Combination weight applied to iterative reconstruction in image reconstruction
View Patent ↗The image generation method and system generates an image using a predetermined iterative reconstruction technique, and an instance of the iteration process is weighted according to a predetermined combination of weights during the reconstruction. The predetermined combination of the weights includes weights based upon a predetermined noise model and a predetermined window function to improve image quality.
1. A method of generating an image, comprising the steps of:
a) generating a combination weight value for measured projection data at each of measured projections based upon at least a predetermined noise model and a predetermined window function; and
b) applying the combination weight values using the measured projection data in one of predetermined iterative reconstruction techniques while an image is being iteratively reconstructed, wherein the predetermined noise model is defined by V=(g I+Ve/I)/I, where the I is a measured signal while Ve and g are respectively the electronic noise variance and the detector gain that is function of channels, segments, a data acquisition system and or collimation.
2. The method of generating an image according to claim 1 wherein the predetermined window function is defined by a smooth PI weighting function w:
w
(
γ
,
v
)
=
{
0
,
v
≤
v
PI
-
-
Δ
v
1
1
2
+
v
-
v
PI
-
2
Δ
v
1
,
v
PI
-
-
Δ
v
1
<
v
<
v
PI
-
+
Δ
v
1
1
,
v
PI
-
+
Δ
v
1
≤
v
≤
v
PI
+
-
Δ
v
2
1
2
-
v
-
v
PI
+
2
Δ
v
2
v
PI
+
-
Δ
v
2
<
v
<
v
PI
+
+
Δ
v
2
0
,
v
≥
v
PI
+
+
Δ
v
2
where (γ, v) are the detector coordinates, γ being a fan angle while v being a vertical coordinate,
v
PI
+
=
H
4
π
(
π
-
2
γ
)
cos
γ
·
v
PI
-
=
H
4
π
(
-
π
-
2
γ
)
cos
γ
=
-
H
4
π
(
π
+
2
γ
)
cos
γ
,
γ
=
-
(
ch
-
Cch
)
×
d
γ
,
d
γ
=
FanAngle
180
π
Nch
,
FanAngle
=
49.2
°
.
Δ
v
1
=
c
×
(
W
+
v
PI
-
)
,
Δ
v
2
=
c
×
(
W
-
v
PI
+
)
,
and c is a smoothing coefficient having a range of 0≦c≦1.
3. The method of generating an image according to claim 1 wherein the predetermined iterative reconstruction techniques include algebraic reconstruction technique (ART) type algorithms, simultaneous algebraic reconstruction technique (SART) type algorithms, ordered-subset simultaneous algebraic reconstruction technique (OS-SART) type algorithms, simultaneous iterative reconstruction technique (SIRT) type algorithms, expectation maximization (EM) type algorithms and penalized least square type algorithms (PLS).
4. The method of generating an image according to claim 1 wherein the predetermined iterative reconstruction technique is ordered subset simultaneous algebraic reconstruction technique (OS-SART), which is weighted by the combination weight value as denoted by d i for ith measured projection of the measured projection data as:
x
j
(
n
+
1
)
=
x
j
(
n
)
+
λ
n
(
∑
i
a
i
,
j
(
d
i
(
b
i
-
∑
k
a
i
,
k
x
k
(
n
)
)
∑
k
a
i
,
k
)
∑
i
a
i
,
j
d
i
)
where x j n+1) is an updated image from an old image x j (n) , λ n is a relaxation factor, a i,j is an element of the system matrix, and b i is after-log data of the measured projection data at an ith detector bin.
5. The method of generating an image according to claim 4 wherein the combination weight value d i is defined by
d
i
=
w
i
V
i
where w i the predetermined window function V i is the predetermined noise model.
6. The method of generating an image according to claim 1 further comprising an additional step of performing image regularization.
7. A system for generating an image, comprising:
a noise reduction device for generating a combination weight value for measured projection data at each of measured projections based upon a combination of a predetermined noise model and a predetermined window function; and
a reconstruction device connected to said noise reduction device for applying the combination weight values using the measured projection data in one of predetermined iterative reconstruction techniques while an image is being iteratively reconstructed, wherein the predetermined noise model is defined by V=(g I+Ve/I)/I, where the I is a measured signal while Ve and g are respectively the electronic noise variance and the detector gain that is function of channels, segments, a data acquisition system and or collimation.
8. The system for generating an image according to claim 7 wherein the predetermined window function is defined by a smooth PI weighting function w:
w
(
γ
,
v
)
=
{
0
,
v
≤
v
PI
-
-
Δ
v
1
1
2
+
v
-
v
PI
-
2
Δ
v
1
,
v
PI
-
-
Δ
v
1
<
v
<
v
PI
-
+
Δ
v
1
1
,
v
PI
-
+
Δ
v
1
≤
v
≤
v
PI
+
-
Δ
v
2
1
2
-
v
-
v
PI
+
2
Δ
v
2
v
PI
+
-
Δ
v
2
<
v
<
v
PI
+
+
Δ
v
2
0
,
v
≥
v
PI
+
+
Δ
v
2
where (γ, v) are the detector coordinates, γ being a fan angle while v being a vertical coordinate,
v
PI
+
=
H
4
π
(
π
-
2
γ
)
cos
γ
·
v
PI
-
=
H
4
π
(
-
π
-
2
γ
)
cos
γ
=
-
H
4
π
(
π
+
2
γ
)
cos
γ
,
γ
=
-
(
ch
-
Cch
)
×
d
γ
,
d
γ
=
FanAngle
180
π
Nch
,
FanAngle
=
49.2
°
.
Δ
v
1
=
c
×
(
W
+
v
PI
-
)
,
Δ
v
2
=
c
×
(
W
-
v
PI
+
)
,
and c is a smoothing coefficient having a range of 0≦c≦1.
9. The system for generating an image according to claim 7 wherein the predetermined iterative reconstruction techniques include algebraic reconstruction technique (ART) type algorithms, simultaneous algebraic reconstruction technique (SART) type algorithms, ordered-subset simultaneous algebraic reconstruction technique (OS-SART) type algorithms, simultaneous iterative reconstruction technique (SIRT) type algorithms, expectation maximization (EM) type algorithms and penalized least square type algorithms (PLS).
10. The system for generating an image according to claim 7 wherein the predetermined iterative reconstruction technique is ordered subset simultaneous algebraic reconstruction technique (OS-SART), which is weighted by the combination weight value as denoted by d i for ith measured projection of the measured projection data as:
x
j
(
n
+
1
)
=
x
j
(
n
)
+
λ
n
(
∑
i
a
i
,
j
(
d
i
(
b
i
-
∑
k
a
i
,
k
x
k
(
n
)
)
∑
k
a
i
,
k
)
∑
i
a
i
,
j
d
i
)
where x j (n+1) is an updated image from an old image x j (n) , λ n is a relaxation factor, a i,j is an element of the system matrix, and b i is after-log data of the measured projection data at an ith detector bin.
11. The system for generating an image according to claim 10 wherein the combination weight value d i is defined by
d
i
=
w
i
V
i
where w i the predetermined window function V i is the predetermined noise model.
12. The system for generating an image according to claim 1 further comprising an additional step of performing image regularization.