CN109472841B

CN109472841B - CBCT three-dimensional reconstruction method based on Gaussian mixture/Poisson maximum likelihood function

Info

Publication number: CN109472841B
Application number: CN201811286785.8A
Authority: CN
Inventors: 田昕; 郑蓉珍; 赵芳; 李波; 李松
Original assignee: Wuhan University WHU
Current assignee: Wuhan University WHU
Priority date: 2018-10-31
Filing date: 2018-10-31
Publication date: 2022-12-02
Anticipated expiration: 2038-10-31
Also published as: CN109472841A

Abstract

The invention discloses a CBCT three-dimensional reconstruction method based on a Gaussian mixture/Poisson maximum likelihood function, which belongs to a statistical iterative reconstruction algorithm. The method comprises the steps of firstly transforming actual measurement projection data which obey Gaussian-Poisson mixed distribution into approximate Gaussian-obeyed distribution through ansscombe transformation, achieving the purpose of stabilizing noise variance, then solving Gaussian mixture/Poisson maximum likelihood function through a gradient descent method, and combining a three-dimensional Total Variation regularization method (3D-Total Variation, 3D-TV) to carry out iterative reconstruction, thereby achieving the purpose of improving the quality of reconstructed images.

Description

CBCT three-dimensional reconstruction method based on Gaussian mixture/Poisson maximum likelihood function

Technical Field

The invention belongs to the technical field of image reconstruction, and mainly relates to a CBCT three-dimensional reconstruction method under Gaussian mixture/Poisson noise.

Background

Computed Tomography (CT) technology acquires information such as internal structure information, material, defects and the like of an object in a nondestructive manner, and is widely applied to the fields of medical auxiliary diagnosis, industrial nondestructive testing, safety inspection and the like. With the rapid development of the technology, a flat panel detector appears, projection data obtained by a Cone Beam Computed Tomography (CBCT) system through the flat panel detector is two-dimensional, a three-dimensional image can be directly obtained by using a three-dimensional reconstruction algorithm, and the system is a real three-dimensional reconstruction. And the CBCT has the obvious advantages of small volume, light weight, flexible movement, high scanning speed, high ray utilization rate, high reconstruction resolution ratio and the like, and is widely applied to interventional operation treatment, nondestructive detection and the like. The CBCT reconstructed image is isotropic, the image accuracy and the reconstruction real-time performance are improved, the focus can be analyzed more accurately and rapidly, and the life quality of a patient is improved. CBCT is low in price, can be compactly installed in oral surgery clinics and private clinics, and provides service for patients more conveniently. In order to reduce the radiation problem of rays in CBCT imaging, a CBCT imaging method with low radiation dose is developed, but the signal-to-noise ratio of signals in the CBCT imaging method is reduced. Therefore, it is very important for the CBCT reconstruction method to effectively remove the noise problem under low dose conditions. The most common noise in the system under low dose conditions includes gaussian noise and poisson noise. Gaussian noise is mainly derived from sensor noise during image acquisition, often due to poor illumination or high temperatures. Poisson noise is caused by the photoelectric conversion process in the image sensor, and the influence is more serious in the low-dose CBCT reconstruction process.

In 1984, feldkamp, davis and Kress proposed the best-known cone-beam three-dimensional image reconstruction algorithm, FDK algorithm, for circular scan trajectories. The method is based on circular trajectory scanning, is an algorithm which is easy to realize and high in reconstruction speed, and is the most classical algorithm in approximation algorithms. Until now, the FDK algorithm is still the mainstream of commercial CT application, and there is no alternative position in the CT reconstruction algorithm. The algorithm is an approximate three-dimensional image reconstruction algorithm, the FDK algorithm has a good reconstruction effect at a small cone angle, but when the cone angle is increased, the reconstruction effect is worse as the distance from the center layer is longer. Aiming at the defects of the FDK algorithm, various FDK algorithm derived algorithms appear, and the reconstructed image quality of the FDK algorithm is improved. The FDK-based analytical algorithm is equivalent to solving an integral equation, and the iterative algorithm is equivalent to solving a large linear equation set. Because the linear equation set is more real than the integral equation in the depiction of the imaging geometric structure and the imaging physical effect, prior knowledge, constraint conditions and the like can be added, the iterative algorithm has smaller dependence on a scanning mode than an analytical algorithm, is more suitable for the actual imaging problem, obtains more accurate results by the iterative algorithm, and has better noise suppression effect. Since the slow reconstruction speed of the iterative algorithm is a fatal defect, many scholars research the acceleration of the iterative algorithm, and the parallel processing capacity of a computer is improved through design, so that the acceleration is performed by using a special image processor or the algorithm is improved and accelerated. With the continuous update of hardware technology and the development of various special servers, the running speed of the computer is higher and higher, and the advantages of the iterative algorithm are better played. The Iterative Reconstruction algorithm is divided into algebraic Reconstruction and Statistical Reconstruction, and the Statistical Iterative Reconstruction algorithm (SIR) is to analyze the Statistical characteristics of projection data to establish a target function and reconstruct a high-quality image by using a certain estimation method. The study of the statistical iterative algorithm is mainly performed on the radiation type CT in China.

The invention utilizes a statistical iterative reconstruction algorithm to reconstruct the cone beam CT, and provides a CBCT three-dimensional reconstruction algorithm based on a Gaussian mixture/Poisson maximum likelihood function, thereby reconstructing a high-quality image.

Disclosure of Invention

The invention provides a CBCT three-dimensional reconstruction algorithm based on a Gaussian mixture/Poisson maximum likelihood function, belongs to a statistical iterative reconstruction algorithm, and aims to reconstruct a high-quality image by analyzing the statistical characteristics of projection data and utilizing a certain estimation method. Mainly comprises the following steps:

step 1, setting system parameters and a reconstructed image estimation value, and loading real projection data;

step 2, performing ansscombe transformation on the real projection data;

step 3, according to the preset iteration times t, if the current iteration times are within the preset iteration times and the iteration termination condition e is not reached, entering an iteration loop specifically including step 4 and step 5, and performing iterative computation on the reconstruction result to approach a more optimal value, otherwise, exiting;

step 4, performing anscombe transformation on the projection data of the estimated value, and solving the maximum likelihood function of the reconstructed image X as an objective function and updating the reconstruction result of the image by the maximum likelihood function on the basis of the anscombe transformation result of the real projection data and the anscombe transformation result of the projection data of the estimated value;

and 5, performing 3DTV regularization smooth denoising on the reconstructed image, optimizing a reconstruction result, updating an iteration step length and performing a new round of iterative computation.

Further, the system parameters set in step 1 include setting of the cone beam CT apparatus, distance from the source to the rotation center and the detector, rotation angle and sampling condition, and detector related parameters.

Further, in step 1, for the real projection data, a reconstructed image is obtained by calling a conventional CBCT reconstruction algorithm FDK as a reconstructed image estimation value.

Further, the specific implementation manner of step 4 is as follows,

s41, setting the estimated value as xk, projecting the estimated value to obtain proj _ xk, and performing anscombe transformation on the projection of the estimated value to obtain proj _ traxk;

s42, taking the maximum likelihood function of the reconstructed image X as the target function for generating the reconstructed image, wherein y is the ith actual measurement projection _i Is subject to a mixed poisson-gaussian distribution, and therefore its maximum likelihood function can be expressed as:

derived based on GAT

The probability density function can be approximated as:

where X represents three-dimensional reconstruction data, A _i ^j J-th row, [ p ], of the projection matrix representing the i-th angle] _j Represents the jth element in the vector p; on this basis, the negative log maximum likelihood function can be expressed as

Wherein M represents the number of projections, N ² Representing the total number of elements on a single projection, and the number of rows of the projection matrix a at the ith projection angle,

means through anThe jth element of the ith projection after scombe transformation;

partial derivatives of X are obtained

According to the above formula, the maximum likelihood function is solved by using the real projection data, the estimated value projection data and the acombe transformation result thereof, which specifically comprises the following steps: solving for

Carrying out zero setting processing on an infinite value and a null value of the solution, cutting off a value with overlarge gradient by using a cut-off function, and carrying out filtering back projection after cutting off to obtain a solution of a maximum likelihood function, namely gradient information gk of the image;

s43, judging whether gk meets the condition of iteration termination, namely whether the module length of the gradient is less than the condition e of iteration termination, if so, terminating the iteration, otherwise, updating the image by utilizing the estimated value xk and the inverse gk to obtain a new estimated value xkj1,

xkj1＝xk-dk*gk (8)

and the initial dk is given as an initial value before iteration loop, the initial loop dk is an initial value, and the non-initial loop is the dk updated in the later period of the last iteration.

Further, the specific implementation manner of step 5 is as follows,

s51, carrying out error evaluation on xkj1 serving as a reconstruction result, judging whether the error is reduced along with the increase of the iteration times, and otherwise, adjusting the iteration step length dk = S × dk through a relaxation factor, wherein S is a constant value initially set; repeating S43 in step 4 until the evaluation error satisfies the condition of reduction;

s52, if the evaluation error meets the reducing condition, carrying out 3DTV regularization smooth denoising on the reconstructed image,

regular term lambda TV (xkj 1)

Wherein k is the pixel index of the image, x, y and z respectively represent three directions of the three-dimensional image, and lambda is a regularization parameter,

representing the full variation of the image xkj1,

gradient information representing the image;

as a total variation constraint regular term, the solution is ensured to have certain regularity, the smoothness of image noise is realized, and the noise is removed;

s53, updating an iteration step, xk = xkj1; gk _1= gk, to perform a new iteration, the iteration step dk is determined by a Barzilar-Borwein method, and when the iteration number k is greater than 1, gk _1 is gk of the previous iteration;

and yk _1 is the difference value of the gradient in the current iteration and the last iteration process, and is used as an intermediate variable for updating the iteration step length.

The method comprises the steps of firstly transforming actual measurement projection data which obey Gaussian-Poisson mixed distribution into approximate Gaussian-obeying distribution through ansscombe transformation to achieve the purpose of stabilizing noise variance, then solving a Gaussian mixture/Poisson maximum likelihood function through a gradient descent method, and performing iterative reconstruction by combining a three-dimensional Total Variation regularization method (3D-Total Variation, 3D-TV), thereby achieving the purpose of improving the quality of reconstructed images.

Drawings

FIG. 1 is a flowchart of a reconstruction method according to an embodiment of the present invention;

FIG. 2 is a reconstruction result of the FDK algorithm under Gaussian Poisson mixed noise models with different sizes;

FIG. 3 is a reconstruction result of the FDK algorithm under Gaussian Poisson mixed noise models with different sizes after projection data BM3D denoising;

FIG. 4 is a reconstructed result of the SART algorithm under Gaussian Poisson mixed noise models with different sizes;

FIG. 5 shows the reconstruction result of the Gaussian Poisson noise mixture models with different sizes according to the method of the present invention;

FIG. 6 shows a comparison of the reconstruction results of the FDK algorithm, BM3D _ FDK, SART, and the method of the present invention under Gaussian Poisson mixed noise models of different sizes.

Fig. 7 is a schematic diagram of the iterative method in step 3.

Detailed Description

The technical solution of the present invention is further explained with reference to the drawings and the embodiments.

The invention relates to CBCT three-dimensional image reconstruction based on a Gaussian mixture/Poisson maximum likelihood function, which utilizes ansscomb transformation to transform actual measurement projection data which obey Gaussian-Poisson mixture distribution into approximate Gaussian mixture, achieves the aim of stabilizing noise variance, solves the Gaussian mixture/Poisson maximum likelihood function through a gradient descent method, combines a three-dimensional Total Variation regularization method (3D-Total Variation, 3D-TV) to carry out iterative reconstruction, fully considers the difference of each iteration estimation value, adjusts iteration step length through a Barzilar-Borwein method, and iterates for multiple times to continuously approach the optimal reconstruction result, thereby improving the quality of the reconstructed image.

Step 1, setting system parameters, including setting of a cone beam CT instrument, the distance from a radiation source to a rotation center and a detector, a rotation angle, sampling conditions and the like, and related parameters of the detector. Acquiring projection data proj, and initializing related parameters of xk, anscombe transformation and the like as the estimated value of the reconstructed image.

And 2, performing ansscombe transformation on the projection data proj. An initial iteration step size is set, and a relaxation factor is added to reduce the step size, so that the algorithm is more stable. The 3DTV regularization rate λ is set. An initial error reference value is set. And (5) setting iteration times t and an iteration termination condition e, and terminating the iteration loop if the iteration termination condition is reached in the range of the iteration times of the step (4) and the step (5).

The ansscombe transformation method is as follows,

due to the fact that

i denotes the ith projection data, y _i Represents the ith actually measured projection,

representing a signal subject to poisson noise, obeys a poisson distribution,

n _i gaussian noise, n, representing the system _i ～Ν(0,δ ² ). Based on GAT (Anscombe Transform) formula (1), we can get

The result of the anscombe transform of the projection data.

a specific iterative method is as follows,

the maximum likelihood function for solving the reconstructed image X is used as an objective function, an external iteration loop is formed based on the objective function, the objective function is solved by using a gradient descent method for each iteration to obtain image gradient information, a reconstructed image is calculated, the reconstructed image is combined with a 3DTV regularization item to form an internal iteration loop, the reconstructed noisy image is subjected to smooth denoising, and the quality of the reconstructed image is improved, as shown in FIG. 7.

And 4, performing anscombe transformation on the projection data of the estimated value, and solving the maximum likelihood function of the reconstructed image X as an objective function on the basis of the anscombe transformation result of the real projection data and the anscombe transformation result of the xk projection data of the estimated value, so as to update the image to obtain the reconstructed result.

The step 4 specifically comprises the following steps:

s41, projecting the estimated value to obtain proj _ xk, and performing anscombe transformation on the projection of the estimated value to obtain proj _ traxk.

derived based on GAT

The probability density function can be approximated as ^[1] ：

[1]MARNISSI Y,ZHENG Y,PESQUEI J.Fast variational Bayesian signal recovery in the presence of Poisson-Gaussian noise[J].ICASSP,IEEE International Conference on Acoustics,Speech and Signal Processing-Proceedings,2016,2016-May:3964-3968.

Where X represents three-dimensional reconstruction data, A _i ^j J-th row, [ p ], of the projection matrix representing the i-th angle] _j Representing the jth element in the vector p. On this basis, the negative log maximum likelihood function can be expressed as

Wherein M represents the number of projections, N ² Representing the total number of elements on a single projection, and also the number of rows of the projection matrix a at the ith projection angle,

refers to the jth element of the ith projection after anscombe transformation.

Partial derivatives of X are obtained

According to the above formula, the maximum likelihood function is solved by using the real and estimated projection data and its ancombe transformation result, which is specifically as follows: solving for

In actual program operation, it is

And carrying out zero setting processing on the infinite value and the null value of the solution, truncating the value with overlarge gradient by adopting a truncation function, and carrying out filtering back projection after truncation to obtain the solution of the maximum likelihood function, namely the gradient information gk of the image.

S43, judging whether gk meets the condition of iteration termination, namely whether the modular length of the gradient is smaller than the condition e of iteration termination. If the new estimated value xkj1 is obtained, terminating iteration, ending program operation, otherwise, updating the image by using the estimated value xk and the inverse gk:

xkj1＝xk-dk*gk (8)

and the initial dk is an initial value given before the iteration loop, the initial loop dk is an initial value, and the non-initial loop is the dk updated in the later period of the last iteration.

The step 5 specifically comprises the following steps:

and S51, evaluating the error of the xkj1 serving as a reconstruction result, judging whether the error is reduced along with the increase of the iteration times, and otherwise, adjusting the iteration step length dk = S × dk through a relaxation factor, wherein S is a constant value initially set by the program. And repeating S3 of the step 4 until the evaluation error meets the reduction condition.

S52, if yes, 3DTV regularization smooth denoising is carried out on the reconstructed image, and the regularization term is lambda TV (xkj 1)

Wherein k is the pixel index of the image, and x, y and z respectively represent three directions of the three-dimensional image. Lambda is a regularization parameter that is,

representing the full variation of the image xkj1,

representing gradient information of the image.

As a total variation constraint regular term, the method ensures that the solution has certain regularity, realizes the smoothness of image noise and removes the noise. The regularization parameter lambda can be used for adjusting the degree of the regularization term, when the value of lambda is large, the degree of the regularization term is high, the smoothing effect is obvious, when the value of lambda is small, the data fidelity degree is high, and the detail area of the edge is easy to maintain. When the noise in the image is larger, a larger lambda value is taken, and when the noise in the image is smaller, a smaller lambda value is taken.

S53, updating an iteration step length, wherein xk = xkj1; gk _1= gk to perform a new iteration. The iteration step dk can be determined by the Barzilar-Borwein method, when the iteration number k > 1: gk _1 is gk for the last iteration,

and yk _1 is the difference value of the gradients in the current iteration and the last iteration process, and is used as an intermediate variable for updating the iteration step length.

The method provided by the invention can realize the process by using a computer software technology. In the embodiment, the modified Shepp-Logan phantom is used for simulating and generating low-dose cT projection data proj, a reconstructed image Reconng is obtained by adopting an approximate reconstruction algorithm FDK based on a circular trajectory and is used as an initial reconstructed image estimated value, a specific explanation is carried out on the process of the invention,

the specific embodiments of the examples are as follows:

and generating low-dose CT projection data by using a modified Shepp-Logan128 x 128 phantom model, setting xk as a reconstructed image estimation value, setting an initial value as FDK to obtain a reconstructed image Recomig, setting dk as an iteration step length, setting s as a relaxation factor for rapidly updating the generation step length, setting t as the iteration times and setting e as an iteration termination condition. Sigma is a parameter of the magnitude of the Gaussian noise added, alpha is the magnitude of the Poisson noise added, and lambda is the regularization rate.

Step 1, loading a Shepp-Logan model, generating 211 pieces of 128 x 128CBCT projection data proj, and calling a CBCT traditional reconstruction algorithm FDK to obtain a reconstructed image which is Recomig and is used as an initial reconstructed image estimated value xk.

And 2, setting parameters for adding noise to the projection data, and respectively setting a Gaussian noise mixture model with sigma of 2,6,10,14,18 and lambda of 1e 5. Setting the initial iteration step dk to 1 and the relaxation factor s =0.5. The 3DTV regularization rate λ is set to 0.01. The initial error reference qm11 is set to 0.2. The number of iterations t =10 and the iteration end condition e =0.2 are set. And setting relevant parameters for ansscomb transformation according to the noise adding condition. The projection data proj is subjected to ansscombe transform to obtain proj _ tra.

And 3, entering an iteration loop if the current iteration number is within the preset iteration number according to the preset iteration number t, and otherwise, exiting the program. When the iteration times are less than or equal to 10, the method enters an iteration cycle, and continuously iterates to calculate the reconstruction result to approach a better value.

Step 4

And S41, entering an iterative loop, and performing ansscombe transformation on the projecture proj _ xk of the reconstructed image estimation value xk to obtain proj _ traxk.

S42, calculating a factor fx1 of the partial derivative of the objective function by utilizing the proj _ tra, the proj _ traxk and the projection data proj, namely:

and carrying out zero setting processing on an infinite value and a null value of a factor of the partial derivative, carrying out truncation by adopting a truncation function, setting the truncation value to be 0.05, and carrying out filtering back projection on the truncated partial derivative factor to obtain a solution gk of the target function.

And S43, if the gk meets the condition of iteration termination, terminating the iteration, ending the program operation, and otherwise, updating the reconstructed image xkj1= xk-dk × gk.

Step 5

And S51, carrying out error evaluation judgment on the reconstructed image xkj1, judging whether the error is reduced along with the increase of the iteration times, otherwise, adjusting the iteration step length dk = S × dk through a relaxation factor, and repeating the step xkj1= xk-dk × gk until the evaluation error meets the reduction condition.

And S52, carrying out 3DTV regularization smoothing denoising on the reconstructed image xkj 1.

S53, updating iteration step length dk, wherein xk = xkj1; gk _1= gk to perform a new iteration.

Example process related data the following table:

CBCT three-dimensional reconstruction using FDK algorithm under different mixed noise models with poisson noise distribution size lambda =1e5, gaussian noise size sigma =2, sigma =6, sigma =10, sigma =14, sigma =18, respectively. The data of the results are shown in Table 1, and the experimental results are shown in FIG. 2.

2 projection data were preprocessed using BM3D under different mixed noise models with a poisson noise distribution size of lambda =1e5, gaussian noise sizes of sigma =2, sigma =6, sigma =10, sigma =14, sigma =18, respectively, and then CBCT three-dimensional reconstruction was performed by FDK algorithm. The data of the results are shown in Table 2, and the results of the experiment are shown in FIG. 3.

3, CBCT three-dimensional reconstruction is carried out by using SART algorithm under different mixed noise models with Poisson noise distribution size of lambda =1e5 and Gaussian noise size of sigma =2, sigma =6, sigma =10, sigma =14 and sigma =18 respectively. The results are shown in Table 3 and the results are shown in FIG. 4.

CBCT three-dimensional reconstruction is carried out by using the algorithm in the text under different mixed noise models with the Poisson noise distribution size of lambda =1e5 and the Gaussian noise size of sigma =2, sigma =6, sigma =10, sigma =14 and sigma =18 respectively, and a CBCT three-dimensional reconstruction algorithm (ML _ TV) based on a mixed Gaussian/Poisson maximum likelihood function is used. The results are shown in Table 4 and the results are shown in FIG. 5.

Comparing the experiment results of FDK, projection data BM3D (three-dimensional block matching) denoising FDK, SART (simultaneous iterative reconstruction iterative algorithm) and the text algorithm (ML _ TV):

TABLE 1 CBCT three-dimensional reconstruction experiment results by FDK algorithm

Sigma-lambda	2-1e5	6-1e5	10-1e5	14-1e5	18-1e5
						RMSE	0.047774	0.052504	0.056828	0.060843	0.064607

TABLE 2 CBCT three-dimensional reconstruction experiment results by BM3D _ FDK algorithm

Sigma-lambda	2-1e5	6-1e5	10-1e5	14-1e5	18-1e5
						RMSE	0.047761	0.048654	0.049515	0.050211	0.050598

TABLE 3 CBCT three-dimensional reconstruction experiment results using SART algorithm

Sigma-lambda	2-1e5	6-1e5	10-1e5	14-1e5	18-1e5
						RMSE	0.040093	0.041942	0.043583	0.04533	0.046899

TABLE 4 results of CBCT three-dimensional reconstruction experiments using the method of the invention (ML _ TV)

Sigma-lambda	2-1e5	6-1e5	10-1e5	14-1e5	18-1e5
						RMSE	0.024242	0.026943	0.030591	0.035602	0.035886
lambda	0.01	0.05	0.05	0.05	0.05
						sigma	40	40	40	42	45

The embodiment process compares the reconstruction results of different reconstruction methods under Gaussian Poisson mixed noise models with different sizes, and relates to a reconstruction result graph as follows: the FDK algorithm is shown in figure 2 in the reconstruction result under Gaussian Poisson mixed noise models with different sizes; the reconstruction result of the projection data BM3D denoised FDK algorithm under Gaussian Poisson mixed noise models with different sizes is shown in figure 3; the reconstruction result of the SART algorithm under Gaussian Poisson mixed noise models with different sizes is shown in FIG. 4; the method of the invention reconstructs the result under Gaussian Poisson mixed noise models with different sizes as shown in figure 5; FDK algorithm, BM3D _ FDK, SART, the invention method in different size Gaussian Poisson mixed noise model under the reconstruction results such as figure 6;

the CBCT three-dimensional reconstruction method is currently divided into an analytic method and an iterative reconstruction method, the FDK algorithm is the most classical analytic reconstruction method, the BM3D is a denoising method with a very good Gaussian noise removing effect at present, projection data are preprocessed through the BM3D and then reconstructed through the FDK, the quality of an FDK reconstructed image is improved after the preprocessing is carried out through the BM3D denoising method as shown in tables 1 and 2, and the effect of optimizing the reconstruction result after the BM3D is applied is shown in a figure 2 and a figure 3. As can be seen from Table 3, the result obtained by the iterative algorithm SART is more accurate, the suppression effect on noise is better, the quality of the reconstructed image is better, even if the FDK reconstruction result of the BM3D denoising method is better than that of the FDK reconstruction result of the BM3D denoising method, and the reconstruction result of the method is better than that of the SART as can be seen from Table 4. The difference of the reconstruction results of the two iterative reconstruction algorithms can be clearly seen from fig. 4 and fig. 5. After the problem of low iterative reconstruction speed is solved through the acceleration of the GPU, the iterative reconstruction algorithm is more suitable for the problem of actual imaging than the analytic algorithm, the result obtained by the iterative algorithm is more accurate, and the noise suppression effect is better. The method provided by the text belongs to a statistical iterative reconstruction method, so that the performance of the reconstructed image is greatly improved, the quality of the reconstructed image is better, and if the method is applied to practice, medical staff can conveniently distinguish the focus.

The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments, or alternatives may be employed, by those skilled in the art, without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims

1. The CBCT three-dimensional reconstruction method based on the Gaussian mixture/Poisson maximum likelihood function is characterized by comprising the following steps of:

step 2, performing ansscombe transformation on the real projection data;

step 3, according to the preset iteration times t, if the current iteration times are within the preset iteration times and the iteration termination condition e is not met, entering an iteration loop specifically including the step 4 and the step 5, performing iterative computation on the reconstruction result to approach a more optimal value, and otherwise, exiting;

2. The CBCT three-dimensional reconstruction method based on gaussian mixture/poisson maximum likelihood function as claimed in claim 1, wherein: the system parameters set in step 1 include the setting of the cone beam CT instrument, the distance between the radiation source and the rotation center and the detector, the rotation angle and the sampling condition, and related parameters of the detector.

3. The CBCT three-dimensional reconstruction method based on gaussian mixture/poisson maximum likelihood function as claimed in claim 1, wherein: in the step 1, aiming at real projection data, a reconstructed image is obtained by calling a CBCT traditional reconstruction algorithm FDK and is used as a reconstructed image estimation value.

4. The CBCT three-dimensional reconstruction method based on gaussian mixture/poisson maximum likelihood function as claimed in claim 1, wherein: the specific implementation of step 4 is as follows,

s41, setting an estimated value as xk, projecting the estimated value to obtain proj _ xk, and performing ansscombe transformation on the projection of the estimated value to obtain proj _ traxk;

derived based on GAT

The probability density function can be approximated as:

the method is characterized in that j element of ith projection after ansscombe transformation is included;

partial derivatives of X are obtained

xkj1＝xk-dk*gk (8)

5. The CBCT three-dimensional reconstruction method based on Gaussian mixture/Poisson maximum likelihood function as claimed in claim 4, characterized in that: the specific implementation of step 5 is as follows,

s52, if the evaluation error meets the reduction condition, 3DTV regularization smooth denoising is carried out on the reconstructed image, and the regularization term lambda TV (xkj 1)

Wherein k is a pixel point index of the image, x, y, z respectively represent three directions of the three-dimensional image, λ is a regularization parameter, | | | | | xkj1| | luminance ₁ Represents the total variation of the image xkj1, and ^ xkj1 represents gradient information of the image; | |. Xkj1| | non-conducting light ₁ As a total variation constraint regular term, the solution is ensured to have certain regularity, the smoothness of image noise is realized, and the noise is removed;