METHODS AND APPARATUS FOR WEIGHTING PROJECTION DATA

• US 20030185337A1
• Filed: 03/29/2002
• Published: 10/02/2003
• Est. Priority Date: 03/29/2002
• Status: Active Grant

• Current Assignee: GE Medical Systems Global Technology Company LLC (GE Healthcare Technologies, Inc.)
• Original Assignee: GE Medical Systems Global Technology Company LLC (GE Healthcare Technologies, Inc.)
• Inventors: Hsieh, Jiang
• Granted Patent: US 6,654,442 B2
• Time in Patent Office: Days
• US Class Current: 378/4
• CPC Class Codes: A61B 6/027 characterised by the use of a particular data acquisition trajectory, e.g. helical or spiral
• CPC Class Codes: G06T 11/005 Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating

Abstract

A method for weighting projection data includes selecting a region that includes a plurality of projection data samples, dividing the region into a plurality of equally sized sub-regions, and weighting the equally sized sub-regions using a location dependent z-smoothing weighting function.

Claims

1. A method for weighting projection data, said method comprising:

selecting a region that includes a plurality of projection data samples;

dividing the region into a plurality of equally sized sub-regions; and

weighting the equally sized sub-regions using a location dependent z-smoothing weighting function.

2. A method in accordance with claim 1 wherein selecting a region that includes a plurality of projection data samples comprises selecting a region that includes a plurality of projection data samples that are within 2π

/N in projection angle β

on either side of a plane of reconstruction.

3. A method in accordance with claim 1 further comprising defining a boundary of the sub-regions in accordance with:

4. A method in accordance with claim 1 further comprising selecting a weighting function that is an even function of a fan angle γ

, parallel to the sub-regions and a summation of the weighting is unity.

5. A method in accordance with claim 4 wherein selecting a weighting function comprises selecting a weighting function in accordance with:

w_k(γ

,β

)=w_k(−

γ

,β

−

γ

) $\underset{n=1}{\overset{4}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f_{n,k}<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\beta <br><br>}+{\mathrm{\beta <br><br>}}_{n,k}-\mathrm{\gamma <br><br>}\right)=1<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>0\le <br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\beta <br><br>}<<br><br>\frac{\mathrm{\pi <br><br>}}{N}$

where;

γ

is a fan angle;

β

is a projection angle change;

n is an index for sub-regions; and

k is the index for detector rows.

6. A method in accordance with claim 1 wherein weighting the equally sized sub-regions using a location dependent z-smoothing weighting function comprises weighting the equally sized sub-regions using a location dependent z-smoothing weighting function in accordance with:

f_1,k(γ

,β

−

β

_1,k)=α

(γ

)η

₁(β

)/[1+2α

(γ

)]f_2,k(γ

,β

−

β

_2,k)={[1−

α

(γ

)]η

₂(β

)+α

(γ

)}/[1+2α

(γ

)]f_3,k(γ

,β

−

β

_3,k)={1−

[1−

α

(γ

)]η

₂(β

)}/[1+2α

(γ

)]f_4,k(γ

,β

−

β

_4,k)=α

(γ

)[1−

η

₂(β

)]/[1+2α

(γ

)]

where;

β

is a projection angle;

β

_n,k is a sub-region boundary;

γ

is a fan angle;

$\begin{array}{c}\mathrm{\alpha <br><br>}<br><br>\left(\mathrm{\gamma <br><br>}\right)=\frac{<br><br>\mathrm{\gamma <br><br>}<br><br>+{\mathrm{\gamma <br><br>}}_b}{2<br><br>\left({\mathrm{\gamma <br><br>}}_m+{\mathrm{\gamma <br><br>}}_b\right)};<br><br>\\ {\mathrm{\eta <br><br>}}_n<br><br>\left(\mathrm{\beta <br><br>}\right)=\frac{\lfloor <br><br>\mathrm{\beta <br><br>}-\left({\mathrm{\beta <br><br>}}_{n,k}-\mathrm{\gamma <br><br>}\right)\rfloor <br><br><br><br>N}{\mathrm{\pi <br><br>}};<br><br>\end{array}$

γ

_b(0≦

γ

_b<

∞

) is a parameter to adjust the variation of the weighting function from the central channels to the boundary channels; and

γ

_m is the maximum detector angle in γ

.

7. A method for weighting projection data, said method comprising:

selecting a region that includes a plurality of projection data samples that are within 2π

/N in projection angle β

on either side of a plane of reconstruction;

dividing the region into a plurality of equally sized sub-regions;

defining a boundary of the sub-regions in accordance with;

${\mathrm{\beta <br><br>}}_{n,k}={\mathrm{\beta <br><br>}}_0+\frac{\left(2<br><br>k-M-1+n\right)<br><br>\mathrm{\pi <br><br>}}{N};<br><br>$

where;

n=−

2, −

1, 0, 1, or 2; and

k=1, . . . ,M; and

wherein;

β

₀ is a projection angle of a center view;

k is a single detector row;

M is a number of detector rows;

n is a sub-region index; and

N is a helical pitch; and

weighting the equally sized sub-regions using a location dependent z-smoothing weighting function in accordance with;

f_1,k(γ

,β

−

β

_1,k)=α

(γ

)η

₁(β

)/[1+2α

(γ

)]f_2,k(γ

,β

−

β

_2,k)={[1−

α

(γ

)]η

₂(β

)+α

(γ

)}/[1+2α

(γ

)]f_3,k(γ

,β

−

β

_3,k)={1−

[1−

α

(γ

)]η

₂(β

)}/[1+2α

(γ

)]f_4,k(γ

,β

−

β

_4,k)=α

(γ

)[1−

η

₂(β

)]/[1+2α

(γ

)]

where;

β

is a projection angle;

β

_n,k is a sub-region boundary;

γ

is a fan angle;

$\begin{array}{c}\mathrm{\alpha <br><br>}<br><br>\left(\mathrm{\gamma <br><br>}\right)=\frac{<br><br>\mathrm{\gamma <br><br>}<br><br>+{\mathrm{\gamma <br><br>}}_b}{2<br><br>\left({\mathrm{\gamma <br><br>}}_m+{\mathrm{\gamma <br><br>}}_b\right)};<br><br>\\ {\mathrm{\eta <br><br>}}_n<br><br>\left(\mathrm{\beta <br><br>}\right)=\frac{\lfloor <br><br>\mathrm{\beta <br><br>}-\left({\mathrm{\beta <br><br>}}_{n,k}-\mathrm{\gamma <br><br>}\right)\rfloor <br><br><br><br>N}{\mathrm{\pi <br><br>}};<br><br>\end{array}$

γ

_b(0≦

γ

_b<

∞

) is a parameter to adjust the variation of the weighting function from the central channels to the boundary channels; and

γ

_m is the maximum detector angle in γ

.

8. A computer for weighting projection data acquired using a medical imaging system, wherein said imaging system comprises a radiation source and a detector, said computer programmed to:

select a region that includes a plurality of projection data samples;

divide the region into a plurality of equally sized sub-regions; and

weight the equally sized sub-regions using a location dependent z-smoothing weighting function.

9. A computer in accordance with claim 8 wherein to select a region that includes a plurality of projection data samples, said computer further programmed to select a region that includes a plurality of projection data samples that are within 2π

/N in projection angle β

on either side of a plane of reconstruction.

10. A computer in accordance with claim 8, said computer further programmed to define a boundary of the sub-regions in accordance with:

11. A computer in accordance with claim 8, said computer further programmed to select a weighting function that is an even function of a fan angle γ

parallel to the sub-regions and a summation of the weighting is unity.

12. A computer in accordance with claim 11 wherein to select a region that includes a plurality of projection data samples, said computer further programmed to select a weighting function in accordance with:

w_k(γ

,β

)=w_k(−

γ

,β

−

γ

) $\underset{n=1}{\overset{4}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f_{n,k}<br><br>\left(\mathrm{\gamma <br><br>},\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\beta <br><br>}+{\mathrm{\beta <br><br>}}_{n,k}-\mathrm{\gamma <br><br>}\right)=1<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>0\le <br><br>\mathrm{\Delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\beta <br><br>}<<br><br>\frac{\mathrm{\pi <br><br>}}{N}$

where;

γ

is a fan angle;

β

is a projection angle change;

n is an index for sub-regions; and

k is the index for detector rows.

13. A computer in accordance with claim 8 wherein to weight the equally sized sub-regions using a location dependent z-smoothing weighting function, said computer further programmed to weight the equally sized sub-regions using a location dependent z-smoothing weighting function in accordance with:

f_1,k(γ

,β

−

β

_1,k)=α

(γ

)η

₁(β

)/[1+2α

(γ

)]f_2,k(γ

,β

−

β

_2,k)={[1−

α

(γ

)]η

₂(β

)+α

(γ

)}/[1+2α

(γ

)]f_3,k(γ

,β

−

β

_3,k)={1−

[1−

α

(γ

)]η

₂(β

)}/[1+2α

(γ

)]f_4,k(γ

,β

−

β

_4,k)=α

(γ

)[1−

η

₂(β

)]/[1+2α

(γ

)]

where;

β

is a projection angle;

β

_n,k is a sub-region boundary;

γ

is a fan angle;

$\begin{array}{c}\mathrm{\alpha <br><br>}<br><br>\left(\mathrm{\gamma <br><br>}\right)=<br><br>\frac{\left|\mathrm{\gamma <br><br>}\right|+{\mathrm{\gamma <br><br>}}_b}{2<br><br>\left({\mathrm{\gamma <br><br>}}_m+{\mathrm{\gamma <br><br>}}_b\right)};<br><br>\\ {\mathrm{\eta <br><br>}}_n<br><br>\left(\mathrm{\beta <br><br>}\right)=<br><br>\frac{\left|\mathrm{\beta <br><br>}-\left({\mathrm{\beta <br><br>}}_{n,\text{\hspace{1em}<br><br>}<br><br>k}-\mathrm{\gamma <br><br>}\right)\right|N}{\mathrm{\pi <br><br>}};<br><br>\end{array}$

γ

_b(0≦

γ

_b<

∞

) is a parameter to adjust the variation of the weighting function from the central channels to the boundary channels; and

γ

_m is the maximum detector angle in γ

.

14. A computed tomographic (CT) imaging system for weighting projection data, said CT system comprising:

a radiation source;

a detector array; and

a computer coupled to said detector array and said radiation source and configured to;

select a region that includes a plurality of projection data samples;

divide the region into a plurality of equally sized sub-regions; and

weight the equally sized sub-regions using a location dependent z-smoothing weighting function.

19. A CT system in accordance with claim 14 wherein to weight the equally sized sub-regions using a location dependent z-smoothing weighting function, said computer further configured to weight the equally sized sub-regions using a location dependent z-smoothing weighting function in accordance with:

f_1,k(γ

,β

−

β

_1,k)=α

(γ

)η

₁(β

)/[1+2α

(γ

)]f_2,k(γ

,β

−

β

_2,k)={[1−

α

(γ

)]η

₂(β

)+α

(γ

)}/[1+2α

(γ

)]f_3,k(γ

,β

−

β

_3,k)={1−

[1−

α

(γ

)]η

₂(β

)}/[1+2α

(γ

)]f_4,k(γ

,β

−

β

_4,k)=α

(γ

)[1−

η

₂(β

)]/[1+2α

(γ

)]

where;

β

is a projection angle;

β

_n,k is a sub-region boundary;

γ

is a fan angle;

$\begin{array}{c}\mathrm{\alpha <br><br>}<br><br>\left(\mathrm{\gamma <br><br>}\right)=<br><br>\frac{\left|\mathrm{\gamma <br><br>}\right|+{\mathrm{\gamma <br><br>}}_b}{2<br><br>\left({\mathrm{\gamma <br><br>}}_m+{\mathrm{\gamma <br><br>}}_b\right)};<br><br>\\ {\mathrm{\eta <br><br>}}_n<br><br>\left(\mathrm{\beta <br><br>}\right)=<br><br>\frac{\left|\mathrm{\beta <br><br>}-\left({\mathrm{\beta <br><br>}}_{n,\text{\hspace{1em}<br><br>}<br><br>k}-\mathrm{\gamma <br><br>}\right)\right|N}{\mathrm{\pi <br><br>}};<br><br>\end{array}$

γ

_b(0≦

γ

_b<

∞

) is a parameter to adjust the variation of the weighting function from the central channels to the boundary channels; and

γ

_m is the maximum detector angle in γ

.

15. A CT system in accordance with 14, said computer further configured to select a region that includes a plurality of projection data samples that are within 2π

/N in projection angle β

on either side of a plane of reconstruction.

16. A CT system in accordance with 14, said computer further configured to define a boundary of the sub-regions in accordance with:

17. A CT system in accordance with 14, said computer further configured to select a weighting function that is an even function of a fan angle γ

parallel to the sub-regions and a summation of the weighting is unity.

18. A CT system in accordance with claim 17 wherein to select a region that includes a plurality of projection data samples, said computer further configured to select a weighting function in accordance with:

w_k(γ

,β

)=w_k(−

γ

,β

−

γ

) $\underset{n=1}{\overset{4}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>f_{n,\text{\hspace{1em}<br><br>}<br><br>k}<br><br>\left(\mathrm{\gamma <br><br>},\text{\hspace{1em}<br><br>}<br><br>\mathrm{\Delta <br><br>\beta <br><br>}+{\mathrm{\beta <br><br>}}_{n,\text{\hspace{1em}<br><br>}<br><br>k}-\mathrm{\gamma <br><br>}\right)=1<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{for}<br><br>\text{\hspace{1em}<br><br>}<br><br>0\le <br><br>\mathrm{\Delta <br><br>\beta <br><br>}<<br><br>\frac{\mathrm{\pi <br><br>}}{N}$

where;

γ

is a fan angle;

β

is a projection angle change;

n is an index for sub-regions; and

k is the index for detector rows.

20. A computed tomographic (CT) imaging system for weighting projection data, said CT system comprising:

a radiation source;

a detector array; and

a computer coupled to said detector array and said radiation source and configured to;

select a region that includes a plurality of projection data samples that are within 2π

/N in projection angle β

on either side of a plane of reconstruction;

divide the region into a plurality of equally sized sub-regions;

define a boundary of the sub-regions in accordance with;

${\mathrm{\beta <br><br>}}_{n,\text{\hspace{1em}<br><br>}<br><br>k}={\mathrm{\beta <br><br>}}_0+\frac{\left(2<br><br>k-M-1+n\right)<br><br>\mathrm{\pi <br><br>}}{N};<br><br>$

where;

n=−

2, −

1, 0, 1, and 2; and

k=1, . . . ,M; and

wherein;

β

₀ is a projection angle of a center view;

k is a single detector row;

M is a number of detector rows;

n is a sub-region index; and

N is a helical pitch; and

weight the equally sized sub-regions using a location dependent z-smoothing weighting function in accordance with;

f_1,k(γ

,β

−

β

_1,k)=α

(γ

)η

₁(β

)/[1+2α

(γ

)]f_2,k(γ

,β

−

β

_2,k)={[1−

α

(γ

)]η

₂(β

)+α

(γ

)}/[1+2α

(γ

)]f_3,k(γ

,β

−

β

_3,k)={1−

[1−

α

(γ

)]η

₂(β

)}/[1+2α

(γ

)]f_4,k(γ

,β

−

β

_4,k)=α

(γ

)[1−

η

₂(β

)]/[1+2α

(γ

)]

where;

β

is a projection angle;

β

_n,k is a sub-region boundary;

γ

is a fan angle;

$\begin{array}{c}\mathrm{\alpha <br><br>}<br><br>\left(\mathrm{\gamma <br><br>}\right)=<br><br>\frac{\left|\mathrm{\gamma <br><br>}\right|+{\mathrm{\gamma <br><br>}}_b}{2<br><br>\left({\mathrm{\gamma <br><br>}}_m+{\mathrm{\gamma <br><br>}}_b\right)};<br><br>\\ {\mathrm{\eta <br><br>}}_n<br><br>\left(\mathrm{\beta <br><br>}\right)=<br><br>\frac{\left|\mathrm{\beta <br><br>}-\left({\mathrm{\beta <br><br>}}_{n,\text{\hspace{1em}<br><br>}<br><br>k}-\mathrm{\gamma <br><br>}\right)\right|N}{\mathrm{\pi <br><br>}};<br><br>\end{array}$

γ

_b(0≦

γ

_b<

∞

) is a parameter to adjust the variation of the weighting function from the central channels to the boundary channels; and

γ

_m is the maximum detector angle in γ

.