CN113393549A - CT image reconstruction method based on flat-panel X-ray source - Google Patents
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Abstract
A CT image reconstruction method based on a flat-panel X-ray source comprises the steps of firstly obtaining empty exposure image data under a non-scanning object and overlapped projection data under N areas when the scanning object is placed, then establishing a flat-panel X-ray source overlapped projection physical model, then combining the empty exposure image data and the overlapped projection data to construct a nonlinear quantity relation of reconstructed projection data and a reconstructed image, comparing the nonlinear quantity relation with a linear formula to obtain a linear correction factor, then establishing a linear flat-panel X-ray source CT reconstruction model according to the linear correction factor, a flat-panel X-ray source system matrix, an image to be reconstructed and the reconstructed projection data, then establishing an iterative updating formula of a flat-panel X-ray source combined iterative reconstruction method and the linear correction factor, and finally reconstructing a flat-panel X-ray source CT image by applying the flat-panel X-ray source combined iterative reconstruction method. The CT image reconstruction method based on the flat-panel X-ray source has low calculation complexity during the reconstruction of the CT image of the flat-panel X-ray source.
Description
Technical Field
The invention relates to the field of image reconstruction, in particular to a CT image reconstruction method based on a flat-panel X-ray source.
Background
The flat-panel X-ray source is a novel X-ray source, is a new leading-edge technology in the field of CT, and has wide application prospect in the fields of medical imaging, safety inspection, industrial flaw detection and the like. The flat-panel X-ray source can realize X-ray emission of the whole plane, and has great advantages in the aspects of reducing the volume of an imaging system, reducing the radiation dose, reducing the mechanical motion of the imaging system and the like.
Projection images generated when a plurality of X-ray sources of the flat-panel X-ray source work simultaneously are overlapped, in the prior art, Lambert beer index accumulation description is applied to the overlapped projection images of the flat-panel X-ray sources, and CT image reconstruction of overlapped projection can be realized. However, when the lambert beer formula is applied to reconstruction of the overlapped projection image of the flat panel X-ray source, logarithmic transformation cannot be eliminated and nonlinear operation exists, and generally, derivative optimization solution is required for the nonlinear operation, so that the calculation amount in the reconstruction process of the overlapped projection image of the flat panel X-ray source is large.
Therefore, it is necessary to provide a CT image reconstruction method based on a flat panel X-ray source to overcome the deficiencies of the prior art.
Disclosure of Invention
The invention aims to avoid the defects of the prior art and provide a CT image reconstruction method based on a flat-panel X-ray source, which converts the nonlinear reconstruction problem of overlapped projection into an approximately linear problem by introducing a linear correction factor when the overlapped projection image of the flat-panel X-ray source is reconstructed, and can reduce the calculation complexity when the overlapped projection image of the flat-panel X-ray source is reconstructed.
The object of the invention is achieved by the following technical measures.
The CT image reconstruction method based on the flat-panel X-ray source comprises the following steps:
s1: under the condition of no scanning object, a flat X-ray source is aligned to a flat detector, a blank exposure area is selected on the flat X-ray source, the blank exposure area exposes the flat detector, and the flat detector acquires blank exposure image data;
s2: placing a scanning object, selecting N areas with different positions and equal sizes on a flat X-ray source, controlling the X-ray sources in the different areas to be exposed in sequence, and acquiring overlapped projection data under the N areas by using a flat detector, wherein N is more than or equal to 10;
s3: establishing a physical model of the overlapped projection of the flat-panel X-ray source according to the Lambert beer law;
s4: constructing a nonlinear quantitative relation between reconstructed projection data and a reconstructed image according to the flat X-ray source overlapped projection physical model, the idle exposure image data and the overlapped projection data, and comparing the nonlinear quantitative relation with a linear formula to construct a linear correction factor;
s5: establishing a linear flat panel X-ray source CT reconstruction model according to the linear correction factor, the flat panel X-ray source system matrix, the image to be reconstructed and the reconstruction projection data;
s6: constructing an iteration updating formula of a flat-panel X-ray source combined iteration reconstruction method and an iteration updating formula of a linear correction factor;
s7: and reconstructing a CT image of the flat-panel X-ray source by using a flat-panel X-ray source combined iterative reconstruction method.
Preferably, K X-ray sources are selected to form a null exposure region in step S1;
the obtained blank exposure image data is
Wherein K is the total number of X-ray sources in the empty exposure area,
and (3) a null exposure image of the X-rays when the K-th X-ray source in the K X-ray sources is exposed independently.
Preferably, the total number and arrangement of the X-ray sources in each of the N regions in step S2 are consistent with those of the blank exposure region in step S1, and the overlapped projection data of the N-th exposure region in the N regions is recorded as In。
Preferably, the physical model of the flat panel X-ray source overlapping projection described in step S3 is
Wherein, I is the total number of voxels, J is the total number of detector units, K is the total number of X-ray sources in the exposure area,
is InThe jth element represents the intensity of the ray received by the jth flat-panel detector unit,
is the exit intensity, X, of the kth X-ray source to the jth detector unitiIs the ith voxel of the reconstructed image, aijkIs the system matrix element of the kth X-ray source and represents the length of a line which the ith voxel is intersected by the X-ray emitted by the kth X-ray source to the jth detector.
Preferably, the construction process of the linear correction factor in step S4 is as follows:
s41: definition of
Wherein, ω isjkRepresenting the contribution of the kth X-ray source to the ray intensity of the jth detector unit;
s42: definition of
Wherein the content of the first and second substances,
is I0The jth element of (1);
by substituting formula (3) and formula (4) into formula (2)
S43: will be provided with
And
obtaining a non-linear quantitative relationship between reconstructed projection data and a reconstructed image by logarithmic transformation
Wherein, bjRepresenting reconstructed projection data;
s44: when K takes any number from 1 to K,
when the value of (a) is not changed,
s45: b is tojAnd
quotient obtaining linear correction factor
Preferably, the linear flat-panel X-ray source CT reconstruction model in step S5 is
λ Ax ═ b … … formula (8)
Wherein λ represents a diagonal element of λjX denotes the vector of the image to be reconstructed and b denotes the element bjA denotes the flat panel X-ray source system matrix, A is specifically
Preferably, in step S6, the single X-ray source system matrix M in the iterative reconstruction formula of the joint iterative reconstruction method of the single X-ray source is replaced by λ a to obtain the iterative update formula of the flat panel X-ray source joint iterative reconstruction method
Updating the reconstructed image xnIterative update formula of linear correction factor obtained by substituting formula (7)
Preferably, step S7 specifically includes:
s71: initializing region projection number n as 1, and image to be reconstructed
And a linear correction factor lambdanE is an identity matrix;
s72: computing reconstructed projection data
S73: at λnA is the flat X-ray source system matrix calculation to-be-reconstructed image
Forward projection of
S74: will reconstruct the projection data bjSubtracting the forward projection p to obtain a residual
S75: and carrying out back projection to update the image to be reconstructed by taking the residual error r as a correction value to obtain a new image to be reconstructed
S76: using new image to be reconstructed
Updating iterative linear correction factor
S77: when N is less than N, taking N as N +1, and returning to the step (2);
s78: and (3) when N is equal to N, if the reconstructed image of the flat-panel X-ray source does not reach the convergence condition, taking N to 1, returning to the step (2), and if the reconstructed image of the flat-panel X-ray source reaches the convergence condition, stopping iteration and obtaining a reconstructed image.
Preferably, the convergence condition of the reconstructed image of the flat-panel X-ray source is that the error of the reconstructed image of two iterations is smaller than a set value.
Preferably, the value range of the set value is 10-4～10-6。
The invention discloses a CT image reconstruction method based on a flat-panel X-ray source, which comprises the following steps: s1: under the condition of no scanning object, a flat X-ray source is aligned to a flat detector, a blank exposure area is selected on the flat X-ray source, the blank exposure area exposes the flat detector, and the flat detector acquires blank exposure image data; s2: placing a scanning object, selecting N areas with different positions and equal sizes on a flat-panel X-ray source, controlling the X-ray sources in the different areas to be sequentially exposed, and acquiring overlapped projection data under the N areas by using a flat-panel detector; s3: establishing a physical model of the overlapped projection of the flat-panel X-ray source according to the Lambert beer law; s4: constructing a nonlinear quantitative relation between reconstructed projection data and a reconstructed image according to the flat X-ray source overlapped projection physical model, the idle exposure image data and the overlapped projection data, and comparing the nonlinear quantitative relation with a linear formula to construct a linear correction factor; s5: establishing a linear flat panel X-ray source CT reconstruction model according to the linear correction factor, the flat panel X-ray source system matrix, the image to be reconstructed and the reconstruction projection data; s6: constructing an iteration updating formula of a flat-panel X-ray source combined iteration reconstruction method and an iteration updating formula of a linear correction factor; s7: and reconstructing a CT image of the flat-panel X-ray source by using a flat-panel X-ray source combined iterative reconstruction method. According to the CT image reconstruction method based on the flat-panel X-ray source, the nonlinear reconstruction problem of the overlapped projection is converted into the approximately linear problem through the linear correction factor, derivative optimization solution is not needed, and the calculation complexity during CT image reconstruction is reduced.
Drawings
The invention is further illustrated by means of the attached drawings, the content of which is not in any way limiting.
Figure 1 is a phantom for the simulated projection of example 2.
Fig. 2 is a geometrical schematic diagram of the acquisition of the projection of the flat panel X-ray source in example 2.
Fig. 3 is a CT reconstructed image of the flat panel X-ray source of example 2.
Detailed Description
The invention is further illustrated by the following examples.
Example 1.
A CT image reconstruction method based on a flat-panel X-ray source comprises the following steps:
s1: under the condition of no scanning object, the flat-panel X-ray source is aligned to the flat-panel detector, a null exposure area is selected on the flat-panel X-ray source, the null exposure area exposes the flat-panel detector, and the flat-panel detector acquires null exposure image data.
S2: placing a scanning object, selecting N areas with different positions and equal sizes on the flat-panel X-ray source, controlling the X-ray sources in the different areas to be exposed in sequence, and acquiring overlapped projection data under the N areas by using a flat-panel detector, wherein N is more than or equal to 10. The plane of the flat-panel X-ray source in the step is parallel to the plane of the flat-panel detector.
S3: and establishing a physical model of the overlapped projection of the flat-panel X-ray source according to the Lambert beer law.
S4: and constructing a nonlinear quantitative relation between the reconstructed projection data and the reconstructed image according to the flat X-ray source overlapped projection physical model, the idle exposure image data and the overlapped projection data, and comparing the nonlinear quantitative relation with a linear formula to construct a linear correction factor. The linear correction factor converts the nonlinear quantitative relation between the reconstructed projection data and the reconstructed image into an approximate linear relation, and reduces the calculation complexity in the CT image reconstruction process of the flat-panel X-ray source.
S5: and establishing a linear flat-panel X-ray source CT reconstruction model according to the linear correction factor, the flat-panel X-ray source system matrix, the image to be reconstructed and the reconstruction projection data.
S6: and constructing an iterative update formula of a flat-panel X-ray source combined iterative reconstruction method and an iterative update formula of a linear correction factor.
S7: and reconstructing a CT image of the flat-panel X-ray source by using a flat-panel X-ray source combined iterative reconstruction method.
In this embodiment, K X-ray sources are selected in step S1 to form a null exposure region;
the obtained blank exposure image data is
Wherein K is the total number of X-ray sources in the empty exposure area,
and (3) a null exposure image of the X-rays when the K-th X-ray source in the K X-ray sources is exposed independently.
In this embodiment, the total number and arrangement of the X-ray sources in each of the N regions in step S2 are consistent with the blank exposure region in step S1, and the overlapping projection data of the nth exposure region in the N regions is denoted as In。
In this embodiment, the physical model of the flat-panel X-ray source overlap projection in step S3 is
Wherein, I is the total number of voxels, J is the total number of detector units, K is the total number of X-ray sources in the exposure area,
is InThe jth element represents the intensity of the ray received by the jth flat-panel detector unit,
is the exit intensity, X, of the kth X-ray source to the jth detector unitiIs the ith voxel of the reconstructed image, aijkIs the system matrix element of the kth X-ray source and represents the length of a line which the ith voxel is intersected by the X-ray emitted by the kth X-ray source to the jth detector.
In this embodiment, the construction process of the linear correction factor in step S4 is as follows:
s41: definition of
Wherein, ω isjkRepresenting the contribution of the kth X-ray source to the ray intensity of the jth detector unit;
s42: definition of
Wherein the content of the first and second substances,
is I0The jth element of (1);
by substituting formula (3) and formula (4) into formula (2)
S43: will be provided with
And
obtaining a non-linear quantitative relationship between reconstructed projection data and a reconstructed image by logarithmic transformation
Wherein, bjRepresenting reconstructed projection data;
s44: when K takes any number from 1 to K,
when the value of (a) is not changed,
s45: b is tojAnd
quotient obtaining linear correction factor
In this embodiment, the linear flat-panel X-ray source CT reconstruction model in step S5 is
λ Ax ═ b … … formula (8)
Wherein λ represents a diagonal element of λjX denotes the vector of the image to be reconstructed and b denotes the element bjA denotes the flat panel X-ray source system matrix, A is specifically
In this embodiment, step S6 is specifically to replace the single X-ray source system matrix M in the joint iterative reconstruction method iterative reconstruction formula of the single X-ray source with λ a to obtain an iterative update formula of the flat panel X-ray source joint iterative reconstruction method
The single X-ray source CT reconstructed image model is generally described by Mx ═ b, M is a single X-ray source system matrix, and the iterative reconstruction formula of the single X-ray source joint iterative reconstruction method is:
wherein M isijAnd (3) representing the elements of the matrix M, and replacing the matrix M with lambda A to obtain an iterative updating formula of the reconstructed image of the flat-panel X-ray source.
The updated reconstructed image x is then processednIterative update formula of linear correction factor obtained by substituting formula (7)
In this embodiment, step S7 specifically includes:
s71: initializing region projection number n as 1, and image to be reconstructed
And a linear correction factor lambdanE is an identity matrix;
s72: computing reconstructed projection data
S73: at λnA is a flat plate XCalculating an image to be reconstructed by using a radiation source system matrix
Forward projection of
S74: will reconstruct the projection data bjSubtracting the forward projection p to obtain a residual
S75: and carrying out back projection to update the image to be reconstructed by taking the residual error r as a correction value to obtain a new image to be reconstructed
S76: using new image to be reconstructed
Updating iterative linear correction factor
S77: when N is less than N, taking N as N +1, and returning to the step (2);
s78: and (3) when N is equal to N, if the reconstructed image of the flat-panel X-ray source does not reach the convergence condition, taking N to 1, returning to the step (2), and if the reconstructed image of the flat-panel X-ray source reaches the convergence condition, stopping iteration and obtaining a reconstructed image.
In this embodiment, the convergence condition of the reconstructed image of the flat panel X-ray source is when the error of the reconstructed image of two iterations is smaller than a set value. The value range of the set value is 10-4～10-6。
According to the CT image reconstruction method based on the flat-panel X-ray source, the nonlinear reconstruction problem of the overlapped projection is converted into the approximately linear problem through the linear correction factor, derivative optimization solution is not needed, and the calculation complexity in the CT image reconstruction process of the flat-panel X-ray source is reduced.
Example 2.
A CT image reconstruction method based on a flat-panel X-ray source has the same other characteristics as embodiment 1, and the difference is that: in this embodiment, a computer simulation experiment is used to generate a finite angle simulated projection of a flat panel X-ray source for a CT image reconstruction experiment.
In this example, the phantom used is a breast phantom as shown in fig. 1, and the dimensions thereof are set to 200mm × 300mm × 50mm, and the voxel size thereof is set to 0.25mm × 0.25mm × 1 mm. The flat panel detector array has a size of 800 x 1440 with each detector pixel having a size of 0.25mm x 0.25 mm. The distance between the flat X-ray source and the detector is 60cm, and the distance between the detector and the center of the object is 6 cm.
In this embodiment, 10 × 10X-ray sources at the middle position are selected as the blank exposure region on the flat panel X-ray source, so that all the X-ray sources on the blank exposure region expose the flat panel detector, and the flat panel detector acquires blank exposure image data. The specific method comprises the following steps: the computer simulates and generates cone-beam empty exposure projection of each X-ray source in an empty exposure area according to the position of the X-ray source, all the projections are superposed to obtain an empty exposure image with the array number of 10 multiplied by 10, the distance between each X-ray source is set to be 1.2mm, and the obtained empty exposure image is marked as I0。
The geometry for generating the projections is shown in fig. 2, and in the present embodiment, the scan object in the geometry for generating the projections is specifically a breast phantom. The flat-panel X-ray source is parallel to the flat-panel detector, a coordinate system is established by using the center of a phantom, the flat-panel X-ray source is vertical to an X axis, 11 areas with different positions and equal sizes are selected at intervals of 20mm in the y axis direction and the z axis direction of the flat-panel X-ray source respectively and are sequentially exposed to obtain 22 overlapped projection images, each area comprises 10X 10X-ray sources, and the interval of each X-ray source is 1.2 mm. The resulting overlapping projections are denoted InAnd n is the number of projected sheets. In this embodiment, the flat panel X-ray source CT reconstruction reconstructed by the flat panel X-ray source combined iterative reconstruction method is finally appliedThe image is shown in figure 3.
According to the CT image reconstruction method based on the flat-panel X-ray source, the nonlinear reconstruction problem of the overlapped projection is converted into the approximately linear problem through the linear correction factor, derivative optimization solution is not needed, and the calculation complexity in the CT image reconstruction process of the flat-panel X-ray source is reduced.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and not for limiting the protection scope of the present invention, and although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.
Claims (10)
1. A CT image reconstruction method based on a flat-panel X-ray source is characterized by comprising the following steps:
s1: under the condition of no scanning object, a flat X-ray source is aligned to a flat detector, a blank exposure area is selected on the flat X-ray source, the blank exposure area exposes the flat detector, and the flat detector acquires blank exposure image data;
s2: placing a scanning object, selecting N areas with different positions and equal sizes on a flat X-ray source, controlling the X-ray sources in the different areas to be exposed in sequence, and acquiring overlapped projection data under the N areas by using a flat detector, wherein N is more than or equal to 10;
s3: establishing a physical model of the overlapped projection of the flat-panel X-ray source according to the Lambert beer law;
s4: constructing a nonlinear quantitative relation between reconstructed projection data and a reconstructed image according to the flat X-ray source overlapped projection physical model, the idle exposure image data and the overlapped projection data, and comparing the nonlinear quantitative relation with a linear formula to construct a linear correction factor;
s5: establishing a linear flat panel X-ray source CT reconstruction model according to the linear correction factor, the flat panel X-ray source system matrix, the image to be reconstructed and the reconstruction projection data;
s6: constructing an iteration updating formula of a flat-panel X-ray source combined iteration reconstruction method and an iteration updating formula of a linear correction factor;
s7: and reconstructing a CT image of the flat-panel X-ray source by using a flat-panel X-ray source combined iterative reconstruction method.
2. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: selecting K X-ray sources to form a null exposure area in the step S1;
the obtained blank exposure image data is
Wherein K is the total number of X-ray sources in the empty exposure area,
and (3) a null exposure image of the X-rays when the K-th X-ray source in the K X-ray sources is exposed independently.
3. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: the total number and arrangement of the X-ray sources in each of the N regions in step S2 are consistent with those of the blank exposure region in step S1, and the overlapping projection data of the nth exposure region in the N regions are marked as In。
4. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: the physical model of the flat-panel X-ray source overlapping projection described in step S3 is
Wherein, I is the total number of voxels, J is the total number of detector units, K is the total number of X-ray sources in the exposure area,
is InThe jth element represents the intensity of the ray received by the jth flat-panel detector unit,
is the exit intensity, X, of the kth X-ray source to the jth detector unitiIs the ith voxel of the reconstructed image, aijkIs the system matrix element of the kth X-ray source and represents the length of a line which the ith voxel is intersected by the X-ray emitted by the kth X-ray source to the jth detector.
5. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: the construction process of the linear correction factor in step S4 is as follows:
s41: definition of
Wherein, ω isjkRepresenting the contribution of the kth X-ray source to the ray intensity of the jth detector unit;
s42: definition of
Wherein the content of the first and second substances,
is I0The jth element of (1);
by substituting formula (3) and formula (4) into formula (2)
S43: will be provided with
And
obtaining a non-linear quantitative relationship between reconstructed projection data and a reconstructed image by logarithmic transformation
Wherein, bjRepresenting reconstructed projection data;
s44: when K takes any number from 1 to K,
when the value of (a) is not changed,
s45: b is tojAnd
quotient obtaining linear correction factor
6. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: in step S5, the linear flat-panel X-ray source CT reconstruction model is
λ Ax ═ b … … formula (8)
Wherein λ represents a diagonal element of λjX denotes the vector of the image to be reconstructed and b denotes the element bjA denotes the flat panel X-ray source system matrix, A is specifically
7. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: step S6 is to replace the single X-ray source system matrix M in the joint iterative reconstruction method iterative reconstruction formula of the single X-ray source with lambda A to obtain the iterative update formula of the flat-panel X-ray source joint iterative reconstruction method
Updating the reconstructed image xnIterative update formula of linear correction factor obtained by substituting formula (7)
8. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: step S7 specifically includes:
s71: initializing region projection number n as 1, and image to be reconstructed
And a linear correction factor lambdanE is an identity matrix;
s72: computing reconstructed projection data
S73: at λnA is the flat X-ray source system matrix calculation to-be-reconstructed image
Forward projection of
S74: will reconstruct the projection data bjSubtracting the forward projection p to obtain a residual
S75: and carrying out back projection to update the image to be reconstructed by taking the residual error r as a correction value to obtain a new image to be reconstructed
S76: using new image to be reconstructed
Updating iterative linear correction factor
S77: when N is less than N, taking N as N +1, and returning to the step (2);
s78: and (3) when N is equal to N, if the reconstructed image of the flat-panel X-ray source does not reach the convergence condition, taking N to 1, returning to the step (2), and if the reconstructed image of the flat-panel X-ray source reaches the convergence condition, stopping iteration and obtaining a reconstructed image.
9. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: the convergence condition of the reconstructed image of the flat-panel X-ray source is that the error of the reconstructed image of two iterations is less than a set value.
10. The flat panel X-ray source-based CT image reconstruction method according to claim 1, characterized in that: the value range of the set value is 10-4～10-6。
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