CN112288762B - Discrete iteration reconstruction method for limited angle CT scanning - Google Patents
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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
Technical Field
The invention relates to a discrete iteration reconstruction method for limited angle CT scanning, belonging to the technical field of medical CT imaging and industrial CT nondestructive testing.
Background
Computer tomography (Computed Tomography, CT) is used as an advanced medical imaging and industrial nondestructive detection technology, can detect defects in the object or measure internal dimensions without damaging the object, is visual in imaging and high in resolution, and has unique advantages in nondestructive detection of complex objects, such as medical diagnosis and treatment, safety inspection, product quality detection control and the like.
The actual X-ray imaging detection process is affected by various factors, the health of patients is generally considered in the medical field, the irradiation dose of the patients is reduced as much as possible or the scanning time is shortened as a criterion, the detection site in the industrial field is often limited by the geometric structure of a detection target, the size of a detector, the detection space, the equipment condition and the like, and complete scanning cannot be performed, so that limited-angle scanning reconstruction becomes the focus of attention of CT detection technology. The limited angle CT scanning angle range is smaller than the theoretical requirement of accurate reconstruction, belongs to the problem of incomplete projection reconstruction, and the direct reconstruction result shows the defects of incomplete structure, fuzzy boundary at a specific angle, low contrast resolution, serious reconstruction artifact and the like, and brings great difficulty to CT image diagnosis, defect identification and other applications, so that the realization of the high-quality imaging technology of the limited angle CT scanning reconstruction is particularly important.
To solve the CT limited angle scan reconstruction problem, 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 algorithm mainly comprises two ideas: one is to use projection data recovery method, and supplement the missing projection data by interpolation or space transformation; the other is to apply constraint limits to the image according to some known conditions in the reconstruction process, such as non-negative limitation of the reconstructed image, limited reconstructed image area, symmetry of the projection image, CAD design model, gradient sparsity, TV constraint or some constraints on structural materials, etc. The iterative algorithm is more effective and practical for solving the incomplete projection problem, the prior knowledge of the image to be reconstructed is converted into the constraint condition, the CT image reconstruction problem is converted into the optimization problem with the constraint condition, and the optimization problem can be solved through a series of mathematical means. The research discovers that the image can be recovered from less projection data by introducing proper constraint conditions and priori knowledge in the process of reconstructing the iterative algorithm, the accuracy of the reconstructed image is improved, the robustness of the algorithm to noise is increased, and remarkable research results are obtained for improving the limited projection reconstruction. According to the sparsity of image gradients, in recent years, it has been found that by using the fact that the material of an object to be reconstructed is limited, discrete gray values are introduced as priori knowledge into reconstruction constraints, images can be recovered from fewer projection data, the accuracy of reconstructed images is improved, and more people begin to pay attention to discrete algebraic reconstruction techniques. In general, image reconstruction algorithms for incomplete projection data have been a research hotspot in the field of image processing. The discrete iteration introduces gray information as constraint into the reconstruction process, and compared with other iterative reconstruction algorithms, the imaging quality is greatly improved, but main technical defects in practical application include:
(1) The prior gray information in the practical application of the discrete iterative algorithm is often difficult to accurately estimate;
(2) The reconstruction algorithm process is greatly influenced by a limited angle range, and a local optimal solution exists in the objective function;
(3) The discrete iterative algorithm relates to image segmentation, and the accuracy of a segmentation threshold value has a large influence on a reconstruction result.
In summary, the existing reconstruction algorithm has certain requirements on the projection range and priori information, and the limited projection reconstruction accuracy is low, so that the actual application requirements of CT high-precision medical imaging and the industrial precision nondestructive detection requirements can not be met.
Disclosure of Invention
Aiming at the practical problems of low image accuracy, large contour error, difficult estimation of gray information and the like of limited angle CT scanning reconstruction, the invention provides a discrete iteration reconstruction method of limited angle CT scanning, which can adaptively acquire optimal gray information and a segmentation threshold value according to an initial reconstruction image of limited scanning projection, improve edge contour distortion caused by limited angle reconstruction, finish high-quality reconstruction and improve reconstruction efficiency.
The technical scheme adopted by the invention for solving the technical problems comprises 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
Step 5: obtaining optimized gray value by L2 norm minimization according to the forward/backward method, and marking as
Step 6: using optimized gray values
Obtaining optimized segmentation threshold value by L2 norm minimization according to the forward/backward method>
Step 7: using threshold values
Dividing the current image to obtain a divided image S;
step 8: selecting an edge point set from S
And fixed point set->
Will->
Endow->
Find->
Corresponding residual projection r, and finishing edge point set updating by utilizing r to obtain +.>
Step 9: merging
And->
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.
In the above step 4, the gray scale value μ is averaged 1 ,μ 2 ,......,μ l Correcting to obtain corrected gray average value
The specific steps of (a) include:
(1) Obtaining a projection weight coefficient matrix w= (W) ij ) N×N Where N represents the size of the reconstructed image, i, j represents the pixel coordinates of the reconstructed image;
(2) Using models
Calculating a relative projection error Δp, where p ij ，w ij ，f ij Respectively representing the projection, the weight coefficient and the numerical value at the position of the coordinate i and the position of the coordinate j of the reconstructed image;
(3) According to the model
A corrected gray average value is obtained.
In the above step 5, the optimized gray value is obtained by L2 norm minimization according to the forward/backward method, and is recorded as
The specific steps of (a) include:
(1) Setting the step delta 1 For correcting gray scale average value
According to->
Performing forward and backward adjustment q times to obtain an adjusted gray level mean +.>
Where k=1, 2, &..i.l, m=1, 2, &..2 q; />
(2) Will be
Imparting current segmentationAn image, noted->
(3) For a pair of
Forward projection, i.e.)>
Making it differ from the actual projection P by the L2 norm minimization function +.>
Obtaining optimized gray level mean->
Where W represents the projection matrix.
In the above step 6, the directions are alternated, and the optimized gray value is used
Obtaining optimized segmentation threshold value by L2 norm minimization according to the forward/backward method>
The specific steps of (a) include:
(1) Setting the step delta 2 Dividing threshold τ 1 ,τ 2 ,......,τ l According to
Performing advance and retreat adjustment q times; obtaining an adjusted segmentation threshold +.>
Where k=1, 2, &..i.l, m=1, 2, &..2 q;
(2) By means of
Dividing the current image, and recording as +.>
(3) For a pair of
Forward projection, i.e.)>
Making it differ from the actual projection P by the L2 norm minimization function +.>
Acquiring an optimized segmentation threshold->
The beneficial effects of the invention are as follows: the discrete iterative reconstruction method of the limited angle CT scanning, provided by the invention, is suitable for the limited angle CT scanning 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.
The invention will be described in detail below with reference to the drawings and the detailed description.
Drawings
FIG. 1 is a flow chart of the algorithm of the present invention.
Detailed Description
The method is used for continuously sampling a single-material industrial object in a limited angle range by the existing industrial cone beam CT equipment (the X-ray source is MXR-451HP/11 of Comet, the flat panel detector is XRD 1621an15 ES of Perkinelmer), and the method is used for carrying out the following steps on a limited projection cone beam CT reconstruction method:
step 1: through industrial cone beam CT equipment, the voltage of a ray source is selected to be 200kV, the current is selected to be 1.6mA, and the scanning geometrical parameters are as follows: the distance from the ray source to the detector is 1212.6mm, the distance from the ray source to the rotation center is 925.1mm, and the reconstruction resolution is 512×512; for single material industrial parts, the angle is 0 DEG to the ultra-range90 projections of CT projection are obtained within the range of 180 degrees, and an iterative reconstruction SIRT algorithm is selected to obtain an initial image f 0 。
Step 2: for the current image f 0 Dividing by using an OTSU clustering algorithm to obtain a division threshold value tau=0.136;
step 3: calculating the gray average value of the current segmented image to obtain;
step 4: correcting the gray average value mu=0.272 to obtain a corrected gray average value
The method comprises the following specific steps:
(1) Obtaining a projection weight coefficient matrix w= (W) ij ) N×N Where n=512 represents the size of the reconstructed image, i, j represents the pixel coordinates of the reconstructed image;
(2) Using models
Calculate the relative projection error Δp=0.281, where p ij ，w ij ，f ij Respectively representing the projection, the weight coefficient and the numerical value at the position of the coordinate i and the position of the coordinate j of the reconstructed image;
(3) According to the model
A corrected gray average value is obtained.
Step 5: obtaining optimized gray value by L2 norm minimization according to the forward/backward method
The method comprises the following steps:
(1) Setting the step delta 1 =0.025 for correction of gray scale mean value
According to
Performing forward and backward adjustment for 2 times to obtain an adjusted gray level mean +.>
Wherein m=1, 2,3,4;
(2) Will be
Giving the current segmented image, noted +.>
(3) For a pair of
Forward projection, i.e.)>
Making it differ from the actual projection P by the L2 norm minimization function +.>
Obtaining optimized gray level mean->
Where W represents the projection matrix.
Step 6: using optimized gray values
Obtaining optimized segmentation threshold by L2 norm minimization according to a forward-backward method
The specific steps of (a) include:
(1) Setting the step delta 2 Division threshold τ=0.136 as per =0.005
Performing advance and retreat adjustment for 2 times; obtaining an adjusted segmentation threshold +.>
Wherein m=1, 2,3,4;
(2) By means of
Dividing the current image, and recording as +.>
(3) For a pair of
Forward projection, i.e.)>
Making it differ from the actual projection P by the L2 norm minimization function +.>
Acquiring an optimized segmentation threshold->
Step 7: using threshold values
Dividing the current image to obtain a divided image S;
step 8: selecting a 3 x 3 gray scale window to select a set of edge points from the segmented image S
And fixed point set->
Will be
Endow->
Find->
Corresponding residual projection r, and finishing edge point set updating by utilizing r to obtain +.>
Step 9: merging
And->
Image, smoothing parameter 0.3 is set, through model +.>
Finishing the smooth operation;
step 10: setting the iteration times of the loop as 100 times, judging whether the loop is completed or not, if the loop is not completed, jumping to the step 2 to continue execution, and if the loop is completed, outputting a discrete iteration 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
Step 5: obtaining optimized gray value by L2 norm minimization according to the forward/backward method, and marking as
Step 6: using optimized gray values
Obtaining optimized segmentation threshold by L2 norm minimization according to a forward-backward method
Step 7: using threshold values
Dividing the current image to obtain a divided image S;
step 8: selecting an edge point set from S
And fixed point set->
Will->
Endow->
Find->
Corresponding residual projection r, and finishing edge point set updating by utilizing r to obtain +.>
Step 9: merging
And->
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
Calculating the relative projection error Δp and then according to the model +.>
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
According to->
Performing forward and backward adjustment q times to obtain an adjusted gray level mean +.>
Where k=1, 2, &..i.l, m=1, 2, &..2 q; then will->
The current segmented image is assigned and recorded as
Finally pair->
Forward projection, i.e.)>
Making it differ from the actual projection P by the L2 norm minimization function +.>
Obtaining optimized gray scale average
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
Obtaining optimized segmentation threshold value by L2 norm minimization according to the forward/backward method>
First set step delta 2 Dividing threshold τ 1 ,τ 2 ,......,τ l According to
Proceeding q times of advancing and retreatingAdjusting; obtaining an adjusted segmentation threshold +.>
Where k=1, 2, &..i.l, m=1, 2, &..2 q; then use->
Segmenting the current image and recording as
Finally pair->
Forward projection, i.e.)>
Making it differ from the actual projection P by the L2 norm minimization function +.>
Obtaining an optimized segmentation threshold
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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