Image reconstruction method and device for tilted helical scan
View Patent ↗Image reconstruction method and device for tilted helical scan are provided. The method includes: acquiring data generated by the tilted helical scan; calculating a ray channel parameter and a slice number corresponding to each pixel position based on a geometric relationship that a ray of the tilted helical scan emitting from a ray source to a detector intersects with a pixel; and performing image reconstruction by using a three-dimensional helical back-projection method based on the acquired data, and the ray channel parameter and the slice number corresponding to each pixel position. With the method and device, there is no need to correct the raw data, which ensures the accuracy of the data, and the artifact is avoided, which ensures the accuracy of the reconstructed image.
1. An image reconstruction method for tilted helical scan, comprising:
acquiring data generated by the tilted helical scan;
calculating a ray channel parameter and a slice number corresponding to each pixel position based on a geometric relationship that a ray of the tilted helical scan emitting from a ray source to a detector intersects with a pixel; and
performing image reconstruction by using a three-dimensional helical back-projection method based on the acquired data, and the ray channel parameter and the slice number corresponding to each pixel position.
2. The method according to claim 1 , wherein the calculating a ray channel parameter and a slice number corresponding to each pixel position based on a geometric relationship that a ray of the tilted helical scan emitting from a ray source to a detector intersects with a pixel comprises:
establishing a ray source parametric mathematical equation, a tilted detector parametric mathematical equation and a target tilted image parametric mathematical equation for a tilted scan system;
calculating a ray equation for a ray from the ray source to a certain pixel position by using the target tilted image parametric mathematical equation and the ray source parametric mathematical equation; and
solving the ray equation and the tilted detector parametric mathematical equation simultaneously for the ray channel parameter and the slice number, based on a geometric relationship that there is an intersection between the ray and the detector.
3. The method according to claim 1 , wherein the acquired data generated by the tilted helical scan is cone-beam data or wedge-beam data.
4. The method according to claim 1 , wherein in the case where the acquired data generated by the tilted helical scan is cone-beam data, the calculating a ray channel parameter and a slice number corresponding to each pixel position based on a geometric relationship that a ray of the tilted helical scan emitting from a ray source to a detector intersects with a pixel comprises:
based on a geometric relationship of the tilted helical scan, establishing a following ray source helical trajectory parametric equation:
S
(
θ
)
=
{
x
F
=
R
sin
θ
y
F
=
R
cos
θ
cos
φ
z
F
=
H
2
π
θ
+
R
cos
θ
sin
φ
,
establishing a following tilted detector parametric equation:
D
(
θ
,
γ
,
m
)
=
{
x
D
=
R
sin
θ
-
R
FD
sin
(
θ
-
γ
)
y
D
=
(
R
cos
θ
-
R
FD
cos
(
θ
-
γ
)
)
cos
φ
-
D
(
m
-
MidSlice
)
sin
φ
z
D
=
H
2
π
θ
+
(
R
cos
θ
-
R
FD
cos
(
θ
-
γ
)
)
sin
φ
+
D
(
m
-
MidSlice
)
cos
φ
,
establishing a following target tilted image parametric equation (for a point (h,v) on an image):
{
x
p
=
(
v
-
Mid
)
*
Δ
p
+
CenterX
y
p
=
(
(
Mid
-
h
)
*
Δ
p
+
CenterY
)
*
cos
φ
z
p
=
(
(
Mid
-
h
)
*
Δ
p
+
CenterY
)
*
sin
φ
+
Z
0
,
wherein θ denotes a projection angle; φ denotes a tilted angle of the detector; R denotes a rotation radius; H denotes an absolute pitch; Z 0 denotes an imaging position for a target image; P*P denotes an image matrix; FOV denotes a field of view for imaging; for the point (h,v) on the image,
Mid
=
P
-
1
2
,
and CenterX and CenterY denote a reconstruction center; Δp denotes width of a single pixel; MidSlice denotes a center slice and has a value of
M
-
1
2
,
wherein M is the total number of slices of two-dimensional detectors; γ denotes a channel angle; and m denotes the slice number;
establishing a following ray equation for a ray from the ray source to a certain pixel position by using the target tilted image parametric equation and the ray source helical trajectory parametric equation:
{
x
=
x
F
+
t
(
x
p
-
x
F
)
y
=
y
F
+
t
(
y
p
-
y
F
)
z
=
z
F
+
t
(
z
p
-
z
F
)
wherein t denotes an intermediate parameter for calculating; and
solving the ray equation and the tilted detector parametric equation for the channel angle, γ, and the slice number, m, based on a geometric relationship that there is an intersection between the ray equation and the tilted detector parametric equation.
5. The method according to claim 1 , wherein in the case where the acquired data generated by the tilted helical scan is wedge-beam data, the calculating a ray channel parameter and a slice number corresponding to each pixel position based on a geometric relationship that a ray of the tilted helical scan emitting from a ray source to a detector intersects with a pixel comprises:
based on a geometric relationship of the tilted helical scan, establishing a following ray source helical trajectory parametric equation:
S
(
θ
,
T
)
=
{
x
F
=
R
sin
(
θ
+
arc
sin
T
R
)
y
F
=
R
cos
(
θ
+
arc
sin
T
R
)
cos
φ
z
F
=
H
2
π
(
θ
+
arc
sin
T
R
)
+
R
cos
(
θ
+
arc
sin
T
R
)
sin
φ
,
establishing a following tilted detector parametric equation:
D
(
θ
,
γ
,
m
)
=
{
x
D
=
R
sin
(
θ
+
arc
sin
T
R
)
-
R
FD
sin
(
θ
)
y
D
=
(
R
cos
(
θ
+
arc
sin
T
R
)
-
R
FD
cos
(
θ
)
)
cos
φ
-
D
(
m
-
MidSlice
)
sin
φ
z
D
=
H
2
π
(
θ
+
arc
sin
T
R
)
+
(
R
cos
(
θ
+
arc
sin
T
R
)
-
R
FD
cos
(
θ
)
)
sin
φ
+
D
(
m
-
MidSlice
)
cos
φ
,
establishing a following target image parametric equation:
{
x
p
=
(
v
-
Mid
)
*
Δ
p
+
CenterX
y
p
=
(
(
Mid
-
h
)
*
Δ
p
+
CenterY
)
*
cos
φ
z
p
=
(
(
Mid
-
h
)
*
Δ
p
+
CenterY
)
*
sin
φ
+
Z
0
,
wherein θ denotes a projection angle; φ denotes a tilted angle of the detector; R denotes a rotation radius; H denotes an absolute pitch; Z 0 denotes an imaging position for a target image; P*P denotes an image matrix; FOV denotes a field of view for imaging; for a point (h,v) on an image,
Mid
=
P
-
1
2
,
and CenterX and CenterY denote a reconstruction center; Δp denotes width of a single pixel; MidSlice denotes a center slice and has a value of
M
-
1
2
,
wherein M is the total number of slices of two-dimensional detectors; T denotes a vertical distance between a central channel and a ray projected onto a center plane; and m denotes the slice number,
establishing a following ray equation for a ray from the ray source to a certain pixel position by using the target image parametric equation and the ray source helical trajectory parametric equation:
{
x
=
x
F
+
t
(
x
D
-
x
F
)
y
=
y
F
+
t
(
y
D
-
y
F
)
z
=
z
F
+
t
(
z
D
-
z
F
)
;
and
solving the ray equation and the tilted detector parametric equation for the channel distance, T, and the slice number, m, based on a geometric relationship that there is an intersection between the ray equation and the tilted detector parametric equation.
6. An image reconstruction device for tilted helical scan, comprising a hardware processor and a memory having processor-executable instructions stored therein, and the instructions when executed by the hardware processor, configure the device to:
acquire data generated by the tilted helical scan;
calculate a ray channel parameter and a slice number corresponding to each pixel position based on a geometric relationship that a ray of the tilted helical scan emitting from a ray source to a detector intersects with a pixel; and
perform image reconstruction by using a three-dimensional helical back-projection method based on the acquired data, and the ray channel parameter and the slice number corresponding to each pixel position.
7. The device according to claim 6 , wherein the device is further configured to:
establish a ray source parameter mathematical equation, a tilted detector parameter mathematical equation and a target tilted image parameter mathematical equation for a scan system;
calculate a ray equation for a ray from the ray source to a certain pixel position by using the target tilted image parameter mathematical equation and the ray source parameter mathematical equation; and
solve the ray equation and the tilted detector parameter mathematical equation simultaneously for the ray channel parameter and the slice number, based on a geometric relationship that there is an intersection between the ray and the detector.
8. The device according to claim 6 , wherein the data generated by the tilted helical scan is cone-beam data or wedge-beam data.
9. The device according to claim 6 , wherein in the case where the data generated by the tilted helical scan is cone-beam data, the device is further configured to:
based on a geometric relationship of the tilted helical scan, establish a following ray source helical trajectory parametric equation:
S
(
θ
)
=
{
x
F
=
R
sin
θ
y
F
=
R
cos
θ
cos
φ
z
F
=
H
2
π
θ
+
R
cos
θ
sin
φ
,
establish a following tilted detector parametric equation:
D
(
θ
,
γ
,
m
)
=
{
x
D
=
R
sin
θ
-
R
FD
sin
(
θ
-
γ
)
y
D
=
(
R
cos
θ
-
R
FD
cos
(
θ
-
γ
)
)
cos
φ
-
D
(
m
-
MidSlice
)
sin
φ
z
D
=
H
2
π
θ
+
(
R
cos
θ
-
R
FD
cos
(
θ
-
γ
)
)
sin
φ
+
D
(
m
-
MidSlice
)
cos
φ
,
establish a following target image parametric equation:
{
x
p
=
(
v
-
Mid
)
*
Δ
p
+
CenterX
y
p
=
(
(
Mid
-
h
)
*
Δ
p
+
CenterY
)
*
cos
φ
z
p
=
(
(
Mid
-
h
)
*
Δ
p
+
Center
Y
)
*
sin
φ
+
Z
0
,
wherein θ denotes a projection angle; φ denotes a tilted angle of the detector; R denotes a rotation radius; H denotes an absolute pitch; Z 0 denotes an imaging position for a target image; P*P denotes an image matrix; FOV denotes a field of view for imaging; for a point (h,v) on an image,
Mid
=
P
-
1
2
,
and CenterX and CenterY denote a reconstruction center; Δp denotes width of a single pixel; MidSlice denotes a center slice and has a value of
M
-
1
2
,
wherein M is the total number of slices of two-dimensional detectors; γ denotes a channel angle; and m denotes the slice number; and
establish a following ray equation for a ray from the ray source to a certain pixel position by using the target image parametric equation and the ray source helical trajectory parametric equation:
{
x
=
x
F
+
t
(
x
p
-
x
F
)
y
=
y
F
+
t
(
y
p
-
y
F
)
z
=
z
F
+
t
(
z
p
-
z
F
)
,
wherein t denotes an intermediate parameter for calculating; and
solve the ray equation and the tilted detector parametric equation for the channel angle, γ, and the slice number, m, based on a geometric relationship that there is an intersection between the ray equation and the tilted detector parametric equation.
10. The device according to claim 6 , wherein in the case where the data generated by the tilted helical scan is wedge-beam data, the device is further configured to:
based on a geometric relationship of the tilted helical scan, establish a following ray source helical trajectory parametric equation:
S
(
θ
,
T
)
=
{
x
F
=
R
sin
(
θ
+
arcsin
T
R
)
y
F
=
R
cos
(
θ
+
arcsin
T
R
)
cos
φ
z
F
=
H
2
π
(
θ
+
arcsin
T
R
)
+
R
cos
(
θ
+
arcsin
T
R
)
sin
φ
,
establish a following tilted detector parametric equation:
D
(
θ
,
γ
,
m
)
=
{
x
D
=
R
sin
(
θ
+
arcsin
T
R
)
-
R
FD
sin
(
θ
)
y
D
=
(
R
cos
(
θ
+
arcsin
T
R
)
-
R
FD
cos
(
θ
)
)
cos
φ
-
D
(
m
-
MidSlice
)
sin
φ
z
D
=
H
2
π
(
θ
+
arcsin
T
R
)
+
(
R
cos
(
θ
+
arcsin
T
R
)
-
R
FD
cos
(
θ
)
)
sin
φ
+
D
(
m
-
MidSlice
)
cos
φ
,
establish a following target image parametric equation:
{
x
p
=
(
v
-
Mid
)
*
Δ
p
+
CenterX
y
p
=
(
(
Mid
-
h
)
*
Δ
p
+
CenterY
)
*
cos
φ
z
p
=
(
(
Mid
-
h
)
*
Δ
p
+
CenterY
)
*
sin
φ
+
Z
0
,
wherein, θ denotes a projection angle; φ denotes a tilted angle of the detector; R denotes a rotation radius; H denotes an absolute pitch; Z 0 denotes an imaging position for a target image; P*P denotes an image matrix; FOV denotes a field of view for imaging; for a point (h,v) on an image,
Mid
=
P
-
1
2
,
and CenterX and CenterY denote a reconstruction center; Δp denotes width of a single pixel; MidSlice denotes a center slice and has a value of
M
-
1
2
,
wherein M is the total number of slices of two-dimensional detectors; T denotes a vertical distance between a central channel and a ray projected onto a center plane; and m denotes the slice number; and
establish a following ray equation for a ray from the ray source to a certain pixel position by using the target image parametric equation and the ray source helical trajectory parametric equation:
{
x
=
x
F
+
t
(
x
D
-
x
F
)
y
=
y
F
+
t
(
y
D
-
y
F
)
z
=
z
F
+
t
(
z
D
-
z
F
)
;
and
solve the ray equation and the tilted detector parametric equation for the channel distance, T, and the slice number, m, based on a geometric relationship that there is an intersection between the ray equation and the tilted detector parametric equation.