CN113392955A - CT reconstruction neural network structure and method based on downsampling imaging geometric modeling - Google Patents
CT reconstruction neural network structure and method based on downsampling imaging geometric modeling Download PDFInfo
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Abstract
A CT reconstruction neural network structure and method based on downsampling imaging geometric modeling are disclosed, wherein the network structure comprises a learning type projection domain filter network module which is used for carrying out filter processing and downsampling processing on CT original projection data to obtain a downsampled projection domain feature map; the system comprises a down-sampling learning type back projection module, a down-sampling learning type back projection module and a down-sampling learning type back projection module, wherein the down-sampling learning type back projection module is used for carrying out back projection operation on a down-sampling projection domain characteristic graph to obtain a down-sampling image domain characteristic graph; the learning type image domain filter network module is used for carrying out filter processing and up-sampling processing on the down-sampled image domain characteristic image to obtain a CT reconstructed image; the learning type back projection module of downsampling is provided with a multichannel downsampling back projection operator. The CT reconstruction neural network structure and the method based on the downsampling imaging geometric modeling have the advantages of low CT image reconstruction calculation complexity, high speed and high accuracy of the obtained CT reconstruction image.
Description
Technical Field
The invention relates to the technical field of image reconstruction, in particular to a CT reconstruction neural network structure and method based on downsampling imaging geometric modeling.
Background
X-ray Computed Tomography (CT) does not inflict invasive injury on the patient while reconstructing the patient's internal anatomy, has become an indispensable imaging modality in modern hospitals and clinics, and is useful for the examination of a variety of diseases. CT image reconstruction requires proper modeling of the relationship between the reconstructed object and the projection space in order to backproject the sinogram data into the image domain space, a process known as imaging geometry modeling.
The existing CT image reconstruction uses a single back projection method, and the CT image reconstruction result obtained by the single back projection CT image reconstruction method has higher precision. However, in the single back projection CT image reconstruction method, the computational complexity is high and the CT image reconstruction speed is slow in the process of reconstructing the CT image.
Therefore, it is necessary to provide a CT reconstruction neural network structure and method based on downsampling imaging geometric modeling 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 reconstruction neural network structure based on the downsampling imaging geometric modeling, which has low calculation complexity and high speed when CT image reconstruction is carried out and the obtained CT reconstruction image has high precision.
The above object of the present invention is achieved by the following technical measures.
A CT reconstruction neural network structure based on down-sampling imaging geometric modeling is provided, which comprises:
the learning type projection domain filter network module is used for carrying out filter processing and downsampling processing on CT original projection data to obtain a downsampled projection domain characteristic diagram;
the system comprises a down-sampling learning type back projection module, a down-sampling learning type back projection module and a down-sampling learning type back projection module, wherein the down-sampling learning type back projection module is used for carrying out back projection operation on a down-sampling projection domain characteristic graph to obtain a down-sampling image domain characteristic graph;
and the learning type image domain filter network module is used for carrying out filter processing and up-sampling processing on the down-sampled image domain characteristic image to obtain a CT reconstructed image.
Preferably, the multi-channel down-sampling back projection operator is:
the construction process of the multi-channel down-sampling back projection operator comprises the following steps:
acquiring CT imaging geometric parameters, and constructing a traditional CT system model according to the CT imaging geometric parameters
The CT imaging geometric parameters are zoomed to obtain the down-sampling CT imaging geometric parameters, and the down-sampling CT imaging geometric parameters are substituted into the traditional CT system model to obtain the down-sampling CT system model
Discretizing the down-sampled CT system model to obtain a multi-channel down-sampled back projection operator;
wherein f (x, y) represents a slice of the object under scanning in the x-y plane, x and y being indices of the object slice in the spatial coordinate system; g (gamma, theta) represents measured chord graph data, gamma is the included angle between the ray reaching any detector and the central ray, and theta is the rotation angle of the radiation source;
to represent
The dirac function of (a) is,
φ＝θ+γ；sγis the physical distance between the detector and the central detector under the included angle of gamma;
γ′、θ′、x′、y′、
s′γand phi' is gamma, theta, x, y, respectively
sγAnd phi scaled down-sampled CT imaging geometry;
Preferably, the CT imaging geometric parameters are the dimension and physical size of the CT image to be reconstructed, the detector dimension and physical size, the scanning angle range and the scanning geometric parameters, the distance from the X-ray source to the rotation center, and the distance from the rotation center to the detector.
Preferably, the ratio of the CT imaging geometric parameters to the downsampled CT imaging geometric parameters is 1-8: 1.
preferably, the learning type projection domain filter network module is provided with at least one filter operator and at least one down-sampling operator.
Preferably, the learning type image domain filter network module is provided with at least one filter operator and at least one up-sampling operator.
Preferably, the filter operator comprises at least one of a convolutional network structure, a residual network structure, a U-net network structure, or an automatic codec network structure.
Preferably, the down-sampling operator is a convolution operation, a posing operation, or a sub-pixel down-sampling operation with a step size greater than 1, and the up-sampling operator is an inverse convolution operation, an interpolation operation, or a sub-pixel up-sampling operation.
The invention relates to a CT reconstruction neural network structure based on downsampling imaging geometric modeling, which comprises the following components: the learning type projection domain filter network module is used for carrying out filter processing and downsampling processing on CT original projection data to obtain a downsampled projection domain characteristic diagram; the down-sampling learning type back projection module is used for carrying out back projection operation on the down-sampling projection domain characteristic diagram to obtain a down-sampling image domain characteristic diagram, and the down-sampling learning type back projection module is provided with a multi-channel down-sampling back projection operator; and the learning type image domain filter network module is used for carrying out filter processing and up-sampling processing on the down-sampled image domain characteristic image to obtain a CT reconstructed image. The multi-channel down-sampling back projection operator only carries out back projection operation once, and the CT image reconstruction result obtained by the CT reconstruction method of single back projection operation has higher precision. In addition, the multi-channel down-sampling back projection operator is low in calculation complexity, and the back projection operation is carried out on the multiple channels simultaneously, so that the down-sampled projection domain characteristic diagram can be rapidly converted into the down-sampled image domain characteristic diagram, and the speed of reconstructing the whole CT image is further improved.
The invention also aims to avoid the defects of the prior art and provide a CT reconstruction method based on the downsampling imaging geometric modeling, which is carried out by adopting a CT reconstruction neural network structure based on the downsampling imaging geometric modeling, and has low calculation complexity, high speed and high precision of the obtained CT reconstruction image when reconstructing the CT image.
The above object of the present invention is achieved by the following technical measures.
A CT reconstruction method based on the down-sampling imaging geometric modeling is provided, and is carried out by adopting a CT reconstruction neural network structure based on the down-sampling imaging geometric modeling.
Preferably, the method comprises the following steps:
s1: constructing a training database;
the training database comprises CT reconstruction contrast images and a large amount of CT original projection data;
s2: training a CT reconstruction neural network structure based on the downsampling imaging geometric modeling by using the CT raw projection data in the step S1;
step S2 is specifically:
s21: inputting the CT original projection data in the step S1 into a learning type projection domain filter network module to obtain a projection domain feature map of downsampling;
s22: inputting the projection domain feature map subjected to down-sampling into a learning type back projection module subjected to down-sampling to obtain an image domain feature map subjected to down-sampling;
s23: inputting the downsampled image domain feature map into a learning type image domain filter network module to obtain a CT reconstructed image;
s24: comparing the CT reconstructed image with the CT reconstructed contrast image by using a root mean square error function to obtain an error between the CT reconstructed image and the CT reconstructed contrast image, wherein when the error is less than 10-5The training of the CT reconstruction neural network structure based on the downsampling imaging geometric modeling is completed; otherwise, go to step S25;
s25: and (5) optimizing the parameters of the CT reconstructed neural network structure based on the down-sampling imaging geometric modeling by using a stochastic gradient descent method, and returning to the step S21.
S3: and inputting the original projection data of the CT to be reconstructed into a trained CT reconstruction neural network structure based on the down-sampling imaging geometric modeling to obtain a CT reconstruction image.
The invention discloses a CT reconstruction method based on downsampling imaging geometric modeling, which is carried out by adopting a CT reconstruction neural network structure based on the downsampling imaging geometric modeling, and the CT reconstruction neural network structure based on the downsampling imaging geometric modeling comprises the following steps: the learning type projection domain filter network module is used for carrying out filter processing and down-sampling processing on CT original projection data to obtain a down-sampled image domain characteristic diagram, and the down-sampled learning type back projection module is provided with a multi-channel down-sampled back projection operator; and the learning type image domain filter network module is used for carrying out filter processing and up-sampling processing on the down-sampled image domain characteristic image to obtain a CT reconstructed image. The multi-channel down-sampling back projection operator only carries out back projection operation once, and the CT image reconstruction result obtained by the CT reconstruction method of single back projection operation has higher precision. In addition, the multi-channel down-sampling back projection operator is low in calculation complexity, and the back projection operation is carried out on the multiple channels simultaneously, so that the down-sampled projection domain characteristic diagram can be rapidly converted into the down-sampled image domain characteristic diagram, and the speed of reconstructing the whole CT image is further improved.
Drawings
The invention is further illustrated by means of the attached drawings, the content of which is not in any way limiting.
Fig. 1 is a schematic structural diagram of a CT reconstructed neural network structure based on downsampling imaging geometric modeling in embodiment 2.
Fig. 2 is a schematic flowchart of a CT reconstruction method based on downsampling imaging geometric modeling in embodiment 4.
Fig. 3 is a CT reconstructed image obtained by the CT reconstruction method based on the down-sampling imaging geometric modeling in embodiment 4.
Fig. 4 is a CT reconstructed image obtained by the filtered back-projection algorithm in example 4.
FIG. 5 is a CT reconstructed image obtained by the image domain filtering method in example 4.
In fig. 1 to 5, there are included:
a first filter operator 100, a second filter operator 200, a third filter operator 300, an up-sampling operator 400, a down-sampling operator 500, a multi-pass down-sampling back-projection operator 600.
Detailed Description
The invention is further illustrated by the following examples.
Example 1.
A CT reconstruction neural network structure based on downsampling imaging geometric modeling, comprising: and the learning type projection domain filter network module is used for carrying out filter processing and downsampling processing on the CT original projection data to obtain a downsampled projection domain characteristic diagram. And the down-sampling learning type back projection module is used for carrying out back projection operation on the down-sampling projection domain characteristic diagram to obtain the down-sampling image domain characteristic diagram. And the learning type image domain filter network module is used for carrying out filter processing and up-sampling processing on the down-sampled image domain characteristic image to obtain a CT reconstructed image. The learning type back projection module of downsampling is provided with a multichannel downsampling back projection operator. The multi-channel down-sampling back projection operator is as follows:
the multi-channel down-sampling back projection operator only carries out back projection operation once, and the CT image reconstruction result obtained by the CT reconstruction method of single back projection operation has higher precision. In addition, the multi-channel down-sampling back projection operator disclosed by the invention is low in calculation complexity, and the back projection operation is simultaneously carried out on a plurality of channels, so that the down-sampled projection domain characteristic diagram can be rapidly converted into the down-sampled image domain characteristic diagram, and the speed of reconstructing the whole CT image is further improved.
In this embodiment, the construction process of the multi-channel downsampling back-projection operator is as follows:
acquiring CT imaging geometric parameters, and constructing a traditional CT system model according to the CT imaging geometric parameters
The CT imaging geometric parameters are zoomed to obtain the down-sampling CT imaging geometric parameters, and the down-sampling CT imaging geometric parameters are substituted into the traditional CT system model to obtain the down-sampling CT system model
Discretizing the CT system model to obtain the multi-channel down-sampling back projection operator
Wherein f (x, y) represents a slice of the object under scanning in the x-y plane, x and y being indices of the object slice in the spatial coordinate system; g (γ, θ) represents measured chord chart data, γ being the ray reaching an arbitrary detector and the central rayThe included angle theta is the rotation angle of the radiation source;
to represent
The dirac function of (a) is,
φ＝θ+γ；sγis the physical distance of the detector from the central detector at the included angle gamma.
γ′、θ′、x′、y′、
s′γAnd phi' are gamma, theta, x, y,
sγand phi scaled down-sampled CT imaging geometry. The ratio of the CT imaging geometric parameters to the downsampled CT imaging geometric parameters is 1-8: 1, scaling the CT imaging geometric parameters by 1-8 times to obtain the down-sampled CT imaging geometric parameters.
In this embodiment, the CT imaging geometric parameters are the dimension and physical size of the CT image to be reconstructed, the dimension and physical size of the detector, the scan angle range, the scan geometric parameters, the distance from the X-ray source to the rotation center, and the distance from the rotation center to the detector.
In this embodiment, the learning-type projection domain filter network module is provided with at least one filter operator and at least one down-sampling operator, and the filter operator and the down-sampling operator perform characteristic change on CT original projection data to obtain a characteristic diagram required by the down-sampling learning-type back projection module. The learning type image domain filter network module is provided with at least one filter operator and at least one up-sampling operator, and the characteristic diagram output by the learning type back projection module is processed through the filter operator and the down-sampling operator, so that a final CT reconstruction image can be obtained.
In this embodiment, the filter operator includes at least one of a convolutional network structure, a residual network structure, a U-net network structure, or an automatic codec network structure. The down-sampling operator is convolution operation, posing operation or sub-pixel down-sampling operation with the step length larger than 1, and the up-sampling operator is deconvolution operation or interpolation operation. It should be noted that the filter operator in this embodiment is not limited to a convolutional network structure, a residual network structure, a U-net network structure, or an automatic codec network structure, and may also be other customized neural network structures. The down-sampling operator in this embodiment is not limited to the convolution operation, the posing operation, or the sub-pixel down-sampling operation with the step size larger than 1, but may be other customized down-sampling operations. The up-sampling operator in this embodiment is not limited to the deconvolution operation or the interpolation operation, and may be other customized up-sampling operations.
According to the CT reconstruction neural network structure based on the downsampling imaging geometric modeling, a plurality of channels of a multi-channel back projection operator can perform single back projection operation at the same time, the used multi-channel back projection operator is low in calculation complexity, the CT image reconstruction speed is high when the CT image is reconstructed, and the obtained CT reconstruction image precision is high.
Example 2.
A CT reconstruction neural network structure based on downsampling imaging geometric modeling, as shown in fig. 1, and the other features are the same as those of embodiment 1, except that: the learning type projection domain filter network module comprises three filter operators and a down-sampling operator 500, wherein the three filter operators are a first filter operator 100, a second filter operator 200 and a third filter operator 300 respectively, and the down-sampling operator 500 is arranged between the first filter operator 100 and the second filter operator 200.
Wherein the first filter operator 100 comprises a convolutional network structure, which is sequentially configured with a convolution operation, a layer normalization operation and an lreol activation function, the convolution operation comprises 16 convolution channels, and a convolution kernel of each convolution channel is 3 × 3 and has a zero padding operator.
The second filter operator 200 comprises a plurality of residual network structures, each of which is sequentially configured with a convolution operation, a layer normalization operation, an lreuu activation function, a convolution operation, a layer normalization operation, and an lreuu activation function, with a short-circuiting path between an input of a first convolution layer and an input of a second lreuu layer. In this embodiment, the second filter operator 200 specifically includes 10 residual network structures, but is not limited to 10, and may also be 8, 9, 11, and the like. The number of channels for both convolution operations is 64, the convolution kernel size is 3 x 3, and with zero padding operators.
The first filter operator 100 comprises a convolutional network structure with a 4-channel convolutional layer with a convolutional kernel size of 1 x 1.
The downsampling operator 500 comprises a sub-pixel downsampling operation that can downsample a feature map of size C × W × H into a feature map of size 4C × W/2 × H/2, where the number of convolution channels of the sub-pixel downsampling operation is 64.
It should be noted that the convolution operations used by the learning-type projection domain filter network module are all 2-dimensional convolutions.
The downsampled learning type back projection module is provided with a multi-channel downsampled back projection operator 600, in this example, a traditional back projection operator is firstly constructed, the matrix size of the traditional back projection operator is 1152 × 736 × 512 × 512, then geometric parameters of the traditional back projection operator are scaled to construct a downsampled back projection operator, the matrix size of the downsampled back projection operator can be 1/16, the matrix size of the downsampled back projection operator can be 576 × 368 × 256 × 256. And setting the number of channels of the down-sampling back projection operator to be 4.
The learning image domain filter network module includes three filter operators and one up-sampling operator 400 that are the same as the learning projection domain filter network module filter operators. The upsampling operator is disposed between the second filter operator 200 and the third filter operator 300, and comprises a sub-pixel based upsampling operation that can upsample a feature map of size 4C × W/2 × H/2 to a feature map of size C × W × H.
This neural network structure is rebuild to CT based on degampling formation of image geometric modeling, the learning-type back projection module of degampling is provided with multichannel degampling back projection operator, and the multiple channels of multichannel back projection operator can carry out single back projection operation simultaneously, and the multichannel back projection operator that uses calculates the complexity and hangs down, and fast and the CT that obtains rebuilds the image precision height when rebuilding the CT image.
Example 3.
A CT reconstruction method based on the downsampling imaging geometric modeling is carried out by adopting a CT reconstruction neural network structure based on the downsampling imaging geometric modeling, and comprises the following steps:
s1: and constructing a training database, wherein the training database comprises CT reconstructed contrast images and a large amount of CT original projection data. The CT raw projection data in the training database may come from the technicians in this field from their own experimental data or from online source databases.
S2: the CT reconstructed neural network structure modeled based on the downsampled imaging geometry is trained using the CT raw projection data in step S1.
Step S2 is specifically:
s21: inputting the CT original projection data in step S1 into the learning type projection domain filter network module to obtain a downsampled projection domain feature map.
S22: and inputting the projection domain feature map subjected to down-sampling into a learning type back projection module subjected to down-sampling to obtain an image domain feature map subjected to down-sampling. The learning type back projection module of downsampling is provided with multichannel downsampling back projection operator 600, and a plurality of passageways of multichannel back projection operator can carry out single back projection operation simultaneously, and has lower computational complexity.
S23: and inputting the downsampled image domain feature map into a learning type image domain filter network module to obtain a CT reconstructed image.
S24: comparing the CT reconstructed image with the CT reconstructed contrast image by using a root mean square error function to obtain an error between the CT reconstructed image and the CT reconstructed contrast image, wherein when the error is less than 10-5The training of the CT reconstruction neural network structure based on the downsampling imaging geometric modeling is completed; otherwise, the process proceeds to step S25.
S25: and (5) optimizing the parameters of the CT reconstructed neural network structure based on the down-sampling imaging geometric modeling by using a stochastic gradient descent method, and returning to the step S21.
S3: and inputting the original projection data of the CT to be reconstructed into a trained CT reconstruction neural network structure based on the down-sampling imaging geometric modeling to obtain a CT reconstruction image.
The CT reconstruction method based on the downsampling imaging geometric modeling has the advantages of low calculation complexity in the reconstruction process, high reconstruction speed and high accuracy of the obtained CT reconstruction image.
Example 4.
A CT reconstruction method based on the down-sampling imaging geometric modeling has the same other characteristics as the embodiment 3, and the difference is that: the method is carried out by adopting a CT reconstruction neural network structure based on the down-sampling imaging geometric modeling in the embodiment 2. As shown in fig. 2, the process of inputting the CT raw projection data to be reconstructed into the trained CT reconstruction neural network structure based on the downsampling imaging geometric modeling includes:
firstly, CT original projection data to be reconstructed are obtained. As shown, the CT raw projection data in this embodiment is derived from the abdomen image of the patient to be reconstructed, and has a size of 512 × 512. The imaging geometry of the X-ray CT scanner used is as follows: the X-ray source is a fan-shaped X-ray source, and the rotation angle is between [0, 2 pi ]. 1152 angles of exposure and sampling of CT projection data are performed over this angular range, each CT projection corresponding to 736 detector units. The size of the image pixel is 0.6641 mm; the size of the detector unit is 0.6848 mm. The distance from the X-ray source to the detector is 600 mm; the distance to the centre of rotation was 550 mm. Therefore, the size of the original projection data of CT to be reconstructed obtained by scanning with the X-ray CT scanner is 1152X 736.
And secondly, inputting original projection data of the CT to be reconstructed with the size of 1152 multiplied 736 into a CT reconstruction neural network structure based on the down-sampling imaging geometric modeling, wherein N is the number of layers to be reconstructed. The CT original projection data to be reconstructed is changed into a feature map with the size of 16 x 1152 x 736 after passing through a first filtering operator 100 of a learning type projection domain filtering network module, the size of the feature map is changed into 64 x 576 x 368 after passing through a down-sampling operator 500, the size of the feature map is kept at 64 x 576 x 368 after passing through a second filtering operator 200, and a feature map with the size of 4 x 576 x 368 is output after passing through a third filtering operator 300. The feature map with the size of 4 × 576 × 368 is subjected to the 4-channel downsampling back-projection operator of the downsampling learning type back-projection module, and then the size becomes 4 × 256 × 256. The feature map with the size of 4 × 256 × 256 passes through the first filter operator 100, the upsampling operator 400, the second filter operator 200 and the third filter operator 300 of the learning type image domain filter network module, and the feature map size is changed into 4 × 256 × 256 → 64 × 256 × 256 → 16 × 512 × 512 → 512 × 512. The feature map with the size of 512 × 512 output by the third filter operator 300 of the learning image domain filter network module is the final CT reconstructed image.
In this embodiment, the number of layers to be reconstructed in the CT original projection data is 1, and a CT reconstructed image obtained by using the CT reconstruction method based on the downsampling imaging geometric modeling in this embodiment with the CT original projection data to be reconstructed having a dose of 1/4 of 1152 × 736 is shown in fig. 3.
The existing single back projection method for CT image reconstruction mainly includes a filtered back projection algorithm and an image domain filtering method, the number of layers to be reconstructed of CT original projection data is 1, a CT reconstructed image obtained by using filtered back projection algorithm on the CT original projection data to be reconstructed with 1/4 dose being 1152 × 736 is shown in fig. 4, and a CT reconstructed image obtained by using image domain filtering method on the CT original projection data to be reconstructed with 1/4 dose being 1152 × 736 is shown in fig. 5.
In addition, the number of layers to be reconstructed of the CT raw projection data is 1, and the CT image reconstruction time using the CT reconstruction method based on the downsampling imaging geometric modeling, the filtered back-projection algorithm, and the image domain filtering method in this embodiment using the CT raw projection data to be reconstructed with the dose of 1/4 of 1152 × 736 is shown in table 1.
TABLE 1 reconstruction time for different CT image reconstruction methods
As can be obtained by combining fig. 3, fig. 4, fig. 5 and table 1, the CT image reconstruction time of the filtered back-projection algorithm is the shortest, but the definition of the CT reconstructed image obtained by the filtered back-projection algorithm is low, and the CT reconstructed image obtained by the image domain filtering method has good definition, but the CT image reconstruction time is long. However, the CT reconstruction method based on the downsampling imaging geometric modeling in the embodiment has the highest accuracy of the obtained CT reconstruction image and short reconstruction time.
According to the CT reconstruction method based on the downsampling imaging geometric modeling, the CT image reconstruction speed is high, and the obtained CT reconstruction image is high in precision.
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 reconstruction neural network structure based on downsampling imaging geometric modeling, comprising:
the learning type projection domain filter network module is used for carrying out filter processing and downsampling processing on CT original projection data to obtain a downsampled projection domain characteristic diagram;
the system comprises a down-sampling learning type back projection module, a down-sampling learning type back projection module and a down-sampling learning type back projection module, wherein the down-sampling learning type back projection module is used for carrying out back projection operation on a down-sampling projection domain characteristic graph to obtain a down-sampling image domain characteristic graph;
and the learning type image domain filter network module is used for carrying out filter processing and up-sampling processing on the down-sampled image domain characteristic image to obtain a CT reconstructed image.
2. The CT reconstruction neural network structure based on downsampling imaging geometric modeling according to claim 1,
the multi-channel down-sampling back projection operator is as follows:
the construction process of the multi-channel down-sampling back projection operator comprises the following steps:
acquiring CT imaging geometric parameters, and constructing a traditional CT system model according to the CT imaging geometric parameters
The CT imaging geometric parameters are zoomed to obtain the down-sampling CT imaging geometric parameters, and the down-sampling CT imaging geometric parameters are substituted into the traditional CT system model to obtain the down-sampling CT system model
Discretizing the down-sampled CT system model to obtain a multi-channel down-sampled back projection operator;
wherein f (x, y) represents a slice of the object under scanning in the x-y plane, x and y being indices of the object slice in the spatial coordinate system; g (gamma, theta) represents measured chord graph data, gamma is the included angle between the ray reaching any detector and the central ray, and theta is the rotation angle of the radiation source;
to represent
The dirac function of (a) is,
φ＝θ+γ；sγis the physical distance between the detector and the central detector under the included angle of gamma;
γ′、θ′、x′、y′、
s′γand phi' are gamma, theta, x, y,
sγand phi scaled down-sampled CT imaging geometry;
3. The neural network structure for CT reconstruction based on downsampling imaging geometry modeling according to claim 2, wherein said CT imaging geometry parameters are dimensions and physical dimensions of the CT image to be reconstructed, detector dimensions and physical dimensions, scan angle range and scan geometry parameters, distance from X-ray source to rotation center and distance from rotation center to detector.
4. The CT reconstruction neural network structure based on the downsampling imaging geometric modeling according to claim 2, wherein the ratio of the CT imaging geometric parameters to the downsampling CT imaging geometric parameters is 1-8: 1.
5. the downsampled imaging geometry modeling-based CT reconstruction neural network structure of claim 1, wherein the learning-type projection domain filter network module is provided with at least one filter operator and at least one downsampling operator.
6. The CT reconstruction neural network structure based on downsampling imaging geometric modeling according to claim 1, wherein the learning type image domain filter network module is provided with at least one filter operator and at least one upsampling operator.
7. The downsampled imaging geometry modeling-based CT reconstructed neural network structure of claim 5 or 6, wherein the filter operator comprises at least one of a convolutional network structure, a residual network structure, a U-net network structure, or an auto-codec network structure.
8. The downsampled imaging geometry modeling-based CT reconstructed neural network structure of claim 7, wherein the downsampling operator is a convolution operation, a pooling operation, or a sub-pixel downsampling operation with a step size greater than 1, and the upsampling operator is an deconvolution operation, an interpolation operation, or a sub-pixel upsampling operation.
9. A CT reconstruction method based on downsampling imaging geometric modeling, characterized by using the CT reconstruction neural network structure based on downsampling imaging geometric modeling according to any one of claims 1 to 8.
10. The method of CT reconstruction based on downsampled imaging geometry modeling according to claim 9, comprising the steps of:
s1: constructing a training database;
the training database comprises CT reconstruction contrast images and a large amount of CT original projection data;
s2: training a CT reconstruction neural network structure based on the downsampling imaging geometric modeling by using the CT raw projection data in the step S1;
step S2 is specifically:
s21: inputting the CT original projection data in the step S1 into a learning type projection domain filter network module to obtain a projection domain feature map of downsampling;
s22: inputting the projection domain feature map subjected to down-sampling into a learning type back projection module subjected to down-sampling to obtain an image domain feature map subjected to down-sampling;
s23: inputting the downsampled image domain feature map into a learning type image domain filter network module to obtain a CT reconstructed image;
s24: comparing the CT reconstructed image with the CT reconstructed contrast image by using a root mean square error function to obtain an error between the CT reconstructed image and the CT reconstructed contrast image, wherein when the error is less than 10-5The training of the CT reconstruction neural network structure based on the downsampling imaging geometric modeling is completed; otherwise, go to step S25;
s25: and (5) optimizing the parameters of the CT reconstructed neural network structure based on the down-sampling imaging geometric modeling by using a stochastic gradient descent method, and returning to the step S21.
S3: and inputting the original projection data of the CT to be reconstructed into a trained CT reconstruction neural network structure based on the down-sampling imaging geometric modeling to obtain a CT reconstruction image.
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