X-ray or gamma ray systems or devices – Specific application – Computerized tomography
Reexamination Certificate
2002-07-22
2003-06-10
Bruce, David V. (Department: 2882)
X-ray or gamma ray systems or devices
Specific application
Computerized tomography
C378S019000, C378S901000
Reexamination Certificate
active
06577701
ABSTRACT:
BACKGROUND OF THE INVENTION
(1) Field of the Invention
This invention relates to section reconstruction methods for projecting radiographic data acquired in each scan position, or filtered radiographic data, as back projection data back to a reconstruction area, and various tomography apparatus for use in the medical, industrial and other fields for radiographing patients or objects under examination and reconstructing sectional images thereof. More particularly, the invention relates to a technique for speeding up the back projections in a reconstruction operation.
(2) Description of the Related Art
FIG. 1
shows a conventional X-ray tomography apparatus. The apparatus includes an X-ray focus f and an X-ray detector
42
, with an array of X-ray detecting elements, opposed to each other across an object or patient. The X-ray focus f and X-ray detector
42
are rotatable synchronously around the object's body axis to radiograph the object intermittently from varied angles of X-ray emission to the object. Radiographic data acquired in each scan position is put to a reconstruction operation to reconstruct sectional images of the object.
As a reconstruction method, what is known as FBP (Filtered Back Projection) is often used. The FBP is a method in which radiographic data for a plurality (Np) of images of the object acquired from different scan positions is put to a filtering correction process to produce back projection data s which is projected back to a reconstruction area B virtually set to a site of interest of the object. To determine a pixel value of point b (x, y) in the reconstruction area B, for example, back projection data s (t (x, y, p)) of detector coordinates t (x, y, p) corresponding to a projection to point b (x, y) in a pth scan position is determined and added up the number of times Np. Thus, a total back projection to point b (x, y) is expressed by the following equation (1):
b
(
x
,
y
)
=
∑
p
=
0
N
p
-
1
s
(
t
(
x
,
y
,
p
)
)
(
1
)
Generally, various parameters are needed to compute detector coordinates t. However, since a scan position is determined by p, the detector coordinates corresponding to the projection to point (x, y) is regarded as t (x, y, p). Further, detector coordinates t (x, y, p) usually is not an integer, and therefore array data s cannot be determined directly. Floating-point interpolation computations are carried out using two adjacent points as shown in FIG.
2
. In
FIG. 2
, u is an integer made by discarding fractional value a of t (x, y, p). An interpolation computation using (u, s (u)) and (u+1, s (u+1)) is expressed by the following equation (2):
b
(
x
,
y
)
=
∑
p
=
0
N
p
-
1
{
(
1
-
α
)
×
s
(
u
)
+
α
×
s
(
u
+
1
)
}
(
2
)
When a computer performs the above equation (2), a computation as expressed by the following equation (3) is carried out the number of projections (Np times):
b
(
x, y
)=
b
(
x, y
)+(1−&agr;)×
s
(
u
)+
&agr;×s
(
u+
1) (3)
Though the same computations as equation (3) above, the following equation (4) is actually used to reduce the number of computations:
b
(
x, y
)=
b
(
x, y
)+&agr;×(
s
(
u+
1)−
s
(
u
))+
s
(
u
) (4)
The above conventional computations has a disadvantage of involving numerous floating point computations, and thus takes a long time in performing reconstruction after a radiographic operation. Particularly, the interpolating computations with floating point in computing back projections are problematic. A floating point interpolation computational complexity will be described in detail.
First, of the computational expression (4) for one back projection to one point in a reconstruction area, computations for interpolation are listed below.
t→u making floating decimals of coordinates into integers . . . one step
u+1 adding integer to coordinates . . . one step
s (u), s (u+1) reading back projection data . . . two steps
&agr;=t−u floating point computation of coordinates . . . one step
floating point multiplication of data . . . one step
floating point addition of data . . . two steps
The above computations provide interpolation data to be added to reconstruction point b (x, y). The interpolating computational complexity is eight steps in total. Next, one step is executed for reading b (x, y), then one step for floating point addition to the interpolation value, and finally one step for writing b (x, y) to complete the computations of equation (4). Thus, the computational complexity of equation (4) is 8+3=11 steps in total. The number of computational steps is shown in the column “equation (4) (1BP)” in FIG.
7
.
The above equation (4) is repeated the number of times corresponding to the number of projections (Np times) to determine a reconstruction pixel value of one point b (x, y). Where the reconstruction area B includes n×n points, the computational complexity corresponding to equation (4) in all reconstruction computations becomes n×n×Np times. This computational complexity is shown in the column “Equation (4) ALL (all BP)” in FIG.
7
. It will be seen that the total computational complexity in the prior art involves 11×n×n×Np steps, thus requiring a long time for the reconstruction computations.
SUMMARY OF THE INVENTION
This invention has been made having regard to the state of the art noted above, and its object is to provide a section reconstruction method and apparatus for speeding up a reconstruction operation.
To fulfill the above object, Inventor has made intensive research and attained the following findings. In the conventional reconstruction computation, data is interpolated in time of the back projection computations. It is time-consuming since the reconstruction requires a great number of floating-point interpolation computations proportional to a product of the number of times of projections Np and the number of section reconstruction pixels (e.g. n×n points). However, it has been found that interpolation computations repeatedly performed from back projection data far less than the reconstruction points include many similar interpolation computations which may be omitted.
In a solution Inventor has found based on this finding, enlarged interpolation data is obtained by enlarging back projection data by m times by interpolating, and thereafter the enlarged interpolation data is directly projected back to a reconstruction area without interpolation computation. In the back projection computation, the back projection data is selected from the enlarged interpolation data by determining by multiplying projection coordinates of reconstruction points by m. Where the enlargement-rate m is infinite, obviously the computations are the same as in the prior art. A finite enlargement-rate m will cause errors. However, by a suitable value m, excellent quality image is reconstructed and such reconstructed images present no problem. This solution reduces the number of interpolation computations to perform a fast reconstruction.
Based on the above finding, this invention provides section reconstruction methods for projecting radiographic data of an object acquired in each scan position back to a reconstruction area, the method comprising the step of generating enlarged interpolation data by interpolating back projection data and then projecting the enlarged interpolation data back to a two-dimensional or three-dimensional reconstruction area virtually set to a region of interest of the object, the back projection data being radiographic data, or data resulting from filtering of the radiographic data, the radiographic data being acquired in each scan position by causing a radiation source and a detector arranged opposite each other across the object to scan the object synchronously, or to scan the object synchronously with rotation of the object, the radiation source irradiating the object with electromagneti
Kishi Taketo
Onishi Shuhei
Shintani Eiichi
Ukita Masaaki
Rader & Fishman & Grauer, PLLC
Shimadzu Corporation
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