CN112288762B - A Discrete Iterative Reconstruction Method for Limited Angle CT Scanning - Google Patents

A Discrete Iterative Reconstruction Method for Limited Angle CT Scanning Download PDF

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CN112288762B
CN112288762B CN202011100141.2A CN202011100141A CN112288762B CN 112288762 B CN112288762 B CN 112288762B CN 202011100141 A CN202011100141 A CN 202011100141A CN 112288762 B CN112288762 B CN 112288762B
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黄魁东
杨富强
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Northwestern Polytechnical University
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Abstract

The invention provides a discrete iterative reconstruction method of limited angle CT scanning, which can adaptively acquire optimal gray information and a segmentation threshold according to an initial reconstruction image of limited scanning projection, improve edge contour distortion caused by limited angle reconstruction and finish high-quality reconstruction. The method provided by the invention is suitable for the limited angle CT projection reconstruction of the measured object with any complex structure, has good reliability, stability and universality, can reduce reconstruction artifacts and image contour distortion to a great extent, and obviously improves the limited angle CT scanning reconstruction quality.

Description

一种有限角度CT扫描的离散迭代重建方法A discrete iterative reconstruction method for finite-angle CT scanning

技术领域Technical Field

本发明涉及一种有限角度CT扫描的离散迭代重建方法，属于医学CT成像和工业CT无损检测技术领域。The invention relates to a discrete iterative reconstruction method for limited-angle CT scanning, and belongs to the technical field of medical CT imaging and industrial CT nondestructive testing.

背景技术Background Art

计算机断层成像(Computed Tomography,CT)作为一种先进的医学成像和工业无损检测技术，可以在不破坏物体的前提下探测其内部的缺陷或者对内部尺寸进行测量，成像直观，分辨率高，在复杂对象的无损检测方面具有独特的优势，如用于医学诊断和治疗、安全检查以及产品质量检测控制等。Computed Tomography (CT) is an advanced medical imaging and industrial non-destructive testing technology that can detect internal defects or measure internal dimensions without destroying the object. It has intuitive imaging and high resolution, and has unique advantages in non-destructive testing of complex objects, such as medical diagnosis and treatment, safety inspections, and product quality inspection and control.

实际X射线成像检测过程中受各种因素影响，医学领域通常考虑病人的健康，以尽量减少病人的照射剂量或缩短扫描时间为准则，工业领域检测现场往往受检测目标的几何结构、探测器大小、检测空间、设备条件等限制而无法进行完整扫描，因此有限角度扫描重建成为CT检测技术关注的焦点。有限角度CT扫描角度范围小于精确重建的理论要求，属于不完全投影重建问题，直接重建结果表现为结构不完整、特定角度边界模糊、对比度分辨力低、重建伪影严重等不足，给CT图像诊断与缺陷识别等应用带来巨大困难，因此实现有限角度CT扫描重建高质量成像技术尤为重要。The actual X-ray imaging detection process is affected by various factors. In the medical field, the health of the patient is usually considered, and the patient's radiation dose or scanning time is minimized as the principle. In the industrial field, the detection site is often limited by the geometric structure of the detection target, the size of the detector, the detection space, the equipment conditions, etc., and it is impossible to perform a complete scan. Therefore, limited angle scanning and reconstruction has become the focus of CT detection technology. The scanning angle range of limited angle CT is smaller than the theoretical requirement for accurate reconstruction, which belongs to the problem of incomplete projection reconstruction. The direct reconstruction results are manifested in incomplete structure, blurred boundaries at specific angles, low contrast resolution, and serious reconstruction artifacts. It brings great difficulties to applications such as CT image diagnosis and defect recognition. Therefore, it is particularly important to realize limited angle CT scanning and reconstruction of high-quality imaging technology.

为了解决CT有限角度扫描重建问题，一些先验信息，如非负性、稀疏性、轮廓或边界信息等常被用来作为求解该问题的约束条件。目前，现有的有限角度CT重建算法主要包括两种思路：一种是采用投影数据恢复的方法，通过插值或空间变换等方法对缺失的投影数据进行补充；另一种是采用迭代法，在重建过程中根据某些已知条件对图像施加约束限制，如重建图像非负有界、重建图像区域有限、投影图像的对称性、CAD设计模型、梯度稀疏、TV约束或结构材质上的一些约束等。迭代类算法对解决不完全投影问题更加有效和实用，通过对待重建图像的先验知识转化为约束条件，将CT图像重建问题转化为求解具有约束条件的优化问题，可以通过一系列数学手段进行求解。研究发现在迭代类算法重建的过程中引入适当的约束条件和先验知识可以从更少的投影数据恢复图像，提高重建图像的精度，增加算法对噪声的鲁棒性，对于改善有限投影重建取得了显著的研究成果。根据图像梯度的稀疏性，近年来，人们发现利用待重建物体材质有限的事实，将离散灰度值作为先验知识引入重建约束，可以从更少的投影数据恢复图像，提高重建图像的精度，越来越多的人开始关注离散代数重建技术。总的来说，不完全投影数据的图像重建算法一直是图像处理领域的研究热点。离散迭代将灰度信息作为约束引入重建过程，相比于其他迭代类重建算法，在成像质量上有了很大的提高，但是在实际应用中主要技术缺点包括：In order to solve the problem of CT limited angle scanning reconstruction, some prior information, such as non-negativity, sparsity, contour or boundary information, is often used as a constraint to solve the problem. At present, the existing limited angle CT reconstruction algorithms mainly include two ideas: one is to use the projection data recovery method to supplement the missing projection data through interpolation or spatial transformation; the other is to use the iterative method to impose constraints on the image according to certain known conditions during the reconstruction process, such as the non-negative boundedness of the reconstructed image, the limited area of the reconstructed image, the symmetry of the projection image, the CAD design model, the gradient sparsity, the TV constraint or some constraints on the structural material. Iterative algorithms are more effective and practical for solving the incomplete projection problem. By converting the prior knowledge of the reconstructed image into constraints, the CT image reconstruction problem is converted into an optimization problem with constraints, which can be solved by a series of mathematical methods. Studies have found that introducing appropriate constraints and prior knowledge in the reconstruction process of iterative algorithms can restore images from less projection data, improve the accuracy of the reconstructed image, and increase the robustness of the algorithm to noise. Significant research results have been achieved in improving limited projection reconstruction. Based on the sparsity of image gradients, in recent years, people have found that by using the fact that the material of the object to be reconstructed is limited and introducing discrete grayscale values as prior knowledge into the reconstruction constraints, images can be restored from less projection data and the accuracy of the reconstructed image can be improved. More and more people have begun to pay attention to discrete algebraic reconstruction technology. In general, image reconstruction algorithms for incomplete projection data have always been a research hotspot in the field of image processing. Discrete iteration introduces grayscale information as a constraint into the reconstruction process. Compared with other iterative reconstruction algorithms, it has greatly improved the imaging quality. However, the main technical disadvantages in practical applications include:

(1)离散迭代算法实际应用中的先验灰度信息往往难以准确估计；(1) The prior grayscale information in the practical application of discrete iterative algorithms is often difficult to accurately estimate;

(2)重建算法过程受有限角度范围影响较大，目标函数存在局部最优解；(2) The reconstruction algorithm process is greatly affected by the limited angle range, and the objective function has a local optimal solution;

(3)离散迭代算法涉及到图像分割，分割阈值的准确性对重建结果影响较大。(3) The discrete iterative algorithm involves image segmentation, and the accuracy of the segmentation threshold has a great impact on the reconstruction results.

综上所述，现有重建算法对投影范围及先验信息有一定要求，有限投影重建精度低，无法满足CT高精准医学成像实际应用要求和工业精密无损检测需求。In summary, the existing reconstruction algorithms have certain requirements on the projection range and prior information. The limited projection reconstruction accuracy is low and cannot meet the practical application requirements of CT high-precision medical imaging and industrial precision non-destructive testing.

发明内容Summary of the invention

针对有限角度CT扫描重建图像精度低、轮廓误差大、灰度信息难以估计等实际问题，本发明提供一种有限角度CT扫描的离散迭代重建方法，该方法能够根据有限扫描投影的初始重建图像，自适应获取最优灰度信息和分割阈值，改善因有限角度重建引起的边缘轮廓扭曲并完成高质量重建，同时提升重建效率。In view of the practical problems of low image accuracy, large contour error, and difficulty in estimating grayscale information in limited-angle CT scanning reconstruction, the present invention provides a discrete iterative reconstruction method for limited-angle CT scanning. The method can adaptively obtain optimal grayscale information and segmentation threshold based on the initial reconstructed image of the limited scanning projection, improve the edge contour distortion caused by limited-angle reconstruction, complete high-quality reconstruction, and improve the reconstruction efficiency.

本发明解决其技术问题所采用的技术方案包括以下步骤：The technical solution adopted by the present invention to solve the technical problem comprises the following steps:

步骤1：获取有限角度CT扫描投影，根据投影进行重建获得初始图像f0；Step 1: Obtain limited-angle CT scan projections, and reconstruct the initial image f 0 based on the projections;

步骤2：对当前图像f0进行多阈值分割，得到分割阈值τ1,τ2,......,τl；Step 2: Perform multi-threshold segmentation on the current image f 0 to obtain segmentation thresholds τ 1 ,τ 2 ,...,τ l ;

步骤3：计算当前分割图像中不同材质类别的灰度均值，记为μ1,μ2,......,μl，其中下标1,2,......,l对应第l种材质类别；Step 3: Calculate the grayscale mean of different material categories in the current segmented image, denoted as μ 1 ,μ 2 ,...,μ l , where the subscripts 1, 2,..., l correspond to the lth material category;

步骤4：对灰度均值μ1,μ2,......,μl进行校正，得到校正灰度均值

Figure GDA0004124910310000021
Step 4: Correct the grayscale mean μ 1 ,μ 2 ,...,μ l to obtain the corrected grayscale mean
Figure GDA0004124910310000021

步骤5：根据进退法利用L2范数最小化求得优化灰度值，记为

Figure GDA0004124910310000022
Step 5: According to the advance-retreat method, the optimal gray value is obtained by minimizing the L2 norm, which is recorded as
Figure GDA0004124910310000022

步骤6：利用优化灰度值

Figure GDA0004124910310000023
根据进退法利用L2范数最小化求得优化分割阈值
Figure GDA0004124910310000031
Step 6: Optimize grayscale values
Figure GDA0004124910310000023
The optimal segmentation threshold is obtained by minimizing the L2 norm according to the advance-retreat method
Figure GDA0004124910310000031

步骤7：利用阈值

Figure GDA0004124910310000032
对当前图像进行分割，得到分割图像S；Step 7: Using Threshold
Figure GDA0004124910310000032
Segment the current image to obtain a segmented image S;

步骤8：从S中选取边缘点集

Figure GDA0004124910310000033
与固定点集
Figure GDA0004124910310000034
将
Figure GDA0004124910310000035
赋予
Figure GDA0004124910310000036
求取
Figure GDA0004124910310000037
对应的残余投影r，并利用r完成边缘点集更新得到
Figure GDA0004124910310000038
Step 8: Select edge point sets from S
Figure GDA0004124910310000033
With fixed point set
Figure GDA0004124910310000034
Will
Figure GDA0004124910310000035
Endow
Figure GDA0004124910310000036
Seek
Figure GDA0004124910310000037
The corresponding residual projection r is used to complete the edge point set update.
Figure GDA0004124910310000038

步骤9：合并

Figure GDA0004124910310000039
与
Figure GDA00041249103100000310
图像，对图像进行平滑；Step 9: Merge
Figure GDA0004124910310000039
and
Figure GDA00041249103100000310
Image, smooth the image;

步骤10：判断是否满足终止条件，若不满足则跳转至步骤2继续执行，若满足则输出离散迭代重建图像。Step 10: Determine whether the termination condition is met. If not, jump to step 2 to continue execution. If it is met, output the discrete iterative reconstructed image.

在上述步骤4中，对灰度均值μ1,μ2,......,μl进行校正，得到校正灰度均值

Figure GDA00041249103100000311
的具体步骤包括：In the above step 4, the grayscale mean values μ 1 , μ 2 , ..., μ l are corrected to obtain the corrected grayscale mean values
Figure GDA00041249103100000311
The specific steps include:

(1)获取投影权重系数矩阵W＝(wij)N×N，其中N表示重建图像的大小，i,j表示重建图像的像素坐标；(1) Obtaining a projection weight coefficient matrix W = ( wij ) N × N , where N represents the size of the reconstructed image, and i, j represents the pixel coordinates of the reconstructed image;

(2)利用模型

Figure GDA00041249103100000312
计算相对投影误差Δp，其中pij，wij，fij分别表示投影、权重系数、重建图像坐标i,j处的数值；(2) Utilization model
Figure GDA00041249103100000312
Calculate the relative projection error Δp, where p ij , w ij , fij represent the projection, weight coefficient, and the value of the reconstructed image coordinate i, j respectively;

(3)根据模型

Figure GDA00041249103100000313
获得校正的灰度均值。(3) According to the model
Figure GDA00041249103100000313
Get the corrected grayscale mean.

在上述步骤5中，根据进退法利用L2范数最小化求得优化灰度值，记为

Figure GDA00041249103100000314
的具体步骤包括：In step 5 above, the optimal grayscale value is obtained by minimizing the L2 norm according to the advance-retreat method, which is recorded as
Figure GDA00041249103100000314
The specific steps include:

(1)设置步进Δ1，对校正灰度均值

Figure GDA00041249103100000315
按照
Figure GDA00041249103100000316
进行q次进退调整，得到调整灰度均值
Figure GDA00041249103100000317
其中k＝1,2,......l，m＝1,2,......,2q；(1) Set the step Δ 1 to correct the grayscale mean
Figure GDA00041249103100000315
according to
Figure GDA00041249103100000316
Perform q times of forward and backward adjustment to obtain the adjusted grayscale mean
Figure GDA00041249103100000317
Where k = 1, 2, ... l, m = 1, 2, ..., 2q;

(2)将

Figure GDA00041249103100000318
赋予当前分割图像，记为
Figure GDA00041249103100000319
(2)
Figure GDA00041249103100000318
Assign the current segmented image, denoted as
Figure GDA00041249103100000319

(3)对

Figure GDA00041249103100000320
进行前向投影，即
Figure GDA00041249103100000321
使之与实际投影P作差，通过L2范数最小化函数
Figure GDA0004124910310000041
获取优化灰度均值
Figure GDA0004124910310000042
其中W表示投影矩阵。(3) Yes
Figure GDA00041249103100000320
Perform forward projection, that is
Figure GDA00041249103100000321
Make a difference with the actual projection P and minimize the function through the L2 norm
Figure GDA0004124910310000041
Get optimized grayscale mean
Figure GDA0004124910310000042
Where W represents the projection matrix.

在上述步骤6中，交替方向，利用优化灰度值

Figure GDA0004124910310000043
根据进退法利用L2范数最小化求得优化分割阈值
Figure GDA0004124910310000044
的具体步骤包括：In step 6 above, alternate directions and use the optimized grayscale value
Figure GDA0004124910310000043
The optimal segmentation threshold is obtained by minimizing the L2 norm according to the advance and retreat method
Figure GDA0004124910310000044
The specific steps include:

(1)设置步进Δ2，对分割阈值τ1,τ2,......,τl按照

Figure GDA0004124910310000045
进行q次进退调整；得到调整分割阈值
Figure GDA0004124910310000046
其中k＝1,2,......l，m＝1,2,......,2q；(1) Set the step Δ 2 and adjust the segmentation thresholds τ 1 , τ 2 , ..., τ l according to
Figure GDA0004124910310000045
Perform q forward and backward adjustments; get the adjusted segmentation threshold
Figure GDA0004124910310000046
Where k = 1, 2, ... l, m = 1, 2, ..., 2q;

(2)利用

Figure GDA0004124910310000047
对当前图像进行分割，记为
Figure GDA0004124910310000048
(2) Utilization
Figure GDA0004124910310000047
Segment the current image, recorded as
Figure GDA0004124910310000048

(3)对

Figure GDA0004124910310000049
进行前向投影，即
Figure GDA00041249103100000410
使之与实际投影P作差，通过L2范数最小化函数
Figure GDA00041249103100000411
获取优化分割阈值
Figure GDA00041249103100000412
(3) Yes
Figure GDA0004124910310000049
Perform forward projection, that is
Figure GDA00041249103100000410
Make a difference with the actual projection P and minimize the function through the L2 norm
Figure GDA00041249103100000411
Get the optimized segmentation threshold
Figure GDA00041249103100000412

本发明的有益效果是：本发明提供的一种有限角度CT扫描的离散迭代重建方法，适用于任意复杂结构被测对象的有限角度CT扫描重建，方法的可靠性、稳定性、通用性好，能够在很大程度上减少重建伪影和图像轮廓畸变，明显改善有限角度CT扫描重建质量。The beneficial effects of the present invention are as follows: the discrete iterative reconstruction method for limited-angle CT scanning provided by the present invention is suitable for limited-angle CT scanning reconstruction of objects with any complex structure. The method has good reliability, stability and versatility, can greatly reduce reconstruction artifacts and image contour distortion, and significantly improve the reconstruction quality of limited-angle CT scanning.

下面结合附图和具体实施方式对本发明进行详细说明。The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为本发明算法流程图。FIG1 is a flow chart of the algorithm of the present invention.

具体实施方式DETAILED DESCRIPTION

通过现有工业锥束CT设备(X射线源为Comet的MXR-451HP/11，平板探测器为PerkinElmer的XRD 1621AN15 ES)，对单材质工业对象进行连续有限角度范围采样，应用本发明方法对有限投影锥束CT重建方法执行以下步骤：By using the existing industrial cone-beam CT equipment (the X-ray source is Comet's MXR-451HP/11, and the flat-panel detector is PerkinElmer's XRD 1621AN15 ES), a single-material industrial object is continuously sampled in a limited angle range, and the limited projection cone-beam CT reconstruction method is applied to perform the following steps:

步骤1：通过工业锥束CT设备，选择射线源电压200kV和电流1.6mA，扫描几何参数为：射线源到探测器距离1212.6mm，射线源到旋转中心距离925.1mm，重建分辨率为512×512；对单材质工业零件在0°～180°范围内获取CT投影90幅投影，选择迭代重建SIRT算法得到初始图像f0。Step 1: Using industrial cone-beam CT equipment, select the source voltage of 200 kV and the current of 1.6 mA, the scanning geometric parameters are: the distance from the source to the detector is 1212.6 mm, the distance from the source to the rotation center is 925.1 mm, and the reconstruction resolution is 512×512; obtain 90 CT projections within the range of 0° to 180° for single-material industrial parts, and select the iterative reconstruction SIRT algorithm to obtain the initial image f 0 .

步骤2：对当前图像f0利用OTSU聚类算法进行分割，得到分割阈值τ＝0.136；Step 2: Use the OTSU clustering algorithm to segment the current image f0 and obtain the segmentation threshold τ = 0.136;

步骤3：计算当前分割图像的灰度均值，得到；Step 3: Calculate the grayscale mean of the current segmented image and obtain;

步骤4：对灰度均值μ＝0.272进行校正，得到校正灰度均值

Figure GDA00041249103100000413
其具体步骤包括：Step 4: Correct the grayscale mean μ = 0.272 to obtain the corrected grayscale mean
Figure GDA00041249103100000413
The specific steps include:

(1)获取投影权重系数矩阵W＝(wij)N×N，其中N＝512表示重建图像的大小，i,j表示重建图像的像素坐标；(1) Obtaining a projection weight coefficient matrix W = ( wij ) N × N , where N = 512 represents the size of the reconstructed image, and i, j represents the pixel coordinates of the reconstructed image;

(2)利用模型

Figure GDA0004124910310000051
计算相对投影误差Δp＝0.281，其中pij，wij，fij分别表示投影、权重系数、重建图像坐标i,j处的数值；(2) Utilization model
Figure GDA0004124910310000051
Calculate the relative projection error Δp=0.281, where p ij , w ij , fij represent the projection, weight coefficient, and the value of the reconstructed image coordinate i, j respectively;

(3)根据模型

Figure GDA0004124910310000052
获得校正的灰度均值。(3) According to the model
Figure GDA0004124910310000052
Get the corrected grayscale mean.

步骤5：根据进退法利用L2范数最小化求得优化灰度值

Figure GDA0004124910310000053
其体步骤包括：Step 5: Use the L2 norm minimization method to obtain the optimal grayscale value
Figure GDA0004124910310000053
The steps include:

(1)设置步进Δ1＝0.025，对校正灰度均值

Figure GDA0004124910310000054
按照
Figure GDA0004124910310000055
进行2次进退调整，得到调整灰度均值
Figure GDA0004124910310000056
其中m＝1,2,3,4；(1) Set the step Δ 1 = 0.025 to correct the grayscale mean
Figure GDA0004124910310000054
according to
Figure GDA0004124910310000055
Perform two forward and backward adjustments to obtain the adjusted grayscale mean
Figure GDA0004124910310000056
Where m = 1, 2, 3, 4;

(2)将

Figure GDA0004124910310000057
赋予当前分割图像，记为
Figure GDA0004124910310000058
(2)
Figure GDA0004124910310000057
Assign the current segmented image, denoted as
Figure GDA0004124910310000058

(3)对

Figure GDA0004124910310000059
进行前向投影，即
Figure GDA00041249103100000510
使之与实际投影P作差，通过L2范数最小化函数
Figure GDA00041249103100000511
获取优化灰度均值
Figure GDA00041249103100000512
其中W表示投影矩阵。(3) Yes
Figure GDA0004124910310000059
Perform forward projection, that is
Figure GDA00041249103100000510
Make a difference with the actual projection P and minimize the function through the L2 norm
Figure GDA00041249103100000511
Get optimized grayscale mean
Figure GDA00041249103100000512
Where W represents the projection matrix.

步骤6：利用优化灰度值

Figure GDA00041249103100000513
根据进退法利用L2范数最小化求得优化分割阈值
Figure GDA00041249103100000523
的具体步骤包括：Step 6: Optimize grayscale values
Figure GDA00041249103100000513
The optimal segmentation threshold is obtained by minimizing the L2 norm according to the advance-retreat method
Figure GDA00041249103100000523
The specific steps include:

(1)设置步进Δ2＝0.005，对分割阈值τ＝0.136按照

Figure GDA00041249103100000514
进行2次进退调整；得到调整分割阈值
Figure GDA00041249103100000515
其中m＝1,2,3,4；(1) Set the step Δ 2 = 0.005, and the segmentation threshold τ = 0.136 according to
Figure GDA00041249103100000514
Perform two forward and backward adjustments to obtain the adjusted segmentation threshold
Figure GDA00041249103100000515
Where m = 1, 2, 3, 4;

(2)利用

Figure GDA00041249103100000516
对当前图像进行分割，记为
Figure GDA00041249103100000517
(2) Utilization
Figure GDA00041249103100000516
Segment the current image, recorded as
Figure GDA00041249103100000517

(3)对

Figure GDA00041249103100000518
进行前向投影，即
Figure GDA00041249103100000519
使之与实际投影P作差，通过L2范数最小化函数
Figure GDA00041249103100000520
获取优化分割阈值
Figure GDA00041249103100000521
(3) Yes
Figure GDA00041249103100000518
Perform forward projection, that is
Figure GDA00041249103100000519
Make a difference with the actual projection P and minimize the function through the L2 norm
Figure GDA00041249103100000520
Get the optimized segmentation threshold
Figure GDA00041249103100000521

步骤7：利用阈值

Figure GDA00041249103100000522
对当前图像进行分割，得到分割图像S；Step 7: Using Threshold
Figure GDA00041249103100000522
Segment the current image to obtain a segmented image S;

步骤8：选择3×3的灰度窗口从分割图像S中选取边缘点集

Figure GDA0004124910310000061
与固定点集
Figure GDA0004124910310000062
将
Figure GDA0004124910310000063
赋予
Figure GDA0004124910310000064
求取
Figure GDA0004124910310000065
对应的残余投影r，并利用r完成边缘点集更新得到
Figure GDA0004124910310000066
Step 8: Select a 3×3 grayscale window to select edge point sets from the segmented image S
Figure GDA0004124910310000061
With fixed point set
Figure GDA0004124910310000062
Will
Figure GDA0004124910310000063
Endow
Figure GDA0004124910310000064
Seek
Figure GDA0004124910310000065
The corresponding residual projection r is used to complete the edge point set update.
Figure GDA0004124910310000066

步骤9：合并

Figure GDA0004124910310000067
与
Figure GDA0004124910310000068
图像，设定平滑参数0.3，通过模型
Figure GDA0004124910310000069
完成平滑运算；Step 9: Merge
Figure GDA0004124910310000067
and
Figure GDA0004124910310000068
Image, set the smoothing parameter to 0.3, through the model
Figure GDA0004124910310000069
Complete smoothing operation;

步骤10：设置循环迭代次数为100次，判断是否完成，若未完成则跳转至步骤2继续执行，若完成则输出离散迭代重建图像。Step 10: Set the number of loop iterations to 100 and determine whether it is completed. If not, jump to step 2 to continue execution. If completed, output the discrete iterative reconstructed image.

Claims (5)

1. A discrete iteration reconstruction method of limited angle CT scanning is characterized by comprising the following steps:
step 1: acquiring limited angle CT scanning projection, and reconstructing according to the projection to obtain an initial image f 0 ；
Step 2: for the current image f 0 Performing multi-threshold segmentation to obtain a segmentation threshold tau 1 ,τ 2 ,......,τ l ；
Step 3: calculating the gray average value of different material categories in the current segmented image, and recording as mu 1 ,μ 2 ,......,μ l Wherein subscripts 1,2 are assigned to each of the group, l corresponds to the first material class;
step 4: for gray scale average mu 1 ,μ 2 ,......,μ l Correcting to obtain corrected gray average value
Figure FDA0004124910300000011
Step 5: obtaining optimized gray value by L2 norm minimization according to the forward/backward method, and marking as
Figure FDA0004124910300000012
Step 6: using optimized gray values
Figure FDA0004124910300000013
Obtaining optimized segmentation threshold by L2 norm minimization according to a forward-backward method
Figure FDA0004124910300000014
Step 7: using threshold values
Figure FDA0004124910300000015
Dividing the current image to obtain a divided image S;
step 8: selecting an edge point set from S
Figure FDA0004124910300000016
And fixed point set->
Figure FDA0004124910300000017
Will->
Figure FDA0004124910300000018
Endow->
Figure FDA0004124910300000019
Find->
Figure FDA00041249103000000110
Corresponding residual projection r, and finishing edge point set updating by utilizing r to obtain +.>
Figure FDA00041249103000000111
Step 9: merging
Figure FDA00041249103000000112
And->
Figure FDA00041249103000000113
An image, smoothing the image;
step 10: and judging whether the termination condition is met, if not, jumping to the step 2 to continue execution, and if so, outputting a discrete iteration reconstructed image.
2. A method of discrete iterative reconstruction of a limited angle CT scan according to claim 1, wherein: in the step 4, the gray scale average value mu 1 ,μ 2 ,......,μ l Correction is performed by first using a model
Figure FDA00041249103000000114
Calculating the relative projection error Δp and then according to the model +.>
Figure FDA00041249103000000115
Obtaining a corrected gray average value, wherein N represents the size of the reconstructed image; wherein p is ij ，w ij ，f ij The values at projection, weight coefficient, reconstructed image coordinates i, j are represented respectively.
3. A method of discrete iterative reconstruction of a limited angle CT scan according to claim 1, wherein: in the step 5, the optimized gray value is obtained by L2 norm minimization according to the advance-retreat method, and the step delta is firstly set 1 For correcting gray scale average value
Figure FDA0004124910300000021
According to->
Figure FDA0004124910300000022
Performing forward and backward adjustment q times to obtain an adjusted gray level mean +.>
Figure FDA0004124910300000023
Where k=1, 2, &..i.l, m=1, 2, &..2 q; then will->
Figure FDA0004124910300000024
The current segmented image is assigned and recorded as
Figure FDA0004124910300000025
Finally pair->
Figure FDA0004124910300000026
Forward projection, i.e.)>
Figure FDA0004124910300000027
Making it differ from the actual projection P by the L2 norm minimization function +.>
Figure FDA0004124910300000028
Obtaining optimized gray scale average
Figure FDA0004124910300000029
4. A method of discrete iterative reconstruction of a limited angle CT scan according to claim 1, wherein: in said step 6, the directions are alternated, using optimized gray values
Figure FDA00041249103000000210
Obtaining optimized segmentation threshold value by L2 norm minimization according to the forward/backward method>
Figure FDA00041249103000000211
First set step delta 2 Dividing threshold τ 1 ,τ 2 ,......,τ l According to
Figure FDA00041249103000000212
Proceeding q times of advancing and retreatingAdjusting; obtaining an adjusted segmentation threshold +.>
Figure FDA00041249103000000213
Where k=1, 2, &..i.l, m=1, 2, &..2 q; then use->
Figure FDA00041249103000000214
Segmenting the current image and recording as
Figure FDA00041249103000000215
Finally pair->
Figure FDA00041249103000000216
Forward projection, i.e.)>
Figure FDA00041249103000000217
Making it differ from the actual projection P by the L2 norm minimization function +.>
Figure FDA00041249103000000218
Obtaining an optimized segmentation threshold
Figure FDA00041249103000000219
5. A method of discrete iterative reconstruction of a limited angle CT scan according to claim 1, wherein: in this embodiment, a discrete iterative reconstruction method for limited angle CT scan is characterized in that:
(1) The algorithm has good reconstruction results for limited angle reconstruction of single-material and multi-material detection objects;
(2) The reconstruction using sparse sampled projections as limited angle projections is equally applicable.
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