Image reconstruction method and system based on limited angle and sparse angle projection of static CT

Abstract

The application discloses an image reconstruction method and system based on limited-angle and sparse-angle projection of static CT. The method first acquires projection data of the static CT, a discrete step number of a stochastic differential equation and a conditional diffusion interval, and then adopts non-conditional reverse diffusion and conditional reverse diffusion alternately to perform data reconstruction on the projection data of the static CT. In the conditional reverse diffusion process, initial neural network parameters are acquired through steps of noise reduction processing, affine set projection, preset neural network learning and implicit neural representation, and the parameters are updated through self-supervised learning, so that a high-quality reconstructed image is finally generated. The application not only significantly improves the quality of the reconstructed image, but also provides a new idea and method for the field of CT image reconstruction.

Description

Technical Field

[0001] This invention relates to an image reconstruction method based on finite-angle and sparse-angle projection of static CT, and also to a corresponding image reconstruction system and a static CT system using the image reconstruction method, belonging to the field of digital image processing technology. Background Technology

[0002] Static CT employs a multi-source ring array and a photon flow detector ring array distributed on different ring planes. Compared to traditional CT, its advantage lies in the fact that each X-ray source only needs to move a small angle to complete the entire scanning process, thus significantly reducing scanning time. This design is of great significance for imaging moving organs and improving temporal resolution.

[0003] However, to further shorten scanning time and improve the temporal resolution of imaging moving parts, it is necessary to address the reconstruction problems of finite and sparse angles. Currently, compressed sensing reconstruction methods constrained by prior images can suppress noise and reduce artifacts under finite and sparse angle conditions, but their main drawback is their heavy reliance on high-quality prior images. Therefore, developing an image reconstruction method that does not rely on high-quality prior images is of great significance for solving this problem. Summary of the Invention

[0004] The primary technical problem to be solved by this invention is to provide an image reconstruction method based on finite-angle and sparse-angle projection of static CT.

[0005] Another technical problem to be solved by the present invention is to provide an image reconstruction system based on static CT with finite angle and sparse angle projection.

[0006] Another technical problem to be solved by the present invention is to provide a static CT system employing the above-described image reconstruction method.

[0007] To achieve the above-mentioned technical objectives, the present invention adopts the following technical solution:

[0008] According to a first aspect of the present invention, an image reconstruction method based on finite-angle and sparse-angle projection of static CT is provided, comprising the following steps:

[0009] The projection data, stochastic differential equation discrete step number, and conditional diffusion interval of static CT are obtained; wherein the projection data is in the form of finite angle plus sparse angle.

[0010] The static CT projection data is reconstructed by alternating between unconditional backdiffusion and conditional backdiffusion; wherein, after every m unconditional backdiffusion data reconstructions, a conditional backdiffusion data reconstruction is performed, where m is a positive integer greater than 1.

[0011] The data reconstruction of the static CT projection data using unconditional back diffusion includes: using the volumetric data x at time t. t Using the scoring function and a preset noise distribution, obtain the volumetric data x at time t-1. t-1 And based on the block data x t-1 Perform data iteration;

[0012] Data reconstruction of the static CT projection data using conditional back diffusion includes:

[0013] For the volumetric data x at time t t Denoising is performed to obtain the denoised reconstructed volume data.

[0014] Based on the noise-reduced reconstructed block data Perform affine set projection so that the projected volumetric data can be transformed using the Radon transformation. Corresponding to the projection data of the static CT scan;

[0015] Based on projected volume data Learn a pre-defined neural network to obtain initial neural network parameters φ. * ; and the projected block data Perform implicit neural representation to obtain the results of implicit neural representation.

[0016] According to the initial neural network parameters φ * Self-supervised learning is performed based on the projection data of the static CT scan to improve the initial neural network parameters φ. * To update and obtain new network parameters φ ** ;

[0017] According to the new network parameter φ ** Volumetric data is generated through the preset neural network.

[0018] For the block data Add noise at time t-1 to form the reconstructed volumetric data x at time t-1. t-1 And based on the block data x t-1 Perform data iteration.

[0019] Preferably, the block data x at time t... t Denoising is performed to obtain the denoised reconstructed volume data. include:

[0020] Based on the size of the projection data of the static CT, an initial noise distribution of the same dimension is obtained; wherein the initial noise distribution follows a normal distribution;

[0021] Based on the initial noise distribution, the noise data at time t is used as the volume data x at time t. t , represented as x t ~N(0,σI);

[0022] Formula (1) is used to analyze the volumetric data x at time t. t Denoising is performed to obtain the denoised reconstructed volume data.

[0023]

[0024] in, Represents the noise figure, s θ* (x t ,t) represents the volumetric data x t The score function at time t, which is the pre-trained network. This represents the reconstructed volume data after noise reduction.

[0025] Preferably, the reconstructed volume data based on the denoised data Perform affine set projection so that the projected volumetric data can be transformed using the Radon transformation. The projection data corresponding to the static CT scan includes:

[0026] Let an affine set C = {x | Px = Y} be defined beforehand. For any x, the projection onto the affine subspace C is defined by the following equation:

[0027] P C (x)=x+A T (AA T ) -1 (Y-Ax) (2)

[0028] Based on the above formulas (1) and (2), The projection is defined by formula (3):

[0029]

[0030] The conjugate gradient (CG) method is used to compute the operator (PP). T The inverse of )

[0031]

[0032] Using formulas (3) and (4), we obtain x. 0t The projection is:

[0033]

[0034] Where Y represents the projection data of static CT; P represents the Radon transform; P T Let P be the transpose of P; x be the reconstructed block; and y be the independent variable to be optimized.

[0035] Preferably, the volumetric data based on the projection Learn a pre-defined neural network to obtain initial neural network parameters φ. * include:

[0036] Select neural network input tensor ∈0(i,j,k)=(i / M,j / N,k / K),i=0,1,...,M-1;j=0,1,...,N-1;k=0,1,...,K-1;where M, N, K represent the number of voxels along the xyz axis;

[0037] Based on a pre-defined neural network F (∈0; Φ), ​​bulk data is obtained. The initial neural network parameters φ are represented. * ;

[0038]

[0039] Where Φ represents the neural network parameters; ∈0 represents the initial noise that conforms to a normal distribution; R represents the regularization function; λ represents the weight coefficient of the regularization term; and arg represents the sign for finding the minimum value.

[0040] Preferably, the projected volumetric data Perform implicit neural representation to obtain the results of implicit neural representation. include:

[0041] Multiple discretization intervals are used to resample the volumetric data of the unit cube;

[0042] Set the encoded tensor ε0 to ε test ∈R rM×rN×rK Where r≥1 is a positive integer r∈N + N+ represents a positive integer;

[0043] Based on the pre-trained neural network, the predicted remodeled volume is obtained, thereby acquiring volumetric data. The results of implicit neural representation

[0044]

[0045] Preferably, the new network parameter φ **Obtain it through the following methods:

[0046] Using the preset implicit neural network F (∈0; Φ) as the initialization model, the neural network is trained using the following objective function to obtain new network parameters φ. ** ;

[0047]

[0048] Preferably, the block data Generate in the following way:

[0049] R λ (Φ) extended to the total variation norm is expressed as: in, Represents the gradient;

[0050] Based on the trained neural network, the volumetric data Represented as:

[0051]

[0052] Where μ > 0 is a hyperparameter used for balancing; R(Φ) represents the regularization term.

[0053] According to a second aspect of the present invention, an image reconstruction system utilizing the above-described image reconstruction method is provided, comprising:

[0054] The parameter acquisition unit is used to acquire the projection data, stochastic differential equation discrete step number, and conditional diffusion interval of static CT; wherein the projection data is in the form of finite angle plus sparse angle.

[0055] An unconditional back diffusion unit is connected to the parameter acquisition unit to reconstruct the projection data of the static CT using unconditional back diffusion.

[0056] A conditional back diffusion unit is connected to the unconditional back diffusion unit to perform data reconstruction on the projection data of the static CT using conditional back diffusion;

[0057] In this process, after every m unconditional backdiffusion data reconstructions, a conditional backdiffusion data reconstruction is performed, where m is a positive integer greater than 1.

[0058] According to a third aspect of the present invention, an image reconstruction system based on finite-angle and sparse-angle projection of static CT is provided, including a processor and a memory; wherein the memory is coupled to the processor and is used to store a computer program, which, when executed by the processor, enables the processor to implement the above-described image reconstruction method.

[0059] According to a fourth aspect of the present invention, a static CT system is provided, wherein the image reconstruction method described above is employed.

[0060] Compared with the prior art, the present invention has the following technical effects:

[0061] (1) By combining deep diffusion image priors, the inherent structural information of the image is captured through a neural network model, thereby providing stronger regularization capabilities in the image reconstruction process and helping to improve the quality of the reconstructed image.

[0062] (2) By introducing implicit neural representation of image information, compared with the traditional explicit voxel representation method, it can capture complex geometric structures and texture details more flexibly, and can output reconstructed images of arbitrary resolution.

[0063] (3) It combines self-supervised learning techniques and uses a pre-trained model to guide the image reconstruction process, thereby helping to achieve more accurate image reconstruction with limited projection data. Attached Figure Description

[0064] Figure 1 The overall flowchart of an image reconstruction method based on finite-angle and sparse-angle projection of static CT provided in the first embodiment of the present invention;

[0065] Figure 2 This is a flowchart illustrating the process of reconstructing projection data from static CT using unconditional back diffusion in the first embodiment of the present invention.

[0066] Figure 3 This is a flowchart illustrating the process of reconstructing projection data from static CT using conditional back diffusion in the first embodiment of the present invention.

[0067] Figure 4 A structural diagram of an image reconstruction system based on finite-angle and sparse-angle projection from static CT, provided in the second embodiment of the present invention;

[0068] Figure 5 This is a structural diagram of an image reconstruction system based on finite-angle and sparse-angle projection of static CT, provided in the third embodiment of the present invention. Detailed Implementation

[0069] The technical content of the present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0070] This invention provides an image reconstruction method based on finite-angle and sparse-angle projection from static CT, primarily applied to cone-beam computed tomography (CBCT) image reconstruction tasks. This method, by combining depth diffusion image priors, implicit neural representations, and self-supervised learning techniques, achieves high-quality image reconstruction under limited projection data conditions. This invention not only significantly improves the quality of reconstructed images but also brings new ideas and methods to the field of CT image reconstruction, as detailed below:

[0071] First Embodiment

[0072] like Figure 1 As shown, the first embodiment of the present invention provides an image reconstruction method based on finite-angle and sparse-angle projection of static CT. This method alternately reconstructs the projection data of static CT using two data reconstruction methods until the final data reconstruction process is completed. Specifically, the two data reconstruction methods are: unconditional backdiffusion and conditional backdiffusion.

[0073] like Figure 1 As shown, after obtaining the projection data of a static CT scan, data reconstruction is performed on the projection data of the static CT scan using alternating unconditional backdiffusion and conditional backdiffusion. In this embodiment, after every m times (for example, m=5, other values ​​can also be used in other embodiments) of unconditional backdiffusion data reconstruction, a conditional backdiffusion data reconstruction is performed, where m is a positive integer greater than 1.

[0074] The following sections will explain in detail how to reconstruct data using the two different data methods:

[0075] (a) Unconditional Backdiffusion

[0076] like Figure 2 As shown, data reconstruction of static CT projection data using unconditional back diffusion includes the following steps:

[0077] S1: Obtain the block data x at time t t The scoring function and the preset noise distribution.

[0078] Specifically, the volumetric data x at time t t The score is determined by a preset scoring function s θ* (x t ,t) is obtained. Wherein, the s θ* (x t ,t) represents the reconstructed volume x t The score function at time t, which is a pre-trained network.

[0079] Furthermore, based on the size of the projection data of static CT, a preset noise distribution is obtained under the same dimension; wherein, the preset noise distribution follows a normal distribution.

[0080] S2: Obtain the block data x at time t-1 t-1 .

[0081] Specifically, the noise at time t-1 is added to the volumetric data x. t On the scoring function, the volumetric data x at time t-1 t-1 .

[0082] S3: Repeat steps S1 to S2 above to iterate the data.

[0083] When the block data x at time t-1 is obtained t-1 Then, using the block data x t-1 Replace the block data x in the original step S1 t To add noise at time t-2 to the volumetric data x t-1 The scoring function is used as the block data at time t-2, and thus iterates continuously m times (specifically 5 times in this embodiment).

[0084] (ii) Conditional Backdiffusion

[0085] like Figure 3 As shown, in this embodiment, conditional backdiffusion is used to reconstruct the projection data of static CT, including the following steps:

[0086] S10: Volume data x at time t t Denoising is performed to obtain the denoised reconstructed volume data.

[0087] Specifically, this includes steps S11 to S13:

[0088] S11: Based on the size of the projection data from static CT, obtain the initial noise distribution of the same dimension; wherein the initial noise distribution follows a normal distribution;

[0089] S12: Based on the initial noise distribution, the noise data at time t is used as the volume data x at time t. t , represented as x t ~N(0,σI);

[0090] S13: Using formula (1) to process the block data x at time t t Denoising is performed to obtain the denoised reconstructed volume data.

[0091]

[0092] in, Represents the noise figure, s θ* (x t ,t) represents the volumetric data x t The score function at time t, which is the pre-trained network. This represents the reconstructed volume data after noise reduction.

[0093] S20: Based on the denoised reconstructed volume data Perform affine set projection so that the projected volumetric data can be transformed using the Radon transformation. Corresponding to the projection data of static CT.

[0094] Specifically, this includes steps S21 to S24:

[0095] S21: Predefine an affine set C = {x | Px = Y}. For any reconstructed volume x, the projection onto the affine subspace C is defined by the following equation:

[0096] P c (x)=x+A T (AA T ) -1 (Y-Ax) (2)

[0097] S22: Based on formulas (1) and (2), The projection is defined by formula (3):

[0098]

[0099] S23: Using the conjugate gradient (CG) method, calculate the operator (PP). T The inverse of )

[0100]

[0101] S24: Using formulas (3) and (4), we obtain x 0t The projection is:

[0102]

[0103] Where Y represents the projection data of static CT; P represents the Radon transform; P T Let P be the transpose of P; x be the reconstructed block; and y be the independent variable to be optimized.

[0104] S30: Based on projected volumetric data Learn a pre-defined neural network to obtain initial neural network parameters φ. * .

[0105] Specifically, this includes steps S31 to S32:

[0106] S31: Selecting the input tensor for the neural network ∈0(i,j,k)=(i / M,j / N,k / K),i=0,1,...,M-1;j=0,1,...,N-1;k=0,1,...,K-1;where M, N, K represent the number of voxels in the three directions of x, y, z of the reconstructed block in the three-dimensional reconstruction coordinate system.

[0107] S32: Based on a preset neural network F (∈0; Φ), ​​acquire volumetric data. The initial neural network parameters φ are represented. * ;

[0108]

[0109] Where Φ represents the neural network parameters; ∈0 represents the initial noise that conforms to a normal distribution; R represents the regularization function; λ represents the weight coefficient of the regularization term; and arg represents the sign for finding the minimum value.

[0110] S40: Projected volumetric data Perform implicit neural representation to obtain the results of implicit neural representation.

[0111] Specifically, this includes steps S41 to S43:

[0112] S41: Use multiple discretization intervals to resample the volume data of the unit cube;

[0113] S42: Set the encoded tensor ε0 to ε test ∈R rM×rN×rK Where r≥1 is a positive integer r∈N + N+ represents a positive integer;

[0114] S43: Based on the pre-trained neural network, obtain the predicted remodeled volume, thereby acquiring volumetric data. The results of implicit neural representation

[0115]

[0116] S50: Based on the results of implicit neural representation Self-supervised learning based on projection data from static CT scans to refine the initial neural network parameters φ * To update and obtain new network parameters φ ** .

[0117] Specifically, the pre-defined implicit neural network F (∈0; Φ) is used as the initialization model, and the neural network is trained using the following objective function to obtain new network parameters φ. ** ;

[0118]

[0119] S60: Based on the new network parameters φ ** Volumetric data is generated through a pre-set neural network.

[0120] Specifically, this includes steps S61 to S63:

[0121] S61: R λ (Φ) extended to the total variation norm is expressed as: in, Represents the gradient;

[0122] S62: Based on the trained neural network, the volumetric data Represented as:

[0123]

[0124] Where μ > 0 is a hyperparameter used for balancing; R(Φ) represents the regularization term.

[0125] S70: Volume data Add noise at time t-1 to form the reconstructed volumetric data x at time t-1. t-1 And based on the volume data x t-1 Perform data iteration.

[0126] It is understandable that step S70 is based on the same principle as steps S2 to S3 in unconditional reverse diffusion, with the main difference being: (1) step S1 directly obtains the volumetric data x at time t. t The score is obtained, while step S70 acquires block data. (2) The noise at time t-1 obtained in step S2 is obtained based on a preset noise distribution, while the noise at time t-1 obtained in step S70 is obtained based on the initial noise distribution formed in step S10.

[0127] It should be noted that the order of steps in the above embodiments can be adjusted according to actual needs, and other steps can be inserted or added, such as preprocessing the projection data of static CT. Moreover, other formulas can be used instead of the calculation formulas, as long as the technical purpose of each step is met.

[0128] Second Embodiment

[0129] like Figure 4 As shown, based on the first embodiment described above, the second embodiment of the present invention provides an image reconstruction system based on finite-angle and sparse-angle projection of static CT. This image reconstruction system includes a parameter acquisition unit 1, an unconditional back diffusion unit 2, and a conditional back diffusion unit 3.

[0130] Specifically, parameter acquisition unit 1 is used to acquire the projection data of static CT, the discrete step number of the stochastic differential equation, and the conditional diffusion interval; wherein, the projection data is in the form of finite angle plus sparse angle. Unconditional back diffusion unit 2 is connected to parameter acquisition unit 1 to reconstruct the projection data of static CT using unconditional back diffusion (corresponding to steps S1 to S3 above). Conditional back diffusion unit 3 is connected to unconditional back diffusion unit 2 to reconstruct the projection data of static CT using conditional back diffusion (corresponding to steps S10 to S70 above).

[0131] When reconstructing CT images, after every m unconditional backdiffusion data reconstructions (m = 5 in this embodiment, but not limited to the specific value of m), a conditional backdiffusion data reconstruction is performed, where m is a positive integer greater than 1.

[0132] Third Embodiment

[0133] like Figure 5 As shown, based on the aforementioned image reconstruction method using finite-angle and sparse-angle projections from static CT, this invention further provides an image reconstruction system based on finite-angle and sparse-angle projections from static CT. This image reconstruction system can be a static CT system, or it can be a security inspection system, a non-destructive testing system, etc. Figure 5 As shown, the image reconstruction system includes one or more processors and a memory. The memory is coupled to the processor and stores one or more programs. When the processor executes these programs, it enables the processor to implement the image reconstruction method based on finite-angle and sparse-angle projection from static CT, as described in the above embodiments.

[0134] The processor controls the overall operation of the image reconstruction system to complete all or part of the steps of the image reconstruction method based on finite-angle and sparse-angle projection of static CT. The processor can be a central processing unit (CPU), graphics processing unit (GPU), field-programmable gate array (FPGA), application-specific integrated circuit (ASIC), digital signal processing (DSP) chip, etc. The memory stores various types of data to support the operation of the image reconstruction system. This data may include, for example, instructions for any application or method operating on the image reconstruction system, as well as application-related data. The memory can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, etc.

[0135] In one exemplary embodiment, the image reconstruction system may be implemented by a computer chip or physical entity, or by a product with certain functions, to perform the image reconstruction method based on finite-angle and sparse-angle projection of static CT described above, and achieve the same technical effect as the method described above. Specifically, the computer may be, for example, a personal computer, a laptop computer, an in-vehicle human-machine interaction device, a cellular phone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or any combination of these devices.

[0136] In another exemplary embodiment, the present invention also provides a computer-readable storage medium including program instructions that, when executed by a processor, implement the steps of the image reconstruction method based on finite-angle and sparse-angle projection of static CT in any of the above embodiments. For example, the computer-readable storage medium may be the memory including the program instructions, which can be executed by the processor of the image reconstruction system to complete the image reconstruction method based on finite-angle and sparse-angle projection of static CT and achieve the same technical effects as the above method.

[0137] Fourth embodiment

[0138] Based on the above embodiments, the fourth embodiment of the present invention also provides a static CT system. This static CT system employs the above-described image reconstruction method based on finite-angle and sparse-angle projection of static CT to complete the CT image reconstruction task.

[0139] It should be noted that the above embodiments are merely illustrative examples. The technical solutions of each embodiment can be combined, and all are within the protection scope of this invention.

[0140] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0141] The image reconstruction method and system based on finite-angle and sparse-angle projection of static CT provided by this invention have been described in detail above. Any obvious modifications made by those skilled in the art without departing from the essence of this invention will constitute an infringement of the patent rights of this invention and will incur corresponding legal liability.

Claims

1. An image reconstruction method based on finite-angle and sparse-angle projection from static CT, characterized in that... Includes the following steps: The projection data, stochastic differential equation discrete step number, and conditional diffusion interval of static CT are obtained; wherein the projection data is in the form of finite angle plus sparse angle. The static CT projection data is reconstructed by alternating between unconditional backdiffusion and conditional backdiffusion; wherein, after every m unconditional backdiffusion data reconstructions, a conditional backdiffusion data reconstruction is performed, where m is a positive integer greater than 1. The data reconstruction of the static CT projection data using unconditional back diffusion includes: using the volumetric data at time t. Using the scoring function and a preset noise distribution, the volumetric data at time t-1 is obtained. And based on the block data Perform data iteration; Data reconstruction of the static CT projection data using conditional back diffusion includes: For volumetric data at time t Denoising is performed to obtain the denoised reconstructed volume data. ; Based on the noise-reduced reconstructed block data Perform affine set projection so that the projected volumetric data can be transformed using the Radon transformation. Corresponding to the projection data of the static CT scan; Based on projected volume data Learn a pre-defined neural network to obtain initial neural network parameters. ; and the projected block data Perform implicit neural representation to obtain the results of implicit neural representation. ; Based on the initial neural network parameters Self-supervised learning is performed based on the projection data of the static CT scan to refine the initial neural network parameters. Update the network parameters to obtain new network parameters. ; According to the new network parameters Volumetric data is generated through the preset neural network. ; For the block data Add noise at time t-1 to form the reconstructed block data at time t-1. And based on the block data Perform data iteration.

2. The image reconstruction method as described in claim 1, characterized in that... The block data at time t Denoising is performed to obtain the denoised reconstructed volume data. Specifically, it includes: Based on the size of the projection data of the static CT, an initial noise distribution of the same dimension is obtained; wherein the initial noise distribution follows a normal distribution; Based on the initial noise distribution, the noise data at time t is used as the volumetric data at time t. , represented as ; Formula (1) is used to analyze the volumetric data at time t. Denoising is performed to obtain the denoised reconstructed volume data. , （1） in, Represents the noise figure. For volume data The score function at time t, which is the pre-trained network. This represents the reconstructed volume data after noise reduction.

3. The image reconstruction method as described in claim 2, characterized in that... The reconstructed block data based on the noise reduction Perform affine set projection so that the projected volumetric data can be transformed using the Radon transformation. The projection data corresponding to the static CT scan includes: Predefine an affine set For any affine subspace The projection onto the surface is defined by the following formula: （2） Based on the above formulas (1) and (2), The projection is defined by formula (3): （3） The operator PP is calculated using the conjugate gradient CG method. T The reverse; (4) Using formulas (3) and (4), we obtain The projection is: Where Y represents the projection data of static CT; P represents the Radon transform; P T Let P be the transpose of P; x be the reconstructed block; and y be the independent variable to be optimized.

4. The image reconstruction method as described in claim 3, characterized in that... The volume data based on projection Learn a pre-defined neural network to obtain initial neural network parameters. Specifically, it includes: Select neural network input tensor , ;in, , , Indicates the number of voxels along the x, y, and z axes; Based on a pre-set neural network Obtain block data The initial neural network parameters are represented. ; in, Represents the parameters of the neural network; This represents the initial noise that conforms to a normal distribution; denoted by ; λ represents the weight coefficient of the regularization term; arg represents the sign for finding the minimum value.

5. The image reconstruction method as described in claim 4, characterized in that... The projected block data Perform implicit neural representation to obtain the results of implicit neural representation. Specifically, it includes: Multiple discretization intervals are used to resample the volumetric data of the unit cube; Encode tensor Set as where r≥1 is a positive integer. N+ represents a positive integer; Based on the pre-trained neural network, the predicted remodeled volume is obtained, thereby acquiring volumetric data. The results of implicit neural representation ; 。 6. The image reconstruction method as described in claim 5, characterized in that... The new network parameters Obtain it through the following methods: Networks with pre-defined implicit neural representations As an initialization model, the following objective function is used to train the neural network, thereby obtaining new network parameters. ; 。 7. The image reconstruction method as described in claim 6, characterized in that... The block data Generate in the following way: Will Extended to the total variation norm, it is expressed as: ;in, Represents the gradient; Based on the trained neural network, the volumetric data Represented as: ， ； in, These are hyperparameters used for balancing; This represents the regularization term.

8. An image reconstruction system based on finite-angle and sparse-angle projection of static CT, used to perform the image reconstruction method as described in any one of claims 1-7, characterized in that... include: The parameter acquisition unit is used to acquire the projection data, stochastic differential equation discrete step number, and conditional diffusion interval of static CT; wherein the projection data is in the form of finite angle plus sparse angle. An unconditional back diffusion unit is connected to the parameter acquisition unit to reconstruct the projection data of the static CT using unconditional back diffusion. A conditional back diffusion unit is connected to the unconditional back diffusion unit to perform data reconstruction on the projection data of the static CT using conditional back diffusion; In this process, after every m unconditional backdiffusion data reconstructions, a conditional backdiffusion data reconstruction is performed, where m is a positive integer greater than 1.

9. An image reconstruction system based on finite-angle and sparse-angle projection from static CT, characterized in that... It includes a processor and a memory; wherein the memory is coupled to the processor and is used to store a computer program, which, when executed by the processor, causes the processor to implement the image reconstruction method according to any one of claims 1 to 7.

10. A static CT system, characterized in that... The image reconstruction method described in any one of claims 1 to 7 is employed.

Images