Computed tomography device and method using circular-pixel position-adaptive interpolation
View Patent ↗A method of computed-tomography and a computed-tomography apparatus where a interpolation kernel width is adaptively determined as a function of the distance from the x-ray source to the reconstruction pixel. The width of the kernel is the projection of the reconstruction pixel on the detector. The method can be implemented in the channel direction. The method can also be implemented in the segment direction, or in the channel and segment directions at the same time. Backprojection is performed using the adaptive kernel width and may by used with helical and circular scanning, and with cone-beam or fan beam x-ray CT.
1. A computed-tomography method, comprising:
determining a channel position located on an x-ray detector using a linear path from an x-ray source through a backprojection pixel;
determining an interpolation kernel width using a distance from said source to said backprojection pixel;
determining a radius P of said pixel having a circular shape with a center at position x i,j , y i,j as
P
=
F
O
V
2
·
MATRIX
where FOV is a reconstruction field of view and MATRIX is a reconstructed image matrix size;
determining a floating point channel position Ch i,j as:
Ch
i
,
j
,
k
=
1
Δγ
tan
-
1
[
x
i
,
j
cos
β
k
+
y
i
,
j
sin
β
k
R
+
x
i
,
j
sin
β
k
-
y
i
,
j
cos
β
k
]
where Δγ is an angular channel width, β k is a view angle at view k, and R is a distance from said x-ray source to isocenter distance; and
determining said kernel width ΔCh i,j as:
Δ
Ch
i
,
j
,
k
=
2
P
Δ
γ
·
L
i
,
j
,
k
where
L
i
,
j
,
k
(
x
i
,
j
,
y
i
,
j
,
β
k
)
=
(
R
sin
β
k
+
x
i
,
j
)
2
+
(
R
cos
β
k
-
y
i
,
j
)
2
.
2. A method as recited in claim 1 , comprising:
calculating a backprojection value PDI as:
PDI
CH
i
,
j
,
k
=
{
PD
(
c
)
if
c
s
=
c
and
c
e
=
c
1
Δ
Ch
i
,
j
,
k
(
δ
s
·
PD
(
c
s
)
+
δ
e
·
PD
(
c
e
)
+
∑
c
′
=
c
s
+
1
c
e
-
1
PD
(
c
′
)
)
otherwise
where PD( ) is raw projection data, c s , c, and c e are integer starting, center, and ending channel indexes of a detector, and
λ
=
Δ
Ch
i
,
j
,
k
2
f
s
=
Ch
i
,
j
-
λ
f
e
=
Ch
i
,
j
+
λ
c
s
=
int
(
f
s
)
c
e
=
int
(
f
e
)
δ
s
=
c
s
+
1
-
f
s
,
and
δ
e
=
f
e
-
c
e
.
3. A non-transitory computer-readable medium containing instructions, wherein the instructions, when executed by a computer, perform a method comprising:
determining a channel position located on a linear path from an x-ray source through a backprojection pixel;
determining an interpolation kernel width using a distance from said source to said backprojection pixel;
determining a radius P of said pixel having a circular shape with a center at position x i,j , y i,j as
P
=
F
O
V
2
·
MATRIX
where FOV is a reconstruction field of view and MATRIX is a reconstructed image matrix size;
determining a floating point channel position Ch i,j as:
Ch
i
,
j
,
k
=
1
Δ
γ
tan
-
1
[
x
i
,
j
cos
β
k
+
y
i
,
j
sin
β
k
R
+
x
i
,
j
sin
β
k
-
y
i
,
j
cos
β
k
]
where Δγ is an angular channel width, β k is a view angle at view k, and R is a distance from said x-ray source to isocenter distance; and
determining said kernel width ΔCh i,j as:
Δ
Ch
i
,
j
,
k
=
2
P
Δ
γ
·
L
i
,
j
,
k
where
L
i
,
j
,
k
(
x
i
,
j
,
y
i
,
j
,
β
k
)
=
(
R
sin
β
k
+
x
i
,
j
)
2
+
(
R
cos
β
k
-
y
i
,
j
)
2
.
4. A non-transitory medium as recited in claim 3 , wherein said method further comprises:
calculating a backprojection value PDI as:
PDI
CH
i
,
j
,
k
=
{
PD
(
c
)
if
c
s
=
c
and
c
e
=
c
1
Δ
Ch
i
,
j
,
k
(
δ
s
·
PD
(
c
s
)
+
δ
e
·
PD
(
c
e
)
+
∑
c
′
=
c
s
+
1
c
e
-
1
PD
(
c
′
)
)
otherwise
where PD( ) is raw projection data, c s , c, and c e are integer starting, center, and ending channel indexes of a detector, and
λ
=
Δ
Ch
i
,
j
,
k
2
f
s
=
Ch
i
,
j
-
λ
f
e
=
Ch
i
,
j
+
λ
c
s
=
int
(
f
s
)
c
e
=
int
(
f
e
)
δ
s
=
c
s
+
1
-
f
s
,
and
δ
e
=
f
e
-
c
e
.