Interpolation interlacing based data upsampling algorithm for cone-beam x-ray CT flying focal spot projection data
View Patent ↗A method of computed-tomography and a computed-tomography apparatus where a flying focal spot x-ray interpolation interlacing is used. Weighted or non-weighted interlacing of zero values is performed, or interpolation interlacing is performed. The interpolation interlacing may be implemented as part of backprojection and or may be a separate process prior to backprojection. In both cases interlacing is performed on post-logged convolved data. The interpolation interlacing may also be incorporated into different parts of the processing chain, such as before convolution.
1. A computed tomography apparatus, comprising:
a flying focal point x-ray source;
an x-ray detector disposed to receive x-rays from said x-ray source;
a unit to collect projection data generated by said detector; and
a processing unit configured to performing interpolation interlacing using said projection data and to reconstruct an image, wherein the processing unit is configured to perform interpolation to obtain interpolated projection data for a view in a manner dependent on a focal spot location of the view, so as to increase sampling in the axial direction without rebinning and resampling into a parallel geometry.
2. An apparatus as recited in claim 1 , wherein said processing unit is configured to interpolate said projection data according to:
PD
II
[
c
,
s
,
v
]
=
W
II
1
·
PD
[
c
,
0
,
v
]
+
s
=
0
W
II
2
·
PD
[
c
,
0
,
v
+
1
]
W
II
1
·
PD
[
c
,
A
,
v
]
+
1
≤
s
<
NSeg
FFS
-
1
;
z
fs
(
v
)
=
+
δ
W
II
2
·
PD
[
c
,
n
,
v
+
1
]
W
II
1
·
PD
[
c
,
n
,
v
]
+
1
≤
s
<
NSeg
FFS
-
1
;
z
fs
(
v
)
=
-
δ
W
II
2
·
PD
[
c
,
n
,
-
even
(
s
)
,
v
+
1
]
W
II
1
·
PD
[
c
,
NSeg
-
1
,
v
]
+
s
=
NSeg
FFS
-
1
W
II
2
·
PD
[
c
,
NSeg
-
1
,
v
+
1
]
where interpolated data PD II [c, s, v] is generated from projection data PD [c, s, v] and PD [c, s, v+1], c is channel, s is segment, v is view,
n
=
int
(
s
2
)
,
A
=
int
(
s
-
1
2
)
,
W II1 and W II2 are interpolation weights, NSeg and NSeg FFS are input and output number of segments, δ is an effect focal spot deviation, and even(s)=1 when s is even; and 0 when s is odd.
3. An apparatus as recited in claim 2 , wherein said interpolation weights W II1 and W II2 are chosen such that W II1 +W II2 =1.
4. An apparatus as recited in claim 2 , wherein W II1 =0.5 and W II2 =0.5.
5. An apparatus as recited in claim 1 , wherein said interpolation interlacing comprises zero interlacing upsampling and interpolates said projection data according to
PD
ZI
[
c
,
s
′
,
v
]
=
{
0
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
+
1
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
0
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
+
1
where interpolated data PD ZI [c, s′, v] is generated from projection data PD [c, s, v], c is channel, s is segment, v is view, z fs is an effective focal spot position, and δ is an effective focal spot deviation.
6. An apparatus as recited in claim 1 , wherein said interpolation interlacing comprises weighted zero interlacing upsampling and interpolates said projection data according to
PD
ZIw
[
c
,
s
′
,
v
]
=
{
W
ZI
·
(
PD
[
c
,
s
,
v
]
+
PD
[
c
,
s
+
1
,
v
]
)
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
+
1
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
W
ZI
·
(
PD
[
c
,
s
,
v
]
+
PD
[
c
,
s
+
1
,
v
]
)
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
+
1
where interpolated data PD ZIw [c, s′, v] is generated from projection data PD [c, s, v], c is channel, s is segment, v is view, z fs is an effective focal spot position, and δ is an effective focal spot deviation and W ZI is a weight.
7. A computed tomography method, comprising:
exposing a subject to x-rays from a flying focal point x-ray source;
collecting projection data from said x-rays; and
performing interpolation interlacing using said projection data and to reconstruct an image, wherein the performing step includes performing interpolation to obtain interpolated projection data for a view in a manner dependent on a focal spot location of the view, so as to increase sampling in the axial direction without rebinning and resampling into a parallel geometry.
8. A method as recited in claim 7 , comprising performing said interpolation interlacing according to:
PD
II
[
c
,
s
,
v
]
=
W
II
1
·
PD
[
c
,
0
,
v
]
+
s
=
0
W
II
2
·
PD
[
c
,
0
,
v
+
1
]
W
II
1
·
PD
[
c
,
A
,
v
]
+
1
≤
s
<
NSeg
FFS
-
1
;
z
fs
(
v
)
=
+
δ
W
II
2
·
PD
[
c
,
n
,
v
+
1
]
W
II
1
·
PD
[
c
,
n
,
v
]
+
1
≤
s
<
NSeg
FFS
-
1
;
z
fs
(
v
)
=
-
δ
W
II
2
·
PD
[
c
,
n
,
-
even
(
s
)
,
v
+
1
]
W
II
1
·
PD
[
c
,
NSeg
-
1
,
v
]
+
s
=
NSeg
FFS
-
1
W
II
2
·
PD
[
c
,
NSeg
-
1
,
v
+
1
]
where interpolated data PD II [c, s, v] is generated from projection data PD [c, s, v] and PD [c, s, v+1], c is channel, s is segment, v is view
n
=
int
(
s
2
)
,
A
=
int
(
s
-
1
2
)
,
W II1 and W II2 are interpolation weights, NSeg and NSeg FFS are input and output number of segments, δ is an effect focal spot deviation, and even(s)=1 when s is even; and 0 when s is odd.
9. A method as recited in claim 8 , comprising selecting said interpolation weights W II1 and W II2 such that W II1 +W II2 =1.
10. A method as recited in claim 8 , comprising selecting W II1 =0.5 and W II2 =0.5.
11. A method as recited in claim 7 , wherein performing said interpolation interlacing comprises performing zero interlacing upsampling according to:
PD
ZI
[
c
,
s
′
,
v
]
=
{
0
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
+
1
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
0
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
+
1
where interpolated data PD ZI [c, s′, v] is generated from projection data PD [c, s, v], c is channel, s is segment, v is view, z fs is an effective focal spot position, and δ is an effective focal spot deviation.
12. A method as recited in claim 7 , wherein performing said interpolation interlacing comprises performing weighted zero interlacing upsampling according to:
PD
ZIw
[
c
,
s
′
,
v
]
=
{
W
ZI
·
(
PD
[
c
,
s
,
v
]
+
PD
[
c
,
s
+
1
,
v
]
)
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
+
1
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
W
ZI
·
(
PD
[
c
,
s
,
v
]
+
PD
[
c
,
s
+
1
,
v
]
)
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
+
1
where interpolated data PD ZIw [c, s′, v] is generated from projection data PD [c, s, v], c is channel, s is segment, v is view, z fs is an effective focal spot position, and δ is an effective focal spot deviation and W ZI is a weight.
13. A non-transitory computer-readable medium storing instructions that, when executed by a computer, cause the computer to perform a method comprising:
collecting projection data associated with x-rays from a flying focal point x-ray source exposing a subject; and
performing interpolation interlacing using said projection data and to reconstruct an image, wherein the performing step includes performing interpolation to obtain interpolated projection data for a view in a manner dependent on a focal spot location of the view, so as to increase sampling in the axial direction without rebinning and resampling into a parallel geometry.
14. A medium as recited in claim 13 , wherein said method comprises performing said interpolation interlacing according to:
PD
II
[
c
,
s
,
v
]
=
W
II
1
·
PD
[
c
,
0
,
v
]
+
s
=
0
W
II
2
·
PD
[
c
,
0
,
v
+
1
]
W
II
1
·
PD
[
c
,
A
,
v
]
+
1
≤
s
<
NSeg
FFS
-
1
;
z
fs
(
v
)
=
+
δ
W
II
2
·
PD
[
c
,
n
,
v
+
1
]
W
II
1
·
PD
[
c
,
n
,
v
]
+
1
≤
s
<
NSeg
FFS
-
1
;
z
fs
(
v
)
=
-
δ
W
II
2
·
PD
[
c
,
n
,
-
even
(
s
)
,
v
+
1
]
W
II
1
·
PD
[
c
,
NSeg
-
1
,
v
]
+
s
=
NSeg
FFS
-
1
W
II
2
·
PD
[
c
,
NSeg
-
1
,
v
+
1
]
where interpolated data PD II [c, s, v] is generated from projection data PD [c, s, v] and PD [c, s, v+1], c is channel, s is segment, v is view,
n
=
int
(
s
2
)
,
A
=
int
(
s
-
1
2
)
,
W II1 and W II2 are interpolation weights, NSeg and NSeg FFS are input and output number of segments, δ is an effect focal spot deviation, and even(s)=1 when s is even, and 0 when s is odd.
15. A medium as recited in claim 14 , wherein said method comprises selecting said interpolation weights W II1 and W II2 such that W II1 +W II2 =1.
16. A medium as recited in claim 14 , comprising selecting W II1 =0.5 and W II2 =0.5.
17. A medium as recited in claim 13 , wherein said method comprises performing said interpolation interlacing comprises performing zero interlacing upsampling according to:
PD
ZI
[
c
,
s
′
,
v
]
=
{
0
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
+
1
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
0
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
+
1
where interpolated data PD ZI [c, s′, v] is generated from projection data PD [c, s, v], c is channel, s is segment, v is view, z fs is an effective focal spot position, and δ is an effective focal spot deviation.
18. A medium as recited in claim 13 , wherein performing said interpolation interlacing comprises performing weighted zero interlacing upsampling according to:
PD
ZIw
[
c
,
s
′
,
v
]
=
{
W
ZI
·
(
PD
[
c
,
s
,
v
]
+
PD
[
c
,
s
+
1
,
v
]
)
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
+
δ
,
s
′
=
2
s
+
1
PD
[
c
,
s
,
v
]
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
W
ZI
·
(
PD
[
c
,
s
,
v
]
+
PD
[
c
,
s
+
1
,
v
]
)
,
z
fs
[
v
]
=
-
δ
,
s
′
=
2
s
+
1
where interpolated data PD ZIw [c, s′, v] is generated from projection data PD [c, s, v], c is channel, s is segment, v is view, z fs is an effective focal spot position, and δ is an effective focal spot deviation and W ZI is a weight.