Dynamic pet parametric image segmentation reconstruction algorithm based on em algorithm

Abstract

The application discloses a dynamic PET parameter image partial reconstruction algorithm based on an EM algorithm and relates to the technical field of medical imaging. The parameter image imaging linear equation obtained by coupling a blood flow physiology model with the parameter image imaging linear equation is disassembled, the reconstruction target image is decomposed into two target images, and the slope image K and the intercept image b are reconstructed through the EM iterative image reconstruction algorithm alternately. The application is based on the EM iterative image reconstruction algorithm and a Patlak mathematical model partial direct dynamic PET parameter image reconstruction method. The slope image and the intercept image of the Patlak curve are partially and alternately iteratively reconstructed in the linear equation, the mutual interference of the slope image and the intercept image in the iterative calculation is greatly reduced, the reconstructed image has higher image quality, the error introduction in the parameter image reconstruction process is greatly reduced, and the obtained parameter image is more favorable for subsequent diagnosis and analysis.

Description

Technical Field

[0001] This invention relates to the field of medical imaging technology, specifically to a dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm. Background Technology

[0002] The key to the application of dynamic PET imaging technology is the quantitative analysis of the patient's physiological metabolism. Post-processing of image sequences based on the Patlak physiological model is currently the mainstream method for dynamic PET data analysis. Indirect parametric image reconstruction involves first reconstructing all dynamic PET image sequences using the projection data obtained from image acquisition. The time-activity curves (TACs) of each tissue in the patient are obtained from the dynamic images. Combining the TACs with the blood input function during imaging, and based on a suitable mode model and the Patlak physiological model, the imaging agent inflow rate Ki of each tissue is calculated, which is the slope of the effective segment of the Patlak curve. Each pixel κ constitutes the dynamic PET parametric image. Beyond the indirect method, leading scientists in dynamic PET have proposed a method to directly calculate parametric images from the projection data obtained from image acquisition, i.e., direct dynamic PET parametric image reconstruction. This method, because it avoids two image estimations, significantly reduces errors and interference information in the parametric image calculation results compared to indirect parametric image reconstruction techniques.

[0003] Indirect methods for reconstructing parametric images involve two image estimation processes: dynamic PET image reconstruction and parametric image reconstruction. This results in significant errors and interference in the reconstructed parametric image. Related techniques using maximum a posteriori (MAP) for direct parametric image reconstruction have greatly reduced these errors and interference. However, this method integrates the slope image κ and intercept image b of the Patlak curve into a single target image for a one-time solution. The large number of unknowns to be solved in the iterations limits the quality of the reconstructed parametric image. Summary of the Invention

[0004] To address the problems in existing technologies, this invention proposes a dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm. This method involves reconstructing the slope image and intercept image of the Patlak curve in a linear equation in an alternating and iterative manner. This greatly reduces the mutual interference between the slope image and the intercept image during iterative calculation, resulting in reconstructed images with higher image quality, which is more conducive to subsequent diagnosis and analysis.

[0005] To achieve the above objectives, this invention provides a dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm, comprising: decomposing the parametric image imaging linear equation obtained by coupling the blood flow physiological model and the imaging linear equation, decomposing the reconstruction target image into two target images, and reconstructing the slope image κ and the intercept image b through an alternating EM iterative image reconstruction algorithm.

[0006] Furthermore, the linear equation for parametric image imaging is decomposed into the following equation:

[0007]

[0008] in, and These are the blood input functions C corresponding to the current dynamic PET imaging task. p The time integral function of (t) and C p The decay integral function of (t); P is the imaging system matrix; r is the scattering and random coincidence time in the projection data; This is the Kronecker product operation; k and b are the slope and intercept images of the Patlak curve to be reconstructed, respectively.

[0009] Furthermore, the time integration function Represented as:

[0010]

[0011] Where n represents a certain time frame, t s,n t is the start time of time frame n; e,n τ is the end time of time frame n; ξ is the integration time variable; ξ is the integration time variable of the inner function; λ is the decay constant of the labeled isotope.

[0012] Furthermore, the attenuation integral function Represented as:

[0013]

[0014] Furthermore, the EM iterative image reconstruction algorithm includes the following slope image κ iterative formula:

[0015]

[0016] Where N is the number of pixels in the target parameter image, 1 N It is a column vector of length N with all elements equal to 1; T represents the matrix transpose.

[0017] Furthermore, the EM iterative image reconstruction algorithm includes the following iterative formula for the intercept image b:

[0018]

[0019] Furthermore, the EM iterative image reconstruction algorithm adopts an alternating iterative formula. After the iterative calculation reaches stable convergence, the directly reconstructed Patlak curve reconstruction slope image κ and intercept image b are obtained.

[0020] Furthermore, the algorithm includes dynamic PET parametric images of the human brain, chest, liver, kidneys, or whole body.

[0021] Furthermore, the PSNR value of the slope image κ reconstructed by the algorithm reaches 28.0636, and the PSNR value of the intercept image b reaches 22.2039.

[0022] Compared with existing technologies, this invention decomposes the parametric image imaging linear equation obtained by coupling the blood flow physiology model with the imaging linear equation, decomposing the reconstructed target image {κ,b} into two target images {κ} and {b}. The slope image κ and intercept image b are then reconstructed using an alternating EM iterative image reconstruction algorithm. This invention, based on the EM iterative image reconstruction algorithm and the Patlak mathematical model, employs a distributed direct dynamic PET parametric image reconstruction method. By iteratively reconstructing the slope and intercept images of the Patlak curve in parts within the linear equation, the mutual interference between the slope and intercept images during iterative calculation is greatly reduced, resulting in higher image quality in the reconstructed image. This significantly reduces the error introduction during the parametric image reconstruction process, making the obtained parametric image more conducive to subsequent diagnosis and analysis. Attached Figure Description

[0023] Figure 1 The figure shows the experimental verification results of the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0025] The embodiments of the present invention provide a dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm, comprising: decomposing the parametric image imaging linear equation obtained by coupling the blood flow physiological model and the imaging linear equation, decomposing the reconstruction target image {κ,b} into two target images {κ} and {b}, and reconstructing the slope image κ and the intercept image b through an alternating EM iterative image reconstruction algorithm.

[0026] The linear equation for parametric image imaging can be decomposed into the following equation:

[0027]

[0028] in, and These are the blood input functions C corresponding to the current dynamic PET imaging task. p The time integral function of (t) and C p The decay integral function of (t); P is the imaging system matrix; r is the scattering and random coincidence time in the projection data; For the Kronecker product operation; κ and b are the slope image and intercept image of the Patlak curve to be reconstructed, respectively.

[0029] Time integral function Represented as:

[0030]

[0031] Where n represents a certain time frame, t s,n t is the start time of time frame n; e,n τ is the end time of time frame n; ξ is the integration time variable; ξ is the integration time variable of the inner function; λ is the decay constant of the labeled isotope.

[0032] decay integral function Represented as:

[0033]

[0034] The EM iterative image reconstruction algorithm includes the following slope image κ iterative formula:

[0035]

[0036] Where N is the number of pixels in the target parameter image, 1 N It is a column vector of length N with all elements equal to 1; T represents the matrix transpose.

[0037] The EM iterative image reconstruction algorithm includes the following iterative formula for the intercept image b:

[0038]

[0039] The EM iterative image reconstruction algorithm uses an alternating iterative formula. After the iterative calculation reaches stable convergence, the reconstructed slope image κ and intercept image b of the Patlak curve are obtained.

[0040] This invention includes dynamic PET parametric images of the human brain, chest, liver, kidneys, or whole body. The PSNR value of the reconstructed slope image κ reaches 28.0636, and the PSNR value of the intercept image b reaches 22.2039.

[0041] To verify the advantages of this invention, reference images were selected, and simulation experiments were conducted using the indirect method, the direct method, and the method of this invention, respectively. The verification results are shown below. Figure 1 .

[0042] Indirect method: The reconstructed parametric image involves two image estimation processes, namely dynamic PET image reconstruction and parametric image reconstruction. Using the projection data obtained from image acquisition, all dynamic PET image sequences are reconstructed first. The time activity curves (TACs) of each tissue in the patient are obtained from the dynamic images. Combining the time activity curves with the blood input function during the imaging process, and based on a suitable mode model and Patlak physiological model, the imaging agent inflow rate Ki of each tissue in the patient is calculated, which is the slope of the effective segment of the Patlak curve. Each pixel κ constitutes the dynamic PET parametric image.

[0043] Direct method: A method that directly reconstructs the parametric image using maximum a posteriori (MAP), based on the formula: The solution is obtained through iterative steps. P is the imaging system matrix, A is the parameter matrix, θ is the image vector with estimated parameters, and r is the scattering and random coincidence time in the projection data. Operations between matrices A and P are performed. For the Kronecker product operation, matrix A is represented as:

[0044]

[0045] Vector θ can be represented as:

[0046] θ=[κ T ,b T ] T

[0047] Where κ and b are the slope and intercept images of the Patlak curve to be reconstructed, respectively, and the symbol T represents matrix transpose. and These are the blood input functions C corresponding to the current dynamic PET imaging task. p The decaying integral function of the time integral of (t) and C p The decay integral function of (t) can be expressed as follows:

[0048]

[0049] and

[0050]

[0051] Based on formula The iterative formula for solving the parametric image θ using the Maximum Likelihood Expectation Maximization (ML-EM) algorithm can be written as:

[0052]

[0053] The Patlak slope image κ and the final image b are integrated into a single target image for a one-time solution.

[0054] See Figure 1 The indirect method yielded a slope image κ with a PSNR of 26.6289 and an intercept image b with a PSNR of 24.5197, indicating significant errors and low image quality. The direct method yielded a slope image κ with a PSNR of 25.6658 and an intercept image b with a PSNR of 20.0284, also failing to meet the required image quality. The method of this invention reconstructs a slope image κ with a PSNR of 28.0636 and an intercept image b with a PSNR of 22.2039, exhibiting high image quality and superior performance.

[0055] This invention employs a method to decompose the parametric imaging linear equation obtained by coupling a blood flow physiology model with the linear equation. The result is that the right-hand side of the linear equation becomes three terms: a slope image term, an intercept image term, and a random event term. The slope image and intercept image are alternately updated using the iterative formula of the Expectation-Maximization (EM) algorithm. The dynamic PET parametric images reconstructed using this method show a significant improvement in image quality compared to parametric images obtained through indirect calculations and direct reconstruction using coupled linear equations. Furthermore, this invention decomposes the coupled linear equation during implementation, and the equivalent imaging system matrix used in subsequent iterations... and Comparing the equivalent imaging system matrix in the original linear equation The matrix size has been reduced by half, which effectively reduces the computational load on the computer when the amount of data in imaging tasks is large.

[0056] The present invention proposes a method to reconstruct the Patlak slope image κ and intercept image b in a linear equation in an alternating iterative manner. This greatly reduces the mutual interference between the κ and b images in the iterative calculation, resulting in a reconstructed image with higher image quality, which is more conducive to subsequent diagnosis and analysis.

[0057] The method of this invention is not limited to dynamic PET imaging of the human brain; it is also applicable to dynamic PET imaging analysis of the chest, liver, or kidneys. The method of this invention can also be extended to whole-body dynamic PET imaging analysis.

[0058] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm, characterized in that, include: The parametric image imaging linear equation obtained by coupling the blood flow physiology model with the imaging linear equation is decomposed, and the linear equation is: in, and These are the blood input functions corresponding to the current dynamic PET imaging task. Time integral function and The decay integral function; For the imaging system matrix; For scattering and random coincidence time in the projected data; For the Kronecker product operation; and These are the slope image and intercept image of the Patlak curve to be reconstructed, respectively. Reconstruct the target image { , Decomposed into two target images { }and{ The EM iterative image reconstruction algorithm is used to obtain the reconstructed slope image by alternately iterating the slope image κ and the intercept image b using the EM iterative image reconstruction algorithm. With intercept image The slope image κ iteration formula is: The iterative formula for the intercept image b is: Where N is the number of pixels in the target parameter image. It is a column vector of length N with all elements equal to 1; T represents the matrix transpose.

2. The dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm according to claim 1, characterized in that, The time integral function Represented as: Where n represents a certain time frame. This represents the start time of time frame n; Let n be the end time of time frame n; For integration time; The time variable for the integration of the inner function; The decay constant is used to label isotopes.

3. The dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm according to claim 1, characterized in that, The attenuation integral function Represented as: 。 4. The dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm according to claim 1, characterized in that, The EM iterative image reconstruction algorithm adopts an alternating iterative formula. After the iterative calculation reaches stable convergence, the directly reconstructed Patlak curve reconstruction slope image κ and intercept image b are obtained.

5. The dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm according to claim 1, characterized in that, The algorithm includes dynamic PET parametric images of the human brain, chest, liver, kidneys, or whole body.

6. The dynamic PET parametric image partial reconstruction algorithm based on the EM algorithm according to claim 1, characterized in that, The algorithm reconstructed a slope image κ with a PSNR value of 28.0636 and an intercept image b with a PSNR value of 22.2039.

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