Method and apparatus for optimizing blocking grating for cone beam CT image scattering correction

Abstract

A method and apparatus for optimizing a blocking grating for cone beam CT image scattering correction, wherein the method comprises: scanning a blocking grating to establish a swinging model thereof; setting initial coordinates of the blocking grating along a longitudinal direction of a detector in an initial projection, and establishing an objective function between CBCT image data missing voxel values and the coordinates of the blocking grating along the longitudinal direction of the detector according to the swinging model; minimizing the objective function with a mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector. The present disclosure proposes a brand new scattering correction method not requiring any source compensation, performs a mathematical optimization modeling of the data missing caused by the blocking grating in the image domain, quantitatively evaluates the influence on the reconstructed image by a blocker, solves a geometric optimal structure of the blocker using a mesh-adaptive direct search algorithm, and lays a solid theory foundation for the scattering correction method based on the blocker measurement.

Claims

1. A method for optimizing a blocking grating for cone beam CT image scattering correction, comprising: scanning a blocking grating to establish a swinging model thereof; setting initial coordinates of the blocking grating along a longitudinal direction of a detector in an initial projection, and establishing an objective function between CBCT image data missing voxel values and the initial coordinates of the blocking grating along the longitudinal direction of the detector according to the swinging model; minimizing the objective function with a mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector.

2. The method for optimizing a blocking grating for cone beam CT image scattering correction according to claim 1, wherein scanning a blocking grating to establish a swinging model comprises: on a projection of the blocking grating, determining an appropriate threshold value of the blocking grating using a maximum between-class variance method, performing an image segmentation based on the appropriate threshold value to generate a binary image, determining a coordinate position of the blocking grating through the generated binary image, and obtaining the swinging model of the blocking grating.

3. The method for optimizing a blocking grating for cone beam CT image scattering correction according to claim 1, wherein setting initial coordinates of the blocking grating along a longitudinal direction of a detector in an initial projection comprises: setting a number of the blocking gratings as n, then coordinates of an i.sup.th blocking grating along the longitudinal direction of the detector in the initial projection are:
G=(g.sub.1,g.sub.2, . . . ,g.sub.n).sup.T.

4. The method for optimizing a blocking grating for cone beam CT image scattering correction according to claim 1, wherein establishing an objective function between CBCT image data missing voxel values and the initial coordinates of the blocking grating along the longitudinal direction of the detector according to the swinging model comprises: simulating a projection image of the blocking grating in each projection according to the swinging model and the initial coordinates; performing a back projection reconstruction for the projection image of each projection; establishing an objective function between missing voxel values of data after reconstructed images of left semi-fan and right semi-fan are fused and the initial coordinates of the blocking grating along the longitudinal direction of the detector according to projection images undergone the back projection reconstruction.

5. The method for optimizing a blocking grating for cone beam CT image scattering correction according to claim 1, wherein minimizing the objective function with a mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector comprises: using initial parameters of the blocking grating as initial values of the mesh-adaptive direct search algorithm to generate the optimized coordinates of the blocking grating along the longitudinal direction of the detector.

6. The method for optimizing a blocking grating for cone beam CT image scattering correction according to claim 5, wherein the initial parameters of the blocking grating are uniformly distributed at an equal interval.

7. An apparatus for optimizing a blocking grating for cone beam CT image scattering correction, comprising a memory, a processor, and a computer program stored in the memory and executable in the processor, wherein the processor performs the following operations when executing the computer program: scanning a blocking grating to establish a swinging model thereof; setting initial coordinates of the blocking grating along a longitudinal direction of a detector in an initial projection, and establishing an objective function between CBCT image data missing voxel values and the initial coordinates of the blocking grating along the longitudinal direction of the detector according to the swinging model; minimizing the objective function with a mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector.

8. The apparatus for optimizing a blocking grating for cone beam CT image scattering correction according to claim 7, wherein the processor further performs the following operations when executing the computer program: on a projection of the blocking grating, determining an appropriate threshold value of the blocking grating using a maximum between-class variance method, performing an image segmentation based on the appropriate threshold value to generate a binary image, determining a coordinate position of the blocking grating through the generated binary image, and obtaining the swinging model of the blocking grating.

9. The apparatus for optimizing a blocking grating for cone beam CT image scattering correction according to claim 7, wherein the processor further performs the following operations when executing the computer program: setting a number of the blocking gratings as n, then coordinates of an i.sup.th blocking grating along the longitudinal direction of the detector in the initial projection are:
G=(g.sub.1,g.sub.2, . . . ,g.sub.n).sup.T; simulating a projection image of the blocking grating in each projection according to the swinging model and the initial coordinates; performing a back projection reconstruction for the projection image of each projection; establishing an objective function between missing voxel values of data after reconstructed images of left semi-fan and right semi-fan are fused and the initial coordinates of the blocking grating along the longitudinal direction of the detector according to projection images undergone the back projection reconstruction.

10. A non-transitory computer readable storage medium, wherein the non-transitory computer readable storage medium stores a computer program, which causes a processor to perform the following operations when being executed: scanning a blocking grating to establish a swinging model thereof; setting initial coordinates of the blocking grating along a longitudinal direction of a detector in an initial projection, and establishing an objective function between CBCT image data missing voxel values and the initial coordinates of the blocking grating along the longitudinal direction of the detector; minimizing the objective function with a mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector.

11. The non-transitory computer readable storage medium according to claim 10, wherein the computer program causes the processor to perform the following operations when being executed: on a projection of the blocking grating, determining an appropriate threshold value of the blocking grating using a maximum between-class variance method, performing an image segmentation based on the appropriate threshold value to generate a binary image, determining a coordinate position of the blocking grating through the generated binary image, and obtaining the swinging model of the blocking grating.

12. The non-transitory computer readable storage medium according to claim 10, wherein the computer program causes the processor to perform the following operations when being executed: setting a number of the blocking gratings as n, then coordinates of an i.sup.th blocking grating along the longitudinal direction of the detector in the initial projection are:
G=(g.sub.1,g.sub.2, . . . ,g.sub.n).sup.T; simulating a projection image of the blocking grating in each projection according to the swinging model and the initial coordinates; performing a back projection reconstruction for the projection image of each projection; establishing an objective function between missing voxel values of data after reconstructed images of left semi-fan and right semi-fan are fused and the initial coordinates of the blocking grating along the longitudinal direction of the detector according to projection images undergone the back projection reconstruction.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In order to more clearly describe the technical solutions in the embodiments of the present disclosure, the drawings to be used in the descriptions of the embodiments will be briefly introduced as follows. Obviously, the drawings in the following descriptions just illustrate some embodiments of the present disclosure, and a person skilled in the art can obtain other drawings from them without paying any creative effort. In which,

(2) FIG. 1 illustrates a processing flowchart of a method for optimizing a blocking grating for cone beam CT image scattering correction in an embodiment of the present disclosure;

(3) FIG. 2 illustrates a principle diagram of a method for optimizing a blocking grating for cone beam CT image scattering correction in an embodiment of the present disclosure;

(4) FIG. 3 illustrates a geometric model of an optimized blocking grating in an embodiment of the present disclosure;

(5) FIG. 4 illustrates a structure diagram of an apparatus for optimizing a blocking grating for cone beam CT image scattering correction in an embodiment of the present disclosure;

(6) FIG. 5 illustrates a comparison diagram of actual correction effects obtained according to a method for optimizing a blocking grating in an embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(7) Next, the technical solutions in the embodiments of the present disclosure will be clearly and completely described with reference to the drawings in the embodiments of the present disclosure. Obviously, those described are just a part rather than all of the embodiments of the present disclosure. Based on the embodiments of the present disclosure, any other embodiment obtained by a person skilled in the art without paying any creative effort shall fall within the protection scope of the present disclosure.

(8) As known to a person skilled in the art, the embodiment of the present disclosure may be implemented as a system, an apparatus, a device, a method or a computer program product. Thus the present disclosure can be specifically implemented as complete hardware, complete software (including firmware, resident software, microcode, etc.), or a combination of hardware and software.

(9) Next, the principle and spirit of the present disclosure are elaborated in details as follows with reference to several representative embodiments of the present disclosure.

(10) The embodiments of the present disclosure propose a mathematical model of an interdigital blocking grating for the quality of a reconstructed image. The mathematical model considers the grating dithering, and introduces a mesh-adaptive direct search algorithm for solving the objective function, so as to obtain a geometric design of a blocking grating suitable for the clinical CBCT scattering correction. Next, the designed blocking grating is placed in front of the ray source, the scattering distribution of each projection is estimated in an interpolation method after the scattering sample is accurately extracted, and finally a scattering corrected image is precisely reconstructed in a semi-fan scanning reconstruction algorithm, thus the clinical CBCT scattering correction is achieved by a single scan.

(11) FIG. 1 illustrates a processing flowchart of a method for optimizing a blocking grating for cone beam CT image scattering correction in an embodiment of the present disclosure. As illustrated in FIG. 1, the method comprising:

(12) step S101: scanning a blocking grating to establish a swinging model thereof;

(13) step S102: setting initial coordinates of the blocking grating along a longitudinal direction of a detector in an initial projection, and establishing an objective function between CBCT image data missing voxel values and the coordinates of the blocking grating along the longitudinal direction of the detector according to the swinging model;

(14) step S103: minimizing the objective function with a mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector.

(15) FIG. 2 illustrates a principle diagram of a method for optimizing a blocking grating for cone beam CT image scattering correction in an embodiment of the present disclosure. Step S101 in FIG. 1 is corresponding to 100 in FIG. 2 (establishment of a grating swinging model), Step S102 in FIG. 1 is corresponding to 200 in FIG. 2 (establishment of a blocking grating mathematical model), and step S103 in FIG. 1 is corresponding to 300 in FIG. 2 (model solution). In the embodiment as illustrated in FIG. 2, ten gratings are used in an example to explain the principle.

(16) In step S101 of this embodiment, with reference to 100 of FIG. 2, a blocking grating firstly shall be designed based on experiences, and then scanned for studying the swinging model of a lead bar projection caused by the isocenter deviation of the cantilever and vibration of the rack in the clinical CBCT. In a preferred embodiment, the designed blocking grating is an interdigital grating.

(17) On the projection of the blocking grating obtained by scanning, an appropriate threshold value of the blocking grating is determined using the maximum between-class variance method (OTSU), an image segmentation is performed based on the threshold value to convert the interested area into a binary image, so as to obtain coordinate values of the central point of the blocking grating in the direction, and acquire the relation between the angle of the rack and the position change of the blocking grating. Namely, the coordinate position of the blocking grating is determined through the generated binary image, and the swinging model of the blocking grating can be obtained according to the coordinate position of the blocking grating.

(18) In step S102 of this embodiment, with reference to 200 of FIG. 2, the objective function of the blocking grating and the number of missing voxels of the image data will be established. The principle is that as the interval between the blocking gratings increases, the number of missing voxels of the image data reconstructed with two groups of semi-fan scanning algorithms decreases. While ensuring the accuracy of scattering estimation, the design of the blocking grating shall ensure the minimization of the number of missing voxels of the image data. Thus, it is possible to design an objective function about the placement position of the blocking grating.

(19) Firstly, the initial coordinates of the blocking grating along the longitudinal direction of the detector in the initial projection shall be set. The number of the blocking gratings may be set as n, then the coordinates of the i.sup.th blocking grating along the longitudinal direction of the detector in the initial projection are:
G=(g.sub.1,g.sub.2, . . . ,g.sub.n).sup.T(1)

(20) Next, the projection image of the blocking grating in each projection is simulated according to the swinging model and the initial coordinates. In the embodiment, the projection image of the blocking grating is simulated, the blocked area is set as 1, and the unblocked area is set as 0. Due to the swinging and the isocenter deviation of the rack, the coordinate position of the blocking grating is different in each projection, wherein d.sub.j is the projection offset in the j.sup.th projection.

(21) $\begin{array}{cc}{p}_{i,j}\left(u,v\right)=\{\begin{array}{cc}1,& -\frac{U}{2}u-\frac{U}{2}+l,g_i+d_{j}v{g}_i+d_j+w_0\\ 0,& \mathrm{otherwise}\end{array}i=1,3,5,\mathrm{.Math.},n-1& \left(2\right)\\ p_{i,j}\left(u,v\right)=\{\begin{array}{cc}1,& \frac{U}{2}-lu\frac{U}{2},g_i+d_{j}v{g}_i+d_j+w_0\\ 0,& \mathrm{otherwise}\end{array}i=2,4,6,\mathrm{.Math.},n& \left(3\right)\end{array}$

(22) p.sub.i,j(u,v) in Equations (2) and (3) are images of singular blocking grating on left and right sides in the j.sup.th projection, U is a horizontal pixel width of the detector, w.sub.0 is a width of the blocking grating, and u and v are horizontal and vertical coordinate values of the detector, respectively.

(23) Equations (2) and (3) are added together to obtain:

(24) $\begin{array}{cc}{P}_j=\underset{i=1}{\overset{n}{.Math.}}{p}_{i,j}& \left(4\right)\end{array}$

(25) P.sub.j is an image of the blocking grating in the j.sup.th projection.

(26) M projections P.sub.j are multiplied by weighting functions f (u, v) and f (u, v), respectively, for a back projection reconstruction to obtain:

(27) $\begin{array}{cc}{M}_l=\mathrm{BP}\left(\underset{j=1}{\overset{m}{.Math.}}\left(P_j.Math.f\left(u,v\right)\right)\right)& \left(5\right)\\ M_r=\mathrm{BP}\left(\underset{j=1}{\overset{m}{.Math.}}\left(P_j.Math.f\left(-u,v\right)\right)\right)& \left(6\right)\end{array}$

(28) It can be found that among M.sub.l and M.sub.r, the voxel value influenced by the blocking grating is non-zero, and the voxel value not influenced by the blocking grating is zero; M.sub.l.Math.M.sub.r is a non-zero area, i.e., the missing voxels of the data after the reconstructed images of the left and right semi-fans are fused. The optimization design of the blocking grating requires that a binarized sum of the missing voxels of the data in the reconstruction volume shall be minimized. The establishment process of the objective function is illustrated in FIG. 2, and the following objective function can be obtained:
g=arg minBNR(M.sub.l).Math.BNR(M.sub.r).sub.1
s.t.
g.sub.i+1g.sub.i>w.sub.0 i=1,2, . . . ,n1
g.sub.mingg.sub.max
g.sub.i+1g.sub.i>w.sub.0 i=1,2, . . . ,n1(7)

(29) wherein g.sub.mingg.sub.max is a constraint condition which means that the left and right gratings must be alternatively distributed, and the vertical coordinate of the gratings cannot exceed a range of the vertical coordinate of the detector.

(30) In step S103 of the embodiment, with reference to 300 of FIG. 2, the initial parameters of the blocking grating are used as the initial values of the mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector, wherein the initial parameters of the blocking grating are uniformly distributed at an equal interval, and of course, other interval may be adopted.

(31) The objective function is solved by introducing the mesh-adaptive direct search algorithm. In the optimization model mentioned herein, the vibration offset d.sub.j of the blocking grating caused by the isocenter deviations of the rack and the vibration is obtained by an object tracking. Currently, the optimization solutions include the mathematical programming method, the heuristic algorithm, the direct search method, etc. The optimization model of the blocking grating is strongly nonlinear, and provides no derivative information, thus the mathematical programming method cannot be employed. Although the heuristic algorithm, such as the simulated annealing algorithm or the genetic algorithm, has a better global search capability, its local search capability is not enough, and the convergence speed is very slow. Since one back projection operation shall be performed each time an objective function is generated, a lot of redundant iterations will occur and much time will be cost, if the objective function of the present disclosure employs the heuristic algorithm. The decision vectors of the mesh-adaptive direct search (MADS) algorithm may be discrete, continuous and binary; the objective function and its constraint condition may be the black box function; the MADS algorithm is adaptive to solve a multivariable mathematical model; thus the present disclosure employs the MADS algorithm to solve the optimization model of the blocking grating. During the solution, in a preferred embodiment, the parameters of the blocking gratings uniformly distributed are used as initial values of the MADS objective function, and the solved grating geometric model is illustrated in FIG. 3.

(32) After the optimized blocking grating structure is obtained in the above steps, it is placed between the ray source and the object to be scanned. After the object projection is collected, the grating position is determined using the image segmentation based on the threshold value, and an interpolative estimation is performed for the scattering distribution using the collected scattering signal. The scattering corrected projection image is obtained by removing the scattering distribution from the original image. Next, the scattering corrected image is reconstructed using the semi-fan scan reconstruction algorithm based on the Parker function.

(33) To be noted, although the operations of the method of the present disclosure are described in a particular sequence in the drawings, it does not requires or implies that those operations must be performed in that particular sequence, or the desired result must be achieved by performing all of the illustrated operations. Additionally or optionally, some steps may be omitted, multiple steps may be merged into one step, and/or one step may be divided into multiple steps.

(34) After the method of the exemplary embodiment of the present disclosure is introduced, an apparatus for optimizing a blocking grating for cone beam CT image scattering correction in an exemplary embodiment of the present disclosure will be described as follows. Please refer to the implementation of the above method for the implementation of the apparatus, and the repeated content is omitted herein.

(35) FIG. 4 illustrates a structure diagram of an apparatus for optimizing a blocking grating for cone beam CT image scattering correction in an embodiment of the present disclosure. As illustrated in FIG. 4, the apparatus comprises a memory 401, a processor 402 and a computer program stored in the memory 401 and executable in the processor 402, wherein the processor 402 performs the following operations when executing the computer program:

(36) scanning a blocking grating to establish a swinging model thereof;

(37) setting initial coordinates of the blocking grating along a longitudinal direction of a detector in an initial projection, and establishing an objective function between CBCT image data missing voxel values and the coordinates of the blocking grating along the longitudinal direction of the detector according to the swinging model;

(38) minimizing the objective function with a mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector.

(39) In the embodiment, the processor 402 further performs the following operations when executing the computer program:

(40) on a projection of the blocking grating, determining an appropriate threshold value of the blocking grating using the maximum between-class variance method, performing an image segmentation based on the threshold value to generate a binary image, determining a coordinate position of the blocking grating through the generated binary image, and obtaining the swinging model of the blocking grating.

(41) In the embodiment, the processor 402 further performs the following operations when executing the computer program:

(42) setting the number of the blocking gratings as n, then coordinates of an i.sup.th blocking grating along the longitudinal direction of the detector in the initial projection are:
G=(g.sub.1,g.sub.2, . . . ,g.sub.n).sup.T;

(43) simulating an projection image of the blocking grating in each projection according to the swinging model and the initial coordinates;

(44) performing a back projection reconstruction for each of the projection images;

(45) establishing an objective function between missing voxel values of data after reconstructed images of left and right semi-fans are fused and the coordinates of the blocking grating along the longitudinal direction of the detector according to the images undergone the back projection reconstruction.

(46) The embodiments of the present disclosure further provide a computer readable storage medium, wherein the computer readable storage medium stores a computer program which causes the processor to perform the following operations when being executed:

(47) scanning a blocking grating to establish a swinging model thereof;

(48) setting initial coordinates of the blocking grating along a longitudinal direction of a detector in an initial projection, and establishing an objective function between CBCT image data missing voxel values and the coordinates of the blocking grating along the longitudinal direction of the detector;

(49) minimizing the objective function with a mesh-adaptive direct search algorithm to generate optimized coordinates of the blocking grating along the longitudinal direction of the detector.

(50) In the embodiment, the computer program further causes the processor to perform the following operations when being executed:

(51) on a projection of the blocking grating, determining an appropriate threshold value of the blocking grating using the maximum between-class variance method, performing an image segmentation based on the threshold value to generate a binary image, determining a coordinate position of the blocking grating through the generated binary image, and obtaining the swinging model of the blocking grating.

(52) In the embodiment, the computer program further causes the processor to perform the following operations when being executed:

(53) setting the number of the blocking gratings as n, then coordinates of an i.sup.th blocking grating along the longitudinal direction of the detector in the initial projection are:
G=(g.sub.1,g.sub.2, . . . ,g.sub.n).sup.T;

(54) simulating an projection image of the blocking grating in each projection according to the swinging model and the initial coordinates;

(55) performing a back projection reconstruction for each of the projection images;

(56) establishing an objective function between missing voxel values of data after reconstructed images of left and right semi-fans are fused and the coordinates of the blocking grating along the longitudinal direction of the detector according to the images undergone the back projection reconstruction.

(57) The blocking grating designed and optimized through the embodiments of the present disclosure has been tested, simulated and used to prove its feasibility. In the CBCT of Varian Trilogy, the Catphan504 die body is used for the test, and the scattering correction is performed using the blocking grating designed and optimized by the present disclosure. The CT error of the interested area drops from 115 HU to 11 HU, while the contrast is increased by 1.45 times. The correction effect is shown in FIG. 5, wherein column (a) is an image before the correction, and column (b) is an image after the correction.

(58) The method and apparatus for optimizing a blocking grating for cone beam CT image scattering correction in the embodiments of the present disclosure propose a brand new scattering correction method not requiring any source compensation and adaptive to the clinical CBCT. The present disclosure establishes the mathematical model for swinging of the projection of the blocking grating caused by the isocenter deviation of the cantilever and the vibration of the rack by means of the image segmentation method, thereby successfully applying the blocking grating into clinical cone beam CT scattering corrections; performs a mathematical optimization modeling of the data missing caused by the blocking grating in the image domain, quantitatively evaluates the influence on the reconstructed image by the blocker, solves the geometric optimal structure of the blocker using a mesh-adaptive direct search algorithm, lays a solid theory foundation for the scattering correction method based on the blocker measurement, and further reveals the importance of the blocker design to the clinical cone beam CT scattering correction.

(59) A person skilled in the art shall understand that the embodiment of the present disclosure can be provided as a method, a system or a computer program product. Therefore, the present disclosure can take the form of a full hardware embodiment, a full software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present disclosure can take the form of a computer program product implemented on one or more computer usable storage mediums (including, but not limited to, a magnetic disc memory, CD-ROM, optical storage, etc.) containing therein computer usable program codes.

(60) The present disclosure is described with reference to a flow diagram and/or block diagram of the method, device (system) and computer program product according to the embodiments of the present disclosure. It shall be understood that each flow and/or block in the flow diagram and/or block diagram and a combination of the flow and/or block in the flow diagram and/or block diagram can be realized by the computer program instructions. These computer program instructions can be provided to a general computer, a dedicated computer, an embedded processor or a processor of other programmable data processing device to generate a machine, such that the instructions performed by the computer or the processor of other programmable data processing devices generate the device for implementing the function designated in one flow or a plurality of flows in the flow diagram and/or a block or a plurality of blocks in the block diagram.

(61) These computer program instructions can also be stored in a computer readable memory capable of directing the computer or other programmable data processing devices to operate in a specific manner, such that the instructions stored in the computer readable memory generate a manufactured article including an instruction device that implements the function(s) designated in one flow or a plurality of flows in the flow diagram and/or a block or a plurality of blocks in the block diagram.

(62) These computer program instructions can also be loaded onto the computer or other programmable data processing devices, such that a series of operation steps is executed on the computer or other programmable devices to generate the processing realized by the computer, therefore the instructions executed on the computer or other programmable devices provide the steps for implementing the function designated in one flow or a plurality of flows in the flow chart and/or a block or a plurality of blocks in the block diagram.

(63) Specific embodiments are used to elaborate the principle and the implementations of the present disclosure. The descriptions of those embodiments just intend to help the understanding of the method and the core idea of the present disclosure. Meanwhile, an ordinary person skilled in the art can change the implementations and the application range based on the idea of the present disclosure. In conclusion, the contents of the Specification shall not be understood as limitations to the present disclosure.