CN1899219A - Rotary symmetric voxel discretization method for CT reestablishing - Google Patents
Rotary symmetric voxel discretization method for CT reestablishing Download PDFInfo
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- CN1899219A CN1899219A CN 200510012250 CN200510012250A CN1899219A CN 1899219 A CN1899219 A CN 1899219A CN 200510012250 CN200510012250 CN 200510012250 CN 200510012250 A CN200510012250 A CN 200510012250A CN 1899219 A CN1899219 A CN 1899219A
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Abstract
The present invention relates to CT image reconstructing technology, and is especially one rotary symmetric voxel discretizing method for CT reconstruction. The method includes the following steps: 1. calculating the sampling step pitch d based on the reconstructing resolution; 2. discretizing the effective reconstructing height in the scan rotating axis direction into discs of thickness d; 3. discretizing each of the scan discs in the scan rotary radius direction into rings; 4. calculating the voxel numbers in each layer; 5. discretizing each ring in circumference direction; 6. calculating system matrix parameters corresponding to any projection angle; 7. calculating projection/back projection in table look up method; and 8. interpolating the reconstructed image based on the display mode. The method can reduce the required calculation amount and memory space of system matrix coefficients and raise CT reconstruction speed while ensuring the required resolution.
Description
Technical field
The present invention relates to fault image reconstruction technique field, the plain discretization method of rotationally symmetric body in rebuilding especially for CT.
Background technology
Along with the progress in epoch, computer tomography technology (CT) has obtained using widely in medical diagnostic techniqu and Non-Destructive Testing.In the CT algorithm for reconstructing, amount of calculation mainly concentrates on projection/back projection's step.Under the certain situation of CT scan systematic parameter, calculate the sytem matrix of using in projection/back projection in advance, realize that with look-up table projection/back projection is the reconstruction accelerated method of using always.The statistics iterative method has remarkable advantages in the calculating of reconstructed image, but repeatedly the required amount of calculation of iteration is very huge, and the normal look-up table that uses can be avoided the double counting of each iterative process to sytem matrix in iterative method.Simultaneously, look-up table also is applicable to the fixed engineering practical application of systematic parameter.Look-up table has proposed the demand to internal memory when reducing amount of calculation, along with the growth of unknown space dimensionality, the required space of storage system matrix exceeds the capacity of present universal computing platform with the sharp increase of power power.So the use of look-up table at present only limits to wisp or low-resolution image is rebuild.In sum, how to construct matrix elements table efficiently, reducing required memory headroom is the key that look-up table is applied to high-resolution and high dimension image reconstruction, also is the important foundation that the statistics iterative method obtains broader applications in practice.The pole of rotation coordinate method is a kind of method of saving the look-up table required memory and improving the speed of tabling look-up that people propose, but stoped the generally use of this method along with the increase resolution of rebuilding radius can descend, and the equal difference ranking method of this being done behind the method improvement obviously increases the complexity of calculating.
Summary of the invention
In order to overcome the deficiency that above-mentioned existing method exists, the purpose of this invention is to provide the plain discretization method of rotationally symmetric body that a kind of CT of being used for rebuilds.It can reduce required sytem matrix coefficient calculations amount and the memory space of projection/back projection in the CT algorithm for reconstructing under the prerequisite that guarantees resolution, improve the CT reconstruction speed.
In order to reach above-mentioned goal of the invention, technical scheme of the present invention realizes as follows:
A kind of plain discretization method of rotationally symmetric body that is used for the CT reconstruction, its key step is:
1) requires calculating sampling step pitch d according to what rebuild resolution;
2) axis direction of edge scanning rotating shaft will effectively be rebuild and highly be separated into the disk that thickness is d;
3) every layer of disk scanned radius of turn direction discretization in diameter of section is the effective coverage of Nd, be separated into the annulus of N/2+1 ring width d;
4) the voxel number in calculating every layer
Θ is the projection number in the 360 degree scopes;
5) in every layer cross section, each annulus is carried out the circumferencial direction discretization, use M
iRepresent that the discrete of each annulus circumferencial direction count:
1. the center diameter is that the circle of d is as voxel, i.e. a M in each layer
0=1;
2. i=1 in each layer, 2 ... Θ/2 a π annulus, all uniform discrete becomes Θ point;
3. i= Θ in each layer/2 π +1, Θ/2 π +2 ... 2 Θ/2 a π annulus, all uniform discrete becomes 2 Θ points;
4. i= 2 Θ in each layer/2 π +1, 2 Θ/2 π +2 ... 3 Θ/2 a π annulus, all uniform discrete becomes 3 Θ points;
5. as above continue, up to N/2 annulus, uniform discrete becomes J
MaxIndividual point;
6) calculate the corresponding down sytem matrix parameter of degree projection angle arbitrarily;
7) use look-up table and calculate projection/back projection:
1. calculate the projection/back projection of first angle by look-up table;
2. to other projection angle:
8) rebuild finish after, according to display mode the image of the plain discretization of rotationally symmetric body is carried out interpolation.
In above-mentioned discretization method, the annulus spacing that described scanning radius of turn direction discretization obtains and the sample rate of circumferencial direction are selected satisfying under the resolution requirement, and have whole symmetry at interval at all angles.
The present invention compares with prior art owing to adopted above-mentioned method step, produces following beneficial effect:
(1) avoids different projection angles are set up the needs of parameter list, thereby made the required parameter item of look-up table reduce by an order of magnitude, dwindled the limited degree of look-up table on internal memory.Suppose that object is H in the discretization number of plies of axis direction, then discrete bodies prime number order and the N in the one deck that obtains by the inventive method
2H is directly proportional, the item number of total sytem matrix parameter look-up table also with N
2H is directly proportional.The discrete bodies prime number order that traditional voxel discretization method obtains also with N
2H is directly proportional, but owing to the parameter that each projection angle is all needed to calculate separately, projection angle number and N are at the same order of magnitude, so the item number and the N of total parameter look-up table usually
3H is directly proportional.The inventive method utilizes rotational symmetry to avoid different projection angles are set up the needs of parameter list, makes the required parameter item of look-up table reduce by an order of magnitude, has reduced amount of calculation, has dwindled the limited degree of look-up table on internal memory.
(2) the inventive method concerns the sytem matrix that just can calculate from the geometrical relationship of a projection angle under all projection angles by simple geometric, can reduce the projection of ordinary meaning and the amount of calculation of back projection, thereby improves the CT reconstruction speed.
(3) the inventive method can adapt to any resolution requirement, can be by other symmetric use be further reduced the amount of tabling look-up, and the inventive method can directly apply to circular scanning and helical scanning simultaneously.
(4) because the discretization process of the inventive method is applicable to different scan modes, be independent of concrete algorithm for reconstructing, therefore can be incorporated into easily in the existing CT reconstruction software and use.
The present invention will be further described below in conjunction with the drawings and specific embodiments.
Description of drawings
Fig. 1 is a scanning radius of turn direction discretization sketch map in the inventive method;
Fig. 2 is a circumferencial direction discretization sketch map in the inventive method;
Fig. 3 is the plain discretization sketch map of rotationally symmetric body in the inventive method;
Fig. 4 is the geometrical relationship that 0 ray a when spending and b pass voxel (i, 0,0) and (i, j, 0) respectively for using the inventive method projection angle;
Fig. 5 is for using the inventive method object θ that turns clockwise
StepBack ray a and b pass the geometrical relationship of voxel (i, Δ, 0) and (i, j+ Δ, 0) respectively.
The specific embodiment
Referring to Fig. 1 to Fig. 3, the inventive method step is:
1) requires calculating sampling step pitch d according to what rebuild resolution.
2) will effectively rebuild height H d along the axis direction of scanning rotating shaft and be separated into the disk that thickness is d.
3) every layer of disk scanned radius of turn direction discretization in diameter of section is the effective coverage of Nd, be separated into the annulus of N/2+1 ring width d, the center is circle, and the outermost layer annulus has only in the inner part
Wide in effective reconstruction regions.
4) the voxel number in calculating every layer
Θ is the projection number in the 360 degree scopes.
5) in every layer cross section, each annulus is carried out the circumferencial direction discretization, use M
iRepresent that the discrete of each annulus circumferencial direction count, i is the subscript of ring:
1. the center diameter is that the circle of d is as voxel, i.e. a M in each layer
0=1.
2. i=1 in each layer, 2 ... Θ/2 a π annulus, all uniform discrete becomes Θ point.
3. i= Θ in each layer/2 π +1, Θ/2 π +2 ... 2 Θ/2 a π annulus, all uniform discrete becomes 2 Θ points.
4. i= 2 Θ in each layer/2 π +1, 2 Θ/2 π +2 ... 3 Θ/2 a π annulus, all uniform discrete becomes 3 Θ points.
5. as above continue, up to N/2 annulus, uniform discrete becomes J
MaxIndividual point.
6) calculate the corresponding down sytem matrix parameter of 0 degree projection angle with pixel driving method or ray-driven method.
7) use look-up table and calculate projection/back projection:
1. calculate the projection/back projection of first angle by look-up table;
2. to other projection angle:
Rearrangement is corresponding to the sytem matrix parameter of first angle.Referring to Fig. 4 and Fig. 5, at the θ that turns clockwise
StepBehind the projection angle, voxel (i, 0,0) and (i, j, 0) is in full accord with the geometrical relationship of ray a and b when the geometrical relationship of voxel (i, Δ, 0) and (i, j+ Δ, 0) and ray a and b and 0 angle projection angle.Therefore, the parameter to other projection angle can obtain from the result of calculation of first angle.The voxel under this different projection angle and the corresponding relation of detector are as shown in table 1, and θ wherein and b represent the ordinal number of projection angle respectively and at the position of detector index of some angles.
| Voxel | Pass the detector of ray correspondence of voxel and their correlation coefficient | |
| The 0th projection angle | (i，j，k) | (0，b)p |
| The 1st projection angle | (i，(j+J i)mod(J iΘ)，k) | (1，b)p |
| The 2nd projection angle | (i，(j+2J i)mod(J iΘ)，k) | (2，b)p |
| θ projection angle | (i，(j+θJ i)mod(J iΘ)，k) | (θ，b)p |
Table 1
Projection/the back projection of the sytem matrix calculation of parameter correspondence that obtains by rearrangement.
8) rebuild finish after, according to display mode the image of the plain discretization of rotationally symmetric body is carried out interpolation.
The special parameter of in the foregoing description, describing, select other parameter also to belong to the scope of protection of the invention as the case may be.
Claims (2)
1, a kind of plain discretization method of rotationally symmetric body that is used for the CT reconstruction, its key step is:
1) requires calculating sampling step pitch d according to what rebuild resolution;
2) axis direction of edge scanning rotating shaft will effectively be rebuild and highly be separated into the disk that thickness is d;
3) every layer of disk scanned radius of turn direction discretization in diameter of section is the effective coverage of Nd, be separated into the annulus of N/2+1 ring width d;
4) the voxel number in calculating every layer
Θ is the projection number in the 360 degree scopes;
5) in every layer cross section, each annulus is carried out the circumferencial direction discretization, use M
iRepresent that the discrete of each annulus circumferencial direction count:
1. the center diameter is that the circle of d is as voxel, i.e. a M in each layer
0=1;
2. i=1 in each layer, 2 ... Θ/2 a π annulus, all uniform discrete becomes Θ point;
3. i= Θ in each layer/2 π +1, Θ/2 π +2 ... 2 Θ/2 a π annulus, all uniform discrete becomes 2 Θ points;
4. i= 2 Θ in each layer/2 π +1, 2 Θ/2 π +2 ... 3 Θ/2 a π annulus, all uniform discrete becomes 3 Θ points;
5. as above continue, up to N/2 annulus, uniform discrete becomes J
MaxIndividual point;
6) calculate the corresponding down sytem matrix parameter of degree projection angle arbitrarily;
7) use look-up table and calculate projection/back projection:
1. calculate the projection/back projection of first angle by look-up table;
2. to other projection angle:
Rearrangement is corresponding to the sytem matrix parameter of first angle;
8) rebuild finish after, according to display mode the image of the plain discretization of rotationally symmetric body is carried out interpolation.
2, the plain discretization method of rotationally symmetric body that is used for the CT reconstruction according to claim 1, it is characterized in that, the annulus spacing that described scanning radius of turn direction discretization obtains and the sample rate of circumferencial direction are selected satisfying under the resolution requirement, and have whole symmetry at interval at all angles.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103181770A (en) * | 2011-12-30 | 2013-07-03 | 上海联影医疗科技有限公司 | Spiral computed tomography (CT) three-dimensional image reconstruction method and minimum projection number determination method in reconstruction |
| CN106575310A (en) * | 2014-06-02 | 2017-04-19 | 赛峰集团 | Method and device for digital reconstruction of an elementary volume representing a microstructure of composite material |
| EP2666122A4 (en) * | 2011-01-21 | 2018-01-24 | Mercury Systems Inc. | Optimized implementation of back projection for computed tomography (ct) |
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| NL7905282A (en) * | 1979-07-06 | 1981-01-08 | Philips Nv | METHOD AND APPARATUS FOR DETERMINING A RADIATION ABSORPTION DISTRIBUTION IN A SURFACE OF A BODY. |
| WO1989009973A1 (en) * | 1988-04-13 | 1989-10-19 | Analogic Corporation | Backprojection apparatus and method |
| JP3604467B2 (en) * | 1995-09-27 | 2004-12-22 | 株式会社東芝 | Myocardial twist correction method |
| JP3751788B2 (en) * | 2000-02-10 | 2006-03-01 | 独立行政法人科学技術振興機構 | CT image reconstruction system |
| CN1140796C (en) * | 2001-06-08 | 2004-03-03 | 清华大学 | Taxonomic real-time reconstruction checking method of large-size workpiece, defect |
| JP4346297B2 (en) * | 2002-10-22 | 2009-10-21 | 株式会社東芝 | X-ray computed tomography apparatus, image processing apparatus, and image processing method |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2666122A4 (en) * | 2011-01-21 | 2018-01-24 | Mercury Systems Inc. | Optimized implementation of back projection for computed tomography (ct) |
| CN103181770A (en) * | 2011-12-30 | 2013-07-03 | 上海联影医疗科技有限公司 | Spiral computed tomography (CT) three-dimensional image reconstruction method and minimum projection number determination method in reconstruction |
| CN103181770B (en) * | 2011-12-30 | 2014-12-17 | 上海联影医疗科技有限公司 | Spiral computed tomography (CT) three-dimensional image reconstruction method and minimum projection number determination method in reconstruction |
| CN106575310A (en) * | 2014-06-02 | 2017-04-19 | 赛峰集团 | Method and device for digital reconstruction of an elementary volume representing a microstructure of composite material |
| US10599791B2 (en) | 2014-06-02 | 2020-03-24 | Safran | Method and device for digital reconstruction of an elementary volume representing a microstructure of composite material |
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