CN116630460A - Detector line differential high-quality image reconstruction method for source linear scanning track - Google Patents

Detector line differential high-quality image reconstruction method for source linear scanning track Download PDF

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CN116630460A
CN116630460A CN202310666193.3A CN202310666193A CN116630460A CN 116630460 A CN116630460 A CN 116630460A CN 202310666193 A CN202310666193 A CN 202310666193A CN 116630460 A CN116630460 A CN 116630460A
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汪志胜
刘悦
崔俊宁
李宗峰
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Harbin Institute of Technology
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Abstract

The method for reconstructing the high-quality image by the line differential of the detector of the source linear scanning track comprises a two-dimensional method and a three-dimensional method, and comprises the following steps: s1, initializing parameters i=1, the number of straight line scanning segments T and the rotation angle interval delta theta, and obtaining a zero space of an image to be reconstructedS2, obtaining projection of linear scanning of the ith section of ray source; s3, pre-weighting projection data; s4, differentiating the weighted projection along the direction of the detector; s5, carrying out weighted back projection on the differential projection to obtain an i-th Hilbert image; s6, carrying out limited Hilbert inverse transformation on the Hilbert image along the ith section of ray source track, and reconstructing an ith section of limited angle imageS7. let i=i+1,s8, if i is less than or equal to T, rotating the linear CT scanning system by an angle (i-1) delta theta, jumping to S2, and sequentially cycling until i is more than T to finish an imageIs performed in the reconstruction of (a). The invention is oriented to a straight line CT scanning track, can directly avoid artifacts caused by truncated projections, can acquire less projections to reconstruct high-quality two-dimensional or three-dimensional images, improves the scanning efficiency and reduces the storage and calculation force requirements on a computing platform.

Description

Detector line differential high-quality image reconstruction method for source linear scanning track
Technical Field
The invention belongs to the field of CT image reconstruction, and particularly relates to a detector line differential high-quality image reconstruction method of a source linear scanning track.
Background
In recent years, in order to meet the higher resolution requirements, a plurality of different CT scanning modes have emerged. Liu Fenglin and Yu Haijun, etc. propose a structure of expanding imaging field of view for linear CT scanning of a radiation source, in which the detector is fixed in imaging geometry, the radiation source is linearly translated in a direction parallel to the detector row, the object to be measured is placed in the center of a turntable, and iterative image reconstruction algorithms based on TV minimization are designed [1,2]. The linear CT scanning structure of the ray source can realize the expansion of imaging vision through controlling the source translation, is easy to realize high-precision control, has great development potential in the technical field of CT scanning, and is sequentially researched along with a series of image reconstruction algorithms suitable for the scanning model.
The iterative image algorithm based on TV minimization is firstly provided, and although the iterative image algorithm can reconstruct an image without artifacts, the reconstruction time is long, the calculation cost is high, and the actual engineering requirements [1,2] are difficult to meet. Although the traditional FBP (filtered back projection) analysis type reconstruction algorithm can perform high-efficiency reconstruction, in the linear CT scanning of the enlarged imaging view field, data truncation exists in the acquired projection data, and then the reconstructed image obtained by the filtered back projection shows serious truncation artifacts [2-5]. In order to avoid truncation artifacts by adopting an FBP type reconstruction algorithm, the prior art adopts a virtual projection mode to realize equivalent global non-truncation projection, and then image reconstruction is carried out [3-5]. Although the method of converting virtual projection can avoid truncation artifacts, a large amount of projection data [5] is required for reconstructing a high-quality image due to the need of filtering along the direction of a source track, so that the scanning efficiency is low, and the storage and calculation power requirements on a computing platform are high.
Reference is made to:
[1] liu Fenglin, yu Haijun, li Lei, tan Chuandong a novel large field-of-view linear scanning CT system and image reconstruction method [ P ]. Chongqing city: CN111839568A,2020-10-30.
[2]H.Yu,L.Li,C.Tan,F.Liu,R.Zhou,X-ray source translation based computed tomography(STCT),Optics Express,29(2021)19743-19758.R.Clackdoyle,F.Noo,A large class of inversion formulae for the 2D Radon transform of functions of compact support,Inverse Problems,20(2004)1281.
[3] Gossypol Wen Jie, yu Haijun, chen Jie, et al source linear scan computed tomography analytical reconstruction based on derivative-hilbert transform-backprojection [ J ]. Optics, 2022,42 (11): 292-303.
[4] Li Lei, yu Haijun, tan Chuandong, duan Xiaojiao, liu Fenglin. Analytical reconstruction algorithm for radiation source translation scanning CT [ J ]. Instructions on instruments and meters, 2022,43 (02): 187-195.DOI:10.19650/j.cnki.cjsi.J2108157.
[5]Yu H,Ni S,Chen J,et al.Analytical reconstruction algorithm for multiple source-translation computed tomography(mSTCT)[J].Applied Mathematical Modelling,2023,117:251-266.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a method for reconstructing a differential high-quality image of a detector of a source linear scanning track, which directly avoids truncation artifacts, reduces the number of projections required for reconstructing a high-resolution image and improves the scanning efficiency of a system.
In order to achieve the above object, the present invention proposes two reconstruction methods, namely a two-dimensional and a three-dimensional method. The two-dimensional method adopts the following technical scheme:
s1, initializing parameters i=1, the number of linear scanning segments T and the rotation angle interval delta theta, and reconstructing a zero space of a two-dimensional image to be reconstructed
S2, acquiring projection of linear scanning of the ith section of ray source
S3, projection of acquisitionPre-weighting to obtain weighted projection +.>
S4, weighting projectionPerforming differential operation along the direction of the detector u;
s5, carrying out weighted back projection operation on the differential projection to obtain an ith Hilbert image
S6, carrying out limited Hilbert inverse transformation on the ith section Hilbert image along the linear translation track direction of the ith section ray source, and reconstructing the ith section limited angle image
S7, executing i=i+1, and finishing superposition of images:
s8, if i is less than or equal to T, rotating the linear CT scanning system by an angle (i-1) delta theta, jumping to S2, and sequentially cycling until i is more than T to finish an imageIs performed in the reconstruction of (a).
Preferably, for a method of reconstructing a detector differentiated high quality two-dimensional image of a source linear scan trajectory, in step S3, the projectionsPre-weighting results in a weighted projection +.>The calculation formula is that
wherein ,θi Is the direction angle theta of the linear scanning track of the ray source i = (i-1) ·Δθ; lambda represents the coordinates of the source on a straight line trajectory, lambda epsilon-s, s]The method comprises the steps of carrying out a first treatment on the surface of the u represents the coordinates of the detector, and u E [ -d, d]D represents half the detector length; l represents the distance from the source to the centre of rotation in the direction perpendicular to the detector; h represents the distance from the center of rotation to the center of the detector;is a redundant weight factor.
Preferably, for the method of reconstructing a detector differential high quality two-dimensional image of a source linear scan trajectory, in step S4, the weighted projectionsDifferential projection is obtained by differential operation in the direction of detector u>The calculation formula is that
wherein ,representing a differential operator, realizing by finite difference operation, wherein data in projection adopts center difference, and data in projection boundary adopts single-side difference; u (u) * Represents crossing the point to be reconstructed->Is used to determine the coordinates of the rays of (a) on the detector,
wherein L represents a point to be reconstructedPerpendicular distance to the source trajectory, l= -x sin θ i +y cosθ i +l; h represents the point to be reconstructed +.>Vertical distance to detector, h=xsin θ i -y cosθ i +h。
Preferably, for a method of reconstructing a detector differential high quality two-dimensional image of a source linear scan trajectory, in step S5, the differential projectionWeighted back projection operation is carried out to obtain i-th Hilbert image +.>The calculation formula is that
in the formula ,representing a point to be reconstructed; s is half of the linear translation length of the ray source; η (eta) i Representing the Hilbert image for the i th segment>A direction angle for performing a limited Hilbert inverse transform; 1/L 2 Weighting factors for the backprojection; the back projection operation is performed in a matrix larger than the image to be reconstructed, i.e. p is added outside each edge of the matrix space of the image to be reconstructed 0 Zero in number =0.5×i, where I is the row or column number of the matrix of images to be reconstructed.
Preferably, for the method of reconstructing a high-quality two-dimensional image of the detector differential of the source linear scan trajectory, in step S6, the pair of i-th segment Hilbert imagesThe limited Hilbert inverse transformation is carried out along the direction of the linear translation track of the ith section ray source, and the ith section limited angle image can be reconstructed>The calculation formula is that
wherein ,y1 Representing the one-dimensional Hilbert transform direction, y 1 ∈[L y +ε y ,U y -ε y], wherein [Ly ,U y ]Representing the finite interval, ε, of the Hilbert transform y Is a small positive number;representing reconstructing an i-th segment limited angle image +.>The unknown constant that needs to be calculated is determined by finding the known +.>Is used as the mean value after being subjected to the finite Hilbert transformationHilbert image of section i->A specific implementation of the limited inverse hilbert transform comprises the steps of:
1) Image of Hilbert section iDot-2 pi and rotate around the center of the image by-eta i Obtaining a rotated Hilbert image +.> wherein ηi ＝θ i Pi/2 (i=1, 2,., T), angle value positive, image counter-clockwise rotation; the angle is negative and the image rotates clockwise;
2) Calculating a weight matrix W mat I.e.
3) Searching for rotated Hilbert imagesThe values of which rows are all 0, and an array R with the elements being row numbers is obtained i ；
4) To rotating Hilbert imagesWeighting W mat And performing Hilbert transform along the matrix array direction to obtain image +.>
5) According to R obtained in step S3 i Numerical value, slave imageThe elements are extracted from the middle rope, and the average value is calculated along the column direction and is inverted to obtain +.>
6) Execution of
7) Will rotate the imageRotation angle eta about the center of the image i To the original state, get ∈>
8) An intermediate image region to be reconstructed is extracted,
the differential high-quality three-dimensional image reconstruction method for the detector of the source linear scanning track adopts the following technical scheme:
s1, initializing parameters i=1, the number of straight line scanning segments T and the rotation angle interval delta theta, and reconstructing a zero space of a three-dimensional image
S2, acquiring cone beam projection of linear scanning of an ith section of ray source
S3, projecting collected cone beamsPre-weighting to obtain weighted cone beam projection +.>
S4, projecting the weighted cone beamsPerforming differential operation along the direction of the panel detector row u;
s5, carrying out weighted back projection operation on the differential cone beam projection to obtain an ith section of three-dimensional Hilbert image
S6, carrying out limited Hilbert inverse transformation on the ith section of three-dimensional Hilbert image layer by layer axially along the direction of linear translation track of the ith section of ray source, and reconstructing the ith section of limited angle three-dimensional image
S7, executing i=i+1, and finishing superposition of three-dimensional images:
s8, if i is less than or equal to T, enabling the linear CT scanning system to rotate by an angle (i-1) delta theta, jumping to S2, and sequentially cycling until i is more than T, and completing the three-dimensional imageIs performed in the reconstruction of (a).
Preferably, for the method of reconstructing a detector differential high quality three-dimensional image of a source linear scan trajectory, in step S3, the cone beam projectionsPre-weighting to obtain weighted cone beam projections +.>The calculation formula is that
wherein ,θi Is the direction angle theta of the linear scanning track of the ray source i = (i-1) ·Δθ; lambda represents the coordinates of the source on a straight line trajectory, lambda epsilon-s, s]The method comprises the steps of carrying out a first treatment on the surface of the u represents the line-wise coordinates of the panel detector, and u E [ -d, d]D represents half of the line length of the panel detector; l represents the distance from the source to the center of rotation in the direction perpendicular to the panel detector; h represents the distance from the center of rotation to the center of the panel detector;is a redundant weight factor.
Preferably, for the method of reconstructing a high quality three-dimensional image of the detector differential of the source linear scan trajectory, in step S4, the weighted cone beam projectionsDifferential operation is performed along the u direction of the panel detector row to obtain differential cone beam projectionThe calculation formula is that
wherein ,the differential operator along the u direction is realized by finite difference operation, the data in the projection adopts center difference, and the data of the projection boundary adopts single-side difference; u (u) * Represents crossing the point to be reconstructed->Is of (2)The line-wise coordinate of the line on the panel detector, v denotes the +.>The column-wise coordinates of the rays of (a) on the panel detector,
wherein L represents a point to be reconstructedPerpendicular distance to the source trajectory, l= -x sin θ i +y cosθ i +l; h represents the point to be reconstructed +.>Vertical distance to panel detector, h=xsin θ i -y cosθ i +h。
Preferably, for the method of reconstructing a detector differential high quality three-dimensional image of a source linear scan trajectory, in step S5, the differential cone beam projectionsPerforming weighted back projection operation to obtain an ith section of three-dimensional Hilbert imageThe calculation formula is that
in the formula ,representing points to be reconstructedThe method comprises the steps of carrying out a first treatment on the surface of the s is half of the linear translation length of the ray source; η (eta) i Representing +.>A direction angle for performing a limited Hilbert inverse transform; 1/L 2 Weighting factors for the backprojection; the back projection operation is completed in a matrix larger than the three-dimensional image to be reconstructed, namely, p is added outside each edge of the matrix space of the three-dimensional image to be reconstructed 0 Zero in number =0.5×i, where I is the number of voxels in a certain dimension of the image to be reconstructed.
Preferably, for the method of reconstructing a high quality three-dimensional image of the detector differential of the source linear scan trajectory, in step S6, the method comprises the step of reconstructing the i-th segment of the three-dimensional Hilbert imageAxially carrying out the inverse Hilbert transformation layer by layer along the linear translation track direction of the ith section of ray source, namely, z by z k (k=1, 2,., I) inverse transforming the two-dimensional Hilbert image layer by layer, thereby reconstructing an I-th limited-angle three-dimensional image +.>The inverse transform of the two-dimensional Hilbert image is also along x j (j=1, 2,., I) one-dimensional processing is performed piece by piece, and the calculation formula is
wherein ,y1 Representing the one-dimensional Hilbert transform direction, y 1 ∈[L y +ε y ,U y -ε y], wherein [Ly ,U y ]Representing the finite interval, ε, of the Hilbert transform y Is a small positive number;representing reconstruction->The unknown constant that needs to be calculated is determined by finding the known +.>Is used as +.>Three-dimensional Hilbert image for the ith segment->Is subjected to a limited Hilbert inverse transformation layer by layer in the axial direction, and comprises the following steps:
1) Three-dimensional Hilbert image of the ith sectionDot-2 pi and rotate around the central axis of the three-dimensional image by-eta i Angle, obtain rotated three-dimensional Hilbert image +.> wherein ηi ＝θ i Pi/2 (i=1, 2,., T), the angle value being positive, the three-dimensional image rotating anticlockwise; the angle is negative, and the three-dimensional image rotates clockwise;
2) Calculate one-dimensional weight sequence W mat I.e.
3) for (k=1; k is less than or equal to I; k++) (i.e., into the for loop body):
3.1 From a rotated three-dimensional Hilbert imageIndexing out a kth layer two-dimensional Hilbert image
3.2 Searching for two-dimensional Hilbert imagesThe values of which rows are all 0, and an array R with the elements being row numbers is obtained i ；
3.3 For two-dimensional Hilbert imageWeighting W mat And performing Hilbert transform along the matrix array direction to obtain image +.>
3.4 According to R obtained in step S3 i Numerical value, slave imageThe elements are extracted from the middle rope, and the average value is calculated along the column direction and is inverted to obtain +.>
3.5 Execution of (1)
3.6 A two-dimensional image to be rotated)Rotation angle eta about the center of the image i To the original state, the reconstructed k layer two-dimensional +.>
4) Extracting intermediate three-dimensional image regions to be reconstructed, i.e.
The invention has the beneficial effects that:
compared with the existing reconstruction algorithm for linear CT scanning of the ray source, the method can utilize truncated projection data to carry out accurate reconstruction, directly avoid truncation artifacts, reconstruct by using less projection data to obtain high-quality images, improve scanning efficiency, and is higher in reconstruction efficiency and more suitable for practical engineering application.
Drawings
Fig. 1 is a schematic flow chart of the present invention.
Fig. 2 is a schematic diagram of a ray source linear CT two-dimensional scanning imaging structure according to the present invention.
FIG. 3 is a flow chart of two-dimensional image reconstruction using a Shepp-Logan phantom as a measured object in the invention.
Fig. 4 is a two-dimensional reconstructed image of different projection numbers of a measured object using a fouild phantom in accordance with the present invention.
Fig. 5 is a schematic diagram of a ray source linear cone beam CT three-dimensional scan trajectory for which the present invention is directed.
Fig. 6 is a schematic representation of the limited inverse Hilbert transform of the three-dimensional Hilbert image of the present invention axially layer by layer.
Fig. 7 is a flow chart of three-dimensional CT image reconstruction of the present invention.
FIG. 8 shows the results of the reconstructed images of the present invention under different projection numbers with a three-dimensional Shepp-Logan phantom as the object under test.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings and examples.
A method for reconstructing a differential high-quality image of a detector of a source linear scan trajectory, as shown in fig. 1, wherein the method for reconstructing a differential high-quality two-dimensional image of a detector of a source linear scan trajectory comprises the following steps:
s1, initializing parameters i=1, the number of linear scanning segments T and the rotation angle interval delta theta, and reconstructing a zero space of a two-dimensional image to be reconstructed
S2, obtainingProjection of linear scan of ith section of ray source
S3, projection of acquisitionPre-weighting to obtain weighted projection +.>
S4, weighting projectionPerforming differential operation along the direction of the detector u;
s5, carrying out weighted back projection operation on the differential projection to obtain an ith Hilbert image
S6, carrying out limited Hilbert inverse transformation on the ith section Hilbert image along the linear translation track direction of the ith section ray source, and reconstructing the ith section limited angle image
S7, executing i=i+1, and finishing superposition of images:
s8, if i is less than or equal to T, rotating the linear CT scanning system by an angle (i-1) delta theta, jumping to S2, and sequentially cycling until i is more than T to finish an imageIs performed in the reconstruction of (a).
Preferably, for a method of reconstructing a detector differentiated high quality two-dimensional image of a source linear scan trajectory, in step S3, the projectionsPre-weighting results in a weighted projection +.>The calculation formula is that
wherein ,θi Is the direction angle theta of the linear scanning track of the ray source i = (i-1) ·Δθ; lambda represents the coordinates of the source on a straight line trajectory, lambda epsilon-s, s]The method comprises the steps of carrying out a first treatment on the surface of the u represents the coordinates of the detector, and u E [ -d, d]D represents half the detector length; l represents the distance from the source to the centre of rotation in the direction perpendicular to the detector; h represents the distance from the center of rotation to the center of the detector;is a redundant weight factor.
Preferably, for the method of reconstructing a detector differential high quality two-dimensional image of a source linear scan trajectory, in step S4, the weighted projectionsDifferential projection is obtained by differential operation in the direction of detector u>The calculation formula is that
wherein ,the differential operator along the u direction is realized by finite difference operation, the data in the projection adopts center difference, and the data of the projection boundary adopts single-side difference; u (u) * Represents crossing the point to be reconstructed->Is used to determine the coordinates of the rays of (a) on the detector,
wherein L represents a point to be reconstructedPerpendicular distance to the source trajectory, l= -x sin θ i +y cosθ i +l; h represents the point to be reconstructed +.>Vertical distance to detector, h=xsin θ i -y cosθ i +h。
Preferably, for a method of reconstructing a detector differential high quality two-dimensional image of a source linear scan trajectory, in step S5, the differential projectionWeighted back projection operation is carried out to obtain i-th Hilbert image +.>The calculation formula is that
in the formula ,representing a point to be reconstructed; s is half of the linear translation length of the ray source; η (eta) i Representing the Hilbert image for the i th segment>A direction angle for performing a limited Hilbert inverse transform; 1/L 2 Is reversely thrownA shadow weighting factor; the back projection operation is performed in a matrix larger than the image to be reconstructed, i.e. p is added outside each edge of the matrix space of the image to be reconstructed 0 Zero in number =0.5×i, where I is the image row or column number to be reconstructed.
Preferably, for the method of reconstructing a high-quality two-dimensional image of the detector differential of the source linear scan trajectory, in step S6, the pair of i-th segment Hilbert imagesThe limited Hilbert inverse transformation is carried out along the direction of the linear translation track of the ith section ray source, and the ith section limited angle image can be reconstructed>The calculation formula is that
wherein ,y1 Representing the one-dimensional Hilbert transform direction, y 1 ∈[L y +ε y ,U y -ε y], wherein [Ly ,U y ]Representing the finite interval, ε, of the Hilbert transform y Is a small positive number;representing reconstructing an i-th segment limited angle image +.>The unknown constant that needs to be calculated is determined by finding the known +.>Is used as the mean value after being subjected to the finite Hilbert transformationHilbert image of section i->A specific implementation of the limited inverse hilbert transform comprises the steps of:
1) Image of Hilbert section iDot-2 pi and rotate around the center of the image by-eta i Obtaining a rotated Hilbert image +.> wherein ηi ＝θ i Pi/2 (i=1, 2,., T), angle value positive, image counter-clockwise rotation; the angle is negative and the image rotates clockwise;
2) Calculating a weight matrix W mat I.e.
3) Searching for rotated Hilbert imagesThe values of which rows are all 0, and an array R with the elements being row numbers is obtained i ；
4) To rotating Hilbert imagesWeighting W mat And performing Hilbert transform along the matrix array direction to obtain image +.>
5) According to R obtained in step S3 i Numerical value, slave imageThe elements are extracted from the middle rope, and the average value is calculated along the column direction and is inverted to obtain +.>
6) Execution of
7) Will rotate the imageRotation angle eta about the center of the image i To the original state, get ∈>
8) An intermediate image region to be reconstructed is extracted,
the differential high-quality three-dimensional image reconstruction method for the detector of the source linear scanning track adopts the following technical scheme:
s1, initializing parameters i=1, the number of straight line scanning segments T and the rotation angle interval delta theta, and reconstructing a zero space of a three-dimensional image
S2, acquiring cone beam projection of linear scanning of an ith section of ray source
S3, projecting collected cone beamsPre-weighting to obtain weighted cone beam projection +.>
S4, projecting the weighted cone beamsDifferential operation along panel detector row u direction；
S5, carrying out weighted back projection operation on the differential cone beam projection to obtain an ith section of three-dimensional Hilbert image
S6, carrying out limited Hilbert inverse transformation on the ith section of three-dimensional Hilbert image layer by layer axially along the direction of linear translation track of the ith section of ray source, and reconstructing the ith section of limited angle three-dimensional image
S7, executing i=i+1, and finishing superposition of three-dimensional images:
s8, if i is less than or equal to T, enabling the linear CT scanning system to rotate by an angle (i-1) delta theta, jumping to S2, and sequentially cycling until i is more than T, and completing the three-dimensional imageIs performed in the reconstruction of (a).
Preferably, for the method of reconstructing a detector differential high quality three-dimensional image of a source linear scan trajectory, in step S3, the cone beam projectionsPre-weighting to obtain weighted cone beam projections +.>The calculation formula is that
wherein ,θi Is the direction angle theta of the linear scanning track of the ray source i = (i-1) ·Δθ; lambda represents the coordinates of the source on a straight line trajectory, lambda epsilon-s, s]The method comprises the steps of carrying out a first treatment on the surface of the u represents the line-wise coordinates of the panel detector, and u E [ -d, d]D represents the panel detectionHalf of the length of the detector in the row direction; l represents the distance from the source to the center of rotation in the direction perpendicular to the panel detector; h represents the distance from the center of rotation to the center of the panel detector;is a redundant weight factor.
Preferably, for the method of reconstructing a high quality three-dimensional image of the detector differential of the source linear scan trajectory, in step S4, the weighted cone beam projectionsDifferential operation is performed along the u direction of the panel detector row to obtain differential cone beam projectionThe calculation formula is that
wherein ,the differential operator along the u direction is realized by finite difference operation, the data in the projection adopts center difference, and the data of the projection boundary adopts single-side difference; u (u) * Represents crossing the point to be reconstructed->The row-wise coordinate of the rays of (2) on the panel detector, v denotes the +.>The column-wise coordinates of the rays of (a) on the panel detector,
wherein L represents a point to be reconstructedPerpendicular distance to the source trajectory, l= -x sin θ i +y cosθ i +l; h represents the point to be reconstructed +.>Vertical distance to panel detector, h=xsin θ i -y cosθ i +h。
Preferably, for the method of reconstructing a detector differential high quality three-dimensional image of a source linear scan trajectory, in step S5, the differential cone beam projectionsPerforming weighted back projection operation to obtain an ith section of three-dimensional Hilbert imageThe calculation formula is that
in the formula ,representing a point to be reconstructed; s is half of the linear translation length of the ray source; η (eta) i Representing +.>A direction angle for performing a limited Hilbert inverse transform; 1/L 2 Weighting factors for the backprojection; the back projection operation is completed in a matrix larger than the three-dimensional image to be reconstructed, namely, p is added outside each edge of the matrix space of the three-dimensional image to be reconstructed 0 Zero in number =0.5×i, where I is the graph to be reconstructedPixel number in a certain dimension direction.
Preferably, for the method of reconstructing a high quality three-dimensional image of the detector differential of the source linear scan trajectory, in step S6, the method comprises the step of reconstructing the i-th segment of the three-dimensional Hilbert imageAxially carrying out the inverse Hilbert transformation layer by layer along the linear translation track direction of the ith section of ray source, namely, z by z k (k=1, 2,., I) inverse transforming the two-dimensional Hilbert image layer by layer, thereby reconstructing an I-th limited-angle three-dimensional image +.>The inverse transform of the two-dimensional Hilbert image is also along x j (j=1, 2,., I) one-dimensional processing is performed piece by piece, and the calculation formula is
wherein ,y1 Representing the one-dimensional Hilbert transform direction, y 1 ∈[L y +ε y ,U y -ε y], wherein [Ly ,U y ]Representing the finite interval, ε, of the Hilbert transform y Is a small positive number; c (C) yi Representation reconstructionThe unknown constant that needs to be calculated is determined by finding the known +.>Is used as +.>Three-dimensional Hilbert image for the ith segment->Is inverse Hilbert-dependent on the axial directionThe specific implementation method comprises the following steps:
1) Three-dimensional Hilbert image of the ith sectionDot-2 pi and rotate around the central axis of the three-dimensional image by-eta i Angle, obtain rotated three-dimensional Hilbert image +.> wherein ηi ＝θ i Pi/2 (i=1, 2,., T), the angle value being positive, the three-dimensional image rotating anticlockwise; the angle is negative, and the three-dimensional image rotates clockwise;
2) Calculate one-dimensional weight sequence W mat I.e.
3) for (k=1; k is less than or equal to I; k++) (i.e., into the for loop body):
3.1 From a rotated three-dimensional Hilbert imageIndexing out a kth layer two-dimensional Hilbert image
3.2 Searching for two-dimensional Hilbert imagesThe values of which rows are all 0, and an array R with the elements being row numbers is obtained i ；
3.3 For two-dimensional Hilbert imageWeighting W mat And performing Hilbert transform along the matrix array direction to obtain image +.>
3.4 According to R obtained in step S3 i Numerical value, slave imageThe elements are extracted from the middle rope, and the average value is calculated along the column direction and is inverted to obtain +.>
3.5 Execution of (1)
3.6 A two-dimensional image to be rotated)Rotation angle eta about the center of the image i To the original state, the reconstructed k layer two-dimensional +.>/>
4) Extracting intermediate three-dimensional image regions to be reconstructed, i.e.
Fig. 2 shows a schematic diagram of the first two-stage scanning in a linear CT two-dimensional scanning structure of a radiation source, which corresponds to the 1 st-stage linear scanning of the radiation source and the 2 nd-stage linear scanning of the radiation source of the present invention.
Fig. 3 shows a two-dimensional image reconstruction process according to the present invention when the Shepp-Logan phantom is used as the object to be measured, and it can be found that the method can reconstruct an image without artifacts.
The number of pixels is 512 by 512 and the size is 8.4mm by 8.4mm using the FORBILD phantom. The image reconstruction effect of the invention is evaluated by quantitative numerical experiments. The result of the reconstructed image is shown in fig. 3, the condition of different projection numbers N under each section of linear CT scan of the radiation source is set, the front projection of the forbid phantom is calculated in a simulation mode and reconstructed by adopting the method, the quality of the reconstructed image is observed, N is respectively set to be 50, 100, 200, 400, 600 and 800, and the parameter settings of the numerical experiment are shown in table 1.
As can be seen from the reconstruction result shown in fig. 4, the present method can clearly see some details from the enlarged image when the number of projections is small, but when the number of projections is reduced to 50, the present method is susceptible to the interference of the artifacts caused by the light sparsity, but can reconstruct the key details, as shown in fig. 4 (a) and fig. 4. Table 2 lists three quantization indices that evaluate the quality of the reconstructed image, including: root Mean Square Error (RMSE), peak signal to noise ratio (PSNR), and Feature Similarity Index (FSIM). The lower the RMSE, the higher the PSNR and FSIM, and the better the reconstructed image quality. It can be seen that the present invention can reconstruct a high quality image with a small number of projections.
Table 1 numerical simulation test parameters
Table 2 quantitative evaluation of reconstructed images
Fig. 5 shows a linear CT scan three-dimensional structure of a radiation source, and fig. 6 shows a three-dimensional Hilbert image for the i-th segmentAnd (3) carrying out finite Hilbert inverse transformation axially layer by layer along the linear translation track direction of the ith section of ray source.
Fig. 7 shows a basic flow of three-dimensional image reconstruction according to the present invention, which can prove the effectiveness of the method, and can reconstruct an image without artifacts.
Further, a three-dimensional Shepp-Logan phantom is used, the number of pixels was 512×512, and the size was 8.4mm×8.4mm. The image reconstruction effect of the invention is evaluated by quantitative numerical experiments. The result of the reconstructed image is shown in fig. 8, the condition of different projection numbers N under each section of ray source straight line CT scan is set, the cone beam orthographic projection of the three-dimensional Shepp-Logan phantom is simulated and calculated, the reconstruction is carried out by adopting the invention, the quality of the reconstructed image is observed, N is set as 200 and 1600 respectively, and the parameter settings of the numerical experiment are shown in table 3. As can be seen from the reconstruction results shown in fig. 8, the present invention can reconstruct a high-quality three-dimensional image with a small number of projections.
Table 3 numerical simulation test parameters
The invention is not limited to the specific embodiments described above, which are intended to be illustrative only and not limiting; those skilled in the art, having the benefit of this disclosure, may make numerous forms without departing from the spirit of the invention and the scope of the claims which follow.

Claims (6)

1. The method for reconstructing the high-quality image by the line differential of the detector of the source linear scanning track is characterized by comprising the following steps of:
s1, initializing parameters i=1, the number of straight line scanning segments T and the rotation angle interval delta theta, and reconstructing a zero space of an image to be reconstructed
S2, acquiring projection of linear scanning of the ith section of ray sourceOr->
S3, projection of acquisitionOr->Pre-weighting to obtain weighted projection +.>Or (b)
S4, weighting projectionOr->Performing differential operation along the direction of the detector u;
s5, carrying out weighted back projection operation on the differential projection to obtain an ith Hilbert image
S6, carrying out limited Hilbert inverse transformation on the ith section Hilbert image along the linear translation track direction of the ith section ray source, and reconstructing the ith section limited angle image
S7, executing i=i+1, and finishing superposition of images:
s8, if i is less than or equal to T, rotating the linear CT scanning system by an angle (i-1) delta theta, jumping to S2, and sequentially cycling until i is more than T to finish an imageIs performed in the reconstruction of (a).
2. The method for reconstructing a high-quality image of a detector line-wise differential of a source linear scan trajectory of claim 1, wherein in step S3, said projectionOr->Pre-weighting results in a weighted projection +.>Or (b)The calculation formula is that
Or (b)
wherein ,θi Is the direction angle theta of the linear scanning track of the ray source i = (i-1) ·Δθ; lambda represents the coordinates of the source on a straight line trajectory, lambda epsilon-s, s]The method comprises the steps of carrying out a first treatment on the surface of the u represents the coordinates of the detector, and u E [ -d, d]D represents half the detector length; l represents the distance from the source to the centre of rotation in the direction perpendicular to the detector; h represents the distance from the center of rotation to the center of the detector;or->Is a redundant weight factor.
3. The method of reconstructing a high quality image of a detector line differential of a source linear scan trajectory of claim 1, wherein in step S4 the weighted projectionsDifferential projection is obtained by differential operation along the direction of the detector uThe calculation formula is that
wherein ,representing a differential operator, realizing by finite difference operation, wherein data in projection adopts center difference, and data in projection boundary adopts single-side difference; u (u) * Represents crossing the point to be reconstructed->Is used to determine the coordinates of the rays of (a) on the detector,
wherein L represents a point to be reconstructedPerpendicular distance to the source trajectory, l= -xsin θ i +ycosθ i +l; h represents the point to be reconstructed +.>Vertical distance to detector, h=xsin θ i -ycosθ i +h。
4. The method for reconstructing a high quality image of a detector line differential of a source linear scan trajectory of claim 1, wherein in step S5, said differential projectionWeighted back projection operation is carried out to obtain i-th Hilbert image +.>The calculation formula is that
in the formula ,representing a point to be reconstructed; s is half of the linear translation length of the ray source; η (eta) i Representing the Hilbert image for the i th segment>A direction angle for performing a limited Hilbert inverse transform; 1/L 2 Weighting factors for the backprojection; the back projection operation is performed in a matrix larger than the image to be reconstructed, i.e. p is added outside each edge of the matrix space of the image to be reconstructed 0 Zero in number =0.5×i, where I is the image row or column number to be reconstructed.
5. The method for reconstructing a high-quality image of a detector line differential of a source linear scan trajectory as set forth in claim 1, wherein in step S6 said pair of i-th segment Hilbert imagesThe limited Hilbert inverse transformation is carried out along the direction of the linear translation track of the ith section ray source, and the ith section limited angle image can be reconstructed>The calculation formula is that
wherein ,y1 Representing the one-dimensional Hilbert transform direction, y 1 ∈[L y +ε y ,U y -ε y], wherein [Ly ,U y ]Representing the finite interval, ε, of the Hilbert transform y Is a small positive number;representing reconstructing an i-th segment limited angle image +.>The unknown constant that needs to be calculated is determined by finding the known +.>Is used as +.>Hilbert image of section i->A specific implementation of the limited inverse hilbert transform comprises the steps of:
1) Image of Hilbert section iDot-2 pi and rotate around the center of the image by-eta i At least one of the first and second end portions,obtaining a rotated Hilbert image-> wherein ηi ＝θ i Pi/2 (i=1, 2,., T), angle value positive, image counter-clockwise rotation; the angle is negative and the image rotates clockwise;
2) Calculating a weight matrix W mat I.e.
3) Searching for rotated Hilbert imagesThe values of which rows are all 0, and an array R with the elements being row numbers is obtained i ；
4) To rotating Hilbert imagesWeighting W mat Hilbert transformation is carried out along the image matrix array direction to obtain an image
5) According to R obtained in step S3 i Numerical value, slave imageThe elements are extracted from the middle rope, and the average value is calculated along the column direction and is inverted to obtain +.>
6) Execution of
7) Will rotate the imageRotation angle eta about the center of the image i To the original state, get ∈>
8) An intermediate image region to be reconstructed is extracted,
6. the method for reconstructing a high-quality three-dimensional image of a detector line differential of a source linear scan trajectory according to claim 1, wherein in step S6, said pair of i-th segment three-dimensional Hilbert imagesAxially carrying out the inverse Hilbert transformation layer by layer along the linear translation track direction of the ith section of ray source, namely, z by z k (k=1, 2,., I) inverse transforming the two-dimensional Hilbert image layer by layer, thereby reconstructing an I-th limited-angle three-dimensional image +.>The inverse transform of the two-dimensional Hilbert image is also along x j (j=1, 2,., I) one-dimensional processing is performed piece by piece, and the calculation formula is
wherein ,y1 Representing the one-dimensional Hilbert transform direction, y 1 ∈[L y +ε y ,U y -ε y], wherein [Ly ,U y ]Representing the finite interval, ε, of the Hilbert transform y Is a small positive number;representing reconstruction->The unknown constant that needs to be calculated is determined by finding the known +.>Is used as +.>Three-dimensional Hilbert image for the ith segment->Is subjected to a limited Hilbert inverse transformation layer by layer in the axial direction, and comprises the following steps:
1) Three-dimensional Hilbert image of the ith sectionDot-2 pi and rotate around the central axis of the three-dimensional image by-eta i Angle, obtain rotated three-dimensional Hilbert image +.> wherein ηi ＝θ i Pi/2 (i=1, 2,., T), the angle value being positive, the three-dimensional image rotating anticlockwise; the angle is negative, and the three-dimensional image rotates clockwise;
2) Calculate one-dimensional weight sequence W mat I.e.
3) for (k=1; k is less than or equal to I; k++) (i.e., into the for loop body):
3.1 From a rotated three-dimensional Hilbert imageTwo-dimensional Hilbert image of the kth layer is indexed out +.>
3.2 Searching for two-dimensional Hilbert imagesThe values of which rows are all 0, and an array R with the elements being row numbers is obtained i ；
3.3 For two-dimensional Hilbert imageWeighting W mat And performing Hilbert transform along the matrix array direction to obtain image +.>
3.4 According to R obtained in step S3 i Numerical value, slave imageThe elements are extracted from the middle rope, and the average value is calculated along the column direction and is inverted to obtain +.>
3.5 Execution of (1)
3.6 A two-dimensional image to be rotated)Rotation angle eta about the center of the image i To the original state, the reconstructed k layer two-dimensional +.>
4) Extracting intermediate three-dimensional image regions to be reconstructed, i.e.
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