WO2021114306A1 - 一种基于gpu加速的高精度pet重建方法及装置 - Google Patents
一种基于gpu加速的高精度pet重建方法及装置 Download PDFInfo
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- the present invention relates to the field of GPU imaging, in particular to a method and device for high-precision PET reconstruction based on GPU acceleration.
- Small animal PET is a miniaturized imaging machine that displays physiological structures in the clinic, enabling researchers to quantify the biochemical activity in a variety of organs. It has been used in preclinical imaging research, biological and medical basic research, and new radiopharmaceutical development. widely used.
- Iterative reconstruction algorithm is one of the mainstream methods in PET reconstruction. Compared with analytical image reconstruction, it can improve the quality of reconstructed images by performing more accurate physical and statistical modeling of the high-energy photon generation and detection process.
- GPU is a highly parallelized multi-threaded multi-core processor designed to solve image processing tasks, and its floating-point computing power is significantly higher than that of the CPU. More and more researchers use GPU for PET reconstruction calculation.
- Zhou Jian et al. use GPU to calculate the forward projection and back projection functions, which proves that it can greatly save the calculation time.
- the traditional iterative reconstruction method uses the CPU to calculate the system matrix and performs forward and back projection of the estimated image. It is close to the true distribution image in iteration.
- the reconstruction speed depends on the dimension of the input sinogram and the dimension of the generated image, as well as the number of iterations.
- the high-precision PET with DOI function can output the depth information of photons in the crystal, and the resolution is higher than that of general small animal PET. Therefore, the dimensionality of the sinogram is very large, and the calculation time of the traditional algorithm takes several days.
- the embodiments of the present invention provide a high-precision PET reconstruction method and device based on GPU acceleration, so as to at least solve the existing technical problem of long calculation time for PET reconstruction using GPU.
- a high-precision PET reconstruction method based on GPU acceleration which includes the following steps:
- S100 Input an initial estimated image, and perform an orthographic projection operation on the estimated image to obtain an estimated projection;
- the method further includes the steps:
- step S500 Return the input estimated image of the next iteration to step S100 for iterative processing, and the estimated image obtained in the last iteration is the result of the final PET reconstruction.
- the method further includes the steps:
- S001 Preprocess the initial estimated image, perform statistics and merge the initial estimated image, and generate a four-dimensional sinogram that meets the preset requirements.
- Each element of the four-dimensional sinogram represents a type of response line Line Of Response, four-dimensional They are the in-plane distance r from the center of the LOR, the in-plane angle phi, the number of the detector ring that receives the first photon, ring1, and the number of the detector ring that receives the second photon, ring2.
- the intensity value x of each voxel in the image is estimated, and a Poisson distribution A with an expected intensity value x is constructed.
- the mathematical model is:
- k is the number of occurrences of the internal source of each voxel in the image
- e is the natural constant
- y is the actual measured projection value
- the matrix p is related to the geometric structure of the detector and indicates the possibility of being detected by the detector at a certain position
- D is the distance from the center in the plane of the LOR;
- N is the normalization correction matrix
- i is the number of iterations
- T is the matrix transposition
- d is the random correction matrix
- x i is the estimated image
- x i+1 is the result of this iteration and also the input of the next iteration.
- the GPU is used to calculate the p T N, and the normalization correction coefficient is back-projected to obtain the sensitivity map of the sensitivity image.
- the image matrix is bound by the three-dimensional texture memory; in the back projection process, the atomic operation is used to ensure the correctness of the calculation: when the atomic operation is executed, the address is locked, and other parallel threads are not allowed Reading and writing operations to the element corresponding to this address can only wait for the end of the current calculation before starting the next access.
- the calculation process of the method steps are all processed in parallel in the GPU, and the kernel function is calculated in parallel in each thread at the same time; when the LOR is calculated online through the voxel depth, the calculation results are repeated more according to the symmetry of the system geometry. Times used.
- the estimated image is first convolved before the projection and after the corrected image is obtained by back-projection. Specifically, the voxel value of each estimated image is compared with the equivalent system function near the voxel value. After multiplying and adding together, the new voxel position image value is obtained.
- the equivalent system response function H(x,y,z) is a three-dimensional Gauss-like function:
- r, t, and a represent the radial, tangential and axial directions of the coordinate axis, respectively.
- the propagation parameter sigma is estimated in the fitting. After obtaining the values of the three parameters ⁇ r , ⁇ t , and ⁇ a, these three The parameters represent the model of the system response function, ⁇ r , ⁇ t , and ⁇ a represent the propagation parameters in the radial, tangential and axial directions, respectively.
- a high-precision PET reconstruction device based on GPU acceleration including:
- the orthographic projection unit is used to input the initial estimated image, and perform orthographic operation on the estimated image to obtain an estimated projection;
- the comparison unit is used to compare the estimated projection obtained with the actual measured projection to obtain a comparison result
- the back-projection unit is used to perform a back-projection operation on the comparison result to obtain a corrected image
- the iterative unit is used to multiply the corrected image and the corresponding voxel of the original image, and then divide the sensitivity image to complete one iteration, and the resulting image is the input estimated image of the next iteration.
- the initial estimated image is input, and the estimated image is subjected to orthographic projection operation to obtain the estimated projection; the obtained estimated projection is compared with the actual measured projection to obtain the comparison Result: Perform back-projection operation on the comparison result to obtain a corrected image; multiply the corrected image with the corresponding voxel of the original image, and then divide the sensitivity image to complete one iteration, and the resulting image is the input estimated image for the next iteration.
- the iterative reconstruction algorithm of PET is improved by GPU acceleration strategy, and fast calculation is performed to obtain high-resolution, high-precision three-dimensional PET images.
- Fig. 1 is a flowchart of a high-precision PET reconstruction method based on GPU acceleration according to the present invention
- FIG. 3 is a graph showing the axial translation characteristics of LOR in the high-precision PET reconstruction method based on GPU acceleration of the present invention
- FIG. 5 is an overall flowchart of the high-precision PET reconstruction method based on GPU acceleration according to the present invention
- Fig. 6 is a block diagram of a high-precision PET reconstruction device based on GPU acceleration according to the present invention.
- Fig. 7 is a preferred module diagram of a high-precision PET reconstruction device based on GPU acceleration of the present invention.
- a high-precision PET reconstruction method based on GPU acceleration is provided.
- the method includes the following steps:
- S100 Input an initial estimated image, and perform an orthographic projection operation on the estimated image to obtain an estimated projection;
- an initial estimated image is input, and the estimated image is subjected to an orthographic projection operation to obtain an estimated projection; the obtained estimated projection is compared with the actual measured projection to obtain a comparison result; Perform a back-projection operation on the comparison result to obtain a corrected image; multiply the corrected image with the corresponding voxel of the original image, and then divide the sensitivity image to complete one iteration, and the resulting image is the input estimated image for the next iteration.
- the iterative reconstruction algorithm of PET is improved by GPU acceleration strategy, and fast calculation is performed to obtain high-resolution, high-precision three-dimensional PET images.
- the method further includes the steps:
- step S500 Return the input estimated image of the next iteration to step S100 for iterative processing, and the estimated image obtained in the last iteration is the result of the final PET reconstruction.
- the method further includes the steps:
- S001 Perform preprocessing on the initial estimated image, perform statistics and merge on the initial estimated image, and generate a four-dimensional chord diagram that meets the preset requirements.
- the high-precision PET reconstruction method based on GPU acceleration proposed in the present invention is divided into preprocessing and iterative reconstruction.
- the preprocessing process is to count and merge all events obtained by the detector to generate a four-dimensional sinogram (Sinogram) that meets the requirements.
- Each element of the chord diagram represents a type of response line (Line Of Response).
- the four dimensions are the distance from the center of the LOR in the plane (r), the angle in the plane (phi), and the number of the detector ring that receives the first photon (ring1). ), the number of the detector ring that receives the second photon (ring2).
- the principle of iterative reconstruction is that the PET data y conforms to the variables of the Poisson distribution and is composed of all the LORs collected by the system. Each LOR represents the sum of the signals generated by its source.
- the present invention needs to estimate the endogenous intensity x of each voxel in the image, and construct a Poisson distribution A whose expectation is x, and its mathematical model is:
- k is the number of occurrences of the internal source of each voxel in the image
- e is the natural constant
- y is the actual measured projection value
- the matrix p is related to the geometric structure of the detector and indicates the possibility of being detected by the detector at a certain position
- D is the distance from the center in the plane of the LOR.
- the present invention needs to find a distribution of x’, x’ is a variable, and its dimension is the same as x, so that P(y
- the maximum expectation method can be used to find the extreme points of formula (4). It is usually used to estimate the parameters of a probability model containing hidden variables or missing data. It is an optimization algorithm for maximum likelihood estimation through iteration. The convergence of the algorithm can be Ensure that the iteration at least approximates the local maximum. Without considering attenuation and scattering:
- N is the normalization correction matrix
- i is the number of iterations
- T is the matrix transposition
- d is the random correction matrix
- x i is the estimated image
- x i+1 is the result of this iteration and also the input of the next iteration.
- the GPU When operating in the computer, input the initial estimated image. Generally, the voxel value of each image is 1. Before the iteration, the GPU is used to calculate the p T N, that is, the normalization correction coefficient is back-projected to obtain the sensitivity image (sensitivity image). map). According to the formula, perform the forward projection operation on the estimated image x i . The estimated projection obtained is compared with the actual measured projection, and the result obtained is subjected to the back projection operation. Then the obtained image is multiplied by the corresponding voxel of the original image, and then divided by the sensitivity map , After completing one iteration, the image obtained is the input estimated image of the next iteration. All processes are calculated in the GPU.
- the principle of GPU parallelism is to calculate the kernel function in parallel in each thread at the same time.
- the estimated image obtained in the last iteration is the final reconstruction result.
- the fast floating-point calculations of the GPU can be fully utilized.
- the present invention uses a three-dimensional texture memory to bind the image matrix.
- Texture memory is a special form of CUDA global memory. Its read and write operations are performed through a special texture cache, which allows multiple threads to access it at the same time, and the access speed is very fast.
- the present invention uses atomic operations to ensure the correctness of the calculation.
- the atomic operation is executed, the address is locked, and other parallel threads are not allowed to read and write the element corresponding to the address, and can only wait for the end of the current calculation to start the next access, ensuring safety.
- the GPU’s simultaneous parallel stream processors are about 1000 to 3000, which means that in fact the GPU can only calculate so many threads at the same time. Therefore, for high-resolution PET systems containing DOI information, it is impossible to calculate all the allocated threads in parallel at the same time. In fact, calculations are performed batch by batch, and this process is serial.
- the method of the present invention utilizes the symmetry of the geometric structure of the system to reduce the total number of LORs that need to be calculated, thereby reducing the number of parallel threads and speeding up the calculation time.
- the consideration of symmetry is that in the process of projection and back-projection, that is, when calculating the depth of LOR through voxels online, the calculation results can be used repeatedly according to the geometric structure characteristics of the system.
- the PET reconstruction method proposed in the present invention not only corrects the uniformity and random events, but also adds the correction of the physical effects of the system's positron free path and photon nonlinearity.
- the method is to measure the point source in the system to reconstruct the image in the system. Function, using these physical effects to the point source image to be equivalent.
- the equivalent system response function H(x,y,z) is a three-dimensional Gauss-like function:
- r, t, and ⁇ represent the radial, tangential, and axial directions of the coordinate axis.
- the propagation parameter sigma is estimated in the fitting. After obtaining the values of the three parameters ⁇ r , ⁇ t , and ⁇ a, these three The parameters can represent the model of the system response function. ⁇ r , ⁇ t , and ⁇ a represent the propagation parameters in the radial, tangential and axial directions, respectively. In the iterative reconstruction process, the estimated image must be convolved before projection.
- the voxel value of each estimated image is multiplied by the equivalent system response function near the voxel value and then added to obtain a new The image value of the voxel position.
- the present invention collects multiple point sources in different positions of the system, and selects representative images among them for fitting to obtain the system response function.
- the overall flow chart of the reconstruction method is shown in Figure 5.
- a high-precision PET reconstruction device based on GPU acceleration See FIG. 6, including:
- the orthographic projection unit 201 is used to input an initial estimated image, and perform an orthographic projection operation on the estimated image to obtain an estimated projection;
- the comparing unit 202 is configured to compare the obtained estimated projection with the actual measured projection to obtain a comparison result
- the back-projection unit 203 is configured to perform a back-projection operation on the comparison result to obtain a corrected image
- the iteration unit 204 is configured to multiply the corrected image and the corresponding voxel of the original image, and then divide the sensitivity image to complete one iteration, and the obtained image is the input estimated image of the next iteration.
- an initial estimated image is input, and the estimated image is subjected to an orthographic projection operation to obtain an estimated projection; the obtained estimated projection is compared with the actual measured projection to obtain a comparison result; Perform a back-projection operation on the comparison result to obtain a corrected image; multiply the corrected image with the corresponding voxel of the original image, and then divide the sensitivity image to complete one iteration, and the resulting image is the input estimated image for the next iteration.
- the iterative reconstruction algorithm of PET is improved by GPU acceleration strategy, and fast calculation is performed to obtain high-resolution, high-precision three-dimensional PET images.
- the device further includes:
- the returning iterative unit 205 is used to return the input estimated image of the next iteration to the orthographic projection unit 201 for iterative processing, and the estimated image obtained in the last iteration is the result of the final PET reconstruction.
- the device further includes:
- the preprocessing unit 200 is configured to preprocess the initial estimated image, perform statistics and merge the initial estimated image, and generate a four-dimensional chord diagram that meets the preset requirements.
- the GPU-accelerated high-precision PET reconstruction device proposed in the present invention is divided into preprocessing and iterative reconstruction.
- the preprocessing unit 200 the preprocessing process is to count and merge all events obtained by the detector to generate a four-dimensional chord diagram that meets the requirements ( Sinogram), each element of the four-dimensional sinogram represents a type of line of response (Line Of Response).
- the four dimensions are the distance from the center in the LOR plane (r), the in-plane angle (phi), and the detection of the first photon received.
- the principle of iterative reconstruction is that the PET data y conforms to the variables of the Poisson distribution and is composed of all the LORs collected by the system. Each LOR represents the sum of the signals generated by its source.
- the present invention needs to estimate the endogenous intensity x of each voxel in the image, and construct a Poisson distribution A whose expectation is x, and its mathematical model is:
- k is the number of occurrences of the internal source of each voxel in the image
- e is the natural constant
- y is the actual measured projection value
- the matrix p is related to the geometric structure of the detector and indicates the possibility of being detected by the detector at a certain position
- D is the distance from the center in the plane of the LOR.
- the present invention needs to find a distribution of x’ to make P(y
- x’ is a variable whose dimension is the same as x
- the likelihood function is:
- the maximum expectation method can be used to find the extreme points of formula (4). It is usually used to estimate the parameters of a probability model containing hidden variables or missing data. It is an optimization algorithm for maximum likelihood estimation through iteration. The convergence of the algorithm can be Ensure that the iteration at least approximates the local maximum. Without considering attenuation and scattering:
- N is the normalization correction matrix
- i is the number of iterations
- T is the matrix transposition
- d is the random correction matrix
- x i is the estimated image
- x i+1 is the result of this iteration and also the input of the next iteration.
- the GPU When operating in the computer, input the initial estimated image. Generally, the voxel value of each image is 1. Before the iteration, the GPU is used to calculate the p T N, that is, the normalization correction coefficient is back-projected to obtain the sensitivity image (sensitivity image). map). According to the formula, perform the forward projection operation on the estimated image x i . The estimated projection obtained is compared with the actual measured projection, and the result obtained is subjected to the back projection operation. Then the obtained image is multiplied by the corresponding voxel of the original image, and then divided by the sensitivity map , After completing one iteration, the image obtained is the input estimated image of the next iteration. All processes are calculated in the GPU.
- the principle of GPU parallelism is to calculate the kernel function in parallel in each thread at the same time.
- the estimated image obtained in the last iteration is the final reconstruction result.
- the fast floating-point calculations of the GPU can be fully utilized.
- the present invention uses a three-dimensional texture memory to bind the image matrix.
- Texture memory is a special form of CUDA global memory. Its read and write operations are performed through a special texture cache, which allows multiple threads to access it at the same time, and the access speed is very fast.
- the present invention uses atomic operations to ensure the correctness of the calculation.
- the atomic operation is executed, the address is locked, and other parallel threads are not allowed to read and write the element corresponding to the address, and can only wait for the end of the current calculation to start the next access, ensuring safety.
- the GPU’s simultaneous parallel stream processors are about 1000 to 3000, which means that in fact the GPU can only calculate so many threads at the same time. Therefore, for high-resolution PET systems containing DOI information, it is impossible to calculate all the allocated threads in parallel at the same time. In fact, calculations are performed batch by batch, and this process is serial.
- the method of the present invention utilizes the symmetry of the geometric structure of the system to reduce the total number of LORs that need to be calculated, thereby reducing the number of parallel threads and speeding up the calculation time.
- the consideration of symmetry is that in the process of projection and back-projection, that is, when calculating the depth of LOR through voxels online, the calculation results can be used repeatedly according to the geometric structure characteristics of the system.
- the PET reconstruction method proposed in the present invention not only corrects the uniformity and random events, but also adds the correction of the physical effects of the system's positron free path and photon nonlinearity.
- the method is to measure the point source in the system to reconstruct the image in the system. Function, using these physical effects to the point source image to be equivalent.
- the equivalent system response function H(x,y,z) is a three-dimensional Gauss-like function:
- r, t, and a represent the radial, tangential and axial directions of the coordinate axis, respectively.
- the propagation parameter sigma is estimated in the fitting. After obtaining the values of the three parameters ⁇ r , ⁇ t , and ⁇ a, these three The parameters can represent the model of the system response function. ⁇ r , ⁇ t , and ⁇ a represent the propagation parameters in the radial, tangential and axial directions, respectively. In the iterative reconstruction process, the estimated image must be convolved before projection.
- the voxel value of each estimated image is multiplied by the equivalent system response function near the voxel value and then added to obtain a new The image value of the voxel position.
- the present invention collects multiple point sources in different positions of the system, and selects representative images among them for fitting to obtain the system response function.
- the overall flow chart of the reconstruction method is shown in Figure 5.
- the present invention uses the iterative reconstruction algorithm in GPU calculations, and considers the geometric symmetry of the system and the CUDA C texture memory acceleration method, and proposes a fast and high-precision high-precision PET reconstruction method based on GPU acceleration.
- Parallel acceleration and the geometric characteristics of the detector parallelize the reconstruction of ultra-large-scale data to perform high-precision and rapid reconstruction, that is, through the GPU acceleration strategy to improve the iterative reconstruction algorithm of PET and perform rapid calculations to obtain high-resolution, high-precision 3D PET image.
- the reconstructed image can be obtained by simply inputting the data collected by the PET system. Improve reconstruction speed and image resolution.
- the protection points of the method and device are: a GPU-based method for accelerating high-definition iterative reconstruction using geometric symmetry; and a system response function calculation method based on actual collected data.
- the disclosed technical content can be implemented in other ways.
- the system embodiment described above is only illustrative.
- the division of units may be a logical function division, and there may be other divisions in actual implementation.
- multiple units or components may be combined or integrated into Another system, or some features can be ignored, or not implemented.
- the displayed or discussed mutual coupling or direct coupling or communication connection may be indirect coupling or communication connection through some interfaces, units or modules, and may be in electrical or other forms.
- the units described as separate components may or may not be physically separate, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple units. Some or all of the units may be selected according to actual needs to achieve the objectives of the solutions of the embodiments.
- the functional units in the various embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units may be integrated into one unit.
- the above-mentioned integrated unit can be implemented in the form of hardware or software functional unit.
- the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer readable storage medium.
- the technical solution of the present invention essentially or the part that contributes to the existing technology or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium.
- a computer device which can be a personal computer, a server, or a network device, etc.
- the aforementioned storage media include: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and other media that can store program codes. .
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Claims (10)
- 一种基于GPU加速的高精度PET重建方法,其特征在于,包括以下步骤:S100:输入初始的估计图像,对估计图像进行正投影操作,获得估计投影;S200:将获得的估计投影与实际测量投影作比较,获得比较结果;S300:对比较结果进行反投影操作,获得校正图像;S400:将校正图像与原始图像对应体素相乘,然后除敏感度图像,完成一次迭代,得到的图像就是下一次迭代的输入估计图像。
- 根据权利要求1所述的基于GPU加速的高精度PET重建方法,其特征在于,所述方法还包括步骤:S500:将下一次迭代的输入估计图像返回步骤S100进行迭代处理,最后一次迭代获得的估计图像即是最终PET重建的结果。
- 根据权利要求2所述的基于GPU加速的高精度PET重建方法,其特征在于,所述方法还包括步骤:S001:对初始的估计图像进行预处理,将初始的估计图像进行统计和合并,生成符合预设要求的四维弦图Sinogram,该四维弦图的每一个元素代表一类响应线Line Of Response,四维分别是LOR的平面内距中心距离r、平面内角度phi、接收第一个光子的探测器环编号ring1、接收第二个光子的探测器环编号ring2。
- 根据权利要求3所述的基于GPU加速的高精度PET重建方法,其特征在于,在迭代过程中估计出图像中每个体素内源的强度值x,构建一个期望是强度值x的泊松分布A,其数学模型为:x和y的期望的关系是:其中,k是图像中每个体素内源的出现次数,e是自然常数,y是实际测量的投影值,矩阵p是与探测器几何结构相关的表示在某一位置被探测器探测到的 可能性,d是LOR的平面内距中心距离;在PET重建中找到一个x’的分布,使得P(y|x’)最大,x’是一个变量,其维度与x相同,似然函数为:利用对数似然函数极值点不变的特性,将公式(2)和公式(3)结合成l(y|x)=logL(y|x),其中:使用最大期望方法求公式(4)的极值点,在不考虑衰减和散射的情况下:其中N是均一化校正矩阵,i是迭代次数,T表示矩阵转置,d是随机校正矩阵,x i为估计图像,x i+1是本次迭代的结果,也是下一次迭代的输入。
- 根据权利要求4所述的基于GPU加速的高精度PET重建方法,其特征在于,进行迭代前先利用GPU计算p TN,把均一化校正系数做反投影,得到敏感度图像sensitivity map。
- 根据权利要求5所述的基于GPU加速的高精度PET重建方法,其特征在于,在正投影过程中,使用三维纹理内存对图像矩阵进行绑定;在反投影过程中,用原子操作来确保计算的正确性:原子操作执行时,锁定该地址,其他并行线程不允许对该地址对应的元素进行读取和写入操作,只能等待当前计算结束才能开始下一次访问。
- 根据权利要求6所述的基于GPU加速的高精度PET重建方法,其特征在于,所述方法步骤的计算过程均在GPU中并行处理,将核函数在每个线程中同时并行计算;在线计算LOR穿过体素深度时,根据系统几何结构的对称性,将计算结果重复多次使用。
- 根据权利要求7所述的基于GPU加速的高精度PET重建方法,其特征在于,迭代重建过程中,在进行投影之前及反投影得到校正图像后先对估计图像进行卷积操作,具体是将每个估计图像体素值与该体素值附近的等效系统函数相乘后相加,得到新的该体素位置图像值。
- 一种基于GPU加速的高精度PET重建装置,其特征在于,包括:正投影单元,用于输入初始的估计图像,对估计图像进行正投影操作,获得估计投影;比较单元,用于将获得的估计投影与实际测量投影作比较,获得比较结果;反投影单元,用于对比较结果进行反投影操作,获得校正图像;迭代单元,用于将校正图像与原始图像对应体素相乘,然后除敏感度图像,完成一次迭代,得到的图像就是下一次迭代的输入估计图像。
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