JPH0675571B2 - Data processing method for image reconstruction - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (Industrial field of use) In the field of imaging such as CT (Computer Tomography), image reconstruction with high spatial resolution is required for clear identification of small objects. The present invention relates to a data processing method for increasing the spatial frequency component (so-called spatial frequency multiplication) required for those high resolution imaging.

(Prior Art) In the Fourier transform in the convolution processing of the conventional high resolution image reconstruction of CT, 0 data is inserted and added based on N sampling data as shown in FIG. In case of multiplying by 3, if N = 1024, it is necessary to add 1024 0 data to 3N = 3072 and directly perform a Fourier transform of the real number of N ′ = 4096 data, which is very long. Calculation time was required. Actually 20
The Fourier transform of 48-point complex number data is performed to reduce the time, but the calculation time is still long.

(Problems to be solved by the invention) In such a Fourier transform for high resolution imaging, a real Fourier transform of 1024 points (actually, a fast Fourier transform of 512 complex numbers is used to increase the processing speed for calculation. Do)
Let T be the processing time of
The processing time of the Fourier transform of 4096 real numbers is 4 × 1.2T =
4.8T (The number of data increases four times, the number of processing loops increases 11
(/ 9 times), and there is a problem that the calculation time increases to about 5 times.

The present invention has been made in view of such a problem, and an object thereof is to provide a data processing method for image reconstruction capable of extremely rapidly multiplying a spatial frequency for high resolution imaging.

(Means for Solving the Problems) A first invention for achieving such an object is to provide N real or complex image reconstruction data (N = 2 ^γ : γ is an integer).
, And before or after or before or after each of this data, a total of m-1 0 data (real number or complex number) sets are inserted, and a total of m · N (m = 2) ^α ; α is an integer)
When performing the Fourier transform of the real number or complex number data of m and increasing the maximum spatial frequency by m times, if the Fourier transform of the m · N data is directly performed, the Fourier transform of the m · N data is performed. The Fourier transform of the N pieces of data appears repeatedly in the data sequence of N, and the Fourier transform of the N pieces of data is first obtained, and then the result is repeatedly used to obtain the m · N Fourier transforms. According to a second aspect of the present invention, N real or complex image reconstruction data (N = 2 ^γ ; γ) is obtained.
Is an integer), and before or after or before or after each of this data, a total of m-1 N data (real or complex number) is inserted, and a total of m · N ( 2 ^β-1 <
m <2 ^β ; β is an integer) real or complex data,
Furthermore, 0 data is added to this data to obtain a total of m ′ · N data (m ′ = 2 ^α ; α ≧ β: α and β are integers) and Fourier transform is performed to increase the maximum spatial frequency by m times. When increasing, the Fourier transform that increases the maximum spatial frequency by m times is replaced by the Fourier transform that increases the maximum spatial frequency by m ′ times, and this Fourier transform is also performed by the N real or complex numbers. Before or after or before or after each of the image reconstruction data of 0, a total of m′−1 0's per set
Insert a set of data (real number or complex number) to obtain a total of m '.
By directly performing the Fourier transform of N real or complex number data, the fact that the Fourier transform of the N data repeatedly appears in the data sequence after the Fourier transform of the m ′ · N data is used. The Fourier transform of the N data is obtained, and the result is repeatedly used to obtain the m ′ ·
It is characterized by obtaining the results of N Fourier transforms.

The image reconstruction data processing method according to the present invention will be described below.

Consider a case where the maximum spatial frequency is increased by m times by Fourier transform based on N pieces of sampling data for image reconstruction. For simplification, N = 2 ^γ and m = 2 ^α (γ and α are integers). The N sampling data are a ₀ , a ₁ , a ₂ ,
, A _N-1 , sampling data b ₀ , b ₁ , of N ′ = m · N = 2 ^{γ + d} with 0 data inserted as shown in FIG.
_{b 2, ..., b N'-} 1 of the Fourier transform A (k) of can be derived as follows.

However k = 0,1,2, ..., N'-1 where Therefore, A (k + lN) = A (k) where k = 0,1,2, ..., N-1 l = 1,2, ..., m-1 (3) Equation (3) is the Fourier transform N ′. In this data string, it is shown that the Fourier transform of the sampling data a ₀ , a ₁ , a ₂ , ..., A _N-1 appears repeatedly. That is (2)
The formula is the Fourier transform of the number of data N '(= mN) 1 / m
It is shown that this can be done by the Fourier transform of the number N of data. Therefore, Fourier transform A (k) (k = 0,1,2, k) based on N sampling data of a ₀ , a ₁ , a ₂ , ..., a _N-1 as shown in FIG.
, N-1), and for N≤k≤N'-1, the result is repeatedly used according to the equation (3).

The Fourier transform (Equation (2)) of the number of data N is a ₀ , a ₁ , a ₂ , a
₃ , ..., a _N-2 , a _N-1 are real numbers, d ₀ = a ₀ + ja ₁ , d ₁ = a ₂
+ Ja ₃ , ..., d _{N / 2-1} = a _N-2 + ja _N-1 is used as a complex number of N / 2 data, and this compression fast Fourier transform (FFT) is performed. As an example, an algorithm in the case of Bese2FFT, the number of actual data N, in Place method, and DIT method is shown.

(B) N / 2 = 2 ^γ-1 , DN = N / 4, l = 1.

(B) K = 0 and M = 0.

(C) The following calculation is performed for k = K, K + 1, K + 2, ..., K + ND-1.

Cl (k) = Cl- ₁ (k) + Cl- ₁ (k + ND) * W (M) (4-1) Cl (k + ND) = Cl- ₁ (k) -Cl- ₁ (k + ND) * W (M) (4-2) where W (M) = cos {2πp / (N / 2)} + j · sin {2πp / (N / 2)} p = Bit Reverse {M}, J ² = -1 Co (k ) = Ck≡a ₂ k + j · a ₂ k _{+ 1} (4-3) (d) M = M + 2, K = K + 2 · ND, and if K <N / 2, return to (c).

(E) Set ND = ND / 2 and l = l + 1, and if l ≤ γ-1 (b)
Return to.

(F) For k = 0, 1, ..., N / 2−1 (normalization of output data array) q = Bit Reverse {k}, and if q> k, G = C _γ−1 (q) C _γ-1 (q) = C _γ-1 (k) C _γ-1 (k) = G (4-4) To obtain the true result from the result of the compression Fourier transform,
According to the following calculation (unpack processing).

(C _γ-1 (k) ≡C (k) = C _R (k) + j · C _I (k)
And) The above description was for the case where m is expressed in the form of 2 ^γ (γ is an integer), that is, the first invention, but m is 2 ^β-1
When expressed in the form of <m < ^2β (β is an integer), the Fourier transform for increasing the maximum spatial frequency by m times as in the second invention is performed by multiplying the maximum spatial frequency by m ′ (m ′ = 2 ^α ; α ≧
If the Fourier transform that increases to β: α is performed as a proxy (it should be noted that proxying in the direction of increasing the maximum spatial frequency produces a rather good result in obtaining the Fourier transform). (Inconvenience does not occur), but it is possible to shorten the time of Fourier transform. For example, in the case of m = 3 described in the section of the conventional art, β is 2, so that the time can be shortened by using the above method with α = 2, that is, m ′ = 4.

(Example) Hereinafter, an example of the present invention will be described in detail with reference to the drawings.

FIG. 1 is an example of the configuration of an X-ray CT that implements the data processing method of the present invention. In the figure, the table gantry TG is
The X-ray generator XG and the X-ray detector S are equipped,
It is configured to lay down (patient). This subject
An X-edge is generated in the PA from the X-ray generation unit XG by a known method to pass the subject PA, and the X-ray detection unit S converts it into an electric signal. This electric signal is amplified and integrated by the data acquisition device DAS, and converted into a digital signal by the A / D converter to obtain perspective image data. This perspective image data is stored in the data storage device DS1.
Then, the preprocessing device PPC performs preprocessing for reconstruction of the cross-sectional image. The data obtained as a result of the preprocessing is temporarily stored in the data storage device DS2. The data stored in the data storage device DS2 is processed by the low frequency band expansion (frequency down) Fourier transform device LFFT and temporarily stored in the data storage device DS3.

This data is subjected to data processing by the Fourier transform device FFT for spatial frequency multiplication according to the method of the present invention, and the result is temporarily stored in the data storage device DS4. The data stored in the data storage device DS4 is filtered by the filter device FILT, further subjected to the inverse Fourier transform process by the inverse Fourier transform device IFFT, and temporarily stored in the data storage device DS5. This data is processed by the back projection control device BPC to become video data, which is stored in the video data storage device IM. This video data is photographed by the image / picture projection device MFC and displayed on the image display device GDC.

A table / gantry controller TGC is connected to the table / gantry TG, and an X-ray generator controller XGC is connected to the X-ray generator XG, which are configured to control X-ray generation and irradiation, respectively. There is.

The table / gantry control unit TGO, the X-ray generator control unit XGC, the data storage units DS1 to DS5, the processing units, the control unit, and the conversion unit are configured to be controlled by the projection control unit SCC. ing.

In the X-ray CT configured as described above, the subject PA is placed on the table gantry TG, and the fluoroscopic image data obtained as a plurality of N sampling data for each cross-sectional portion of the subject PA is collected in many angular directions. Data storage device DS
After being stored in 1, and subjected to preprocessing, low-frequency expansion processing is executed by the low-frequency expansion Fourier transform device LFFT. The result is stored in DS3. With respect to the data, the Fourier transform device FFT performs data processing based on the above-mentioned method to obtain Fourier image data on the cross-section. This data is stored in the data storage device DS4, subjected to the filtering process by the filter device FILT and the inverse Fourier transform process by the inverse Fourier transform device IFFT to become the data corresponding to the radiation absorption coefficient, and the back projection control device BPC performs the back projection. Then, the image data that forms the distribution of the radiation absorption coefficient of each part is obtained. This is displayed on the image display device GDC and is also photographed by the image photographing device MFC.

The present invention is not limited to the above embodiment.
For example, you can do the following:

(1) Modification of FFT algorithm Basically, this method is followed, but when the FFT algorithm is different (a) When the DIF (Decimation In Frequency) method is used (b) When Base such as Base 4 or Base 8 is different (c) Original If the number of data N ₁ is not N ₁ ≠ 2 ^γ (N ₂ 0
By adding data and setting N ₁ + N ₂ = N = 2 ^γ , etc.) (2) Various configurations can be modified in application to CT equipment.

(Effects of the Invention) As described above, the present invention has the following effects.

(1) The data processing time for spatial frequency multiplication can be minimized, and the data processing speed can be dramatically increased. For example, when the number of data N = 1024,4 times (m = 4) frequency multiplication, by adopting this method, a processing speed (processing time 1/5) about 5 times that of the conventional method can be obtained. This has 409 data
This is because the number of loops in the Fast Fourier Transform (FFT) is reduced from 6 to 1024 (1/4) from 11 to 9 (1 / 1.2). The method of the present invention is a Forward F in Bony Target Reconstruction which is a high resolution image enlargement reconstruction of X-ray CT.
It can be applied to FT, etc., and the above performance can be expected to be dramatically improved.

(2) Higher performance can be achieved without side effects (such as deterioration of CT image quality).

[Brief description of drawings]

FIG. 1 is a block diagram of an X-ray CT using the method of the present invention, and FIG.
FIG. 4 and FIG. 4 are views showing a data array in the conventional Fourier transform, and FIG. 3 is a view showing a data array in the method of the present invention. XG: X-ray generator XGC: X-ray generator controller TGC: Table / gantry controller IM: Video data storage device DS1 to DS5: Data storage device S: X-ray detector, PA: Cover Sample DAS …… Data collection device PPC …… Preprocessing device LFFT …… Low-frequency expansion Fourier transform device FFT …… Fourier transform device FILT …… Filter device IFFT …… Inverse Fourier transform device BPC …… Backprojection device, GDC …… Image display device MFC …… Image photography device SCC …… Shooting control device

Claims (4)

[Claims] 1. N real or complex image reconstruction data (N = 2 ^γ : γ is an integer) are obtained, and before or after or before or after each of these data, a total of m-1 per set is obtained. Insert a set of 0 data (real number or complex number) for each m, N in total
(M = 2 ^α ; α is an integer) Fourier transform of real or complex data is performed, and when the maximum spatial frequency is increased by m times, the Fourier transform of the m · N data is directly performed. Utilizing the fact that the Fourier transform of the N data repeatedly appears in the data string after the Fourier transform of the m · N data, first the Fourier transform of the N data is obtained, and then the result is repeated. Used as above, m · N
A data processing method for image reconstruction, characterized in that the result of each Fourier transform is obtained. 2. In order to obtain the N real or complex image reconstruction data, N ₁ real or complex image reconstruction data (N ₁ ≠ 2 ^γ ; γ is an integer) Patented that N ₂ pieces of 0 data (real number or complex number) are inserted before or after or before and after to obtain the N pieces of image reconstruction data (N = N ₁ + N ₂ ). The data processing method for image reconstruction according to claim 1. 3. When obtaining the Fourier transform of the N data, if the image reconstruction data is a real number, the N data are treated as N / 2 sets of complex number data to perform the Fourier transform. The image processing method for image reconstruction according to claim 1, wherein the Fourier transform of the N pieces of data is obtained. 4. N real or complex image reconstruction data (N = 2 ^γ ; γ is an integer) are obtained, and before or after or before or after each of these data, a total of m-1 per set is obtained. Insert a set of 0 data (real number or complex number) for each m, N in total
(2 ^β-1 <m <2 ^β ; β is an integer) real or complex data is obtained, and 0 data is further added to this data to make a total of m ′ · N data (m ′ = 2 ^α , α ≧ β: α, β
Is an integer) and Fourier transform is performed, and when the maximum spatial frequency is increased by m times, the Fourier transform that increases the maximum spatial frequency by m times is performed by the Fourier transform that increases the maximum spatial frequency by m ′ times. The Fourier transform is also performed on behalf of the real-time or complex-number image reconstruction data before or after or before or after each of the N real or complex image reconstruction data.
-By inserting a set of 0 data (real number or complex number) one by one and directly performing a Fourier transform of a total of m ′ · N real or complex data, after the Fourier transform of m ′ · N data By utilizing the fact that the Fourier transform of the N data repeatedly appears in the data string of, the Fourier transform of the N data is first obtained, and then the result is repeatedly used to obtain the m ′ · N data. A data processing method for image reconstruction, characterized by obtaining a result of Fourier transform.