A sparse helical CT image reconstruction method based on a differentiable helical reconstruction operator

Abstract

A kind of sparse helical CT image reconstruction method based on differentiable helical reconstruction operator, first, the real helical scanning geometry parameter of image and corresponding full-angle helical projection data are acquired, and through 7 steps, the final reconstructed image is acquired.The present application uses the real scanning geometry to carry out forward projection to the reconstructed sparse angle image, provides geometric prior guidance for missing projection;At the same time, according to the similarity and redundancy characteristics of adjacent projection of helical scanning, a projection completion network is constructed, the bidirectional motion field of adjacent angle is learned, combined with geometric prior projection, to jointly synthesize intermediate missing projection data;And realize the recovery of image global strip artifact;Finally, the joint training of projection domain and image domain is realized, which is conducive to the overall recovery of projection-image dual-domain information, and the data collected in two pitch is used for recovery, which effectively avoids excessive calculation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of deep learning and computed tomography, and particularly relates to a sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator. BACKGROUND

[0002] As a high-contrast, non-invasive fast imaging technology, computer tomography (CT) has been widely used in medical image diagnosis, surgical positioning and navigation, radiotherapy planning, etc. However, studies have shown that when exposed to a large amount of X-ray radiation, it can cause systemic acute and chronic radiation damage, DNA and cell damage, etc., greatly increasing the risk of cancer in the future. However, reducing the X-ray radiation dose will inevitably lead to degradation of CT image quality, affecting the effectiveness of diagnosis and treatment. Therefore, to achieve low-dose CT high-quality imaging and ensure that the clinical diagnosis and treatment needs are met, is a frontier scientific problem in the field of high-end medical CT research. In order to alleviate the harm of medical CT to the human body, a variety of low-dose CT scanning protocols have been proposed. At present, low-milliampere scanning protocols combined with advanced reconstruction algorithms can achieve conventional low-dose clinical task scanning, but such methods are limited by hardware, and when the X-ray photon dose is further reduced, the measured projection data may experience a "photon starvation" effect, that is, the amount of X-ray photons generated by ultra-low milliampere is not enough to penetrate the object or the amount of X-ray photons is extremely low, resulting in that the detector cannot collect effective and sufficient X-ray signals, so that the reconstructed image structure is submerged in noise artifacts and difficult to recover.

[0003] In terms of ultra-low dose CT imaging, sparse angle scanning protocol is one of the most promising technologies. It reduces the radiation dose by reducing the projection exposure angle, and keeps the tube voltage and tube current of each projection exposure at a normal dose level. Compared with low-milliampere scanning protocols, this protocol has the following advantages: 1. It can effectively avoid the photon starvation effect and avoid modeling complex noise; 2. It can avoid the problem of model performance degradation caused by the domain difference between simulated low-dose data and real low-dose data; 3. It can effectively shorten the scanning time. However, the existing sparse angle scanning still cannot meet the current clinical diagnosis and treatment needs. When the scanning projection angle is reduced, the sampling rate does not meet the classical Shannon sampling theorem, making the image reconstruction degenerate into an ill-posed inverse problem, and using classical filtered back projection for reconstruction is easy to introduce artifacts in the image.

[0004] With the rapid development of deep learning, there are currently a large number of deep learning-based methods to effectively improve image quality. According to the different strategies and modeling objects, these methods can be divided into four categories: (1) sparse angle CT imaging based on projection interpolation, this kind of method relies on the correlation between the projection angles, learns the mapping between the sparse angle projection and the full angle projection, and then uses the filtered back projection algorithm to reconstruct the target image. However, due to the characteristics of the FBP reconstruction algorithm, one data point in the projection data corresponds to all pixel values in a whole ray path through the CT image, so the error caused by projection interpolation is easy to introduce new artifacts in the image domain which is difficult to handle, which is the main reason why this kind of method is difficult to break through; 2, sparse angle CT imaging based on image domain post-processing, this kind of method directly learns the mapping between sparse angle image and full angle image, although this kind of method can effectively remove most of the noise and artifacts in the image, but due to the convolution in the recovery process equivalent to the filtering process, it is inevitable to cause the loss of structural detail information in the image, and the improvement of image quality is limited; 3, sparse angle CT imaging based on projection-image cross-domain recovery, this kind of method learns the mapping between sparse angle projection data and full angle image data, effectively combines the projection domain and image domain data information, and can obtain better imaging performance than the projection domain or image domain alone.

[0005] Current research on sparse angles is mostly focused on fan beams under a circular scanning trajectory, and its sparse angle simulation process mainly includes two types: 1. Starting from the acquired image data, the image is fan-beam forward projected to obtain its simulated fan-beam projection data, and the projection data is uniformly sampled to obtain its corresponding sparse angle projection. This kind of method lacks analysis of real scanning geometry and spiral projection data, and is difficult to be directly applied to clinical practice; 2. Starting from real spiral projection data, the spiral projection data is rearranged into fan-beam projection, and the fan-beam projection is uniformly sampled to obtain its corresponding sparse angle projection. Although this kind of method starts from real projection data, its recovery performance will be greatly reduced in the case of large pitch. There is almost no detailed work on the sparse angle CT reconstruction algorithm and system directly from spiral projection data at present, so it cannot be directly applied to clinical diagnosis and treatment.

[0006] Therefore, in view of the deficiencies of the prior art, it is very necessary to provide a sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator to solve the deficiencies of the prior art. SUMMARY

[0007] The present application aims to avoid the deficiencies of the prior art and provides a sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction algorithm.

[0008] The above-mentioned object of the present application is achieved by the following technical measures:

[0009] The present application provides a sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction algorithm, comprising the following steps:

[0010] S1, obtaining the real spiral scanning geometry parameters of an object and the corresponding full-angle spiral projection data;

[0011] S2, uniformly and sparsely sampling the full-angle spiral projection data obtained in S1 to obtain simulated sparse-angle spiral projection data and simulated sparse scanning geometry parameters;

[0012] S3, reconstructing a full-angle spiral CT image by a weighted filtered back-projection algorithm according to the real spiral scanning geometry parameters and the full-angle spiral projection data in S1, and reconstructing a sparse-angle spiral CT image by the weighted filtered back-projection algorithm according to the simulated sparse-angle spiral projection data and the simulated sparse scanning geometry parameters obtained in S2;

[0013] S4, performing 3D forward projection on the sparse-angle spiral CT image obtained in S3 to obtain the corresponding geometric prior projection by using the real spiral scanning geometry parameters in S1;

[0014] S5, restoring the projection data of the missing angles in the geometric prior projection obtained in S4 by using the trained projection completion deep learning model to obtain initial completed projection data, and then replacing the corresponding positions in the simulated sparse-angle spiral projection data in S3 with the completed projection data to obtain final completed projection data;

[0015] S6, connecting the real spiral scanning geometry parameters in S1 and the final completed projection data obtained in S5 in the projection domain to the image domain by using the differentiable spiral reconstruction algorithm to obtain the initial recovered image data after projection completion;

[0016] S7, performing detail recovery and residual artifact recovery on the sparse-angle spiral CT image obtained in S3 and the initial recovered image data obtained in S6 by using the trained image domain deep learning model to obtain the final reconstructed image.

[0017] The sparse spiral CT image reconstruction method based on the differentiable spiral reconstruction operator of the application, the trained projection completion deep learning model and the trained image domain deep learning model are obtained by joint training, wherein each joint training is performed according to the following steps:

[0018] A1, obtaining the real spiral scanning geometric parameters of the object and the corresponding full-angle spiral projection data;

[0019] A2, uniformly and sparsely sampling the full-angle spiral projection data obtained in A1 to obtain simulated sparse-angle spiral projection data and simulated sparse scanning geometric parameters;

[0020] A3, reconstructing the full-angle spiral CT image by a weighted filtered back-projection algorithm according to the real spiral scanning geometric parameters and the full-angle spiral projection data in A1, and reconstructing the sparse-angle spiral CT image by a weighted filtered back-projection algorithm according to the simulated sparse-angle spiral projection data and the simulated sparse scanning geometric parameters obtained in A2;

[0021] A4, performing 3D forward projection on the sparse-angle spiral CT image obtained in A3 by the real spiral scanning geometric parameters in A1 to obtain the corresponding geometric prior projection;

[0022] A5, restoring the projection data of the missing angles in the geometric prior projection obtained in A4 by the projection completion deep learning model to obtain initial completed projection data, and then replacing the corresponding positions in the completed projection data with the simulated sparse-angle spiral projection data in A3 to obtain the final completed projection data;

[0023] A6, performing projection domain to image domain cross-domain connection on the real spiral scanning geometric parameters in A1 and the final completed projection data obtained in A5 by the differentiable spiral reconstruction operator to obtain the initial recovered image data after projection completion;

[0024] A7, performing detail recovery and residual artifact recovery on the sparse-angle spiral CT image obtained in A3 and the initial recovered image data obtained in A6 by the image domain deep learning model to obtain the final reconstructed image;

[0025] A8, calculating the loss by a loss function, wherein the loss is obtained by comparing the final completed projection data obtained in A5 with the full-angle spiral projection data in A1 wherein the loss is obtained by comparing the gradient of the final completed projection data obtained in A5 with the gradient of the full-angle spiral projection data in A1 wherein the loss is obtained by comparing the initial recovered image data obtained in A6 with the full-angle spiral CT image in A3 wherein the loss is obtained by comparing the final reconstructed image obtained in A7 with the full-angle spiral CT image in A3

[0026] A9、the update of the image domain deep learning model is to directly backpropagate the loss to the image domain deep learning model to update the parameters of the image domain deep learning model; the update of the projection completion deep learning model is to directly backpropagate the loss to the projection completion deep learning model, and simultaneously backpropagate the loss to the projection completion deep learning model, and simultaneously backpropagate the loss to the projection completion deep learning model, and simultaneously backpropagate the loss to the projection completion deep learning model through a 3D differentiable gradient backpropagation operator, and finally update the parameters of the projection completion deep learning model.

[0027] In S2 or A2, the uniform sparse sampling is specifically uniform sampling in the angle direction on the full-angle projection data, which is represented by formula (1):

[0028]

[0029] wherein P SV is the simulated sparse angle helical projection data, P FV is the full-angle helical projection data, is a uniform sampling process in the angle direction, and N is a sparse sampling interval.

[0030] The weighted filtered backprojection algorithm reconstruction process in S3 or A3 is represented by formula (2) and formula (3):

[0031]

[0032] wherein I FV is the full-angle helical CT image, I SV is the sparse angle helical CT image, a is the real helical scanning geometry parameter, a ′ is the simulated sparse scanning geometry parameter, is the full-angle reconstruction using the real helical scanning geometry parameter, is the sparse angle reconstruction using the simulated sparse scanning geometry parameter.

[0033] In S4 or A4, the geometric prior projection is to obtain the projection initial value of the missing angle in the sparse angle scanning by using the prior information of the real helical scanning geometry parameter and the sparse angle CT image, which is represented by formula (4):

[0034]

[0035] wherein P GPP is the geometric prior projection, is the 3D forward projection under the real helical scanning geometry parameter.

[0036] In S5 or A5, a projection completion deep learning model Φ is projected, the projection completion deep learning model synthesizes the intermediate missing projection by learning the motion field between adjacent angles, and the projection completion deep learning model is represented by formula (5):

[0037] P Φ = Φ (P SV , P GPP , θ) …… formula (5);

[0038] Wherein, P Φ is the final completed projection data, and θ is a learnable parameter of the projection completion deep learning model.

[0039] In S6, the differentiable spiral reconstruction operator is composed of a 3D spiral reconstruction operator, and in A6, the differentiable spiral reconstruction operator is composed of a 3D spiral reconstruction operator and a 3D forward projection operator.

[0040] Preferably, the above-mentioned 3D spiral reconstruction operator transforms the completed projection data from the projection domain to the image domain to obtain initial recovered image data, and the 3D spiral reconstruction operator is represented by formula (6):

[0041]

[0042] Wherein, I Φ is the initial recovered image data, is the 3D spiral reconstruction operator.

[0043] Preferably, the above-mentioned 3D forward projection operator transforms the initial recovered image data from the image domain to the projection domain, and is represented by formula (7):

[0044]

[0045] Wherein, is the 3D forward projection operator, P ′ Φ is the projection data obtained by 3D forward projection on the initial recovered image data, and I is the data needed to be back-propagated from the image to the projection.

[0046] In S7 or A7, the image domain deep learning model utilizes the sparse angle CT image and the image data after projection completion to perform detail recovery and residual artifact recovery, adopts a multi-scale algorithm to extract global information of the image, simultaneously utilizes a channel attention module to extract information between different layers, and obtains a final reconstructed image; the image domain deep learning model is represented by formula (8):

[0047]

[0048] Wherein, is the image domain deep learning model, and ω is a learnable parameter of the image domain deep learning model. For the final reconstructed image.

[0049] The loss function described in A8 is represented by equations (9)-(13):

[0050]

[0051]

[0052] in, Let β1 be the total loss function, and β1 be the loss function. The corresponding weights, β2 is the loss. The corresponding weights, β3 is the loss. The corresponding weights, β4 is the loss. The corresponding weight, N D M represents the total number of angles corresponding to the full-angle spiral projection data. D This represents the number of images corresponding to a full-angle spiral CT image. To reconstruct the operator.

[0053] In A9, gradient backpropagation involves backpropagating the gradients of the learnable parameters, and applying the projection domain Φ to the loss function. The relevant learnable parameters are defined as θ, and the projection domain is... With loss loss and loss The relevant learnable parameter is defined as ω;

[0054] In A9, the update of the image domain deep learning model is represented by equation (14):

[0055]

[0056] In A9, the update of the projection completion deep learning model is represented by equations (15) and (16):

[0057]

[0058] Among them, I loss The loss between the current image and the full-angle spiral CT image, and in Middle I loss for exist Middle I loss for

[0059] The actual helical scanning geometry parameters in S1 or A1 are the distance from the X-ray source to the detector and the center of rotation, the detector size, the detector element size, the number of exposure angles per revolution, the collimator width, the pitch, and the starting scan angle.

[0060] The sparse spiral CT image reconstruction method based on the differentiable spiral reconstruction operator of the application comprises the following steps: S1, obtaining the real spiral scanning geometric parameters of an object and corresponding full-angle spiral projection data; S2, uniformly and sparsely sampling the full-angle spiral projection data obtained in S1 to obtain simulated sparse angle spiral projection data and simulated sparse scanning geometric parameters; S3, reconstructing a full-angle spiral CT image by a weighted filtered back-projection algorithm according to the real spiral scanning geometric parameters and the full-angle spiral projection data in S1, and reconstructing a sparse angle spiral CT image by a weighted filtered back-projection algorithm according to the simulated sparse angle spiral projection data and the simulated sparse scanning geometric parameters obtained in S2; S4, performing 3D forward projection on the sparse angle spiral CT image obtained in S3 by using the real spiral scanning geometric parameters in S1 to obtain corresponding geometric prior projection;

[0061] S5, restoring the projection data of the missing angle in the geometric prior projection obtained in S4 by using the trained projection completion deep learning model to obtain initial completion projection data, and then replacing the corresponding positions in the completion projection data with the simulated sparse angle spiral projection data in S3 to obtain final completion projection data; S6, performing cross-domain connection from the projection domain to the image domain on the real spiral scanning geometric parameters in S1 and the final completion projection data obtained in S5 by using the differentiable spiral reconstruction operator to obtain the initial recovery image data after projection completion; S7, performing detail recovery and residual artifact recovery on the sparse angle spiral CT image obtained in S3 and the initial recovery image data obtained in S6 by using the trained image domain deep learning model to obtain the final reconstructed image. Compared with the prior art, the application has the following beneficial effects: 1. By constructing the geometric prior forward projection, the real scanning geometry is used to perform forward projection on the reconstructed sparse angle image to provide geometric prior guidance for the missing projection; 2. According to the similarity and redundancy characteristics of adjacent projections in spiral scanning, a projection completion network is constructed, the bidirectional motion field of adjacent angles is learned, and the intermediate missing projection data is synthesized together with the geometric prior projection; 3. An image domain fine-tuning module is constructed to realize the recovery of global strip artifacts in the image; 4. In view of the problems of the loss gradient during the dual-domain training, such as the inability to return and the large amount of calculation, on the one hand, the differentiable spiral reconstruction operator capable of gradient return is constructed to realize the joint training of the projection domain and the image domain, which is beneficial to the overall recovery combining the projection-image dual-domain information; on the other hand, only the data collected within two pitches is used for recovery during the training process, which effectively avoids the excessive calculation amount. BRIEF DESCRIPTION OF DRAWINGS

[0062] The application is further described with reference to the accompanying drawings, but the content in the drawings does not constitute any limitation on the application.

[0063] Figure 1A flow chart of a sparse helical CT image reconstruction method based on a differentiable helical reconstruction operator.

[0064] Figure 2 A flow chart of joint training.

[0065] Figure 3 A comparison chart of results before and after the algorithm of the present application. DETAILED DESCRIPTION

[0066] The technical solutions of the present application are further illustrated in combination with the following examples.

[0067] Example 1

[0068] A sparse helical CT image reconstruction method based on a differentiable helical reconstruction operator, as shown in the figure, includes the following steps: Figure 1

[0069] S1, obtaining the real helical scanning geometry parameters of the image and the corresponding full-angle helical projection data;

[0070] S2, uniformly and sparsely sampling the full-angle helical projection data obtained in S1 to obtain simulated sparse-angle helical projection data and simulated sparse scanning geometry parameters;

[0071] S3, reconstructing a full-angle helical CT image by a weighted filtered back-projection algorithm according to the real helical scanning geometry parameters and the full-angle helical projection data in S1, and reconstructing a sparse-angle helical CT image by a weighted filtered back-projection algorithm according to the simulated sparse-angle helical projection data and the simulated sparse scanning geometry parameters obtained in S2;

[0072] S4, performing 3D forward projection on the sparse-angle helical CT image obtained in S3 by the real helical scanning geometry parameters in S1 to obtain the corresponding geometric prior projection;

[0073] S5, restoring the projection data of the missing angles in the geometric prior projection obtained in S4 by the trained projection completion deep learning model to obtain initial completion projection data, and then replacing the corresponding positions in the completion projection data with the simulated sparse-angle helical projection data in S3 to obtain the final completion projection data, so as to maintain the consistency before and after the measurement data recovery, wherein the projection completion deep learning model is constructed according to the similarity and redundancy characteristics between adjacent projections of helical scanning;

[0074] S6, performing cross-domain connection from the projection domain to the image domain on the real helical scanning geometry parameters in S1 and the final completion projection data obtained in S5 by the differentiable helical reconstruction operator to obtain the initial recovery image data after projection completion;

[0075] ​S7, performing detail recovery and residual artifact recovery on the sparse angle spiral CT image obtained in S3 and the initial recovered image data obtained in S6 through the trained image domain deep learning model, to obtain a final reconstructed image.

[0076] The trained projection completion deep learning model and the trained image domain deep learning model are obtained through joint training, wherein each joint training is performed according to the following steps, as shown in Figure 2

[0077] A1, obtaining real spiral scanning geometric parameters of an object and corresponding full-angle spiral projection data;

[0078] A2, performing uniform sparse sampling on the full-angle spiral projection data obtained in A1 to obtain simulated sparse angle spiral projection data and simulated sparse scanning geometric parameters;

[0079] A3, reconstructing a full-angle spiral CT image through a weighted filter back-projection algorithm according to the real spiral scanning geometric parameters and the full-angle spiral projection data in A1, and reconstructing a sparse angle spiral CT image through the weighted filter back-projection algorithm according to the simulated sparse angle spiral projection data and the simulated sparse scanning geometric parameters obtained in A2;

[0080] A4, performing 3D forward projection on the sparse angle spiral CT image obtained in A3 through the real spiral scanning geometric parameters in A1 to obtain corresponding geometric prior projection;

[0081] A5, recovering projection data of missing angles in the geometric prior projection obtained in A4 through a projection completion deep learning model to obtain initial completion projection data, and then replacing the simulated sparse angle spiral projection data in A3 with the corresponding positions in the completion projection data to obtain final completion projection data, so as to maintain consistency before and after the measurement data recovery, wherein the projection completion deep learning model is constructed according to the similarity and redundancy characteristics between adjacent projections of spiral scanning;

[0082] A6, performing cross-domain connection from the projection domain to the image domain on the real spiral scanning geometric parameters in A1 and the final completion projection data obtained in A5 through a differentiable spiral reconstruction operator to obtain initial recovered image data after projection completion;

[0083] A7, performing detail recovery and residual artifact recovery on the sparse angle spiral CT image obtained in A3 and the initial recovered image data obtained in A6 through an image domain deep learning model to obtain a final reconstructed image;

[0084] A8, calculating a loss through a loss function, wherein the loss is obtained by comparing the final completion projection data obtained in A5 with the full-angle spiral projection data in A1 ​Wherein the gradient of the final complete projection data of A5 is compared with the gradient of the full-angle spiral projection data of A1 to obtain the loss Wherein the initial recovered image data of A6 is compared with the full-angle spiral CT image of A3 to obtain the loss Wherein the final reconstructed image of A7 is compared with the full-angle spiral CT image of A3 to obtain the loss

[0085] A9, the update of the image domain deep learning model is to update the parameters of the image domain deep learning model by the loss Direct gradient backpropagation to the image domain deep learning model updates the parameters of the image domain deep learning model; the update of the projection completion deep learning model is to update the parameters of the projection completion deep learning model by the loss And the loss Direct gradient backpropagation to the projection completion deep learning model, while the loss And the loss Through the 3D differentiable gradient backpropagation operator, the gradient is backpropagated to the projection completion deep learning model, and finally the parameters of the projection completion deep learning model are updated.

[0086] It should be noted that the training of the present application is completed when the projection completion deep learning model and the image domain deep learning model are trained for multiple times until convergence, and the condition of convergence can be that the number of training reaches a predetermined number, and the predetermined number is determined according to the data volume and the network size.

[0087] In S2 or A2, the uniform sparse sampling is specifically uniform sampling in the angle direction of the full-angle projection data, which is represented by formula (1):

[0088]

[0089] Wherein, P SV is the simulated sparse angle spiral projection data, P FV is the full-angle spiral projection data, is the uniform sampling process in the angle direction, and N is the sparse sampling interval.

[0090] The weighted filtered backprojection algorithm reconstruction process in S3 or A3 is represented by formula (2) and formula (3):

[0091]

[0092] Wherein, I FV is the full-angle spiral CT image, I SV is the sparse angle spiral CT image, alpha is the real spiral scanning geometry parameter, alpha ′ is the simulated sparse scanning geometry parameter, is the full-angle reconstruction using the real spiral scanning geometry parameter, For sparse angle reconstruction using simulated sparse scanning geometry parameters.

[0093] It should be noted that, since the sampling rate of sparse angle projection data does not meet the Shannon sampling theorem, directly using the traditional filtered back projection algorithm for reconstruction, a large number of stripe artifacts and noise will appear in the image, affecting clinical diagnosis, therefore the application carries out weighted filtered back projection algorithm reconstruction.

[0094] In S4 or A4, the geometric prior projection is to obtain the projection initial value of the missing angle in the sparse angle scanning by using the real spiral scanning geometry parameters and the prior information of the sparse angle CT image, which is represented by formula (4):

[0095]

[0096] Wherein, P GPP is the geometric prior projection, is the 3D forward projection under the real spiral scanning geometry parameters.

[0097] It should be noted that the geometric prior projection is beneficial to guide the recovery of the missing angle

[0098] In S5 or A5, the projection completion deep learning model Φ is used, the projection completion deep learning model is used to synthesize the intermediate missing projection by learning the motion field between adjacent angles, and the projection completion deep learning model is represented by formula (5):

[0099] P Φ = Φ (P SV , P GPP , θ) …… formula (5);

[0100] Wherein, P Φ is the final completed projection data, and θ is the learnable parameter of the projection completion deep learning model. The final completed projection data still retains the original measured data at the real sparse scanning angle position, and the data consistency before and after the projection recovery can be maintained.

[0101] In S6, the differentiable spiral reconstruction operator is composed of a 3D spiral reconstruction operator, and in A6, the differentiable spiral reconstruction operator is composed of a 3D spiral reconstruction operator and a 3D forward projection operator.

[0102] The 3D spiral reconstruction operator transforms the completed projection data from the projection domain to the image domain to obtain the initial recovered image data, and the 3D spiral reconstruction operator is represented by formula (6):

[0103]

[0104] Wherein, I Φ is the initial recovered image data, is the 3D spiral reconstruction operator,

[0105] The 3D forward projection operator transforms the initial reconstructed image data from the image domain to the projection domain, which is represented by equation (7);

[0106]

[0107] wherein, is a 3D forward projection operator, P ′ Φ is the projection data obtained by 3D forward projection on the initial reconstructed image data, I Φ is the data that needs to be back-projected from the image domain to the projection domain.

[0108] It should be noted that the projection data P ′ Φ Since there is data truncation in the z-axis of the image, compared with P Φ There is data truncation in the detector channel direction, but this part of the data truncation has no effect on the image to be reconstructed.

[0109] In S7 or A7, the image domain deep learning model uses the sparse angle CT image and the image data after projection completion to perform detail recovery and residual artifact recovery, adopts a multi-scale algorithm to extract global information of the image, simultaneously uses a channel attention module to extract information between different layers, and obtains a final reconstructed image; the image domain deep learning model is represented by equation (8) as:

[0110]

[0111] wherein, is an image domain deep learning model, ω is a learnable parameter of the image domain deep learning model, is a final reconstructed image.

[0112] In A8, the loss function is represented by equations (9)-(13):

[0113]

[0114] wherein, is a total loss function, β1 is a corresponding weight of the loss , β2 is a corresponding weight of the loss , β3 is a corresponding weight of the loss , β4 is a corresponding weight of the loss , N D is a total number of angles corresponding to the full-angle helical projection data, M D is a number of images corresponding to the full-angle helical CT image, is a reconstruction operator.

[0115] It should be noted that in A9, gradient backpropagation refers to backpropagating the gradients of the learnable parameters, and the loss is calculated by projecting the domain Φ and the learnable parameters θ. Related, the projection domain Learnable parameters ω and loss loss and loss Related. Since θ and ω are learnable parameters, it is necessary to calculate... and

[0116] In A9, the update of the image domain deep learning model is represented by equation (14):

[0117]

[0118] In A9, the update of the projection completion deep learning model is represented by equations (15) and (16):

[0119]

[0120] Among them, I loss The loss between the current image and the full-angle spiral CT image, and in Middle I loss for exist Middle I loss for

[0121] The actual helical scanning geometric parameters in S1 or A1 are the distance from the X-ray source to the detector and the center of rotation, the detector size, the detector unit size, the number of exposure angles in one revolution, the collimator width, the pitch, and the starting scanning angle; wherein the helical projection data of the present invention, such as full-angle helical projection data, sparse-angle helical projection data, etc., refers to the projection data after logarithmic transformation.

[0122] Both the projection completion deep learning model and the image domain deep learning model are U-net models.

[0123] This sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator achieves joint training from real spiral projection data to 3D images by constructing a differentiable spiral reconstruction operator. It fully utilizes the information from both domains of the projection image for diagnostic-level image reconstruction. Simultaneously, it leverages the redundant information between adjacent spiral projection data to recover missing angles, fully utilizing the information in the projection data and significantly improving projection recovery performance. Furthermore, this invention can be directly applied to clinical scanning. During clinical spiral scanning, by inputting the scanning parameters and sparse spiral projection data for each case into this invention, the final CT image can be obtained. This invention is directly applicable to clinical CT scanning and is suitable for different scanning conditions and scanning models.

[0124] The sparse spiral CT image reconstruction method based on the differentiable spiral reconstruction operator has the following advantages: 1. By constructing a geometric prior preprojection, the reconstructed sparse angle image is preprojected using the real scan geometry, providing geometric prior guidance for missing projections; 2. Based on the similarity and redundancy characteristics of adjacent projections in spiral scanning, a projection completion network is constructed. By learning the bidirectional motion field of adjacent angles and combining it with the geometric prior projection, intermediate missing projection data is synthesized together; 3. An image domain fine-tuning module is constructed to realize the recovery of global strip artifacts in the image; 4. To address the problems of loss gradient not being able to be backpropagated and large computational load during dual-domain training, on the one hand, a differentiable spiral reconstruction operator with gradient backpropagation is constructed to realize joint training of the projection domain and the image domain, which is beneficial for overall recovery by combining projection-image dual-domain information; on the other hand, during the training process, only data collected within two pitches is used for recovery, effectively avoiding excessive computational load.

[0125] Example 2

[0126] A sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator is provided. Other features are the same as in Example 1. In this example, the actual spiral scanning geometric parameters in S1 and A1 are: the distances from the X-ray source to the rotation center and the detector are 1085.6 mm and 595 mm, respectively; the exposure angle for one revolution is 1152°; the detector size is 736×64; and the detector element size is 1.2858×1.0947.

[0127] In S2 and A2, uniform sparse sampling is performed using a sparse factor of 1 / 6 (192 angles, N=6). In S4 and A4, to balance memory usage and network performance, two-ring projection data is used for restoration, i.e., sparse projection data 384*736*64 is completed into full-angle projection data 2304*736*64. During model training, a strategy of interpolating the missing frame by projecting between two adjacent frames is adopted. Due to the large amount of data, the data is adjusted to 384*1*736*64 during training, and the data of different adjacent frames are restored in parallel to reduce the amount of computation and achieve spiral projection completion, laying the foundation for subsequent reconstruction.

[0128] In S6 and A6, the final size of the completed projection data is 32*512*512. In S7 and A7, in order to reduce the number of parameters of the image domain deep learning model during image domain training, this embodiment selects a 2.5D training strategy, that is, placing the data of different slices in the channel direction.

[0129] exist Figure 3The first column is full angle spiral CT abdominal cross-sectional and coronal sectional images in S3, the second column is sparse angle (N=6) spiral CT abdominal cross-sectional and coronal sectional images in S3, and the third column is the reconstructed abdominal cross-sectional and coronal sectional images in the present application under sparse angle (N=6). By Figure 3 It can be seen that there are more noises and artifacts in the cross-sectional and coronal sectional images of the sparse angle spiral CT images, resulting in image distortion. These artifacts overlap and cover the real tissue structure, affecting the doctor's diagnosis. After the application of the method of the present application, the images in the above-mentioned images have changed significantly. The corrected images can effectively remove a large amount of noise and strip artifacts in the sparse angle spiral CT images, making the tissue details clear and visible. Figure 3

[0130] It should be finally pointed out that the above examples are only used to illustrate the technical solutions of the present application and not to limit the protection scope of the present application. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced equivalently without departing from the essence and scope of the technical solutions of the present application.​

Claims

1. A sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator, characterized in that, Includes the following steps: S1. Obtain the actual spiral scanning geometric parameters and the full-angle spiral projection data corresponding to the object; S2. Perform uniform sparse sampling on the full-angle spiral projection data obtained in S1 to obtain simulated sparse angle spiral projection data and simulated sparse scanning geometric parameters. S3. Reconstruct the full-angle spiral CT image by weighted filtering back projection algorithm based on the real spiral scanning geometric parameters and full-angle spiral projection data obtained in S1; and reconstruct the sparse-angle spiral CT image by weighted filtering back projection algorithm based on the simulated sparse-angle spiral projection data and simulated sparse scanning geometric parameters obtained in S2. S4. Using the actual spiral scanning geometric parameters of S1, perform 3D front projection on the sparse angle spiral CT image obtained in S3 to obtain the corresponding geometric prior projection. S5. The projection data of the missing angles in the geometric prior projection obtained in S4 is recovered by the trained projection completion deep learning model to obtain the initial completed projection data. Then, the simulated sparse angle spiral projection data in S2 is replaced to the corresponding positions in the completed projection data to obtain the final completed projection data. S6. Using the differentiable spiral reconstruction operator, the real spiral scanning geometric parameters in S1 and the final completed projection data obtained in S5 are connected across the projection domain to the image domain to obtain the initial restored image data after projection completion. S7. The trained image domain deep learning model is used to perform detail restoration and residual artifact restoration on the sparse angle spiral CT image obtained in S3 and the initial restored image data obtained in S6 to obtain the final reconstructed image. The trained projection completion deep learning model and the trained image domain deep learning model are obtained through joint training, with each joint training session performed according to the following steps: A1. Obtain the actual spiral scanning geometric parameters and the full-angle spiral projection data corresponding to the object; A2. Perform uniform sparse sampling on the full-angle spiral projection data obtained in A1 to obtain simulated sparse angle spiral projection data and simulated sparse scanning geometric parameters. A3. Reconstruct the full-angle spiral CT image by weighted filtering back projection algorithm based on the real spiral scanning geometric parameters and full-angle spiral projection data obtained in A1; and reconstruct the sparse-angle spiral CT image by weighted filtering back projection algorithm based on the simulated sparse-angle spiral projection data and simulated sparse scanning geometric parameters obtained in A2. A4. Using the actual spiral scanning geometric parameters of A1, perform 3D front projection on the sparse angle spiral CT image obtained in A3 to obtain the corresponding geometric prior projection. A5. The projection data of the missing angles in the geometric prior projection obtained in A4 is recovered by the projection completion deep learning model to obtain the initial completed projection data. Then, the simulated sparse angle spiral projection data of A2 is replaced in the corresponding position in the completed projection data to obtain the final completed projection data. A6. By using the differentiable spiral reconstruction operator, the real spiral scanning geometric parameters in A1 and the final completed projection data obtained in A5 are connected across the projection domain to the image domain to obtain the initial restored image data after projection completion. A7. Using an image domain deep learning model, detail restoration and residual artifact restoration are performed on the sparse angle spiral CT image obtained in A3 and the initial restored image data obtained in A6 to obtain the final reconstructed image. A8. Calculate the loss using the loss function, where the final completed projection data obtained from A5 is compared with the full-angle spiral projection data from A1 to obtain the loss. The gradient of the final completed projection data obtained from A5 is compared with the gradient of the full-angle spiral projection data from A1 to obtain the loss. The initial restored image data from A6 was compared with the full-angle spiral CT image from A3 to obtain the loss. The final reconstructed image from A7 was compared with the full-angle spiral CT image from A3 to obtain the loss. A9. The update of an image domain deep learning model involves applying the loss... Gradient backpropagation is performed directly to the image domain deep learning model to update its parameters; the update of the projection-complete deep learning model involves applying the loss function. and loss The gradient is directly backpropagated to the projection-complete deep learning model, while the loss is... and loss The gradient is backpropagated to the projection-complete deep learning model through the 3D differentiable gradient backpropagation operator, and finally the parameters of the projection-complete deep learning model are updated. The actual helical scanning geometry parameters are: distance from the X-ray source to the detector and the center of rotation, detector size, detector unit size, number of exposure angles per revolution, collimator width, pitch, and starting scan angle. The reconstruction process of the S3 weighted filtering back projection algorithm is represented by equations (2) and (3): Among them, I FV For full-angle spiral CT images, I SV These are sparse angle spiral CT images, where α is the true spiral scan geometry parameter. ′ To simulate sparse scan geometry parameters, To achieve full-angle reconstruction using true helical scanning geometry parameters, To reconstruct sparse angles using simulated sparse scan geometry parameters, P SV To simulate sparse angle spiral projection data; In S4 or A4, the geometric prior projection is obtained by using the prior information of the real spiral scan geometric parameters and sparse angle CT images to obtain the initial projection value of the missing angle in the sparse angle scan, which is expressed by equation (4): Among them, P GPP For geometric prior projection, To perform 3D front projection under the actual helical scanning geometry parameters; In S6, the differentiable spiral reconstruction operator consists of a 3D spiral reconstruction operator, while in A6, the differentiable spiral reconstruction operator consists of a 3D spiral reconstruction operator and a 3D forward projection operator. The image domain deep learning model is represented by equation (8): in, Let ω be a deep learning model in the image domain, and let ω be a learnable parameter of the deep learning model in the image domain. For the final reconstructed image; In S5 or A5, the projection completion deep learning model Φ synthesizes the intermediate missing projection by learning the motion field between adjacent angles. The projection completion deep learning model is represented by equation (5): P Φ = Φ(P SV , P GPP , θ)…… Equation (5); Among them, P Φ For the final completed projection data, θ is the learnable parameter of the projection completion deep learning model; The 3D spiral reconstruction operator transforms the completed projection data from the projection domain to the image domain to obtain the initial restored image data. The 3D spiral reconstruction operator is represented by equation (6). Among them, I Φ To initially recover image data, For 3D spiral reconstruction operators, The 3D forward projection operator transforms the initial recovered image data from the image domain to the projection domain, as expressed by equation (7); in, For 3D front projection operator, P ′ Φ I represents the projection data obtained by 3D pre-projection of the initial restored image data, where I is the data that needs to be gradient-backpropagated from the image domain to the projection domain.

2. The sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator according to claim 1, characterized in that: In S2 or A2, uniform sparse sampling specifically involves uniformly sampling the full-angle projection data along the angular direction, as represented by equation (1): Among them, P FV This is full-angle spiral projection data. For a uniform sampling process in the angular direction, N is the sparse sampling interval.

3. The sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator according to claim 2, characterized in that: In S7 or A7, the image domain deep learning model uses sparse angle CT images and image data after projection completion to restore details and recover residual artifacts. It employs a multi-scale algorithm to extract global information of the image and uses a channel attention module to extract information between different layers to obtain the final reconstructed image.

4. The sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator according to claim 3, characterized in that: The loss function described in A8 is represented by equations (9)-(13): in, Let β1 be the total loss function, and β1 be the loss function. The corresponding weights, β2 is the loss. The corresponding weights, β3 is the loss. The corresponding weights, β4 is the loss. The corresponding weight, N D M represents the total number of angles corresponding to the full-angle spiral projection data. D This represents the number of images corresponding to a full-angle spiral CT image. To reconstruct the operator.

5. The sparse spiral CT image reconstruction method based on a differentiable spiral reconstruction operator according to claim 4, characterized in that: In A9, the update of the image domain deep learning model is represented by equation (14): In A9, the update of the projection completion deep learning model is represented by equations (15) and (16): Among them, I loss The loss between the current image and the full-angle spiral CT image, and in Middle I loss for exist Middle I loss for The actual helical scanning geometry parameters in S1 or A1 are the distance from the X-ray source to the detector and the center of rotation, the detector size, the detector element size, the number of exposure angles per revolution, the collimator width, the pitch, and the starting scan angle.

Images