X-ray or gamma ray systems or devices – Specific application – Computerized tomography
Reexamination Certificate
2002-06-27
2003-12-16
Bruce, David V. (Department: 2882)
X-ray or gamma ray systems or devices
Specific application
Computerized tomography
C378S901000
Reexamination Certificate
active
06665369
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to reconstruction software for causing a computer to perform back projection computations for projecting radiographic data of each scan position back to a reconstruction area, a recording medium storing the software, 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 method for speeding up back projection computations (main part of reconstruction computations) on radiographic data or filtered radiographic data.
2. Description of the Related Art
FIG. 1
schematically shows a X-ray tomography apparatus. The apparatus includes an X-ray tube X-ray focus f) and an X-ray detector
42
opposed to each other across an object or patient. The X-ray tube and X-ray detector
42
are rotatable synchronously about the patient's body axis to radiograph the patient intermittently from varied angles of X-ray emission from the X-ray tube to the patient. Radiographic data acquired in each scan position is put to an FBP (Filtered Back Projection) to reconstruct images of a region of interest of the patient. The FBP is a method in which radiographic data for a plurality of images of the patient acquired from different angles is put to a filtering correction process to produce data S which is projected back to a reconstruction area B virtually set to the region of interest of the patient.
To determine a reconstruction pixel value of point b(x, y) in the two-dimensional reconstructing area B, for example, value s (t(x, y, p) of detecting coordinates t(x, y, p) corresponding to a pth projection from point b(x, y), is added up the number of times of projection (Np times). This is expressed by equation (1) below and the value s is one of S. Here, t is usually calculated complicatedly from various positional information such as an X-ray focus position, a detector position and a scan angle. However, the representation t(x, y, p causes no problem since a scanning orbit is usually fixed and scan angle is calculated from p.
b
(
x
,
y
)
=
∑
p
=
0
N
p
-
1
s
(
t
(
x
,
y
,
p
)
)
(
1
)
In the above equation (1), usually t is not an integer and array value s (t(x, y, p) cannot be determined directly. Therefore, an interpolating calculation is carried out using two adjacent points as shown in FIG.
2
. This is expressed by the following equation (2):
b
(
x
,
y
)
=
∑
p
=
0
N
p
-
1
{
(
1
-
a
)
×
s
(
u
)
+
a
×
s
(
u
+
1
)
}
(
2
)
When a computer performs an integrating operation as expressed by the above equation (2), a computation as expressed by the following equation (3) is carried out the number of times of projection (Np times):
b
(
x, y
)=
b
(
x, y
)+(1
−a
)×
s
(
u
)+
a×s
(
u+
1) (3)
FIG. 3
shows a conventional example of program code relating to the above equation (3). In u=INT (t(x, y, p) and a=t(x, y, p)−u, function t(x, y, p) is a function for calculating original data coordinates for back projection by floating point. Function INT ( ) is a function for rounding down to make an integer. Such reconstruction computations are extremely time-consuming, and usually a dedicated DSP board or the like is used for the computations. However, with personal computers (hereinafter abbreviated “PC” as appropriate) with ever-increasing high-speed features, radiographic apparatus have been developed with PCs for performing such reconstructing computations.
A PC today is made up of a CPU (central processing unit), memory, a hard disk (HD), IOs (input/output ports) and peripherals such as a keyboard and a mouse. Usually software and data are stored on the hard disk, which are loaded into the memory and processed by the CPU. The latest CPU chip operates faster than the memory. To demonstrate this high-speed capability, improvement has been made in performance by introducing a high-speed memory called cache memory between the CPU and memory. The cache memory is often mounted on the same semiconductor chip on which the CPU is mounted. The term CPU often embraces the cache memory. However, since high speed is required, the cache memory is more expensive than the main memory, and its storage capacity is usually small. Operation of this cache memory will be described now. When a necessary program or data is not present in the cache memory, the CPU automatically loads the program or data from the memory to the cache memory. Meanwhile, the CPU can perform a different task, thereby increasing overall efficiency. When the cache memory is full, unused old data is successively written into the memory, or data not overwritten is simply discarded. In this way, the cache memory is constantly filled with latest data needed by the CPU.
A relatively high performance PC today may have a 20 GB hard disk, a 1 GB memory, a 400 MHz CPU, and a 512 KB cache memory. In such a PC, read and write performance between CPU and cache memory is about 3200 MB/sec, and read and write performance between cache memory and memory is about 800 MB/sec. In a transfer time of 4 byte floating point data, the read and write time between CPU and cache memory is 1.25 nsec/float, and read and write time between cache memory and memory is 5 nsec/float. Thus, the cache memory is about four times as fast.
A simplified example of caching operation will be described based on an addition of all pixels in image data (1 Mbytes) of 512×512 pixels with floating point values (4 bytes). The image data is too large to store in the above 512 Kbyte cache memory. The CPU adds up the pixels while the first half of the image data in 512 Kbytes is loaded into the cache memory at 512 kbytes/800 Mbytes =640 &mgr;sec. However, the data is transferred between the cache memory and CPU at a fast rate of 512 kbytes/3200 Mbytes=160 &mgr;sec. Thus, the CPU just waits for the data for 640−160=480 &mgr;sec. and stands idle without adding pixels. Next, when the CPU requests the second half of the image data in 512 Kbytes, the cache memory data is replaced successively from old data, and after 512 kbytes/800 Mbytes=640 &mgr;sec, the cache memory has the second half of the image data in 512 Kbytes. However, the CPU remains idle for 480 &mgr;sec. as above.
The prior art has the following drawback. The latest PCs incorporate improvement such as cache memory regarding memory accessing. However, as shown in
FIG. 3
, only computations “for the direction along x-axis, and then for the direction along y-axis” are performed for the back projection computations. This fails to make good use of the computing capability of the CPU. A long time is taken in reconstruction computations as described below. Two-dimensional and three-dimensional reconstructions will particularly be described hereinafter.
The number of times of and a time taken in data reading and writing needed for computations to reconstruct a two-dimensional sectional image will be described first.
The foregoing equation (3) is used to determine the number of memory accesses needed to compute a section reconstruction for one point for one back projection. Value b(x, y) of point (x, y) in the section reconstructing area B is read once, then added and written. Thus, memory access occurs twice. For radiographic data S after a filtering correction, two data are read for interpolation, and thus memory access occurs twice. This requires memory access to be made a total of four times (2+2=4).
Next, for one back projection to the reconstruction area B of the size Nx×Ny, memory access is required Nx×Ny×4 times. Further, when the back projection is made Np times, memory access is required Nx×Ny×4×Np times in total. Usually, data is represented by 4 byte floating point numbers for computations. The number of memory accesses required is Nx×Ny×4×Np×4 bytes.
A mem
Bruce David V.
Rader & Fishman & Grauer, PLLC
Shimadzu Corporation
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