections calculated from the modified estimated cross-sectional image and the radiographic projections, a standard deviation of a local region of the modified estimated cross-sectional image, and an entropy of the local region of the modified estimated cross-sectional image.
[claim5]
5. The image reconstructing device of claim 1, comprising: instead of the means (a), (c) and (d),
means (h) for calculating DELTA H using [Expression 1], and obtaining DELTA E (DELTA E=DELTA H+ . . . ) including the calculated DELTA H as a component,
(Equation image 12 not included in text) where, when the current estimated cross-sectional image of the object is represented by f(x, y) and the portion modified by the means (b) is represented by DELTA f(x, y), DELTA f(x, y) is a cross-sectional image having a value of DELTA mu only at a coordinate point (x0, y0) and zero elsewhere, and p(r, theta ) represents a projection calculated from the current estimated cross-sectional image of the object, p0(r, theta ) represents a radiographic projection of the object, r represents a channel position of a one-dimensional detector taking the projection, theta represents a projection angle, and r(theta )=x0 cos theta +y0 sin theta .
[claim6]
6. The image reconstructing device of claim 5, wherein the means (h) calculates DELTA sigma using [Expression 3], and obtains DELTA E (DELTA E=DELTA H+cDELTA sigma + . . . ) including as a component a sum of a product (cDELTA sigma ) of the calculated DELTA sigma and a coefficient c, and the DELTA H,
(Equation image 13 not included in text) where sigma represents a standard deviation of luminance values of d * d pixels around the coordinate point (x0, y0) and is calculated by [Expression 4], and fi and fj represent values of f(x0, y0) before and after the modification by the means (b),
(Equation image 14 not included in text)
[claim7]
7. The image reconstructing device of claim 5, wherein the means (h) calculates DELTA S using [Expression 7], and obtains DELTA E (DELTA E=DELTA H-TDELTA S+ . . . ) including as a component a sum of a product (-TDELTA S) of the calculated DELTA S and the temperature parameter (T), and the DELTA H,
DELTA S=k ln Ni-k ln(Nj+1) [Expression 7]
where S represents an entropy of a local region image of d * d pixels around the coordinate point (x0, y0) and is calculated by [Expression 8],
(Equation image 15 not included in text) where
N: a total number of pixels in the local region image,
Ni: a total number of pixels whose pixel value is a digital value of i,
Nj: a total number of pixels whose pixel value is a digital value of j,
k: a constant,
a pixel value is changed from the digital value i to the digital value j by the modification by the means (b).
[claim8]
8. The image reconstructing device of claim 1, comprising: instead of the means (a), (c) and (d),
means (h) for calculating DELTA H using [Expression 1], and obtaining DELTA E (DELTA E=DELTA H+ . . . ) including the calculated DELTA H as a component,
(Equation image 16 not included in text) where, when the current estimated cross-sectional image of the object is represented by f(x, y) and the portion modified by the means (b) is represented by DELTA f(x, y), DELTA f(x, y) is a cross-sectional image having a value of DELTA mu only at a coordinate point (x0, y0) and zero elsewhere, and p(r, theta ) represents a projection calculated from the current estimated cross-sectional image of the object, p0(r, theta ) represents a radiographic projection of the object, r represents a channel position of a one-dimensional detector taking the projection, theta represents a projection angle, r(theta )=x0 cos theta +y0 sin theta , and M represents the number of projection angles.
[claim9]
9. The image reconstructing device of claim 8, wherein the means (h) calculates DELTA sigma using [Expression 3], and obtains DELTA E (DELTA E=DELTA H+cDELTA sigma + . . . ) including as a component a sum of a product (cDELTA sigma ) of the calculated DELTA sigma and a coefficient c, and the DELTA H,
(Equation image 17 not included in text) where sigma represents a standard deviation of luminance values of d * d pixels around the coordinate point (x0, y0) and is calculated by [Expression 4], and fi and fj represent values of f(x0, y0) before and after the modification by the means (b),
(Equation image 18 not included in text)
[claim10]
10. The image reconstructing device of claim 8, wherein the means (h) calculates DELTA S using [Expression 7], and obtains DELTA E (DELTA E=DELTA H-TDELTA S+ . . . ) including as a component a sum of a product (-TDELTA S) of the calculated DELTA S and the temperature parameter (T), and the DELTA H,
DELTA S=k ln Ni-k ln(Nj+1) [Expression 7]
where S represents an entropy of a local region image of d * d pixels around the coordinate point (x0, y0) and is calculated by [Expression 8],
(Equation image 19 not included in text) where
N: a total number of pixels in the local region image,
Ni: a total number of pixels whose pixel value is a digital value of i,
Nj: a total number of pixels whose pixel value is a digital value of j,
k: a constant,
a pixel value is changed from the digital value i to the digital value j by the modification by the means (b).
[claim11]
11. The image reconstructing device of claim 1, comprising: instead of the means (e) and (f), means (e1) for determining whether or not the modification is to be accepted, based on an acceptance function using the differential (DELTA E) and a temperature parameter (T) for controlling an acceptance probability, and reserving reflection of a result of determination on the current estimated cross-sectional image; and
means (f1) for reflecting the reservation(s) in the means (e1) on the current estimated cross-sectional image and changing a value of the temperature parameter (T) every time the number of iterations of a series of processes of the means (a) to (d) and (e1) reaches a predetermined value.
[claim12]
12. An image reconstructing device for obtaining a cross-sectional image of an object from projections obtained by irradiating the object with a beam of radiation, comprising: means (m1) for calculating a back projection g0(x, y) of a radiographic projection p0(r, theta ) of the object by a back projection operation without filtering;
means (m2) for calculating a projection p(r, theta ) from a current estimated cross-sectional image f(x, y) of the object, and calculating a back projection g(x, y) of the projection p(r, theta ) by a back projection operation without filtering;
means (m3) for generating an image DELTA mu (x, y) whose pixel value is a change value of the current estimated cross-sectional image f(x, y) of the object;
means (m4) for generating an image DELTA H(x, y) by applying [Expression 9] to each pixel value,
DELTA H=MDELTA mu 2+2DELTA mu {g(x0, y0)-g0(x0, y0)} [Expression 9]
where
M: the number of projection angles;
means (m5) for calculating DELTA E(x, y) using the DELTA H(x, y),
where
DELTA E(x, y) represents a differential between evaluation functions E0(x, y) and E1(x, y),
E0(x, y) represents an evaluation function including a difference between the projection p(r, theta ) calculated from the estimated cross-sectional image f(x, y) and the radiographic projection p0(r, theta ), and
E1(x, y) represents an evaluation function including a difference between a projection {p(r, theta )+DELTA p(r, theta )}, calculated from a sum {f(x, y)+DELTA mu (x, y)} of the estimated cross-sectional image f(x, y) and the image DELTA mu (x, y) obtained by the means (m3), and the radiographic projection p0(r, theta );
means (m6) for setting the DELTA mu (x, y) to 0 at a coordinate point (x, y) where the DELTA E is positive; and
means (m7) for setting a sum of the estimated cross-sectional image f(x, y) and the image DELTA mu (x, y) obtained by the means (m6) as a new estimated cross-sectional image f(x, y) and repeating processes of the means (m2) to (m6) with respect to the new estimated cross-sectional image f(x, y).
[claim13]
13. An image reconstructing device for obtaining a cross-sectional image of an object from projections obtained by irradiating the object with a beam of radiation, comprising: means (m1) for calculating a back projection g0(x, y) of a radiographic projection p0(r, theta ) of the object using [Expression 10]
(Equation image 20 not included in text) r: a channel position of a one-dimensional detector taking the projection,
theta : a projection angle,
means (m2) for calculating a projection p(r, theta ) from a current estimated cross-sectional image f(x, y) of the object, and calculating a back projection g(x, y) of the projection p(r, theta ) using [Expression 11]
(Equation image 21 not included in text) means (m3) for generating an image DELTA mu (x, y) whose pixel value is a change value of the current estimated cross-sectional image f(x, y) of the object;
means (m4) for generating an image DELTA H(x, y) by applying [Expression 12] to each pixel value,
DELTA H=MDELTA mu 2+2 DELTA mu {g(x0, y0)-g(x0, y0)} [Expression 12]
where
M: the number of projection angles;
means (m5) for generating DELTA sigma (x, y) by applying [Expression 13] to each pixel value,
(Equation image 22 not included in text) where sigma represents a standard deviation of luminance values of d * d pixels around a coordinate point (x0, y0) and is calculated by [Expression 14], and fi and fj represent values of f(x0, y0) before and after a change,
(Equation image 23 not included in text) means (m6) for generating an image DELTA S by applying [Expression 17] to each value,
DELTA S=k ln Ni-k ln(Nj+1) [Expression 17]
where S represents an entropy of a local region image of d * d pixels around the coordinate point (x0, y0) and is calculated by [Expression 18],
(Equation image 24 not included in text) where
N: a total number of pixels in the local region image,
Ni: a total number of pixels whose pixel value is a digital value of i,
Nj: a total number of pixels whose pixel value is a digital value of j,
k: a constant,
a pixel value is changed from the digital value i to the digital value j by the modification by the means (b);
means (m7) for calculating DELTA E(x, y) based on [Expression 19],
DELTA E=DELTA H+cDELTA sigma -TDELTA S [Expression 19]
where
c: a coefficient,
T: a virtual temperature (temperature parameter),
means (m8) for setting the DELTA mu (x, y) to 0 at a coordinate point (x, y) where the DELTA E is positive;
means (m9) for setting a sum of the estimated cross-sectional image f(x, y) and the image DELTA mu (x, y) obtained by the means (m8) as a new estimated cross-sectional image f(x, y); and
means (m10) for multiplying the T by alpha (alpha <1), and repeating processes of the means (m2) to (m9).
[claim14]
14. A method for obtaining a cross-sectional image of an object from projections (hereinafter referred to as "radiographic projections") obtained by irradiating the object with a beam of radiation, comprising the steps of: (a) obtaining an evaluation function (hereinafter referred to as an "energy") (E0) including differences between projections calculated from a current estimated cross-sectional image of the object and the radiographic projections;
(b) modifying a portion of the current estimated cross-sectional image;
(c) obtaining an energy (E1) including differences between projections calculated from the modified estimated cross-sectional image and the radiographic projections;
(d) obtaining a differential (DELTA E) between the energy (E0) and the energy (E1);
(e) determining whether or not the modification is to be accepted, based on an acceptance function using the differential (DELTA E) and a temperature parameter (T) for controlling an acceptance probability;
(f) reflecting a result of the determination on the current estimated cross-sectional image, and returning to the step (a);
(g) changing a value of the temperature parameter (T) every time the number of iterations of the steps (a) to (f) reaches a predetermined value; and
(h) determining whether or not the result of the determination in the step (e) satisfies predetermined stop conditions, and if the result of the determination in the step (e) satisfies predetermined stop conditions, ending the process.
[claim15]
15. An image reconstructing program for obtaining a cross-sectional image of an object from projections (hereinafter referred to as "radiographic projections") obtained by irradiating the object with a beam of radiation, wherein the program causes a computer to execute the steps of:
(a) obtaining an evaluation function (hereinafter referred to as an "energy") (E0) including differences between projections calculated from a current estimated cross-sectional image of the object and the radiographic projections;
(b) modifying a portion of the current estimated cross-sectional image;
(c) obtaining an energy (E1) including differences between projections calculated from the modified estimated cross-sectional image and the radiographic projections;
(d) obtaining a differential (DELTA E) between the energy (E0) and the energy (E1);
(e) determining whether or not the modification is to be accepted, based on an acceptance function using the differential (DELTA E) and a temperature parameter (T) for controlling an acceptance probability;
(f) reflecting a result of the determination on the current estimated cross-sectional image, and returning to the step (a); and
(g) changing a value of the temperature parameter (T) every time the number of iterations of the steps (a) to (f) reaches a predetermined value.
[claim16]
16. A CT apparatus comprising: means (A) for obtaining projections by irradiating an object with a beam of radiation; and
means (B) for obtaining a cross-sectional image of the object from the projections,
wherein the means (B) includes: means (b1) for obtaining an evaluation function (hereinafter referred to as an "energy") (E0) including differences between projections calculated from a current estimated cross-sectional image of the object and the projections by irradiating the object with the beam of radiation (hereinafter referred to as "radiographic projections");
means (b2) for modifying a portion of the current estimated cross-sectional image;
means (b3) for obtaining an energy (E1) including differences between projections calculated from the modified estimated cross-sectional image and the radiographic projections;
means (b4) for obtaining a differential (DELTA E) between the energy (E0) and the energy (E1);
means (b5) for determining whether or not the modification is to be accepted, based on an acceptance function using the differential (DELTA E) and a temperature parameter (T) for controlling an acceptance probability, and reflecting a result of the determination on the current estimated cross-sectional image; and
means (b6) for changing a value of the temperature parameter (T) every time the number of iterations of a series of processes of the means (b1) to (b5) reaches a predetermined value.
  • Inventor, and Inventor/Applicant
  • NISHIKAWA YUKIHIRO
  • KYOTO INSTITUTE OF TECHNOLOGY
IPC(International Patent Classification)
U.S. Cl./(Sub)
  • A61B006/03B
  • A61B006/03D
  • G06T011/00T3
  • S06T211/424
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