Motion weighting in computed tomography (CT) with cone angle
View Patent ↗Embodiments and processes of computer tomography perform tasks associated with weighting projection data based upon at least one motion index such as electrocardiogram gated reconstruction, view-based motion map and ray-based motion map. Other embodiments and processes of computer tomography perform tasks associated with weighting projection data based upon at least one motion index and another index that is associated with certain geometric characteristics of a cone beam.
1. A method of weighting projection data in a computed tomography (CT) system, comprising the steps of:
acquiring projection data using a cone beam along a circular trajectory in the CT system;
determining a weight value according to a normalized electrocardiogram gated reconstruction (EGR) weighting function, w EGR (β,γ) based upon an EGR weighting function u EGR (φ(β)) at a cardiac phase φ and a view angle β, said u EGR (φ(β)) being normalized by a summation of u EGR (φ(β n C )) from n=−N PI to n=N PI for complementary view angles (β n C ) during the cardiac phase φ, wherein said determining step determines said weight value according to a FB+EGR weighting function w FB+EGR (β,γ) based upon said u EGR (φ(β)) and a fan beam (FB) weighting function u FB (β) at the view angle β, a product of said u EGR (φ(β)) and said u FB (β) being normalized by the summation of a product of u FB (β n C ,γ n C ) and u EGR (φ(β n C )) from n=−N PI to n=N PI for the complementary view angles (α n C ) and complementary fan angles (γ n C ); and
weighting each of the projection data by said weight value as determined by said w EGR (β,γ) for the CT system, where γ is a fan angle of the cone beam.
2. The method of weighting projection data according to claim 1 wherein said u EGR (φ(β)) is defined as
exp
(
-
(
φ
(
β
)
-
φ
0
)
2
σ
EGR
2
)
,
where a slice is reconstructed at a phase φ 0 while σ EGR is a predetermined empirical parameter.
3. The method of weighting projection data according to claim 1 wherein said u FB (β) is defined as:
u
FB
(
β
)
=
{
0
,
β
<
β
start
p
(
β
-
β
start
Δβ
)
,
β
start
≤
β
<
β
start
+
Δβ
1
,
β
start
+
Δβ
≤
β
≤
β
end
-
Δβ
p
(
β
end
-
β
Δβ
)
,
β
end
-
Δβ
<
β
≤
β
end
0
,
β
>
β
end
where Δβ is a predetermined smoothing interval, β start and β end are respectively a start and an end of an image reconstruction view range.
4. The method of weighting projection data according to claim 3 wherein said function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
5. The method of weighting projection data according to claim 1 wherein said determining step determines said weight value according to a FB+EGR+vMMAP weighting function w FB+EGR+vMMAP (β,γ) based upon said u EGR (φ(β)) said u FB (β) and a view-based motion map (vMMAP) weighting function u vMMAP (β) at the view angle β, a product of said u EGR (φ(β)), said u FB (β, v) and said u vMMAP (β) being normalized by the summation of a product of said u FB (β n C ,γ n C ), said u EGR (φ(β n C )) and a u vMMAP (β n C ) from n=−N PI to n=N PI or the complementary view angles (β n C ) and the complementary fan angles (γ n C ).
6. The method of weighting projection data according to claim 5 wherein said u vMMAP (β) is defined as
p
(
maxMmap
-
MMAP
(
β
)
maxMmap
-
minMmap
)
,
where
vMMAP
(
β
)
=
∑
ch
abs
(
diff
[
ch
,
β
]
)
,
ch is a channel, maxMmap=max(MMAP(β)), minMmap=min(MMAP(β)), p( ) is generally a function that satisfies the following conditions: p( 0 )=0, p( 1 )=1, and p(x) also monotonically increases from 0 to 1 as the variable x increases.
7. The method of weighting projection data according to claim 1 wherein said weighting step takes place before backprojection.
8. A method of weighting projection data in a computed tomography (CT) system, comprising the steps of:
acquiring projection data using a cone beam along a circular trajectory in the CT system;
determining a weight value according to a normalized view-based motion map (vMMAP) weighting function w vMMAP (β,γ) at a view angle β, a vMMAP weighting function u vMMAP (β) being normalized by a summation of u vMMAP (β n C ) from n=−N PI to n=N PI for complementary view angles (β n C ), wherein said determining step determines said weight value according to a FB+vMMAP weighting function w FB+vMMAP (β,γ) based upon said u vMMAP (β) and a fan beam (FB) weighting function u FB (β) at the view angle β, a product of said u vMMAP (β) and said u FB (β) being normalized by the summation of a product of u FB (β n C ,γ n C ) and u vMMAP (β n C ) from n=−N PI to n=N PI for the complementary view angles (β n C ) and complementary fan angles (γ n C ); and
weighting each of the projection data by said weight value as determined by said w vMMAP (β,γ) for the CT system, where γ is a fan angle of the cone beam.
9. The method of weighting projection data according to claim 8 wherein said u vMMAP (β) is defined as
p
(
maxMmap
-
MMAP
(
β
)
maxMmap
-
minMmap
)
,
where
vMMAP
(
β
)
=
∑
ch
abs
(
diff
[
ch
,
β
]
)
,
ch is a channel, maxMmap=max(MMAP(β)), minMmap=min(MMAP(β)), p( ) is generally a function that satisfies the following conditions: p( 0 )=0, p( 1 )=1, and p(x) also monotonically increases from 0 to 1 as the variable x increases.
10. The method of weighting projection data according to claim 8 wherein said u FB (β) is defined as:
u
FB
(
β
)
=
{
0
,
β
<
β
start
p
(
β
-
β
start
Δβ
)
,
β
start
≤
β
<
β
start
+
Δβ
1
,
β
start
+
Δβ
≤
β
≤
β
end
-
Δβ
p
(
β
end
-
β
Δβ
)
,
β
end
-
Δβ
<
β
≤
β
end
0
,
β
>
β
end
where Δβ is a predetermined smoothing interval, β start and β end are respectively a start and an end of an image reconstruction view range.
11. The method of weighting projection data according to claim 10 wherein said function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
12. The method of weighting projection data according to claim 8 wherein said weighting step takes place before backprojection.
13. A method of weighting projection data in a computed tomography (CT) system, comprising the steps of:
acquiring projection data using a cone beam along a circular trajectory in the CT system;
determining a weight value according to a normalized ray-based motion map (rMMAP) weighting function w rMMAP (β,γ) at a view angle β and a fan angle γ, a rMMAP weighting function u rMMAP (β,γ) being normalized by a summation of u rMMAP (β n C ,γ n C ) from n=−N PI to n=N PI for complementary view and fan angles (β n C ,γ n C ); and
weighting each of the projection data by said weight value as determined by said w rMMAP (β,γ) for the CT system.
14. The method of weighting projection data according to claim 13 wherein said u rMMAP (β,γ) is assigned a weight value of 1 if a view is the closest to an image plane, while other views are each assigned a value that is determined by an amount of motion between two complementary rays AB and BA, the amount of motion being defined by m(AB)=f(|g(BA)−g(AB)|), where g(.) is measured raw while f(.) is a predetermined function such that f( 0 )=1 and f(t)→0 as t increases.
15. The method of weighting projection data according to claim 13 wherein said determining step determines said weight value according to a FB+rMMAP weighting function w FB+rMMAP (β,γ) based upon said u rMMAP (β,γ) and a fan beam (FB) weighting function u FB (β), a product of said u rMMAP (β,γ) and said u FB (β) being normalized by the summation of a product of u FB (β n C ,γ n C ) and u rMMAP (γ n C ,γ n C ) from n=−N PI to n=N PI for the complementary view angles (β n C ) and complementary fan angles (γ n C ).
16. The method of weighting projection data according to claim 15 wherein said u FB (β) is defined as:
u
FB
(
β
)
=
{
0
,
β
<
β
start
p
(
β
-
β
start
Δβ
)
,
β
start
≤
β
<
β
start
+
Δβ
1
,
β
start
+
Δβ
≤
β
≤
β
end
-
Δβ
p
(
β
end
-
β
Δβ
)
,
β
end
-
Δβ
<
β
≤
β
end
0
,
β
>
β
end
where Δβ is a predetermined smoothing interval, β start and β end are respectively a start and an end of an image reconstruction view range.
17. The method of weighting projection data according to claim 16 wherein said function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
18. The method of weighting projection data according to claim 15 wherein said determining step determines said weight value according to a FB+EGR+rMMAP weighting function w FB+EGR+rMMAP (β,γ) based upon an electrocardiogram gated reconstruction (EGR) u EGR (φ(β)), said u FB (β) and said u rMMAP (β,γ), a product of said u FB (β,v), said u EGR (φ(β)) and said u rMMAP (β,γ) being normalized by a summation of a product of said u FB (β n C ,γ n C ), said u rMMAP (β n C ,γ n C ) and a u EGR (φ(β n C )) from n=−N PI to n=N PI for the complementary view angles (β n C ) and the complementary fan angles (γ n C ).
19. The method of weighting projection data according to claim 13 wherein said weighting step takes place before backprojection.
20. A method of weighting projection data in a computed tomography (CT) system, comprising the steps of:
acquiring projection data using a cone beam along a helical trajectory in the CT system;
determining a weight value according to a normalized cone beam and electrocardiogram gated reconstruction (CBW+EGR) weighting function w CBW+EGR (β,γ,v) based upon an EGR weighting function u EGR (φ(β)) and a cone beam weighting function, u CBW (β,v) at a view angle β, a cardiac phase φ, a fan angle γ and a vertical coordinate v, said u EGR (φ(β)) and said u CBW (β,v) being normalized by a summation of u EGR (φ(β n C )) and u CBW (β n C ,γ n C ,v n C ) from n=−N PI to n=N PI for complementary view and fan angles and complementary vertical coordinate (β n C ,γ n C ,v n C ), wherein said u CBW (β, v) is defined by a product of u FB (β,γ) and u CB (v) where said u FB is a fan beam; and
weighting each of the projection data by said weight value as determined by said w CBW+EGR (β,γ,v) for the CT system.
21. The method of weighting projection data according to claim 20 wherein said u EGR (φ(β)) is defined as
exp
(
-
(
φ
(
β
)
-
φ
0
)
2
σ
EGR
2
)
,
where a slice is reconstructed at a phase φ 0 while σ EGR is a predetermined empirical parameter.
22. The method of weighting projection data according to claim 20 wherein said u FB (β) is defined as:
u
FB
(
β
)
=
{
0
,
β
<
β
start
p
(
β
-
β
start
Δβ
)
,
β
start
≤
β
<
β
start
+
Δβ
1
,
β
start
+
Δβ
≤
β
≤
β
end
-
Δβ
p
(
β
end
-
β
Δβ
)
,
β
end
-
Δβ
<
β
≤
β
end
0
,
β
>
β
end
where Δβ is a predetermined smoothing interval, β start and β end are respectively a start and an end of an image reconstruction view range.
23. The method of weighting projection data according to claim 20 wherein said function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
24. The method of weighting projection data according to claim 20 wherein said u CB (v), is defined as:
u
CB
(
v
)
=
{
0
,
v
≤
-
W
p
(
W
+
v
Δ
v
)
,
-
W
<
v
<
-
W
+
Δ
v
1
,
-
W
+
Δ
v
≤
v
≤
W
-
Δ
v
p
(
W
-
v
Δ
v
)
W
-
Δ
v
<
v
<
W
0
,
v
≥
W
Where the function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
25. The method of weighting projection data according to claim 20 wherein said determining step determines said weight value according to a CBW+EGR+vMMAP weighting function w CBW+vMMAP+EGR (β,γ,v) based upon said u EGR (φ(β)), said u CBW (β,v) and a view-based motion map (vMMAP) weighting function u vMMAP (β) at the view angle β, a product of said u EGR (φ(β)), said u CBW (β,v) and said u vMMAP (β) being normalized by the summation of a product of said u CBW (β n C ,γ n C ,v n C ), said u EGR (φ(β n C )) and said u vMMAP (β n C ) from n=−N PI to n=N PI for the complementary view and fan angles and the complementary vertical coordinate (β n C ,γ n C ,v n C ).
26. The method of weighting projection data according to claim 25 wherein said u vMMAP (β) is defined as
P
(
maxMmap
-
MMAP
(
β
)
maxMmap
-
minMmap
)
,
where
vMMAP
(
β
)
=
∑
ch
abs
(
diff
[
ch
,
β
]
)
,
ch is a channel, maxMmap=max(MMAP(β)), minMmap=min(MMAP(β)), p( ) is generally a function that satisfies the following conditions: p( 0 )=0, p( 1 )=1, and p(x) also monotonically increases from 0 to 1 as the variable x increases.
27. The method of weighting projection data according to claim 20 wherein said weighting-step takes place before backprojection.
28. A method of weighting projection data in a computed tomography (CT) system, comprising the steps of:
acquiring projection data using a cone beam along a helical trajectory in the CT system;
determining a weight value according to a normalized cone beam and view-based motion map (CBW+vMMAP) weighting function w CBW+vMMAP (β,γ,v) based upon a vMMAP weighting function u vMMAP (β) and a cone beam weighting function u CBW (β,v) at a view angle β, a fan angle γ and a vertical coordinate v, said u vMMAP (β) and said u CBW (β,v) being normalized by a summation of u vMMAP (β n C ) and u CBW (β n C ,γ n C ,v n C ) from n=−N PI to n=N PI for complementary view and fan angles and complementary vertical coordinate (β n C ,γ n C ,v n C ), wherein said u CBW (β,v) is defined by a product of u FB (β,γ) and u CB (v) where said u FB is a fan beam; and
weighting each of the projection data by said weight value as determined by said w CBW+vMMAP (β,γ,v) for the CT system.
29. The method of weighting projection data according to claim 28 wherein said u FB (β) is defined as:
u
FB
(
β
)
=
{
0
,
β
<
β
start
p
(
β
-
β
start
Δβ
)
,
β
start
≤
β
<
β
start
+
Δβ
1
,
β
start
+
Δβ
≤
β
≤
β
end
-
Δβ
p
(
β
end
-
β
Δβ
)
β
end
-
Δβ
<
β
≤
β
end
0
,
β
>
β
end
where Δβ is a predetermined smoothing interval, β start and β end are respectively a start and an end of an image reconstruction view range.
30. The method of weighting projection data according to claim 29 wherein said function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
31. The method of weighting projection data according to claim 28 wherein said u CB (v) is defined as:
u
CB
(
v
)
=
{
0
,
v
≤
-
W
p
(
W
+
v
Δ
v
)
,
-
W
<
v
<
-
W
+
Δ
v
1
,
-
W
+
Δ
v
≤
v
≤
W
-
Δ
v
p
(
W
-
v
Δ
v
)
W
-
Δ
v
<
v
<
W
0
,
v
≥
W
where the function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
32. The method of weighting projection data according to claim 28 wherein said u vMMAP (β) is defined as
P
(
maxMmap
-
MMAP
(
β
)
maxMmap
-
minMmap
)
,
where
vMMAP
(
β
)
=
∑
ch
abs
(
diff
[
ch
,
β
]
)
,
ch is a channel, maxMmap=max(MMAP(β)), minMmap=min(MMAP(β)), p( ) is generally a function that satisfies the following conditions: p( 0 )=0, p( 1 )=1, and p(x) also monotonically increases from 0 to 1 as the variable x increases.
33. The method of weighting projection data according to claim 28 wherein said weighting step takes place before backprojection.
34. A method of weighting projection data in a computed tomography (CT) system, comprising the steps of:
acquiring projection data using a cone beam along a helical trajectory in the CT system;
determining a weight value according to a normalized cone beam and ray-based motion map (CBW+rMMAP) weighting function w CBW+rMMAP (β,γ,v) based upon a rMMAP weighting function u rMMAP (β,γ) and a cone beam weighting function u CBW (β,v) at a view angle β, a fan angle γ and a vertical coordinate v, said u rMMAP (β,γ) and said u CBW (β,v) being normalized by a summation of u rMMAP (β n C ,γ n C ) and u CBW (β n C ,γ n C ,v n C ) from n=−N PI to n=N PI for complementary view and fan angles and complementary vertical coordinate (β n C ,γ n C ,v n C ), wherein said u CBW (β,v) is defined by a product of u FB (β,γ) and u CB (v) where said u FB is a fan beam; and
weighting each of the projection data by said weight value as determined by said w CBW+rMMAP (β,γ,v) for the CT system.
35. The method of weighting projection data according to claim 34 wherein said u FB (β) is defined as:
u
FB
(
β
)
=
{
0
,
β
<
β
start
p
(
β
-
β
start
Δβ
)
,
β
start
≤
β
<
β
start
+
Δβ
1
,
β
start
+
Δβ
≤
β
≤
β
end
-
Δβ
p
(
β
end
-
β
Δβ
)
β
end
-
Δβ
<
β
≤
β
end
0
,
β
>
β
end
where Δβ is a predetermined smoothing interval, β start and β end are respectively a start and an end of an image reconstruction view range.
36. The method of weighting projection data according to claim 35 wherein said function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
37. The method of weighting projection data according to claim 34 wherein said u CB (v), is defined as:
u
CB
(
v
)
=
{
0
,
v
≤
-
W
p
(
W
+
v
Δ
v
)
,
-
W
<
v
<
-
W
+
Δ
v
1
,
-
W
+
Δ
v
≤
v
≤
W
-
Δ
v
p
(
W
-
v
Δ
v
)
W
-
Δ
v
<
v
<
W
0
,
v
≥
W
where the function p( ) includes
p
(
x
)
=
x
,
p
(
x
)
=
3
x
2
-
2
x
3
,
p
(
x
)
=
1
2
(
1
-
cos
(
π
x
)
)
and
p
(
x
)
=
sin
2
(
π
x
2
)
.
38. The method of weighting projection data according to claim 34 wherein said u rMMAP (β,γ) is assigned a weight value of 1 if a view is the closest to an image plane, while other views are each assigned a value that is determined by an amount of motion between two complementary rays AB and BA, the amount of motion being defined by m(AB)=f(|g(BA)−g(AB)|), where g(.) is measured raw while f(.) is a predetermined function such that f( 0 )=1 and f(t)→0 as t increases.
39. The method of weighting projection data according to claim 34 wherein said determining step determines said weight value according to a CBW+EGR+rMMAP weighting function w CBW+EGR+rMMAP (β,γ,v) based upon an electrocardiogram gated reconstruction (EGR) u EGR (φ(β)), said u CBW (β,v) and said u rMMAP (β,γ), a product of said u CBW (β,v), said u EGR (φ(β)) and said u CBW (β,γ) being normalized by a summation of a product of said u CBW (β n C ,γ n C ,v n C ), said u rMMAP (β n C ,γ n C ), and a u EGR (φ(β n C )) from n=−N PI to n=N PI for the complementary view and fan angles and the complementary vertical coordinate (β n C ,γ n C ,v n C ).
40. The method of weighting projection data according to claim 34 wherein said weighting step takes place before backprojection.