Limited angle and sparse angle projection image reconstruction method and system based on static CT

Abstract

The invention discloses an image reconstruction method and system for limited angle and sparse angle projection based on static CT (Computed Tomography). The method comprises the following steps: firstly, acquiring projection data of static CT, a stochastic differential equation distance step number and a conditional diffusion interval, and then performing data reconstruction on the projection data of the static CT by adopting non-conditional reverse diffusion and conditional reverse diffusion alternation. In the conditional reverse diffusion process, initial neural network parameters are obtained through the steps of noise reduction processing, affine set projection, preset neural network learning, implicit neural representation and the like, the parameters are updated through self-supervised learning, and finally a high-quality reconstructed image is generated. According to the method, the quality of the reconstructed image is remarkably improved, and a new thought and method are provided for the field of CT image reconstruction.

Description

Technical Field

[0001] The present invention relates to an image reconstruction method based on limited angle and sparse angle projection of static CT, and also relates to a corresponding image reconstruction system and a static CT system using the image reconstruction method, belonging to the technical field of digital image processing. Background Art

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

[0003] However, in order to further shorten the scanning time and improve the temporal resolution of imaging of moving parts, it is necessary to solve the reconstruction problem of limited angles and sparse angles. At present, the compressed sensing reconstruction method constrained by prior images can suppress noise and reduce artifacts under limited angles and sparse angles, but its main drawback is that it heavily relies on high-quality prior images. Therefore, it is of great significance to develop an image reconstruction method that does not rely on high-quality prior images to solve this problem. Summary of the invention

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

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

[0007] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

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

[0009] Acquire static CT projection data, stochastic differential equation discrete steps and conditional diffusion interval; wherein the projection data is in the form of finite angle plus sparse angle data;

[0010] Unconditional reverse diffusion and conditional reverse diffusion are used alternately to reconstruct the projection data of the static CT; wherein, after each m times of unconditional reverse diffusion data reconstruction, conditional reverse diffusion data reconstruction is performed once, where m is a positive integer greater than 1;

[0011] The data reconstruction of the static CT projection data by using unconditional reverse diffusion includes: using the block data x at time t t The scoring function and the preset noise distribution are used to obtain the block data x at time t-1. t-1 , and based on the block data x t-1 Perform data iteration;

[0012] The data reconstruction of the static CT projection data by conditional reverse diffusion includes:

[0013] For the block data x at time t t Perform denoising to obtain denoised reconstructed volume data

[0014] Based on the reconstructed block data after denoising Perform affine set projection to make the projected block data corresponding to the projection data of the static CT;

[0015] Based on the projected block data Perform learning of the preset neural network to obtain the initial neural network parameters φ * ; and the projected block data Perform implicit neural representation to obtain implicit neural representation results

[0016] According to the initial neural network parameter φ * , self-supervised learning is performed based on the projection data of the static CT to adjust the initial neural network parameters φ * Update to obtain the new network parameter φ ** ;

[0017] According to the new network parameter φ ** , generate volume data through the preset neural network

[0018] For the block data Add the noise at time t-1 to form the reconstructed block data x at time t-1 t-1 , and based on the block data x t-1 Iterate over the data.

[0019] Preferably, the block data x at time t is t Perform noise reduction to obtain the reconstructed block data after noise reduction include:

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

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

[0022] Formula (1) is used to calculate the block data x at time t t Perform noise reduction to obtain the reconstructed block data after noise reduction

[0023]

[0024] in, represents the noise factor, s θ* (x t ,t) is the block data x t The score function at time t is the pre-trained network. Represents the reconstructed block data after denoising.

[0025] Preferably, the reconstructed block data after noise reduction is Perform affine set projection to make the projected block data The projection data corresponding to the static CT include:

[0026] An affine set C = {x|Px = Y} is defined in advance. For any x, the projection on the affine subspace C is defined by the following formula:

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

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

[0029]

[0030] The conjugate gradient (CG) method is used to calculate the operator (PP T )

[0031]

[0032] By using the formula (3) and formula (4), we can get x 0t The projection is:

[0033]

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

[0035] Preferably, the projected block data Perform learning of the preset neural network to obtain the initial neural network parameters φ * include:

[0036] Selecting neural network input tensors ∈ 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 xyz axis;

[0037] Based on the preset neural network F(∈ 0 ; Φ), ​​get the block data The initial neural network parameters φ are represented by * ;

[0038]

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

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

[0041] Using multiple discretization intervals, resample the block data of the unit cube;

[0042] The encoded tensor ε 0 Set 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 reconstruction volume is obtained, thereby obtaining the volume block data The implicit neural representation results

[0044]

[0045] Preferably, the new network parameter φ ** Obtained through:

[0046] The preset implicit neural network F(∈ 0 Φ) as the initialization model, the following objective function is used to train the neural network to obtain the new network parameter φ ** ;

[0047]

[0048] Preferably, the block data Generated by:

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

[0050] Based on the trained neural network, the block data It is expressed as:

[0051]

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

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

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

[0055] An unconditional reverse diffusion unit, connected to the parameter acquisition unit, to reconstruct the projection data of the static CT by using unconditional reverse diffusion;

[0056] A conditional back diffusion unit connected to the unconditional back diffusion unit to reconstruct the projection data of the static CT by using conditional back diffusion;

[0057] After each m-times of data reconstruction by unconditional reverse diffusion, a data reconstruction by conditional reverse diffusion is performed, where m is a positive integer greater than 1.

[0058] According to a third aspect of an embodiment of the present invention, there is provided an image reconstruction system based on limited angle and sparse angle projection of static CT, comprising a processor and a memory; wherein the memory is coupled to the processor and is used to store a computer program, and when the computer program is executed by the processor, the processor implements the above-mentioned image reconstruction method.

[0059] According to a fourth aspect of an embodiment of the present invention, a static CT system is provided, in which the above-mentioned image reconstruction method is adopted.

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

[0061] (1) Combined with the deep diffusion image prior, the neural network model is used to capture the intrinsic structural information of the image, thereby providing stronger regularization capabilities in the image reconstruction process and helping to improve the quality of the reconstructed image;

[0062] (2) The introduction of implicit neural representation of image information can more flexibly capture complex geometric structures and texture details compared to traditional explicit voxel representation methods, and can output reconstruction images of arbitrary resolution;

[0063] (3) It combines self-supervised learning technology to guide the image reconstruction process through a pre-trained model, thereby helping to achieve more accurate image reconstruction with limited projection data. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 An overall flow chart of an image reconstruction method based on limited angle and sparse angle projection of static CT provided in the first embodiment of the present invention;

[0065] Figure 2 This is a flow chart of reconstructing static CT projection data using unconditional reverse diffusion in the first embodiment of the present invention;

[0066] Figure 3 This is a flow chart of reconstructing static CT projection data using conditional reverse diffusion in the first embodiment of the present invention;

[0067] Figure 4 A structural diagram of an image reconstruction system based on limited angle and sparse angle projection of 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 limited angle and sparse angle projection of static CT provided in the third embodiment of the present invention. DETAILED DESCRIPTION

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

[0070] The embodiment of the present invention provides an image reconstruction method based on limited angle and sparse angle projection of static CT, which is mainly used in cone beam computed tomography (CBCT) image reconstruction tasks. The method can achieve high-quality image reconstruction under limited projection data conditions by combining deep diffusion image priors, implicit neural representations and self-supervised learning technology. The present invention not only significantly improves the quality of reconstructed images, but also brings new ideas and methods to the field of CT image reconstruction, which are specifically described as follows:

[0071] First embodiment

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

[0073] like Figure 1 As shown, after the projection data of the static CT is acquired, the projection data of the static CT is reconstructed by alternately using unconditional reverse diffusion and conditional reverse diffusion. In this embodiment, after each m times (for example, m=5, other values ​​may also be used in other embodiments) of data reconstruction by unconditional reverse diffusion, a data reconstruction by conditional reverse diffusion is performed, where m is a positive integer greater than 1.

[0074] The following is a detailed description of how to reconstruct data in two data modes:

[0075] 1. Unconditional reverse diffusion

[0076] like Figure 2 As shown, the projection data of static CT is reconstructed using unconditional reverse diffusion, including the following steps:

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

[0078] Specifically, the block data x at time t t The score is calculated by the preset score function s θ* (x t ,t) to obtain. Among them, the s θ* (x t ,t) is the reconstructed block x t The score function at time t is a pre-trained network.

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

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

[0081] Specifically, the noise at time t-1 is added to the block data x t The score function is used as the block data x at time t-1. t-1 .

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

[0083] When the block data x at time t-1 is obtained t-1 After that, the block data x t-1 Replace the block data x in the original step S1 t , to add the noise at time t-2 to the block data x t-1 The score function is used as the volume block data at time t-2, thereby continuously iterating m times (specifically 5 times in this embodiment).

[0084] (II) Conditional reverse diffusion method

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

[0086] S10: for the block data x at time t t Perform noise reduction to obtain the reconstructed block data after noise reduction

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

[0088] S11: based on the size of the static CT projection data, obtaining an initial noise distribution of the same dimension; wherein the initial noise distribution obeys a normal distribution;

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

[0090] S13: Use formula (1) to calculate the block data x at time t t Perform noise reduction to obtain the reconstructed block data after noise reduction

[0091]

[0092] in, represents the noise factor, s θ* (x t ,t) is the block data x t The score function at time t is the pre-trained network. Represents the reconstructed block data after denoising.

[0093] S20: Reconstructed block data based on denoising Perform affine set projection to make the projected block data Corresponds to the projection data of static CT.

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

[0095] S21: predefine an affine set C = {x|Px = Y}. For any reconstructed block x, the projection on the affine subspace C is defined by the following formula:

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

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

[0098]

[0099] S23: Using the conjugate gradient (CG) method, the operator (PP T )

[0100]

[0101] S24: Through formula (3) and formula (4), we can get x 0t The projection is:

[0102]

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

[0104] S30: Based on the projected block data Perform learning of the preset neural network to obtain the initial neural network parameters φ * .

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

[0106] S31: 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;wherein, M, N, K represent the number of voxels in the three directions of x, y and z axes of the reconstructed block in the three-dimensional reconstruction coordinate system.

[0107] S32: Based on the preset neural network F(∈ 0 ; Φ), ​​get the block data The initial neural network parameters φ are represented by * ;

[0108]

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

[0110] S40: Projected block data Perform implicit neural representation to obtain implicit neural representation results

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

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

[0113] S42: Encode the tensor ε 0 Set 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, the predicted reconstruction model is obtained, thereby obtaining the data for the volume block. The implicit neural representation results

[0115]

[0116] S50: Based on the results of implicit neural representation Self-supervised learning based on static CT projection data is used to adjust the initial neural network parameters φ * Update to obtain the new network parameter φ ** .

[0117] Specifically, the preset implicit neural representation network F(∈ 0 Φ) as the initialization model, the following objective function is used to train the neural network to obtain the new network parameter φ ** ;

[0118]

[0119] S60: According to the new network parameter φ ** , generate volume data through preset neural network

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

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

[0122] S62: Based on the trained neural network, the volume data It is expressed as:

[0123]

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

[0125] S70: Block data Add the noise at time t-1 to form the reconstructed block data x at time t-1 t-1 , and based on the block data x t-1 Iterate over the data.

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

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

[0128] Second embodiment

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

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

[0131] When reconstructing a CT image, after every m (in this embodiment, m=5, but not limited to the specific value of m) unconditional reverse diffusion data reconstructions, a conditional reverse diffusion 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 above-mentioned image reconstruction method based on limited angle and sparse angle projection of static CT, the present invention further provides an image reconstruction system based on limited angle and sparse angle projection of static CT. The image reconstruction system can be a static CT system, or 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 is used to store one or more programs. When the one or more programs are executed by the processor, the processor implements the image reconstruction method based on limited angle and sparse angle projection of static CT in the above embodiment.

[0134] The processor is used to control the overall operation of the image reconstruction system to complete all or part of the steps of the above-mentioned image reconstruction method based on limited angle and sparse angle projection of static CT. The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), a digital signal processing (DSP) chip, etc. The memory is used to store various types of data to support the operation of the image reconstruction system, and these data can include, for example, instructions for any application or method used to operate on the image reconstruction system, and 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 memory, flash memory, etc.

[0135] In an exemplary embodiment, the image reconstruction system can be implemented by a computer chip or entity, or by a product with a certain function, for executing the above-mentioned image reconstruction method based on static CT limited angle and sparse angle projection, and achieving the same technical effect as the above-mentioned method. Specifically, the computer can be, for example, a personal computer, a laptop computer, a vehicle-mounted human-computer interaction device, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0136] In another exemplary embodiment, the present invention further provides a computer-readable storage medium including program instructions, which, when executed by a processor, implements the steps of the image reconstruction method based on limited angle and sparse angle projection of static CT in any of the above embodiments. For example, the computer-readable storage medium may be the above-mentioned memory including program instructions, and the above-mentioned program instructions may be executed by a processor of an image reconstruction system to complete the above-mentioned image reconstruction method based on limited angle and sparse angle projection of static CT, and achieve the technical effect consistent with the above-mentioned method.

[0137] Fourth embodiment

[0138] Based on the above embodiments, the fourth embodiment of the present invention further provides a static CT system, which adopts the above image reconstruction method based on limited angle and sparse angle projection of static CT to complete the task of CT image reconstruction.

[0139] It should be noted that the above embodiments are only examples, and the technical solutions of the various embodiments can be combined, all within the protection scope of the present invention.

[0140] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0141] The above is a detailed description of the image reconstruction method and system based on limited angle and sparse angle projection of static CT provided by the present invention. For those skilled in the art, any obvious changes made to it without departing from the essence of the present invention will constitute an infringement of the patent right of the present invention and will bear the corresponding legal liability.

Claims

1. An image reconstruction method based on limited angle and sparse angle projection of static CT, characterized in that The steps include: Acquire static CT projection data, stochastic differential equation discrete steps and conditional diffusion interval; wherein the projection data is in the form of finite angle plus sparse angle data; Unconditional reverse diffusion and conditional reverse diffusion are used alternately to reconstruct the projection data of the static CT; wherein, after each m times of unconditional reverse diffusion data reconstruction, conditional reverse diffusion data reconstruction is performed once, where m is a positive integer greater than 1; The data reconstruction of the static CT projection data by using unconditional reverse diffusion includes: using the block data x at time t t The scoring function and the preset noise distribution are used to obtain the block data x at time t-1. t-1 , and based on the block data x t-1 Perform data iteration; The data reconstruction of the static CT projection data by conditional reverse diffusion includes: For the block data x at time t t Perform noise reduction to obtain the reconstructed block data after noise reduction Based on the reconstructed block data after denoising Perform affine set projection to make the projected block data corresponding to the projection data of the static CT; Based on the projected block data Perform learning of the preset neural network to obtain the initial neural network parameters φ * ; and the projected block data Perform implicit neural representation to obtain implicit neural representation results According to the initial neural network parameter φ * , self-supervised learning is performed based on the projection data of the static CT to adjust the initial neural network parameters φ * Update to obtain the new network parameter φ ** ; According to the new network parameter φ ** , generating volume data through the preset neural network For the block data Add the noise at time t-1 to form the reconstructed block data x at time t-1 t-1 , and based on the block data x t-1 Iterate over the data.

2. The image reconstruction method according to claim 1, characterized in that The block data x at time t t Perform noise reduction to obtain the reconstructed block data after noise reduction Specifically include: Based on the size of the static CT projection data, an initial noise distribution of the same dimension is obtained; wherein the initial noise distribution obeys a normal distribution; Based on the initial noise distribution, the noise data at time t is used as the block data x at time t. t , denoted by x t ~N(0,σI); Formula (1) is used to calculate the block data x at time t t Perform noise reduction to obtain the reconstructed block data after noise reduction in, represents the noise factor, s θ* (x t ,t) is the block data x t The score function at time t is the pre-trained network. Represents the reconstructed block data after denoising.

3. The image reconstruction method according to claim 2, characterized in that The reconstructed block data based on the noise reduction Perform affine set projection to make the projected block data The projection data corresponding to the static CT include: An affine set C = {x|Px = Y} is defined in advance. For any x, the projection on the affine subspace C is defined by the following formula: Based on the above formula (1) and formula (2), The projection of is defined by formula (3): The conjugate gradient (CG) method is used to calculate the operator (PP T ) By using the formula (3) and formula (4), we can get x 0t The projection is: Where Y represents the projection data of static CT; P represents Radon transform; P T represents the transpose of P; x represents the reconstructed block; y represents the independent variable to be optimized.

4. The image reconstruction method according to claim 3, characterized in that Based on the projected block data Perform learning of the preset neural network to obtain the initial neural network parameters φ * , specifically including: Selecting neural network input tensors ∈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 xyz axis; Based on the preset neural network F(∈0;Φ), the block data is obtained The initial neural network parameters φ are represented by * ; Among them, Φ represents the neural network parameters; ∈0 represents the initial noise that conforms to the normal distribution; R represents the regularization function; λ represents the weight coefficient of the regularization term; arg represents the symbol for solving the minimum value.

5. The image reconstruction method according to claim 4, characterized in that The projected block data Perform implicit neural representation to obtain implicit neural representation results Specifically include: Using multiple discretization intervals, resample the block data of the unit cube; Set the encoding tensor ε0 to ε test ∈R rM×rN×rK , where r ≥ 1 is a positive integer r ∈ N + ; N+ represents a positive integer; Based on the pre-trained neural network, the predicted reconstruction volume is obtained, thereby obtaining the volume block data The implicit neural representation results 6. The image reconstruction method according to claim 5, characterized in that The new network parameter φ ** Obtained through: The preset implicit neural network F(∈0;Φ) is used as the initialization model, and the following objective function is used to train the neural network to obtain a new network parameter φ ** ; 7. The image reconstruction method according to claim 6, characterized in that The block data Generated by: R λ (Φ) is expanded to the total variation norm, expressed as: in, represents the gradient; Based on the trained neural network, the block data It is expressed as: Among them, μ>0 is a hyperparameter used for balancing; R(Φ) represents the regularization term.

8. An image reconstruction system based on limited angle and sparse angle projection of static CT, characterized in that include: A parameter acquisition unit, used to acquire static CT projection data, stochastic differential equation discrete steps and conditional diffusion interval; wherein the projection data is in the form of finite angle plus sparse angle data; An unconditional reverse diffusion unit, connected to the parameter acquisition unit, to reconstruct the projection data of the static CT by using unconditional reverse diffusion; A conditional back diffusion unit connected to the unconditional back diffusion unit to reconstruct the projection data of the static CT by using conditional back diffusion; After each m-times of data reconstruction by unconditional reverse diffusion, a data reconstruction by conditional reverse diffusion is performed, where m is a positive integer greater than 1.

9. An image reconstruction system based on limited angle and sparse angle projection of static CT, characterized in that It comprises a processor and a memory; wherein the memory is coupled to the processor and is used to store a computer program, and when the computer program is executed by the processor, the processor implements 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 according to any one of claims 1 to 7 is adopted.

Images