CN105354868B - Limited angle conical beam CT image rebuilding method based on several picture square - Google Patents

Limited angle conical beam CT image rebuilding method based on several picture square Download PDF

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CN105354868B
CN105354868B CN201510644674.XA CN201510644674A CN105354868B CN 105354868 B CN105354868 B CN 105354868B CN 201510644674 A CN201510644674 A CN 201510644674A CN 105354868 B CN105354868 B CN 105354868B
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radon data
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戴修斌
刘天亮
胡栋
晏善成
石丹丹
邓黄建
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Nanjing Post and Telecommunication University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/008—Specific post-processing after tomographic reconstruction, e.g. voxelisation, metal artifact correction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T15/00—3D [Three Dimensional] image rendering
    • G06T15/06—Ray-tracing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10081—Computed x-ray tomography [CT]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10116—X-ray image
    • G06T2207/10124—Digitally reconstructed radiograph [DRR]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2211/00—Image generation
    • G06T2211/40—Computed tomography
    • G06T2211/416—Exact reconstruction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2215/00—Indexing scheme for image rendering
    • G06T2215/06—Curved planar reformation of 3D line structures

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Abstract

The invention discloses the limited angle conical beam CT image rebuilding methods based on several picture square, step is followed successively by, known Radon data are converted by the cone beam projection data of acquisition, obtain the perspective geometry square transformation of known Radon data, several picture square is calculated according in the transformation of the perspective geometry square of known Radon data, go out the perspective geometry square transformation of unknown Radon data according to several picture moments estimation, unknown Radon data are found out through inverse transformation, known Radon data will be walked and unknown Radon data carry out data split, obtain the three-dimensional Radon data and CT image reconstruction of completion.The present invention can reconstruct the conical beam CT image for meeting clinical diagnosis requirement, high quality under conditions of reducing scanning range.

Description

Limited angle conical beam CT image rebuilding method based on several picture square
Technical field
The present invention relates to a kind of medical image method for reconstructing, in particular to a kind of CT image rebuilding method.
Background technique
As a kind of current effective clinical medicine diagnostic tool of routine, X ray computer tomography technology (X-ray Computerized Tomography, CT) for the diagnosis of clinician provide human organ organizational information abundant.But Shown by correlative study：Primary complete CT scan is usually along with the ionising radiation of higher degree, and high dose ionising radiation The diseases such as human metabolism's exception or even cancer, leukaemia can be induced.Therefore, how the same of X-ray dosage is being reduced When, guarantee the emphasis that reconstructed image quality meets clinical diagnosis requirement as field of medical image processing research.
Clinically reducing one of the important method of sufferer amount of radiation is exactly to reduce CT scan range, i.e., by the rotation of detector Angular range is limited in some and is less than in the section of standard, so that x-ray radiation suffered by patient be greatly reduced on the whole. Although limitation CT equipment scanning range can reduce x-ray radiation suffered by patient, obtained CT data for projection will cause simultaneously Excalation, that is, what is obtained is incomplete data for projection, is decreased obviously CT image reconstruction quality, so that it cannot meet clinical The needs of diagnosis.
The iterative reconstruction approach of statistical model is mainly based upon for limited angle CT image rebuilding method at present.Although should Method remains to obtain preferable reconstructed results in the limited situation of scanning angle, but this method needs to carry out objective function Up to a hundred iterative solutions, CT image reconstruction required calculating time are significantly increased, considerably beyond classical analytic reconstruction method, no It is able to satisfy the requirement of Clinical CT real-time visualization.
Although classical analytic reconstruction method reconstruction speed is fast, image can be lost in the limited situation of scanning angle Original detailed information has seriously affected the resolution to characteristic point so as to cause occurring a large amount of artifacts and noise in reconstruction image.
Summary of the invention
In order to solve the technical issues of above-mentioned background technique proposes, the present invention is intended to provide based on the limited of several picture square Angle conical beam CT image rebuilding method, can be in reduction scanning range --- i.e. symbol is reconstructed under the conditions of incomplete projection data Close the conical beam CT image of clinical diagnosis requirement, high quality.
In order to achieve the above technical purposes, the technical scheme is that：
Limited angle conical beam CT image rebuilding method based on several picture square, includes the following steps：
(1) the incomplete cone beam projection data under the limited angle condition of scanning is obtained；
(2) known three-dimensional Radon number is converted by the cone beam projection data that step (1) obtains using Grangeat formula According to；
(3) transformation of perspective geometry square is carried out to the known three-dimensional Radon data that step (2) obtain；
(4) between the transformation of perspective geometry square and several picture square of the known three-dimensional Radon data that establishment step (3) obtains Relational expression；
(5) relational expression established using step (4), the perspective geometry of the known three-dimensional Radon data obtained from step (3) Several picture square is calculated in square transformation；
(6) relational expression between unknown three-dimensional Radon data and several picture square is established；
(7) relational expression established according to step (6) estimates unknown three-dimensional from the several picture square that step (5) obtain The perspective geometry square of Radon data converts；
(8) the perspective geometry square of the unknown three-dimensional Radon data obtained using the inverse transformation of perspective geometry square from step (7) is become Unknown three-dimensional Radon data are found out in changing；
(9) by the known three-dimensional Radon data that step (2) obtains and the unknown three-dimensional Radon data that step (8) obtains into Row data split obtains the three-dimensional Radon data of completion；
(10) by three-dimensional Radon inverse transformation, the three-dimensional Radon data reconstruction of the completion obtained according to step (9) goes out CT Image.
Further, in step (1), refer under the limited angle condition of scanningRange inward turning Turn scanning, wherein
Further, detailed process is as follows for step (2)：
One of known three-dimensional Radon data about ρ is converted by cone beam projection data first with Grangeat formula Order derivative：
In formula (1),It is first derivative of the known three-dimensional Radon data about ρ, cos β=SO/SCD, CDIt is to put The intersection point of ray and detector plane, then SCDIt is radioactive source S and intersection point CDThe distance between, SO is radioactive source S and coordinate origin O The distance between, ρ is the distance between coordinate origin O and characteristic point C；For from coordinate origin O be directed toward characteristic point C unit to Amount；It is the projection number after the incomplete cone beam projection data obtained in step (1) is weighted According to value, straight line t and line segment OCDVertically, and the vertical range of coordinate origin O to straight line t is s, and p, q are respectively detector plane Axis of abscissas and axis of ordinates, α are line segment OCDWith the angle of detector plane axis of abscissas p；
Then the first derivative to known three-dimensional Radon data about ρIt is integrated, that is, is obtained known three-dimensional Radon data, the three-dimensional Radon data definition are：
In formula (2),It is that 3-D image f existsThe gray value at place,θ It is unit vectorWith the angle of reference axis z.
Further, using SO/SA as weight, the incomplete cone beam projection data obtained in step (1) is added Power obtains projection data values after calculatingWherein, SA is on radioactive source S and straight line t at a distance from the A of arbitrary point.
Further, in the step (3) perspective geometry square transformation definition be：
In formula (3),For in directionOn p rank perspective geometry square convert data.
Further, the definition of the several picture square in the step (4) is：
In formula (4), f (x, y, z) is gray value of the 3-D image f at point (x, y, z).
Then the relational expression between the transformation of p rank perspective geometry square and several picture square of known three-dimensional Radon data is：
Wherein,
Further, detailed process is as follows for the step (5)：
Formula (5) is rewritten into the matrix form as shown in formula (7) first：
Wherein,
M is the maximum order of geometric moment used；
Then matrix division is used to formula (7), obtains several picture square vector：
Further, the perspective geometry square for establishing several picture square Yu unknown three-dimensional Radon data in the step (6) Relational expression between transformation is：
It is the perspective geometry square transformation of unknown Radon data in formula (12),For within the scope of non-scanning angle Vector, i.e.,
Further, the detailed process of the step (7) is：
Formula (12) is rewritten into the matrix form as shown in formula (13) first：
Wherein,
Then several picture square vector Ψ step (5) obtainedMSubstitution formula (13) calculates unknown three-dimensional Radon number According to perspective geometry square transformation
Further, the formula of perspective geometry square inverse transformation is in the step (8)：
Wherein,It is unknown three-dimensional Radon data；
The formula of three-dimensional Radon inverse transformation is in the step (10)：
Wherein,It is the CT image rebuild.
Bring beneficial effect by adopting the above technical scheme：
(1) present invention can be reducing scanning range --- i.e. and it is reconstructed under the conditions of incomplete projection data and meets clinic and examine It is disconnected require, the conical beam CT image of high quality；
(2) since the present invention is not related to interative computation, so calculating the time less than statistics alternative manner；
(3) the conical beam CT image of the invention that less cone beam projection data can be used to reconstruct high quality, therefore this hair It is bright to efficiently reduce x-ray radiation suffered by patient under the premise of guaranteeing CT image reconstruction quality.
Detailed description of the invention
Fig. 1 is the basic procedure schematic diagram of the method for the present invention；
Fig. 2 is the CT image-forming principle schematic diagram of cone-beam projections；
Fig. 3 is unit vector in step (2)Geometrical relationship schematic diagram；
Fig. 4 is the geometrical relationship schematic diagram of straight line t in step (2)；
Fig. 5 is the reconstruction image obtained using traditional filter back-projection reconstruction algorithm；
Fig. 6 is the reconstruction image obtained using the present invention.
Specific embodiment
Below with reference to attached drawing, technical solution of the present invention is described in detail.
Limited angle conical beam CT image rebuilding method based on several picture square, as shown in Figure 1, including the following steps：
Using three-dimensional S hepp-logan head model as computer simulation experiment object, having a size of 512*512*60, CT machine is simulated The distance of x-ray source to rotation center and detector be respectively 570mm and 1040mm.Cone beam CT apparatus rotational scan range For [γ, 360 ° of-γ], wherein γ=50 °；Angular samples value is 1160；Corresponding 672 detector cells in each sampling angle, are visited The size for surveying device unit is 1.407mm.
Step (1) obtains the cone beam projection data under the limited angle condition of scanningSuch as attached drawing 2,3,4 Shown, ρ is the distance between coordinate origin O and characteristic point C, straight line t and line segment OCDVertically, and coordinate origin O is to straight line t's Vertical range is s；For from coordinate origin O be directed toward characteristic point C unit vector, Due to CT equipment not routinely along track [0 °, 360 °) rotary scanning one is enclosed in range, and only limited angle [γ, 360 ° of-γ] rotary scanning in range.Therefore, for acquired cone beam projection dataIts corresponding list Bit vectorParameterIt is worth noting that,WithIn angular range Cone beam projection data is unknown.
Step (2) converts known three-dimensional Radon data for known cone beam projection data using Grangeat formula and closes In the first derivative of ρ.Grangeat formula is：
Wherein,It is first derivative of the known three-dimensional Radon data about ρ；As shown in attached drawing 2,3,4, cos β= SO/SCD, SO is the distance between radioactive source S and coordinate origin O, CDIt is the intersection point of radioactive ray and detector plane, then SCDIt is to put Penetrate source S and intersection point CDThe distance between；ρ is the distance between coordinate origin O and characteristic point C；It is special to be directed toward from coordinate origin O Levy the unit vector of point C；It is to the incomplete cone beam projection data obtained in step (1)Projection data values after being weighted；Weight used is preferably SO/SA, SA be radioactive source S with The distance put on straight line t；Straight line t and line segment OCDVertically, and the vertical range of coordinate origin O to straight line t is s, and p, q are respectively The axis of abscissas and axis of ordinates of detector plane, α are line segment OCDWith the angle of detector plane axis of abscissas p；
Then the first derivative to known three-dimensional Radon data about ρCarrying out integral can be obtained known three-dimensional Radon data
Step (3) calculates known three-dimensional Radon dataPerspective geometry square transformation for mula be：
Wherein,For in directionOn P rank perspective geometry square transformation.
A series of perspective geometry squares transformation that order P is respectively [0,1,2 ..., M] is calculated by formula (2), M is is used Geometric moment maximum order.M=20 in this example.Then, these perspective geometry square transformed values are formed in certain sequence Vector
Step (4), for scanning angle range, design factor matrix
Wherein,
Step (5), it is known that the perspective geometry square of three-dimensional Radon data converts the rectangular of the relationship between several picture square Formula is：
Several picture square vector, which then can be obtained, using formula (5) is：
Several picture square vector ΨMIt is no more than the several picture square G of M by a series of ordersmnqComposition, as follows：
Step (6), for non-scanning angle range, design factor matrix
Wherein,For the vector within the scope of non-scanning angle, i.e., Or
Step (7), the matrix form of relationship between the perspective geometry square transformation of unknown Radon data and several picture square For：
Because of the calculated several picture square Ψ of step (5)MWithIt is unrelated, so step (5) can be obtained several What image moment ΨMAnd the coefficient matrix that step (6) obtainsIt substitutes into formula (9), unknown Radon data can be calculated Perspective geometry square transformationIt is a series of perspective geometry square that orders are not more than MThe vector of composition (0≤p≤M)。
Step (8), perspective geometry square inverse transformation formula are as follows：
Then obtained using formula (10) and step (7)Unknown Radon data can be acquired
Step (9) merges the unknown Radon data estimated according to scanning angle sequence and known Radon data, i.e., It can get the Radon data of completion.
Step (10), three-dimensional Radon inverse transformation formula are as follows：
Using three-dimensional Radon inverse transformation CT image can be reconstructed from the Radon data of completion
In order to compare the effect of method shown in the present invention, using traditional filter back-projection reconstruction algorithm to incomplete taper Beam data for projection is rebuild, and obtained reconstruction image is as shown in Figure 5；And the reconstruction image for using the method for the present invention to obtain is as schemed Shown in 6.Compare the reconstructed results of Fig. 5 and Fig. 6, it can be seen that artifact is relatively fewer in the method for the present invention acquired results, Er Qietou The profile of model is more complete and clear.It can be considered that the condition weight that the method for the present invention can be lacked in part data for projection Build out that artifact is less, the better result of picture quality.
The above examples only illustrate the technical idea of the present invention, and this does not limit the scope of protection of the present invention, all According to the technical idea provided by the invention, any changes made on the basis of the technical scheme each falls within protection model of the invention Within enclosing.

Claims (10)

1. the limited angle conical beam CT image rebuilding method based on several picture square, which is characterized in that include the following steps：
(1) the incomplete cone beam projection data under the limited angle condition of scanning is obtained；
(2) known three-dimensional Radon data are converted by the cone beam projection data that step (1) obtains using Grangeat formula；
(3) transformation of perspective geometry square is carried out to the known three-dimensional Radon data that step (2) obtain；
(4) pass between the transformation of perspective geometry square and several picture square of the known three-dimensional Radon data that establishment step (3) obtains It is formula；
(5) the perspective geometry square of the relational expression established using step (4), the known three-dimensional Radon data obtained from step (3) is become Several picture square is calculated in changing；
(6) relational expression between unknown three-dimensional Radon data and several picture square is established；
(7) relational expression established according to step (6) estimates unknown three-dimensional Radon from the several picture square that step (5) obtain The perspective geometry square of data converts；
(8) using the inverse transformation of perspective geometry square from the transformation of the perspective geometry square for the unknown three-dimensional Radon data that step (7) obtains Find out unknown three-dimensional Radon data；
(9) the unknown three-dimensional Radon data that known three-dimensional Radon data and step (8) that step (2) obtains obtain are counted According to split, the three-dimensional Radon data of completion are obtained；
(10) by three-dimensional Radon inverse transformation, the three-dimensional Radon data reconstruction of the completion obtained according to step (9) goes out CT image.
2. the limited angle conical beam CT image rebuilding method based on several picture square as described in claim 1, it is characterised in that： In step (1), refer under the limited angle condition of scanningRotary scanning in range, wherein
3. the limited angle conical beam CT image rebuilding method based on several picture square as claimed in claim 2, which is characterized in that Detailed process is as follows for step (2)：
Known three-dimensional Radon data are converted by cone beam projection data first with Grangeat formula to lead about the single order of ρ Number：
In formula (1),It is first derivative of the known three-dimensional Radon data about ρ, cos β=SO/SCD, CDIt is radioactive ray With the intersection point of detector plane, then SCDIt is radioactive source S and intersection point CDThe distance between, SO is between radioactive source S and coordinate origin O Distance, P be the distance between coordinate origin O and characteristic point C,For from coordinate origin O be directed toward characteristic point C unit vector,It is the projection data values after the incomplete cone beam projection data obtained in step (1) is weighted, Straight line t and line segment OCDVertically, and the vertical range of coordinate origin O to straight line t is s, and p, q are respectively the horizontal seat of detector plane Parameter and axis of ordinates, a are line segment OCDWith the angle of detector plane axis of abscissas p；
Then the first derivative to known three-dimensional Radon data about ρIt is integrated, that is, obtains known three-dimensional Radon Data, the three-dimensional Radon data definition are：
In formula (2),It is that 3-D image f existsThe gray value at place,θ is single Bit vectorWith the angle of reference axis z.
4. the limited angle conical beam CT image rebuilding method based on several picture square as claimed in claim 3, it is characterised in that： Using SO/SA as weight, projection number is obtained after the incomplete cone beam projection data obtained in step (1) is weighted According to valueWherein, SA is on radioactive source S and straight line t at a distance from the A of arbitrary point.
5. the limited angle conical beam CT image rebuilding method based on several picture square as claimed in claim 3, which is characterized in that In the step (3) perspective geometry square transformation definition be：
In formula (3),For in directionOn p rank perspective geometry square convert data.
6. the limited angle conical beam CT image rebuilding method based on several picture square as claimed in claim 5, which is characterized in that The definition of several picture square in the step (4) is：
In formula (4), f (x, y, z) is gray value of the 3-D image f at point (x, y, z)；
Then the relational expression between the transformation of p rank perspective geometry square and several picture square of known three-dimensional Radon data is：
Wherein,
7. the limited angle conical beam CT image rebuilding method based on several picture square as claimed in claim 6, which is characterized in that Detailed process is as follows for the step (5)：
Formula (5) is rewritten into the matrix form as shown in formula (7) first：
Wherein,
G(k)=[GK,0,M-K,GK-1,1,M-K,…,G1,K-1,M-K,G0,K,M-K]t (9)
M is the maximum order of geometric moment used；
Then matrix division is used to formula (7), obtains several picture square vector：
8. the limited angle conical beam CT image rebuilding method based on several picture square, feature exist as claimed in claims 6 or 7 In the relationship between the perspective geometry square transformation for establishing several picture square and unknown three-dimensional Radon data in the step (6) Formula is：
In formula (12),It is the perspective geometry square transformation of unknown Radon data,For the vector within the scope of non-scanning angle, I.e.
9. the limited angle conical beam CT image rebuilding method based on several picture square as claimed in claim 8, which is characterized in that The detailed process of the step (7) is：
Formula (12) is rewritten into the matrix form as shown in formula (13) first：
Wherein,
G(K)=[GK,0,M-K,GK-1,1,M-K,…,G1,K-1,M-K,G0,K,M-K]t (15)
Then several picture square vector Ψ step (5) obtainedMSubstitution formula (13) calculates the throwing of unknown three-dimensional Radon data The transformation of shadow geometric moment
10. the limited angle conical beam CT image rebuilding method based on several picture square, feature exist as claimed in claim 9 In the formula of perspective geometry square inverse transformation is in the step (8)：
Wherein,It is unknown three-dimensional Radon data；
The formula of three-dimensional Radon inverse transformation is in the step (10)：
Wherein,It is the CT image rebuild.
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