CN113554729B - CT image reconstruction method and system - Google Patents
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Abstract
The invention discloses a CT image reconstruction method and a system, wherein the method comprises the following steps: collecting projection data and inputting related parameters; respectively carrying out one-dimensional Fourier transform on the projection data under different irradiation angles to obtain distribution data of the projection data in a frequency domain; according to the Fourier center slicing theorem, rearranging the projection data under different irradiation angles in a frequency domain to corresponding straight lines under a rectangular coordinate system respectively, wherein each straight line passes through the origin of the rectangular coordinate system and the slope corresponds to the surface slope of the detector under each irradiation angle respectively, so that the distribution of the distribution data of the projection data in the frequency domain under the rectangular coordinate system is obtained; by utilizing a convolutional neural network, taking the distribution of the distribution data of the projection data in the frequency domain under a rectangular coordinate system as input, and outputting the frequency domain distribution of the reconstructed image; then performing two-dimensional Fourier inverse transformation to generate a reconstructed image in a die body time domain; and outputting the reconstructed image of the phantom. The invention makes the process of CT image reconstruction easier.
Description
Technical Field
The invention relates to the technical field of CT image reconstruction, in particular to a CT image reconstruction method and a system.
Background
Since the X-ray Computed Tomography (CT) technology has great advantages in disease screening and diagnosis, the technology becomes an indispensable imaging means in clinical practice in modern hospitals, including whole body diagnosis CT, C-arm CT interventional imaging, dental CT, and the like. The main factors affecting the widespread use of CT technology in clinical practice are two-fold: the quality of the reconstructed image and the speed of image reconstruction obviously improve the quality of the CT image along with the development of a deep learning technology in recent years; with the development of GPU hardware acceleration technology, the time required by CT image reconstruction is obviously shortened.
Originally, the deep learning technique was directly used to enhance the image obtained by the conventional CT image reconstruction method, and improve the visual effect of the reconstructed image. And then, the deep learning technology is gradually applied to the CT image reconstruction process, so that the quality of the reconstructed image is further improved. Methods for directly reconstructing CT images using a deep learning technique can be classified into three categories: (1) a full-connection method, (2) an iterative expansion method, and (3) an analytical operator method.
The deep learning refers to a machine learning method which is formed by simple operations and has a multilayer network structure, namely a machine learning method based on a convolutional neural network. Because the projection data and the reconstructed image are not in the same image domain, the convolutional neural network is directly used for carrying out cross-image domain connection, and the feature extraction capability and the feature expression capability of the convolutional neural network are seriously reduced. To overcome this problem, Zhu et al uses a fully-connected layer to connect the projection data with the reconstructed image, implementing a depth-learning-based CT image reconstruction. According to the method, three full-connection layers are used for realizing connection between different image domains, so that the difficulty of network training is increased. Li et al use a full link layer to achieve the connection of projection data and tomographic images, reducing the difficulty of network training. The CT image reconstruction network using the full-connection structure is not a multi-layer network with a simple structure any more, so that the advantages of a deep learning technology are weakened, and the difficulty of network training is increased.
To avoid using fully connected layers in the CT reconstruction process, some scholars construct convolutional neural networks using iterative unfolding methods. The general idea is to ensure that the forward/backward projection process in the iterative process is unchanged, and to mine useful information in projection data and a back-projected image by using a deep learning technology. Some methods directly utilize a convolutional neural network to realize a regular term of an objective function in a traditional iteration method; other methods divide the objective function of the conventional iterative method into several sub-objective functions, and for the sub-objective functions related to projection data or a back-projected image, a convolutional neural network is used for implementation. Although the iterative expansion method avoids using a full connection layer in a neural network, the corresponding CT image reconstruction network is very huge, and the network training difficulty is high.
In order to fully exploit the potential of the deep learning technology in CT image reconstruction, a back projection network layer without variable parameters is constructed by using an analysis operator, so that the connection from a projection domain to an image domain is realized; and extracting image information in a projection domain and an image domain by using a convolutional neural network respectively. Burfl et al preprocess (filter) the projection data with one full link layer; and reconstructing an image by utilizing a back projection network layer. He et al preprocess (filter) projection data using two fully connected layers or two convolutional neural networks; reconstructing an image by utilizing a back projection network layer; and the reconstructed image is processed by using the convolutional neural network, so that the quality of the reconstructed image is further improved. Zhang et al use the back projection network layer to reconstruct the image; and (3) processing the projection data and the reconstructed image by using a convolutional neural network, further retaining the details of the reconstructed image and removing the image artifact. Zheng et al constructs a backprojection network layer using an ideal ramp filter and an operator of the analysis operation. Although the back projection network layer realizes the connection of the projection domain and the image domain and reduces the complexity of the CT image reconstruction network structure, the whole CT image reconstruction network is divided into two convolution neural networks, and the feature extraction capability and the feature expression capability of the reconstruction network are reduced.
Therefore, there is a need for a CT image reconstruction method and system that can make the CT image reconstruction process simpler and easier.
Disclosure of Invention
The present invention has been made in view of the above problems. The invention aims to provide a CT image reconstruction method and a system, which overcome the defects and make the CT image reconstruction process easier.
In order to achieve the above purpose, the solution of the invention is: a CT image reconstruction method, comprising the steps of:
step 1: inputting projection data and system parameters, wherein a detector on CT equipment receives X-ray irradiation and then generates numerical values, or a computer simulates the detector to receive the X-ray irradiation and generate numerical values to form the projection data, and the system parameters comprise the size of the detector, the sampling interval of the detector, the number of the projection data, the irradiation angle of the X-ray and the detector relative to a die body, the size of a reconstructed die body and the sampling interval of the reconstructed die body;
step 2: respectively carrying out one-dimensional Fourier transform on projection data under different illumination angles, and calculating to obtain distribution data of the projection data in a frequency domain;
and step 3: according to the Fourier center slicing theorem, rearranging the projection data under different irradiation angles in a frequency domain to corresponding straight lines under a rectangular coordinate system respectively, wherein each straight line passes through the origin of the rectangular coordinate system and the slope of each straight line is correspondingly the same as the slope of the surface of the detector under each irradiation angle, so that the distribution of the distribution data of the projection data in the frequency domain under the rectangular coordinate system is obtained;
and 4, step 4: under a rectangular coordinate system, extracting useful information in the rearranged projection data by using the trained convolutional neural network to generate a reconstructed image, and outputting the frequency domain distribution of the reconstructed image;
and 5: performing two-dimensional Fourier inverse transformation on the frequency domain distribution of the reconstructed image in the rectangular coordinate system to generate a reconstructed image of the phantom in a time domain;
step 6: and outputting the reconstructed image of the phantom.
Further, in step 3, when the distribution data of the projection data in the frequency domain is arranged to the rectangular coordinate system, the projection data and the origin are arranged at a certain distance and are arranged outwards at equal intervals along the corresponding straight line from the origin.
Further, when the distribution data of the projection data in the frequency domain is arranged to the rectangular coordinate system, the data arrangement sampling intervals on the lines with different slopes are not all the same.
Further, the straight line linearly increases from 1 pixel long to 45 ° in data interval within a rotation angle range of 0 ° to 45 °
One pixel long; from 45 to 90 rotation angles
The one pixel length is linearly decreased to 1 pixel length.
Further, when the distribution data of the projection data is arranged in the rectangular coordinate system in the frequency domain, the arrangement is started with an interval of 100 pixels from the origin of the rectangular coordinate system.
Further, the convolutional neural network is a U-Net network.
A CT image reconstruction system comprising:
an information input module: the system comprises a computer, a CT device and a reconstruction module, wherein the computer is used for inputting projection data and system parameters, the projection data are values generated after a detector on the CT device receives X-ray irradiation, or the values generated after the detector simulates the detector to receive the X-ray irradiation through the computer, and the system parameters comprise the size of the detector, the sampling interval of the detector, the number of the projection data, the irradiation angle of the X-ray and the detector, the size of the reconstruction module and the sampling interval of the reconstruction module;
a Fourier transform module: the X-ray detector is used for performing one-dimensional Fourier transform on projection data of the X-ray and the detector relative to the die body under different irradiation angles so as to calculate distribution data of the projection data in a frequency domain;
a data rearrangement module: the distribution of the projection data of the X-ray and the detector pair mold body under different irradiation angles is rearranged to corresponding straight lines under the rectangular coordinate system in the frequency domain to obtain the distribution of the projection data under the rectangular coordinate system in the frequency domain;
a convolutional neural network module: under a rectangular coordinate system, mining useful information in rearranged projection data by using the trained convolutional neural network to generate a reconstructed image, and outputting frequency domain distribution of the reconstructed image;
an inverse Fourier transform module: the system comprises a two-dimensional Fourier transformation module, a reconstruction module and a reconstruction module, wherein the two-dimensional Fourier transformation module is used for performing two-dimensional Fourier inverse transformation on the frequency domain distribution of the reconstruction image in the rectangular coordinate system to generate the reconstruction image in the time domain;
an information output module: for outputting reconstructed phantom images.
After the scheme is adopted, the invention has the beneficial effects that:
according to the Fourier center slicing theorem, the projection data distribution under different irradiation angles is rearranged on the corresponding straight lines under the rectangular coordinate system in the frequency domain, each straight line passes through the origin of the rectangular coordinate system, and the slope of each straight line is respectively corresponding to the same slope of the surface of the detector under each irradiation angle, so that the distribution of the projection data under the rectangular coordinate system in the frequency domain is obtained, the frequency domain distribution of the reconstructed image is also under the rectangular coordinate system, the useful information in the rearranged projection data can be directly mined by using a convolutional neural network to generate the frequency domain distribution of the reconstructed image, and the reconstructed phantom image can be obtained through two-dimensional inverse Fourier transform; the CT reconstructed image is directly constructed by using the convolutional neural network in the same image domain, so that the problem of complex learning task of the convolutional neural network caused by the conversion from a projection domain to the image domain is solved, the visual quality of the reconstructed image is improved, and the process of reconstructing the CT image is easier.
Drawings
FIG. 1 is a flow chart of a CT image reconstruction method and system according to the present invention;
FIG. 2 is a schematic diagram of the calculation of a data module according to the present invention;
FIG. 3 is a schematic diagram of the computation of a convolutional neural network of the present invention;
fig. 4 is a schematic diagram of an embodiment of the convolutional neural network of the present invention.
Detailed Description
The invention is described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the present invention provides a CT image reconstruction method, which includes the following steps:
step 1: inputting projection data and system parameters, wherein a detector on CT equipment receives X-ray irradiation and then generates numerical values, or a computer simulates the detector to receive the X-ray irradiation and generate numerical values to form the projection data, and the system parameters comprise the detector size, the detector sampling interval, the number of the projection data, the irradiation angle of the X-ray and the detector, the size of a reconstructed phantom and the sampling interval of the reconstructed phantom; in the embodiment, a parallel X-ray is used for irradiating a die body, a flat panel detector is used for imaging, the X-ray penetrates through the die body and then irradiates on the flat panel detector, the X-ray generates attenuation with different degrees when penetrating through different positions of the die body, so that the X-ray intensity received by different positions on the flat panel detector is different, the flat panel detector generates numerical values reflecting the X-ray intensity of each position, the numerical values on the flat panel detector under different irradiation angles of the X-ray relative to the die body are extracted to form projection data, in the embodiment, the sampling interval when the irradiation angles of the X-ray and the detector are rotated is 1 degree, the number of projections is N-360, and the projection data under each irradiation angle of the X-ray and the detector relative to the die body are correspondingly obtained, and in the embodiment, only a fault plane where a rotation center is located is reconstructed; the length of the projection data is 768 mm, the sampling interval is 1.0mm, and the length corresponds to the size of the detector, the sampling interval of the detector and the number of the projection data;
step 2: performing one-dimensional fourier transform on the projection data of the X-ray and the detector at different irradiation angles, and calculating to obtain distribution data of the projection data in a frequency domain, wherein in this embodiment, the frequency domain distribution length of the projection data at each irradiation angle is 768, and the 0 frequency component is at the 385 th sampling position;
and step 3: as shown in fig. 2, the relationship between the distribution of the projection data in the frequency domain and the reconstructed image can be known according to the fourier center slice theorem, the projection data in the polar coordinate system is sampled, and the obtained frequency domain distribution in the rectangular coordinate is the frequency domain distribution of the reconstructed image; therefore, the CT image reconstruction task can be simplified into the conversion of projection data in a polar coordinate system in a frequency domain to a reconstructed image in a rectangular coordinate system, the data conversion in the two coordinate systems is realized by directly using a convolutional neural network due to the limitation of the inconsistency of the data sampling modes in the two coordinate systems, in order to overcome the problem of the data conversion, the projection data in the polar coordinate system is rearranged to the rectangular coordinate system according to a certain rule so as to obtain the distribution of the projection data in the rectangular coordinate system, the distribution data of the projection data in the frequency domain under different irradiation angles are respectively arranged to corresponding straight lines in the rectangular coordinate system in the frequency domain according to the Fourier center slicing principle, the straight lines pass through the origin of the rectangular coordinate system, and the slopes of the straight lines are respectively corresponding to the slopes of the detector surfaces under the irradiation angles, so as to obtain the distribution data of the projection data in the frequency domain under the rectangular coordinate system, in this embodiment, the distribution of the projection data in the frequency domain is shown in the left diagram in fig. 2, each line of data is the frequency domain distribution data of the projection data at a certain projection angle, each line of data is mapped to the straight line of the corresponding slope in the rectangular coordinate system, because of the polar coordinate systemThe sampling precision of the original point is high, which is easy to cause the phenomenon of data aliasing at the original point after data rearrangement, so when the distribution data of the projection data in the frequency domain is arranged to the rectangular coordinate system, the data and the original point are arranged at a certain distance, and are arranged outwards from the original point at equal intervals along the corresponding straight line, in this embodiment, when the distribution data of the projection data in the frequency domain is arranged to the rectangular coordinate system, 100 pixels at the original point of the rectangular coordinate system are arranged at intervals; in the rectangular coordinate system, because the intersecting length of the straight line passing through the origin point with different slopes and the pixel is different, the use of the same sampling interval in the rearrangement process of the projection data is easy to cause the mixing of adjacent rearranged data, in order to overcome the problem, when the distribution data of the projection data in the frequency domain is arranged to the rectangular coordinate system, the intervals of the data on different straight lines of the rectangular coordinate system are not all the same when the data are arranged, the sampling interval of the data arrangement on the straight line passing through the origin point is corrected along with the different rotation angles of the straight line, in the embodiment, the data sampling interval of the straight line is linearly increased from 1 pixel length to 45 degrees within the rotation angle range of the straight line from 0 degree to 45 degrees
One pixel long; from 45 to 90 rotation angles
The length of each pixel is linearly decreased to 1 pixel; in the other quadrants, as in the case of the first quadrant, not specifically illustrated;
and 4, step 4: in a rectangular coordinate system, mining useful information in rearranged projection data to generate a reconstructed image by using a trained convolutional neural network, and outputting frequency domain distribution of the reconstructed image, wherein the convolutional neural network comprises a plurality of network layers, basic operations of the convolutional neural network comprise convolution, activation, pooling, up-sampling (or deconvolution), error feedback and the like, the plurality of layers of convolutional neural network layers are more than 2 layers, and the convolutional neural network model is formed by using the basic operations, as shown in fig. 3, in the process of forward transfer processing of data in the plurality of network layers of the convolutional neural network, the projection data sequentially passes through each basic operation of the convolutional neural network in sequence to generate the reconstructed image; constructing a loss function in the reverse transfer process of data in a plurality of network layers of the convolutional neural network, calculating the value of the whole network loss function by using an image and a real image which are reconstructed by the convolutional neural network, reversely passing the gradient information of the loss function through each network layer of the convolutional neural network, calculating the gradient information of each network layer and updating the parameter value of each network layer;
as shown in fig. 4, in the present embodiment, the convolutional neural network is constructed by using a U-Net network structure, the overall network structure is an end-to-end network structure, and in the present embodiment, the rearranged back projection is a two-dimensional image with a size of 1024 × 1024; the reconstructed data is also a two-dimensional image with a size of 512x512, so that two-dimensional data operation mode is adopted in the convolutional neural network to input data for processing, and the convolution operation, the pooling operation and the upsampling operation are all processed by adopting a two-dimensional template, and a specific data operation mode is shown in fig. 4, wherein the size of the template of the convolutional layer is 3x 3; the template size of the pooling layer is 2x2, and the step size is 2x 2; the upsampled template size is 2x2 with a step size of 2x 2. The loss function can be constructed using point-to-point pixel differences or image structure similarity, such as L1Norm loss function, L2The norm loss function and the SSIM (structural similarity index) loss function can also be constructed by using a convolutional neural network for extracting image structure characteristics, such as a VGG loss function, in the embodiment, L is used2In the implementation case, the convolutional neural network is trained independently, the rearranged projection data is positioned under a rectangular coordinate system, the reconstructed image is also positioned under the rectangular coordinate system, and then the input data and the output data of the convolutional neural network module are positioned under the same rectangular coordinate system, so that the feature extraction and feature expression capability of the convolutional neural network can be directly utilized to mine useful information in the projection data to generate the reconstructed image;
and 5: performing two-dimensional Fourier inverse transformation on the frequency domain distribution of the reconstructed image in the rectangular coordinate system to generate a reconstructed image of the phantom in a time domain;
step 6: and outputting the reconstructed image.
The present invention also provides a CT image reconstruction system, including:
an information input module: the system comprises a computer, a CT device and a reconstruction module, wherein the computer is used for inputting projection data and system parameters, the projection data are values generated after a detector on the CT device receives X-ray irradiation, or the values generated after the detector simulates the detector to receive the X-ray irradiation through the computer, and the system parameters comprise the size of the detector, the sampling interval of the detector, the number of the projection data, the irradiation angle of the X-ray and the detector, the size of the reconstruction module and the sampling interval of the reconstruction module;
a Fourier transform module: the X-ray detector is used for performing one-dimensional Fourier transform on projection data of the X-ray and the detector relative to the die body under different irradiation angles so as to calculate distribution data of the projection data in a frequency domain;
a data rearrangement module: the distribution of the projection data of the X-ray and the detector pair mold body under different irradiation angles is rearranged to corresponding straight lines under the rectangular coordinate system in the frequency domain to obtain the distribution of the projection data under the rectangular coordinate system in the frequency domain;
a convolutional neural network module: under a rectangular coordinate system, mining useful information in rearranged projection data by using the trained convolutional neural network to generate a reconstructed image, and outputting frequency domain distribution of the reconstructed image;
an inverse Fourier transform module: the system comprises a two-dimensional Fourier transformation module, a reconstruction module and a reconstruction module, wherein the two-dimensional Fourier transformation module is used for performing two-dimensional Fourier inverse transformation on the frequency domain distribution of the reconstruction image in the rectangular coordinate system to generate the reconstruction image in the time domain;
an information output module: for outputting reconstructed phantom images.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the design of the present invention, and all equivalent changes made in the design key point of the present invention fall within the protection scope of the present invention.
Claims (2)
1. A CT image reconstruction method, comprising the steps of:
step 1: inputting projection data and system parameters, wherein a detector on CT equipment receives X-ray irradiation and then generates numerical values, or a computer simulates the detector to receive the X-ray irradiation and generate numerical values to form the projection data, and the system parameters comprise the size of the detector, the sampling interval of the detector, the number of the projection data, the irradiation angle of the X-ray and the detector relative to a die body, the size of a reconstructed die body and the sampling interval of the reconstructed die body;
step 2: respectively carrying out one-dimensional Fourier transform on projection data under different illumination angles, and calculating to obtain distribution data of the projection data in a frequency domain;
and step 3: according to the Fourier center slicing theorem, rearranging the projection data under different irradiation angles in a frequency domain to corresponding straight lines under a rectangular coordinate system respectively, wherein each straight line passes through the origin of the rectangular coordinate system and the slope of each straight line is correspondingly the same as the slope of the surface of the detector under each irradiation angle, so that the distribution of the distribution data of the projection data in the frequency domain under the rectangular coordinate system is obtained; when the distribution data of the projection data in the frequency domain is arranged to a rectangular coordinate system, the projection data and an origin point are arranged at an interval of 100 pixels, the projection data and the origin point are arranged outwards at equal intervals along corresponding straight lines from the origin point, the data arrangement sampling intervals on straight lines with different slopes are not all the same, and the data sampling intervals of the straight lines are linearly increased from 1 pixel to 45 degrees within the rotation angle range of 0 degree to 45 degrees
One pixel long, ranging from 45 DEG to 90 DEG of rotation angle
The length of each pixel is linearly decreased to 1 pixel;
and 4, step 4: under a rectangular coordinate system, extracting useful information in the rearranged projection data by using the trained convolutional neural network to generate a reconstructed image, and outputting the frequency domain distribution of the reconstructed image;
and 5: performing two-dimensional Fourier inverse transformation on the frequency domain distribution of the reconstructed image in the rectangular coordinate system to generate a reconstructed image of the phantom in a time domain;
step 6: and outputting the reconstructed image of the phantom.
2. A CT image reconstruction method as claimed in claim 1, characterized in that: the convolutional neural network is a U-Net network.
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