Restoring CT scan data
View Patent ↗A method for restoring CT scan data is disclosed. The method may comprise: building a data collecting model with respect to a specific direction of a detector based a response curve of the detector. In some examples, the specific direction can indicate a channel direction and a slice direction of the detector. During a CT scanning, based on the data collecting model, X-ray intensity values detected by the detectors in the specific direction can be acquired. A function can be determined such that it satisfies the data collecting model, a continuity condition and a boundary condition, An X-ray intensity value can be obtained by substituting the coordinate value of a point in the specific direction into the function.
1. A method for restoring CT scan data, the method comprises:
building a data collecting model with respect to a specific direction of a detector based on a response curve of the detector, wherein the specific direction indicates a channel direction and/or a slice direction of the detector;
acquiring, based on the data collecting model, X-ray intensity values detected by the detector in the specific direction during a CT scanning;
determining a function which satisfies a relationship of the data collecting model with respect to the acquired X-ray intensity values in the specific direction, a continuity condition and a boundary condition; and
calculating an X-ray intensity value of a point in the specific direction by substituting a coordinate value of the point into the function.
2. The method of claim 1 , wherein the data collecting model is a data collecting model with respect to a channel direction of the detector and is defined by the following equation:
y
ij
=
∫
x
=
x
i
x
=
x
i
+
1
K
ij
(
x
)
A
ij
(
x
)
d
x
;
wherein, x represents the coordinate value in a channel direction of the detector,
i represents a channel index and is an integer ranging from 1 to a maximum value of N,
j represents a slice index and is an integer ranging from 1 to a maximum value of M,
y ij represents an X-ray intensity value detected by the detector at the j th slice and the i th channel,
K ij (x) represents a response curve in a channel direction of the detector at the j th slice and the i th channel,
A ij (x) represents a real X-ray intensity value in a channel direction of the detector at the j th slice and the i th channel,
x i represents a minimum coordinate value in a channel direction of the detector at the i th channel, and
x i+1 represents a minimum coordinate value in a channel direction of the detector at the (i+1) th channel.
3. The method of claim 1 , wherein the data collecting model is a data collecting model with respect to the slice direction of the detector and is defined by the following equation:
y
ij
=
∫
z
=
z
j
z
=
z
j
+
1
K
ij
(
z
)
A
ij
(
z
)
d
z
;
wherein, z represents a coordinate value in a slice direction of the detector,
i represents a channel index and is an integer ranging from 1 to a maximum value of N,
j represents a slice index and is an integer ranging from 1 to a maximum value of M,
y ij represents an X-ray intensity value detected by the detector in at j th slice and the i th channel,
K ij (z)represents a response curve in a slice direction of the detector at the j th slice and the i th channel,
A ij (z) represents a real X-ray intensity value in a slice direction of the detector at the j th slice and the i th channel,
z j represents a minimum coordinate value in a slice direction of the detectors at the j th slice, and
z j+1 represents a minimum coordinate value in a slice direction of the detectors at the (j+1) th slice.
4. The method of claim 1 , wherein, the data collecting model is a data collecting model with respect to a channel direction and the slice direction of the detector and is defined by the following equation:
y
ij
=
∫
x
=
x
i
x
=
x
i
+
1
∫
z
=
z
j
z
=
z
j
+
1
K
ij
(
x
,
z
)
A
ij
(
x
,
z
)
d
x
d
z
;
wherein, x represents a coordinate value in a channel direction of the detector,
z represents a coordinate value in a slice direction of the detector,
i represents a channel index and is an integer ranging from 1 to the maximum value of N,
j represents a slice index and is an integer ranging from 1 to the maximum value of M,
y ij represents an X-ray intensity value detected by the detector at the j th slice and the i th channel,
K ij (x, z) represents a response curve in a channel direction and a slice direction of the detector at the j th slice and the i th channel,
A ij (x, z) represents an real X-ray intensity value in a channel direction and a slice direction of the detector at the j th slice and the i th channel,
x i represents a minimum coordinate value in a channel direction of the detectors at the i th channel,
x i+1 represents a minimum coordinate value in a channel direction of the detectors at the (i+1) th channel,
z j represents a minimum coordinate value in a slice direction of the detectors at the j th slice, and
z j+1 represents a minimum coordinate value in a slice direction of the detectors at the (j+1) th slice.
5. The method of claim 2 , wherein, said determining the function which satisfies the data collecting model, the continuity condition and the boundary condition includes:
constructing an equation set as follows:
continuity condition: P ij (x i+1 )=P (i+1)j (x i+1 );
boundary condition:
P
1
j
(
x
1
)
=
y
1
j
x
2
-
x
1
;
a relationship of the acquired X-ray intensity values in the channel direction with respect to the data collecting model:
∫
x
=
x
i
x
=
x
i
+
1
K
ij
(
x
)
P
ij
(
x
)
d
x
=
y
ij
;
and
determining a function P ij (x) which satisfies above conditions by solving the above equation set.
6. The method of claim 3 , wherein, said determining the function which satisfies the data collecting model, the continuity condition and the boundary condition includes:
constructing an equation set as follows:
continuity condition: P ij (z j+1 )=P i(j+1) (z j+1 );
boundary condition:
P
i
1
(
z
1
)
=
y
i
1
z
2
-
z
1
;
a relationship of the acquired X-ray intensity values in the slice direction with respect to the data collecting model:
∫
z
=
z
j
z
=
z
j
+
1
K
ij
(
z
)
P
ij
(
z
)
d
z
=
y
ij
;
and
determining a function P ij (z) which satisfies above conditions by solving the above equation set.
7. The method of claim 4 , wherein, said determining the function which satisfies the data collecting model, the continuity condition and the boundary condition includes:
constructing an equation set as follows:
continuity condition: P ij (x i+1 , z j )=P (i+1)j (x i+1 , z j );
P ij (x i , z j+1 )=P i(j+1) (x i , z j+1 );
boundary condition:
P
1
j
(
x
1
,
z
j
)
=
y
1
j
x
2
-
x
1
;
P
i
1
(
x
i
,
z
1
)
=
y
i
1
z
2
-
z
1
;
a relationship of the acquired X-ray intensity values in the channel direction and the slice direction with respect to the data collecting model:
∫
x
=
x
i
x
=
x
i
+
1
∫
z
=
z
j
z
=
z
j
+
1
K
ij
(
x
,
z
)
P
ij
(
x
,
z
)
d
x
d
z
=
y
ij
;
and
determining a function P ij (x, z) which satisfies above conditions by solving the above equation set.
8. The method of claim 5 , wherein the function further satisfies a smoothness condition, and wherein,
when determining the function P ij (x), the smoothness condition is {dot over (P)} ij (x i+1 )={dot over (P)} (i+1)j (x i+1 ), wherein {dot over (P)} ij (x) is the first order derivative of P ij (x);
when determining the function P ij (x), the smoothness condition is {dot over (P)} ij (z j+1 )={dot over (P)} i(j+1) (z j+1 ), in which {dot over (P)} ij (z) is the first order derivative of P ij (z); and
when determining the function P ij (x, z), the smoothness condition is
∂
P
ij
(
x
i
+
1
,
z
j
)
∂
x
=
∂
P
(
i
+
1
)
j
(
x
i
+
1
,
z
j
)
∂
x
and
∂
P
ij
(
x
i
,
z
j
+
1
)
∂
z
=
∂
P
i
(
j
+
1
)
(
x
i
,
z
j
+
1
)
∂
z
,
wherein in
∂
P
ij
(
x
,
z
)
∂
x
is the first order partial derivative of P ij (x, z) with respect to x, and
∂
P
ij
(
x
,
z
)
∂
z
is the first order partial derivative of P ij (x, z) with respect to z.
9. The method of claim 6 , wherein the function further satisfies a smoothness condition, and wherein,
when determining the function P ij (x), the smoothness condition is {dot over (P)} ij (x i+1 )={dot over (P)} (i+1)j (x i+1 ), wherein {dot over (P)} ij (x) is the first order derivative of P ij (x);
when determining the function P ij (z), the smoothness condition is {dot over (P)} ij (z j+1 )={dot over (P)} i(j+1) (z j+1 ), wherein {dot over (P)} ij (z) is the first order derivative of P ij (z); and
when determining the function P ij (x, z), the smoothness condition is
∂
P
ij
(
x
i
+
1
,
z
j
)
∂
x
=
∂
P
(
i
+
1
)
j
(
x
i
+
1
,
z
j
)
∂
x
and
∂
P
ij
(
x
i
,
z
j
+
1
)
∂
z
=
∂
P
i
(
j
+
1
)
(
x
i
,
z
j
+
1
)
∂
z
,
wherein
∂
P
ij
(
x
,
z
)
∂
x
is the first order partial derivative of P ij (x, z) with respect to x, and
∂
P
ij
(
x
,
z
)
∂
z
is the first order partial derivative of P ij (x, z) with respect to z.
10. The method of claim 7 , wherein the function further satisfies a smoothness condition, and wherein
when determining the function P ij (x), the smoothness condition is {dot over (P)} ij (x i+1 )={dot over (P)} (i+1)j (x i+1 ), wherein {dot over (P)} ij (x) is the first order derivative of P ij (x);
when determining the function P ij (z) , the smoothness condition is {dot over (P)} ij (z j+1 )={dot over (P)} i(j+1) (z j+1 ), wherein {dot over (P)} ij (z); and
when determining the function P ij (x, z), the smoothness condition is
∂
P
ij
(
x
i
+
1
,
z
j
)
∂
x
=
∂
P
(
i
+
1
)
j
(
x
i
+
1
,
z
j
)
∂
x
and
∂
P
ij
(
x
i
,
z
j
+
1
)
∂
z
=
∂
P
i
(
j
+
1
)
(
x
i
,
z
j
+
1
)
∂
z
,
wherein
∂
P
ij
(
x
,
z
)
∂
x
is the first order partial derivative of P ij (x, z) with respect to x, and
∂
P
ij
(
x
,
z
)
∂
z
is the first order partial derivative of P ij (x, z) with respect to z.
11. A device for restoring CT scan data, the device comprising:
a processor configured to execute machine readable instructions corresponding to a control logic for restoring CT scan data stored on a storage medium, wherein when the machine-readable instructions are executed by the processor, the machine-readable instructions cause the processor to:
build a data collecting model with respect to a specific direction of the detector according to a response curve of the detector, wherein the specific direction is selected from a group including a channel direction and a slice direction;
acquire, based on the data collecting model, X-ray intensity values detected by the detector in the specific direction during a CT scanning;
determine a function which satisfies a relationship of the data collecting model with respect to the acquired X-ray intensity values in the specific direction, a continuity condition and a boundary condition; and
calculate an X-ray intensity value of a point in the specific direction by substituting a coordinate value of the point into the function.
12. The device of claim 11 , wherein the data collecting model is a data collecting model with respect to a channel direction of the detector and is defined by the following equation:
y
ij
=
∫
x
=
x
i
x
=
x
i
+
1
K
ij
(
x
)
A
ij
(
x
)
d
x
;
wherein, x represents the coordinate value in a channel direction of the detector,
i represents a channel index and is an integer ranging from 1 to a maximum value of N,
j represents a slice index and is an integer ranging from 1 to a maximum value of M,
y ij represents an X-ray intensity value detected by the detector at the j th slice and the i th channel,
K ij represents a response curve in a channel direction of the detector at the j th slice and the i th channel,
A ij (x) represents a real X-ray intensity value in a channel direction of the detector at the j th slice and the i th channel,
x i represents a minimum coordinate value in a channel direction of the detector at the i th channel, and
x i+1 represents a minimum coordinate value in a channel direction of the detector at the (i+1) th channel.
13. The device of claim 11 , wherein the data collecting model is a data collecting model with respect to the slice direction of the detector and is defined by the following equation:
y
ij
=
∫
z
=
z
j
z
=
z
j
+
1
K
ij
(
z
)
A
ij
(
z
)
d
z
;
wherein, z represents a coordinate value in a slice direction of the detector,
i represents a channel index and is an integer ranging from 1 to a maximum value of N,
j represents a slice index and is an integer ranging from 1 to a maximum value of M,
y ij represents an X-ray intensity value detected by the detector in at i th slice and the i th channel,
K ij (z) represents a response curve in a slice direction of the detector at the j th slice and the i th channel,
A ij (x) represents a real X-ray intensity value in a slice direction of the detector at the j th slice and the i th channel,
z j represents a minimum coordinate value in a slice direction of the detectors at the j th slice, and
z j+1 represents a minimum coordinate value in a slice direction of the detectors at the (j+1) th slice.
14. The device of claim 11 , wherein, the data collecting model is a data collecting model with respect to a channel direction and the slice direction of the detector and is defined by the following equation:
y
ij
=
∫
x
=
x
i
x
=
x
i
+
1
∫
z
=
z
j
z
=
z
j
+
1
K
ij
(
x
,
z
)
A
ij
(
x
,
z
)
d
x
d
z
;
wherein, x represents a coordinate value in the channel direction of the detector,
z represents a coordinate value in a slice direction of the detector,
i represents a channel index and is an integer ranging from 1 to the maximum value of N,
j represents a slice index and is an integer ranging from 1 to the maximum value of M,
y ij represents an X-ray intensity value detected by the detector at the j th slice and the i th channel,
K ij (x, z) represents a response curve in a channel direction and a slice direction of the detector at the j th slice and the i th channel,
A ij (x, z) represents an real X-ray intensity value in a channel direction and a slice direction of the detector at the j th slice and the i th channel,
x i represents a minimum coordinate value in a channel direction of the detectors at the i th channel,
x i+1 represents a minimum coordinate value in a channel direction of the detectors at the (i+1) th channel,
z j represents a minimum coordinate value in a slice direction of the detectors at the j th slice, and
z j+1 represents a minimum coordinate value in a slice direction of the detectors at the (j+1) th slice.
15. The device of claim 12 , wherein, said machine readable instructions further cause the processor to:
construct an equation set as follows:
continuity condition: P ij (x i+1 )=P (i+1)j (x i+1 );
boundary condition:
P
1
j
(
x
1
)
=
y
1
j
x
2
-
x
1
;
a relationship of the acquired X-ray intensity values in the channel direction with respect to the data collecting model:
∫
x
=
x
i
x
=
x
i
+
1
K
ij
(
x
)
P
ij
(
x
)
d
x
=
y
ij
;
and
determine a function P ij (x) which satisfies above conditions by solving the above equation set.
16. The device of claim 13 , wherein, said machine readable instructions further cause the processor to:
construct an equation set as follows:
continuity condition: P ij (z j+1 )=P i(j+1) (z j+1 );
boundary condition:
P
i
1
(
z
1
)
=
y
i
1
z
2
-
z
1
;
a relationship of the acquired X-ray intensity values in the slice direction with respect to the data collecting model:
∫
z
=
z
j
z
=
z
j
+
1
K
ij
(
z
)
P
ij
(
z
)
d
z
=
y
ij
;
and
determine a function P ij (z) which satisfies above conditions by solving the above equation set.
17. The device of claim 14 , wherein, said machine readable instructions further cause the processor to:
construct an equation set as follows:
continuity condition: P ij (x i+1 , z j )=P (i+1)j (x i+1 , z j );
P ij (x i , z j+1 )=P i(j+1) (x i , z j+1 );
boundary condition:
P
1
j
(
x
1
,
z
j
)
=
y
1
j
x
2
-
x
1
;
P
i
1
(
x
i
,
z
1
)
=
y
i
1
z
2
-
z
1
;
a relationship of the acquired X-ray intensity values in the channel direction and the slice direction with respect to the data collecting model:
∫
x
=
x
i
x
=
x
i
+
1
∫
z
=
z
j
z
=
z
j
+
1
K
ij
(
x
,
z
)
P
ij
(
x
,
z
)
d
x
d
z
=
y
ij
;
and
determine a function P ij (x, z) which satisfies above conditions by solving the above equation set.
18. The device of claim 15 , wherein the function further satisfies a smoothness condition, and wherein;
when determining the function P ij (x), the smoothness condition is {dot over (P)} ij (x i+1 )={dot over (P)} (i+1)j (x i+1 ), in which {dot over (P)} ij (x) is the first order derivative of P ij (z); and
when determining the function P ij (z) , the smoothness condition is {dot over (P)} ij (z j+1 )={dot over (P)} i(j+1) (z j+1 ), in which {dot over (P)} ij (z) is the first order derivative of P ij (z); and
when determining the function P ij (x, z), the smoothness condition is
∂
P
ij
(
x
i
+
1
,
z
j
)
∂
x
=
∂
P
(
i
+
1
)
j
(
x
i
+
1
,
z
j
)
∂
x
and
∂
P
ij
(
x
i
,
z
j
+
1
)
∂
z
=
∂
P
i
(
j
+
1
)
(
x
i
,
z
j
+
1
)
∂
z
;
in which
∂
P
ij
(
x
,
z
)
∂
x
is the first order partial derivative of P ij (x, z) with respect to x, and
∂
P
ij
(
x
,
z
)
∂
z
is the first order partial derivative of P ij (x, z) with respect to z.
19. The device of claim 16 , wherein the function further satisfies a smoothness condition, and wherein;
when determining the function P i,j (x), the smoothness condition is {dot over (P)} ij (x i+1 )={dot over (P)} (i+1)j (x i+1 ), wherein {dot over (P)} ij (x) is the first order derivative of P ij (x);
when determine the function P ij (z), the smoothness condition is {dot over (P)} ij (z j+1 )={dot over (P)} i(j+1) (z j+1 ), wherein {dot over (P)} ij (z) is the first order derivative of P ij (z); and
when determining the function P ij (x, z), the smoothness condition is
∂
P
ij
(
x
i
+
1
,
z
j
)
∂
x
=
∂
P
(
i
+
1
)
j
(
x
i
+
1
,
z
j
)
∂
x
and
∂
P
ij
(
x
i
,
z
j
+
1
)
∂
z
=
∂
P
i
(
j
+
1
)
(
x
i
,
z
j
+
1
)
∂
z
,
wherein
∂
P
ij
(
x
,
z
)
∂
x
is the first order partial derivative of P ij (x, z) with respect to x, and
∂
P
ij
(
x
,
z
)
∂
z
is the first order partial derivative of P ij (x, z) with respect to z.
20. The device of claim 17 , wherein the function further satisfies a smoothness condition, and wherein;
when determining the function P ij (x), the smoothness condition is {dot over (P)} ij (x i+1 )={dot over (P)} (i+1)j (x i+1 ), wherein {dot over (P)} ij (x) is the first order derivative of P ij (x);
when determine the function P ij (z), the smoothness condition is {dot over (P)} ij (z j+1 )={dot over (P)} i(j+1) (z j+1 ), wherein {dot over (P)} ij (z) is the first order derivative of P ij (z); and
when determining the function P ij (x, z), the smoothness condition is
∂
P
ij
(
x
i
+
1
,
z
j
)
∂
x
=
∂
P
(
i
+
1
)
j
(
x
i
+
1
,
z
j
)
∂
x
and
∂
P
ij
(
x
i
,
z
j
+
1
)
∂
z
=
∂
P
i
(
j
+
1
)
(
x
i
,
z
j
+
1
)
∂
z
,
wherein
∂
P
ij
(
x
,
z
)
∂
x
is the first order partial derivative of P ij (x, z) with respect to x, and
∂
P
ij
(
x
,
z
)
∂
z
is the first order partial derivative of P ij (x, z) with respect to z.