Method for circular scan reconstruction in computed tomography and computed tomographic device
View Patent ↗A method of computed-tomography and a computed-tomography apparatus where the portion of the field of view of a subject were full scan data is available is reconstructed using a full-scan algorithm. In the areas where full scan data is not available, half-scanning is used. Data is also extrapolated from the full scan data. The extrapolated data overlaps a portion of the half-scanning data. The extrapolated data and the overlapped portion of the half-scanning data are feathered. The image is reconstructed using the full-scan, half-scan and feathered data. Corner regions in an image are exposed and reconstructed to produce more uniform z-coverage of the reconstruction field of view.
1. A computed-tomography method, comprising:
scanning an object with x-rays to obtain projection data;
reconstructing a first part of an image of the object where full scan data is available;
reconstructing a second part of the image using half-scanning where full scan data is not available;
reconstructing a third part of the image using data extrapolated from the full scan data;
combining weighted sums of overlapping portions of the second and third parts; and
obtaining the image using the first to third parts and the combined weighted sums.
2. A method as recited in claim 1 , wherein an angular range of the half-scanning for a pixel located at (r, φ) is given by:
β start ( r,φ,z )=φ+π−Δβ( r,z )/2
β end ( r,φ,z )=φ+π+Δβ( r,z )/2=β start ( r,φ,z )+Δβ( r,z )
where:
Δβ( r,z )=π+2θ
θ
=
π
2
-
ϕ
,
ϕ
=
arcsin
(
d
R
sin
γ
)
γ
=
arccos
(
r
2
+
d
2
-
R
2
2
rd
)
and
d
=
R
z
W
,
with:
R being a distance from an x-ray source to a center an x-ray detector,
W being a half-width of the detector at the center of the x-ray detector, and
z is an axial direction of the object.
3. A method as recited in claim 1 , comprising:
applying redundancy weighting to each pixel.
4. A method as recited in claim 3 , wherein applying redundancy weighting to said pixels comprises using:
w
N
(
β
,
γ
)
=
c
(
β
)
∑
n
=
-
N
N
c
(
β
n
,
γ
n
)
where
:
(
β
n
,
γ
n
)
=
{
(
β
+
π
n
,
γ
)
n
is
even
(
β
+
π
n
+
2
γ
,
-
γ
)
n
is
odd
,
N=1, 2, . . . and is a number of 1π arcs used for image reconstruction,
c
(
β
)
=
{
cos
2
π
(
β
start
+
σ
-
β
)
2
σ
,
β
start
≤
β
≤
β
start
+
σ
1
,
β
start
+
σ
≤
β
≤
β
end
-
σ
cos
2
π
(
β
-
β
end
+
σ
)
2
σ
,
β
end
-
σ
≤
β
≤
β
end
,
σ= k (Δβ( r,z ))×Δβ( r,z ), and
k
(
Δβ
(
r
,
z
)
)
=
k
min
+
Δβ
(
r
,
z
)
-
Δβ
π
(
r
)
2
π
-
Δβ
π
(
r
)
(
k
max
-
k
min
)
,
for k min =0.05 and k max =0.5.
5. A method as recited in claim 3 , wherein the redundancy weighting is dependent upon angular positions of reconstruction pixels.
6. A method as recited in claim 3 , wherein the redundancy weighting is dependent upon radial positions of reconstruction pixels.
7. A method as recited in claim 3 , wherein the redundancy weighting is dependent upon a z-direction position of reconstruction pixels.
8. A method as recited in claim 1 , comprising:
determining a first portion of the second part which overlaps a first portion of the third part;
combining weighted sums of the first portions to produce a fourth part;
determining second portions of the second and third parts which do not overlap; and
obtaining the image using the first part, second portions and the fourth part.
9. A method as recited in claim 1 , wherein said combining comprises:
feathering together said second and third parts.
10. A method as recited in claim 9 , comprising:
assigning a weight w=1 to data located at a first border between said first and second parts;
assigning a weight w=0 to data located at a second border between said second and third parts;
smoothly varying said weight w between 0 and 1 across said second part;
combining said second and third parts using:
Img= w ×Img2+( w− 1)×Img3,
where Img is a combined image, Img2 is image data from said second part and Img3 is image data from said third part at a given pixel.
11. A method as recited in claim 10 , comprising combining weighted sums of overlapping portions of the first and second parts.
12. A method as recited in claim 11 , wherein data is extrapolated over a region of said image adjacent to where said full scan data is available and which overlaps said half-scan data, said method comprising:
assigning a weight w=1 to data located at one edge of said region adjacent to said full scan data;
assigning a weight w=0 to data located at the farthest extent of said region intersecting with said half-scan data;
smoothly varying said weight w between 1 and 0 across said region;
combining said second and third parts using:
Img= w ×Img2+( w− 1)×Img3,
where Img is a combined image, Img2 is extrapolated image data and Img3 is half-scan at a given pixel.
13. A computed-tomography apparatus, comprising:
an x-ray source;
an x-ray detector; and
a reconstruction processor for reconstructing an image of an subject from data collected by said x-ray detector, wherein the processor
reconstructs a first part of the image where full scan data is available;
reconstructs a second part of the image using half-scanning data where full scan data is not available;
reconstructs a third part of the image using data extrapolated from the full scan data;
combines weighted sums of overlapping portions of the second and third parts; and
reconstructs the image using the first to third parts and combined weighted sums.
14. An apparatus as recited in claim 13 , comprising:
wherein said processor applies redundancy weighting to each pixel.
15. An apparatus as recited in claim 14 , wherein said processor applies redundancy weighting to said pixels comprises using:
w
N
(
β
,
γ
)
=
c
(
β
)
∑
n
=
-
N
N
c
(
β
n
,
γ
n
)
where
:
(
β
n
,
γ
n
)
=
{
(
β
+
π
n
,
γ
)
n
is
even
(
β
+
π
n
+
2
γ
,
-
γ
)
n
is
odd
,
N=1, 2, . . . and is a number of 1π arcs used for image reconstruction,
c
(
β
)
=
{
cos
2
π
(
β
start
+
σ
-
β
)
2
σ
,
β
start
≤
β
≤
β
start
+
σ
1
,
β
start
+
σ
≤
β
≤
β
end
-
σ
cos
2
π
(
β
-
β
end
+
σ
)
2
σ
,
β
end
-
σ
≤
β
≤
β
end
,
σ= k (Δβ( r,z ))×Δβ( r,z ), and
k
(
Δβ
(
r
,
z
)
)
=
k
min
+
Δβ
(
r
,
z
)
-
Δβ
π
(
r
)
2
π
-
Δβ
π
(
r
)
(
k
max
-
k
min
)
,
for k min =0.05 and k max =0.5.
16. An apparatus as recited in claim 15 , wherein the redundancy weighting is dependent upon angular positions of reconstruction pixels.
17. An apparatus as recited in claim 15 , wherein the processor applies redundancy weighting dependent upon radial positions of reconstruction pixels.
18. An apparatus as recited in claim 15 , wherein the processor applies redundancy weighting dependent upon a z-direction position of reconstruction pixels.
19. An apparatus as recited in claim 15 , comprising:
determining a first portion of the second part which overlaps a first portion of the third part;
combining weighted sums of the first portions to produce a fourth part;
determining second portions of the second and third parts which do not overlap; and
obtaining the image using the first part, second portions and the fourth part.
20. An apparatus as recited in claim 13 , wherein said processor feathers together said second and third parts.
21. An apparatus as recited in claim 13 , wherein said processor:
assigns a weight w=1 to data located at a first border between said first and second parts;
assigns a weight w=0 to data located at a second border between said second and third parts;
smoothly varies said weight w between 0 and 1 across said second part; and
combines said second and third parts using:
Img= w ×Img2+( w− 1)×Img3,
where Img is a combined image, Img2 is image data from said second part and Img3 is image data from said third part at a given pixel.