CT metal artifact correction method based on back projection tensor coding

Abstract

A CT metal artifact correction method based on back projection tensor coding comprises the steps that an original chordal graph is filtered through a Ramp filter, and finally a trained parameterized residual network based on Fourier series expansion is input to obtain a metal artifact correction image. According to the method, the back projection tensor and the rotation isovariant convolution are combined together, the back projection tensor can provide uncompressed lossless information compared with projection data or image data, the back projection tensor influenced by metal is used as network input, and an image without artifacts is obtained through reconstruction. Priori information of a rotational symmetry structure exists in a back projection tensor slice and between slices, so that a rotation equivariant convolution kernel is used for replacing common convolution to code the back projection tensor. According to the CT metal artifact correction method based on back projection tensor coding, image information can be recovered to obtain a high-quality CT image, meanwhile, the number of network parameters can be reduced, and the generalization of the network is improved.

Description

Technical Field

[0001] The invention relates to the technical field of medical imaging quality control, and in particular to a CT metal artifact correction method based on back-projection tensor coding. Background Art

[0002] Computed Tomography (CT) can provide more detailed and accurate images than traditional X-rays, which is very valuable for diagnosing various diseases, such as tumors, vascular diseases, and internal organ damage. During CT scanning, if the patient has metal implants in the body, such as oral fillers, artificial joints, pacemakers, etc., metal artifacts will be generated in the reconstructed image, causing image distortion.

[0003] At present, the methods of metal artifact correction are mainly divided into three categories: projection completion method, iterative reconstruction method and deep learning-based algorithm. The first method, projection completion method, refers to the use of normal projection data near the metal trajectory in the projection domain to interpolate and complete the metal area, and then reconstruct the metal artifact correction image through the filtered back projection algorithm. The projection interpolation-based method is simple and efficient, but it will inevitably cause problems such as too smooth tissue around the metal and failure to maintain tissue structure due to ignoring the hidden structural information in the metal trajectory. In addition, secondary artifacts are easily introduced due to the discontinuity between the interpolated projection and the adjacent projection. The second method, iterative metal artifact removal method, refers to adding a regularization term based on prior knowledge to the iterative reconstruction algorithm, and obtaining a metal artifact correction image through optimization solution. The iterative reconstruction method is usually better than the projection completion method and performs well in removing metal artifacts. However, due to the large amount of calculation and long time consumption of the algorithm, it is difficult to promote in clinical practice. The third method, deep learning, as a branch of machine learning, has experienced rapid development in recent years. Its core lies in building a deep neural network to learn the complex patterns and features of big data. In the metal artifact correction method based on the image domain, it is necessary to restore the tissue structure of the area covered by the metal artifact. However, it is difficult for the deep learning network to completely separate the light and dark stripes in the metal artifact from the normal tissue. In the metal artifact correction method based on the projection domain, many scholars have introduced various prior information to partially complete the metal trajectory in the chord diagram domain, but there is still a problem of inconsistency between the completed part and the normal tissue, which is further amplified after filtering, resulting in the appearance of secondary artifacts.

[0004] Therefore, in view of the shortcomings of the prior art, it is necessary to provide a CT metal artifact correction method based on back-projection tensor encoding to solve the shortcomings of the prior art. Summary of the invention

[0005] The purpose of the present invention is to avoid the shortcomings of the prior art and provide a CT metal artifact correction method based on back-projection tensor coding. The CT metal artifact correction method based on back-projection tensor coding is conducive to restoring image information to obtain high-quality CT images, and can also reduce the number of network parameters and improve the generalization of the network.

[0006] The above-mentioned purpose of the present invention is achieved by the following technical measures:

[0007] A CT metal artifact correction method based on back-projection tensor coding is provided, and the following steps are obtained:

[0008] S1, filtering the original chord graph through a ramp filter to obtain a filtered chord graph;

[0009] S2, back-projecting the filtered chord diagram obtained in S1 angle by angle, and stacking the back-projected data in the projection angle direction in the order of angles to obtain three-dimensional back-projected tensor data;

[0010] S3. Use the back-projection tensor obtained in S2 as the input of the trained residual network parameterized based on Fourier series expansion to obtain a metal artifact corrected image.

[0011] Preferably, the above-mentioned residual network parameterized based on Fourier series expansion is to replace the convolution in the ordinary convolutional network with a rotational equivariant convolution operator, so as to obtain the residual network parameterized based on Fourier series expansion composed of a rotational equivariant convolution operator FConv and a residual block ResBlock.

[0012] Preferably, the above rotational equivariant convolution operator is expressed by equation (1) and equation (2);

[0013]

[0014] in and are all two-dimensional basis functions, x i and x j are the two-dimensional spatial coordinates, Ω(x) is the radial mask function, and Ω(x) ≥ 0, h is the image pixel size, and p is the back-projection tensor slice size; I p (m) is a periodic function of the Fourier series, and I p (m) is represented by formula (3);

[0015]

[0016] The CT metal artifact correction method based on back-projection tensor coding of the present invention pre-builds a training database, and then uses the training database to train a parameterized residual network based on Fourier series expansion.

[0017] Preferably, the training database is provided with a plurality of pairs of paired data, and each pair of paired data is metal back-projection tensor data of the same object and the same slice and a CT image without metal artifacts.

[0018] Preferably, the above-mentioned residual network parameterized based on Fourier series expansion is trained by the following steps:

[0019] A1. Inputting the metal back-projection tensor data in the training database into a residual network parameterized based on Fourier series expansion to obtain a metal artifact corrected image;

[0020] A2, using a root mean square error function to compare the metal artifact corrected image obtained in A1 with the CT image without metal artifacts in the same pair of paired data, to obtain the error between the metal artifact corrected image and the CT image without metal artifacts;

[0021] A3, judge the size of the error obtained in A2 and the error threshold. When the error is greater than the equal error threshold, enter A4; when the error is less than the error threshold, enter A5, and the error threshold is greater than 0;

[0022] A4. Use the optimizer AdamW to optimize the parameters of the residual network parameterized based on Fourier series expansion, and then return to A1;

[0023] A5. After the training is completed, the current residual network parameterized based on Fourier series expansion is used as the residual network parameterized based on Fourier series expansion after training.

[0024] Preferably, the training database is constructed by the following steps:

[0025] B1. Acquire multiple metal-containing clinical data images, and segment the metal-containing clinical data images using a threshold value to obtain multiple metal masks;

[0026] B2. Perform threshold segmentation on the CT images without metal artifacts in the Mayo public data set to obtain the water-based image and bone-based image corresponding to the CT images without metal artifacts;

[0027] B3. The simulation process of each pair of paired data is as follows: randomly select one metal mask from the multiple metal masks obtained in B1, and then simulate it with the water-based image and bone-based image corresponding to a CT image without metal artifacts to obtain three-dimensional metal back-projection tensor data; the CT image without metal artifacts and the metal back-projection tensor data constitute a pair of paired data.

[0028] The simulation in B3 is performed by the following steps:

[0029] C1. Multiply a randomly selected metal mask by the density corresponding to the selected metal artifact simulation material to obtain the metal base map ρm , and then calculate the number of emitted photons I by formula (4) out ;

[0030]

[0031] Among them, I in (E) is the number of incident photons at energy E, E max is the maximum energy and E max =120, L is the X-ray projection path, μ(E) is the linear attenuation coefficient, and μ(E) is obtained by formula (5);

[0032] μ(E)=μ′ w (E)ρ w +μ′ b (E)ρ b +μ′ m (E)ρ m ...Formula (5);

[0033] Among them, μ′ w (E) is the mass attenuation coefficient of water under energy E, μ′ b (E) is the mass attenuation coefficient of bone at energy E, μ′ m (E) is the mass attenuation coefficient of metal under energy E, ρ w is the water-based image corresponding to the CT image without metal artifacts, ρ b It is the bone base image corresponding to the CT image without metal artifacts;

[0034] C2, the number of emitted photons I obtained for C1 out Add Poisson noise and scattering, expressed by equation (6);

[0035] I′ out ~Poisson(I out )+ξ……Formula (6);

[0036] Where Poisson is the Poisson noise function, ξ is the scattering, I′ out is the number of outgoing photons obtained by adding Poisson noise and scattering to the number of outgoing photons;

[0037] C3, I′ obtained from C2 out The projection P under multi-energy conditions is obtained by formula (7);

[0038]

[0039] Among them I in is the number of incident photons; I in From formula (8), we get:

[0040]

[0041] C4, filtering the projection P obtained in C3 through a ramp filter, and then performing angle-by-angle back-projection to obtain three-dimensional metal back-projection tensor data.

[0042] In A4, the L1 norm is used as the loss function Loss to optimize the parameters of the residual network parameterized based on Fourier series expansion, which is expressed by formula (9);

[0043]

[0044] Where N is the number of samples, I pred is the metal artifact correction image, I ref These are CT images without metal artifacts in the same pair of paired data.

[0045] Preferably, the back-projection tensor data includes texture structure information in the image domain and imaging geometry information in the projection domain.

[0046] Preferably, the metal artifact simulation material is titanium.

[0047] Preferably, the above error threshold is 10 -4 .

[0048] The present invention discloses a CT metal artifact correction method based on back-projection tensor coding, which is obtained by the following steps: S1, filtering the original chord diagram through a ramp filter to obtain a filtered chord diagram; S2, back-projecting the filtered chord diagram obtained by S1 angle by angle, and stacking the back-projection data in the projection angle direction in order of angles to obtain three-dimensional back-projection tensor data; S3, using the back-projection tensor obtained by S2 as the input of a trained Fourier series expansion-based parameterized residual network to obtain a metal artifact correction image. The present invention filters the original chord diagram to eliminate the smear caused by back-projection. The back-projection tensor data of the present invention contains both texture structure information in the image domain and imaging geometry information in the projection domain, which enables the network to better restore tissue details and has stronger metal artifact correction performance compared with projection domain data and image domain data. In the back-projection tensor slice, metal and its artifacts are clearly demarcated from normal tissues, which are manifested as overly bright or overly dark stripe structures, and have simpler morphological features, making it easier for the network to reconstruct an image without artifacts. The present invention combines the back-projection tensor with the rotational equivariant convolution at the same time. Since the back-projection tensor can provide uncompressed lossless information compared with the projection data or image data, the back-projection tensor affected by metal is used as the network input to reconstruct the prior information of the rotationally symmetric structure of the back-projection tensor slices and between slices of the image without artifacts. Therefore, the parameterized residual network based on Fourier series expansion of the present invention uses the rotational equivariant convolution kernel to replace the ordinary convolution to encode the back-projection tensor. The CT metal artifact correction method based on the back-projection tensor encoding is conducive to restoring image information to obtain high-quality CT images, and can also reduce the number of network parameters and improve the generalization of the network. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The present invention is further described with reference to the accompanying drawings, but the contents in the accompanying drawings do not constitute any limitation to the present invention.

[0050] Figure 1 The flowchart of a CT metal artifact correction method based on back-projection tensor encoding is shown.

[0051] Figure 2 This is a diagram of the residual network structure parameterized based on Fourier series expansion.

[0052] Figure 3 This is the metal artifact image before correction in Example 2. Figure 4 This is the metal artifact correction image of Example 2. DETAILED DESCRIPTION

[0053] The technical solution of the present invention is further described in conjunction with the following embodiments.

[0054] Example 1

[0055] A CT metal artifact correction method based on back-projection tensor coding, such as Figure 1 As shown, due to the steps:

[0056] S1, filtering the original chord graph through a ramp filter to obtain a filtered chord graph;

[0057] S2, back-projecting the filtered chord diagram obtained in S1 angle by angle, and stacking the back-projected data (also called VVBP data) in the projection angle direction in the order of angles to obtain three-dimensional back-projected tensor data (also called VVBP tensor);

[0058] S3. Using the back-projected tensor obtained in S2 as the input of a trained Fourier series expansion-based parameterized residual network (also called F-ResNet) to obtain a metal artifact corrected image.

[0059] like Figure 2 As shown, the residual network parameterized based on Fourier series expansion is to replace the convolution in the convolution network with a rotation equivariant convolution operator, and the residual network parameterized based on Fourier series expansion consisting of a rotation equivariant convolution operator FConv and a residual block ResBlock can be obtained. The convolution network of the present invention is an ordinary convolution network, which only has translation equivariance, while the VVBP tensor has the characteristic of rotation. Therefore, the residual network parameterized based on Fourier series expansion of the present invention replaces ordinary convolution with rotation equivariant convolution, and the purpose of Fourier series expansion is to realize rotation equivariant convolution.

[0060] It should be noted that the back-projection tensor data of the present invention contains texture structure information in the image domain and imaging geometry information in the projection domain, so the back-projection tensor data can enable the network to better restore tissue details and have stronger metal artifact correction performance compared with the projection domain data and the image domain data. In addition, in the back-projection tensor slices, there is a clear boundary between metal and its artifacts and normal tissues, which appear as overly bright or overly dark stripe structures, and have simpler morphological features, making it easier for the network to reconstruct artifact-free images. Since the back-projection tensor has prior information of rotationally symmetric structures within and between slices, the parameterized residual network based on Fourier series expansion of the present invention uses rotationally equivariant convolution kernels instead of ordinary convolutions to encode VVBP-Tensor, which is conducive to restoring image information, reducing the number of network parameters, and improving the generalization of the network.

[0061] It should also be noted that there are radial stripes with similar and different tilt angles in the back-projection tensor slices, and due to the CT rotation scanning, the back-projection tensor slices are rotated by a certain angle compared with the adjacent slices, so the back-projection tensor has rotational symmetry characteristics within and between slices. Based on this characteristic, the present invention introduces a rotational equivariant convolution operator to realize the rotational equivariant convolution in the network.

[0062] Since rotation equivariance is proposed based on the translation equivariance of existing convolutional neural networks, filter parameterization is an important strategy to achieve rotation equivariant convolution. The basic idea is to define the filter to be learned as a linear combination of a set of basis functions and learn the combination coefficients. The rotation basis function is the rotation filter, which realizes the construction of rotation equivariant convolution. Since the two-dimensional discrete Fourier transform can be equivalently expressed as a Fourier series expansion, the Fourier series expansion is selected as the basis function of the filter to construct a parameterized filter based on the Fourier series expansion, which can also be called a rotation equivariant convolution operator. In order to represent a discrete filter This can be done by [-(p-1)h / 2,(p-1)h / 2] 2 Discretize a two-dimensional function by uniformly sampling the area within h is the image pixel size, and p is the back-projection tensor slice size:

[0063]

[0064] Among them, x represents the two-dimensional space coordinate, and represents the two-dimensional basis function, m qt and n qt Represents the expansion coefficient. In the traditional Fourier series, the basis functions that can be selected are as follows:

[0065]

[0066] Among them, when ||x||≥((p+1) / 2)h, Ω(x)=0.

[0067] However, when x rotates, the two-dimensional function of Fourier series always presents an aliasing effect. In order to solve this problem, the present invention modifies the above two equations to obtain the rotational equivariant convolution operator of the present invention, which is represented by equations (1) and (2);

[0068]

[0069] in and are all two-dimensional basis functions, x i and x jare the two-dimensional spatial coordinates, Ω(x) is the radial mask function, and Ω(x) ≥ 0, h is the image pixel size, and p is the back-projection tensor slice size; I p (m) is a periodic function of the Fourier series, and I p (m) is represented by formula (3);

[0070]

[0071] The present invention pre-builds a training database, and then uses the training database to train a parameterized residual network based on Fourier series expansion; the training database is provided with multiple pairs of paired data, and each pair of paired data is metal back-projection tensor data of the same object and the same slice and a CT image without metal artifacts.

[0072] The training database is set with multiple pairs of paired data, and each pair of paired data is the metal back-projection tensor data of the same object and the same slice and the CT image without metal artifacts.

[0073] The residual network parameterized by Fourier series expansion is trained through the following steps:

[0074] A1. Input the metal back-projection tensor data in the training database into the residual network parameterized based on Fourier series expansion to obtain a metal artifact corrected image;

[0075] A2, using a root mean square error function to compare the metal artifact corrected image obtained in A1 with the CT image without metal artifacts in the same pair of paired data, to obtain the error between the metal artifact corrected image and the CT image without metal artifacts;

[0076] A3: Determine the difference between the error obtained in A2 and the error threshold. When the error is greater than the error threshold, proceed to A4. When the error is less than the error threshold, proceed to A5. The error threshold is greater than 0. The error threshold in this embodiment is specifically 10. -4 ;

[0077] A4. Use the optimizer AdamW to optimize the parameters of the residual network parameterized based on Fourier series expansion, and then return to A1;

[0078] A5. After the training is completed, the current residual network parameterized based on Fourier series expansion is used as the residual network parameterized based on Fourier series expansion after training.

[0079] In A4, the L1 norm is used as the loss function Loss to optimize the parameters of the residual network parameterized by Fourier series expansion, which is expressed by formula (9);

[0080]

[0081] Where N is the number of samples, Ipred is the metal artifact correction image, I ref These are CT images without metal artifacts in the same pair of paired data.

[0082] The training database is constructed through the following steps:

[0083] B1. Acquire multiple metal-containing clinical data images, and use thresholds to segment the metal-containing clinical data images to obtain multiple metal masks;

[0084] B2. Perform threshold segmentation on the CT images without metal artifacts in the Mayo public data set to obtain the water-based image and bone-based image corresponding to the CT images without metal artifacts;

[0085] B3. The simulation process of each pair of paired data is as follows: randomly select one metal mask from the multiple metal masks obtained in B1, and then simulate it with the water-based image and bone-based image corresponding to a CT image without metal artifacts to obtain three-dimensional metal back-projection tensor data; the CT image without metal artifacts and the metal back-projection tensor data constitute a pair of paired data.

[0086] It should be noted that since the present invention uses the Mayo public data set, the data is scanned at 120kVp and cannot achieve traditional base material decomposition. Therefore, threshold segmentation is used to obtain soft tissue and bone, which are used as water-based images and bone-based images, and simulated with the metal mask segmented from the metal-containing chest and abdomen data images. In order to make the artifact representation of the simulation data more similar to the clinical data, the simulation process of the present invention uses GE geometry, and the imaging geometry is fan beam.

[0087] The simulation in B3 is performed in the following steps:

[0088] C1. Multiply a randomly selected metal mask by the density corresponding to the selected metal artifact simulation material to obtain the metal base map ρ m , and then calculate the number of emitted photons I by formula (4) out ;

[0089]

[0090] Among them, I in (E) is the number of incident photons at energy E, E max is the maximum energy and E max =120, L is the X-ray projection path, μ(E) is the linear attenuation coefficient, and μ(E) is obtained by formula (5);

[0091] μ(E)=μ′ w (E)ρ w +μ′ b (E)ρ b +μ′m (E)ρ m ...Formula (5);

[0092] Among them, μ′ w (E) is the mass attenuation coefficient of water under energy E, μ′ b (E) is the mass attenuation coefficient of bone at energy E, μ′ m (E) is the mass attenuation coefficient of metal under energy E, ρ w is the water-based image corresponding to the CT image without metal artifacts, ρ b It is the bone-based image corresponding to the CT image without metal artifacts; the water-based image and bone-based image are derived from the base material decomposition of dual-energy data.

[0093] C2, the number of emitted photons I obtained for C1 out Add Poisson noise and scattering, expressed by equation (6);

[0094] I′ out ~Poisson(I out )+ξ……Formula (6);

[0095] Where Poisson is the Poisson noise function, ξ is the scattering, I′ out is the number of outgoing photons obtained by adding Poisson noise and scattering to the number of outgoing photons;

[0096] C3, I′ obtained from C2 out The projection P under multi-energy conditions is obtained by formula (7);

[0097]

[0098] Among them I in is the number of incident photons; I in From formula (8), we get:

[0099]

[0100] C4, filtering the projection P obtained in C3 through a ramp filter, and then performing angle-by-angle back-projection to obtain three-dimensional metal back-projection tensor data.

[0101] The CT metal artifact correction method based on back-projection tensor encoding filters the original chord diagram to eliminate the smear caused by back-projection. The back-projection tensor data of the present invention contains both texture structure information in the image domain and imaging geometry information in the projection domain. Compared with projection domain data and image domain data, the network can better restore tissue details and has stronger metal artifact correction performance. In the back-projection tensor slice, there is a clear boundary between metal and its artifacts and normal tissue, which is manifested as an overly bright or overly dark stripe structure, and has simpler morphological characteristics, making it easier for the network to reconstruct an artifact-free image. The present invention also combines the back-projection tensor with rotational equivariant convolution. Since the back-projection tensor can provide uncompressed lossless information compared with projection data or image data, the back-projection tensor affected by metal is used as the network input to reconstruct the artifact-free image back-projection tensor slice with prior information having a rotationally symmetric structure within and between slices. Therefore, the Fourier series expansion-based parameterized residual network of the present invention uses a rotationally equivariant convolution kernel instead of ordinary convolution to encode the back-projection tensor. This CT metal artifact correction method based on back-projection tensor coding is conducive to restoring image information to obtain high-quality CT images, while also reducing the number of network parameters and improving the generalization of the network.

[0102] Example 2

[0103] A CT metal artifact correction method based on back-projection tensor encoding, other features are the same as those in Example 1. In this example, the image size of the CT image without metal artifacts in the Mayo public data set is 512×512, the exposure angle of the tube scanning a circle is 984, the distance from the source to the scanned object is 538.52mm, the distance from the scanned object to the detector is 408.23mm, the number of detector units is 1776, and the size of the detector unit is 1.024mm. A total of 2156 sets of paired metal-containing projections P are simulated, and the projections P are filtered and back-projected angle by angle to obtain three-dimensional back-projection tensor data, 1781 sets are used for training, 155 sets are used for verification, and 220 sets are used for testing.

[0104] Moreover, the metal-containing clinical data image of this embodiment is a metal-containing chest and abdomen data image, and the metal artifact simulation material is titanium, which is the most commonly used in clinical metal implant surgery, and its density is 4.54g / cm 3 It should be noted that the metal-containing clinical data images of this embodiment are selected from metal-containing chest and abdomen data images, in which the CT metal artifact correction method corresponds to the original chord diagram of the chest and abdomen; when metal-containing clinical data images of other parts are used, the original chord diagram corresponding to the correction is also the original chord diagram of the part.

[0105] This embodiment uses Figure 3The original chord diagram of the metal artifact image of the chest before correction is subjected to the CT metal artifact correction method based on back-projection tensor coding, and the obtained Figure 4 Metal artifact corrected image. Figure 3 and Figure 4 In the figure, the light grey box is the magnified image of the ROI area, and the dark grey part represents the metal area. Figure 3 and Figure 4 By comparison, it can be seen that there are many light and dark stripe artifacts around the metal in the uncorrected image, and the surrounding tissue is blurred, while the corrected image removes most of the light and dark artifacts caused by the metal and is able to maintain the surrounding tissue structure, indicating the effectiveness of the present invention.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present invention.

Claims

1. A CT metal artifact correction method based on back-projection tensor coding, characterized in that: As the steps get: S1, filtering the original chord graph through a ramp filter to obtain a filtered chord graph; S2, back-projecting the filtered chord diagram obtained in S1 angle by angle, and stacking the back-projected data in the projection angle direction in the order of angles to obtain three-dimensional back-projected tensor data; S3. Use the back-projection tensor obtained in S2 as the input of the trained residual network parameterized based on Fourier series expansion to obtain a metal artifact corrected image.

2. The CT metal artifact correction method based on back-projection tensor coding according to claim 1, characterized in that: The residual network parameterized based on Fourier series expansion is to replace the convolution in the convolutional network with a rotational equivariant convolution operator, so as to obtain the residual network parameterized based on Fourier series expansion composed of a rotational equivariant convolution operator FConv and a residual block ResBlock.

3. The CT metal artifact correction method based on back-projection tensor coding according to claim 2, characterized in that: The rotational equivariant convolution operator is expressed by equation (1) and equation (2); in and are all two-dimensional basis functions, x i and x j are the two-dimensional spatial coordinates, Ω(x) is the radial mask function, and Ω(x) ≥ 0, h is the image pixel size, and p is the back-projection tensor slice size; I p (m) is a periodic function of the Fourier series, and I p (m) is represented by formula (3); 4. The CT metal artifact correction method based on back-projection tensor coding according to claim 3, characterized in that: Pre-building a training database, and then using the training database to train a residual network parameterized based on Fourier series expansion; The training database is provided with a plurality of pairs of paired data, and each pair of paired data is metal back-projection tensor data of the same slice of the same object and a CT image without metal artifacts.

5. The CT metal artifact correction method based on back-projection tensor coding according to claim 4, characterized in that: The Fourier series expansion-based parameterized residual network is trained by the following steps: A1. Inputting the metal back-projection tensor data in the training database into a residual network parameterized based on Fourier series expansion to obtain a metal artifact corrected image; A2, using a root mean square error function to compare the metal artifact corrected image obtained in A1 with the CT image without metal artifacts in the same pair of paired data, to obtain the error between the metal artifact corrected image and the CT image without metal artifacts; A3, judge the size of the error obtained in A2 and the error threshold. When the error is greater than the equal error threshold, enter A4; when the error is less than the error threshold, enter A5, and the error threshold is greater than 0; A4. Use the optimizer AdamW to optimize the parameters of the residual network parameterized based on Fourier series expansion, and then return to A1; A5. After the training is completed, the current residual network parameterized based on Fourier series expansion is used as the residual network parameterized based on Fourier series expansion after training.

6. The CT metal artifact correction method based on back-projection tensor coding according to claim 5, characterized in that: The training database is constructed by the following steps: B1. Acquire multiple metal-containing clinical data images, and segment the metal-containing clinical data images using a threshold value to obtain multiple metal masks; B2. Perform threshold segmentation on the CT images without metal artifacts in the Mayo public data set to obtain the water-based image and bone-based image corresponding to the CT images without metal artifacts; B3. The simulation process of each pair of paired data is as follows: randomly select one metal mask from the multiple metal masks obtained in B1, and then simulate it with the water-based image and bone-based image corresponding to a CT image without metal artifacts to obtain three-dimensional metal back-projection tensor data; the CT image without metal artifacts and the metal back-projection tensor data constitute a pair of paired data.

7. The CT metal artifact correction method based on back-projection tensor coding according to claim 6, characterized in that: The simulation in B3 is performed by the following steps: C1. Multiply a randomly selected metal mask by the density corresponding to the selected metal artifact simulation material to obtain the metal base map ρ m , and then calculate the number of emitted photons I by formula (4) out ; Among them, I in (E) is the number of incident photons at energy E, E max is the maximum energy and E max =120, L is the X-ray projection path, μ(E) is the linear attenuation coefficient, and μ(E) is obtained by formula (5); μ(E)=μ′ w (E)r w +μ′ b (E)r b +μ′ m (E)r m ……expression(5); Among them, μ′ w (E) is the mass attenuation coefficient of water under energy E, μ′ b (E) is the mass attenuation coefficient of bone at energy E, μ′ m (E) is the mass attenuation coefficient of metal under energy E, ρ w is the water-based image corresponding to the CT image without metal artifacts, ρ b It is the bone base image corresponding to the CT image without metal artifacts; C2, the number of emitted photons I obtained for C1 out Add Poisson noise and scattering, expressed by equation (6); I′ out ~Poisson(I out ) + ζ …… Equation (6); Where Poisson is the Poisson noise function, ξ is the scattering, I′ out is the number of outgoing photons obtained by adding Poisson noise and scattering to the number of outgoing photons; C3, I′ obtained from C2 out The projection P under multi-energy conditions is obtained by formula (7); Among them I in is the number of incident photons; I in From formula (8), we get: C4, filtering the projection P obtained in C3 through a ramp filter, and then performing angle-by-angle back-projection to obtain three-dimensional metal back-projection tensor data.

8. The CT metal artifact correction method based on back-projection tensor coding according to claim 7, characterized in that: In A4, the L1 norm is used as the loss function Loss to optimize the parameters of the residual network parameterized based on Fourier series expansion, which is expressed by formula (9); Where N is the number of samples, I pred is the metal artifact correction image, I ref These are CT images without metal artifacts in the same pair of paired data.

9. The CT metal artifact correction method based on back-projection tensor coding according to claim 1, characterized in that: The back-projection tensor data contains texture structure information in the image domain and imaging geometry information in the projection domain.

10. The CT metal artifact correction method based on back-projection tensor coding according to claim 8, characterized in that: The metal artifact simulation material is titanium; The error threshold is 10 -4 .

Images