CN114549680A - Method for eliminating truncation artifacts in limited view angle tomography - Google Patents

Method for eliminating truncation artifacts in limited view angle tomography Download PDF

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CN114549680A
CN114549680A CN202210145816.8A CN202210145816A CN114549680A CN 114549680 A CN114549680 A CN 114549680A CN 202210145816 A CN202210145816 A CN 202210145816A CN 114549680 A CN114549680 A CN 114549680A
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袁杰
蔡昀烨
沈恩翔
陶超
刘晓峻
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Nanjing University
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Abstract

The invention provides a method for eliminating truncation artifacts in limited-view tomography. The method comprises the following steps: respectively placing an X-ray emitter and a receiver above and below a target tissue, scanning the X-ray emitter and the receiver at a limited angle and receiving projection data; performing primary reconstruction by using an SART reconstruction algorithm to obtain a primary reconstruction image; projecting the primary reconstruction data, and completing the original projection data by utilizing gradient information of the projection data; performing SART reconstruction on the supplemented projection data; and iterating the steps for multiple times to obtain a finite angle CT imaging result for eliminating truncation artifacts. The invention completes the original projection data by utilizing the projection gradient information of the SART reconstructed image, thereby enabling each iteration to contain all voxels and solving the problem that the edge of the finite angle CT image reconstruction has a strip truncation artifact.

Description

Method for eliminating truncation artifacts in limited view angle tomography
Technical Field
The invention relates to the field of image processing, in particular to a method for eliminating truncation artifacts in limited-view tomography.
Background
In a conventional CT (Computed Tomography) imaging technique, a conical X-ray emitter is used to emit X-rays 180 ° around a target tissue at regular intervals, and an X-ray receiver is used to receive signals from the other side of the target tissue, so as to obtain a plurality of sets of projection data, and the internal structure of the target tissue is reconstructed according to the characteristic that different portions of the target tissue absorb or attenuate X-rays with different coefficients.
In practical applications, it is often difficult to scan the target tissue in a full angular range due to the difference of the target tissue structure and the restriction of the application environment, so the limited view angle CT imaging technology is often adopted in practical applications. Unlike conventional CT techniques, which require acquisition of a 180 ° complete data set, limited view CT imaging techniques typically reconstruct images based on projection data acquired over a limited angular range from 15 ° to 60 °. The traditional finite angle CT reconstruction method comprises an iterative algorithm and a non-iterative algorithm. The non-iterative algorithm includes a BP (Back Projection) algorithm, and a FBP (Filtered Back Projection) algorithm. The reconstruction speed of the BP algorithm is high, but the quality of the reconstructed image is poor. The FBP algorithm uses a filter for filtering noise information in the BP reconstruction process based on the BP algorithm, and can provide satisfactory image quality while having a fast calculation speed, but the method is limited by the imaging geometry, for example, in some systems using a very narrow projection angle range, a non-uniform angle sampling scheme and a fixed detector, the calculation of the FBP is more complicated, and the calculation error also reduces the image quality. Iterative algorithms, such as SART (singular adaptive Reconstruction Technique) and statistical model-based algorithms such as ML-convex (Maximum Likelihood convex function) can adapt to limited-view tomography without being limited to geometric shapes, and can effectively enhance the edges and contrast of target tissue images. Along with the upgrading of computer hardware and the improvement of parallel computing efficiency, the reconstruction speed of the iterative algorithm is also improved to a certain extent.
However, due to the limited size of the detector and the point light source, the receiver cannot receive the complete projection data when a part of large-angle projections are projected, the corresponding PVs (projection views) are truncated, and after the truncated PVs are updated, the voxel values outside the FOV (field of view) are not updated, which results in discontinuity of edge voxel values, and if no correction is performed, TPA (truncated projection artifacts) will appear in the reconstructed image. TPA significantly affects the quality of the reconstructed image.
Disclosure of Invention
The purpose of the invention is as follows: the invention provides a method for eliminating truncation artifacts in limited view angle tomography, aiming at the problem that discontinuous strip truncation artifacts appear at the edge of a limited view angle CT imaging result.
In order to achieve the purpose, the method comprises the following specific steps:
step 1, respectively placing an X-ray emitter and a receiver on the upper part and the lower part of a target tissue;
step 2, using an X-ray emitter to move around the tissue and emit X-rays within a limited angle, and simultaneously collecting original projection data by a receiver;
step 3, reconstructing the original projection data to obtain a reconstructed image;
step 4, carrying out projection transformation on the reconstructed image to obtain complete projection data; obtaining gradient information of the complete projection data;
step 5, complementing the original projection data by using the gradient information to obtain complemented projection data;
and 6, reconstructing the completed projection data to obtain a limited angle CT reconstructed image with the truncation artifacts eliminated.
In the invention, preferably, in step 4, the SART reconstructed image is subjected to projection transformation to obtain complete projection data; the complete projection data is not truncated. Taking gradient information for the complete projection data comprises:
aligning the complete projection data with the original projection data according to the relative position of the complete projection data and the original projection data, and extracting a required part of the complete projection data, wherein the part consists of a left block and a right block which are respectively a non-zero part from a cut-off part of the original projection data relative to the complete projection data to two sides of the complete projection dataHere, as left reconstructed projection data fLAnd right reconstructed projection data fR；
Reconstructing projection data f to the leftLAnd right reconstructed projection data fRTaking gradient information in the x direction and reconstructing projection data f on the left sideLMiddle, pixel (x)l,yn) Gradient value g in x-directionL(xl,yn) Comprises the following steps:
gL(xl,yn)＝fL(xl+1,yn)-fL(xl,yn)
reconstructing projection data f to the rightRPixel point (x)r,yn) The gradient values in the x-direction are:
gR(xr,yn)＝fR(xr,yn)-fR(xr-1,yn)
where l denotes the left reconstructed projection data fLPosition index in the middle x-direction, r represents the right reconstructed projection data fRThe x-direction position index, and n represents the y-direction position index.
The area of the receiver can be artificially enlarged by carrying out projection transformation on the reconstructed image, so that the projection data is not truncated any more, and the generation of artifacts is fundamentally avoided. The projection graph obtained by the method has more commonalities with the original projection data, and the original projection data can be better complemented.
In the present invention, it is preferable that in the step 5, the projection data f is reconstructed from the left sideLAnd right reconstructed projection data fRThe missing part of the original projection data is completed from the inner side to the two sides by the gradient information of the projection data, and the completed projection data is obtained.
In the present invention, preferably, the step 5 includes:
the projection data after the completion of the recording is f0Compensated projection data f0In the middle, original projection data are in the middle; the original projection data is completed from the middle to two sides, and the parts needing to be completed at two sides are respectively iterated as follows：
For the left region ynLine data, there are:
f0(xl+1,yn)＝f0(xl,yn)+gL(xl,yn)
wherein, l ═ l0Processing the projection data to obtain a compensation value according to the formula
Figure BDA0003508870560000031
Then obtaining the result according to the formula
Figure BDA0003508870560000032
Until the iteration is finished;
for the right region ynLine data, there are:
f0(xr-1,yn)＝f0(xr,yn)-gR(xr,yn)
wherein r is r0Processing the projection data to obtain a compensation value according to the formula
Figure BDA0003508870560000033
Then obtaining the result according to the formula
Figure BDA0003508870560000034
Until the iteration is finished;
and (4) performing iteration of the left area and the right area on each row to complete the completion of the original projection data.
In step 5, the gradient information is adopted to complement the projection data, so that the discontinuity of the projection data at the truncation position is avoided, and compared with the existing projection data expansion method, the adopted data complementation method can better recover the truncated projection data, the recovered data is closer to the true value, and a good image can be finally reconstructed. Compared with the existing method using pixel compensation, the method has the advantages that the reconstructed image is more real, information covered by the artifact can be completely reserved, and jagged artifacts cannot be caused at the edge of the image.
In the present invention, preferably, the method further includes a step 7 of performing more than one cycle of the steps 4 to 6 to obtain a limited angle CT reconstructed image with the truncation artifact removed, where the reconstructed image input in the step 4 in the cycle process is the limited angle CT reconstructed image with the truncation artifact removed, obtained in the step 6 in the previous cycle. When the slice with a lower position is concerned, the step 1 to the step 6 can effectively eliminate the strip truncation artifact at the edge of the image; when the slice with a higher position is focused, step 7 is executed to carry out a plurality of cycles on steps 4 to 6, so that the strip truncation artifact at the edge of the high-level image can be effectively reduced.
In the present invention, preferably, the X-ray emitter in step 1 should be located above the receiver, so that the X-ray beam covers the target tissue as much as possible.
In the present invention, preferably, in the step 2, a straight line in the plane of the receiver is taken as a rotation axis, the X-ray emitter makes a limited-angle circular arc-shaped movement around the rotation axis in a movement plane perpendicular to the plane of the receiver, and an angle range is represented by a central angle determined by boundary points of left and right movement of the emitter, wherein the left and right boundary points are symmetrical about the center of the trajectory. In the acquisition process, the X-ray emitter moves from an initial end point to another moving end point, and when the X-ray emitter moves for a certain angle, the X-ray emitter emits X-rays to the receiver, and the receiver receives the X-rays and acquires a group of projection data. The scanning process, step 2, is complete and several sets of raw projection data are acquired.
In the present invention, preferably, in step 3, an SART reconstruction algorithm is used to reconstruct the reconstruction region, so that the final result meets the optimization condition, and a first limited view angle CT imaging result is obtained, where the imaging result has a strip truncation artifact at the edge.
In the present invention, preferably, in step 6, the supplemented projection data is reconstructed by using an SART algorithm, so as to obtain a limited-angle CT reconstructed image with truncation artifacts removed.
Has the advantages that:
the invention provides a method for eliminating truncation artifacts in limited-view tomography, which is based on a traditional SART reconstruction algorithm, completes truncated original projection data by utilizing gradient information of a projection value of a reconstructed image, and performs SART reconstruction on the completed projection data to obtain a limited-view CT reconstruction result for eliminating the truncation artifacts, thereby solving the problem that the edge of the reconstructed image has strip truncation artifacts due to the fact that a receiver cannot receive all x-rays to cause real projection data loss in CT image reconstruction under a limited view.
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The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of the raw projection data acquisition process of the present invention.
Fig. 3 is raw projection data in an embodiment of the present application.
Fig. 4 is a diagram obtained by performing initial SART algorithm reconstruction on original projection data in the embodiment of the present application.
Fig. 5 is a projection data diagram of a primary reconstructed image in an embodiment of the present application.
Fig. 6 is a schematic diagram of a completion process in an embodiment of the present application.
Fig. 7 is a diagram of the completed projection data in the embodiment of the present application.
Fig. 8 is a diagram obtained by performing SART algorithm reconstruction on the projection data after completion in the embodiment of the present application.
Detailed Description
Embodiments of the present invention will be described below with reference to the accompanying drawings.
As shown in fig. 1, the method for eliminating truncation artifacts in limited view tomography proposed by the present invention comprises the following steps:
step 1, respectively placing an X-ray emitter and a receiver on the upper part and the lower part of a target tissue;
step 2, using an X-ray emitter to move around the tissue and emit X-rays within a limited angle, and simultaneously acquiring original projection data by a receiver;
step 3, reconstructing the original projection data to obtain a reconstructed image;
step 4, carrying out projection transformation on the reconstructed image to obtain complete projection data; obtaining gradient information of the complete projection data;
step 5, complementing the original projection data by using the gradient information to obtain complemented projection data;
and 6, reconstructing the supplemented projection data to obtain a limited-angle CT reconstructed image with truncated artifacts eliminated.
In this embodiment, in step 1, the X-ray receiver has a length of 23.04cm and a width of 19.20cm, and each pixel has a size of a square with a side of 0.1mm, so that each time projection data is received, a plan view with a resolution of 1920 × 2304 is obtained. The target tissue is placed between the X-ray emitter and the receiver and close to the plane of the receiver, the distance between the bottom surface of the object and the plane of the receiver is 2cm, and the distance between the X-ray emitter and the rotating fulcrum is 64 cm. The placement positions of the X-ray emitter, the receiver and the object are shown in fig. 2.
In this embodiment, in step 2, as shown in fig. 2, the center of the circular arc motion track is located at a point P, the rotation pivot point P' is a projection of the point P on the rotation axis, the initial position of the X-ray emitter is located at a left end point L of the motion track, and the end point of the motion is a right end point R. In the motion plane, the X-ray emitter takes a point P 'as a rotation center and makes arc motion around the point, the central angle of the arc is 60 degrees, and a left endpoint L and a right endpoint R are axisymmetric with PP' and respectively form 30 degrees with a central axis. The X-ray emitter starts from a left end point L and moves in an arc shape towards a right end point R, X-rays are emitted to the X-ray receiver once every 3 degrees, and data received by the receiver serve as a group of projection values of the angle. When the emitter reaches the point R, the scanning process is ended, and 21 sets of projection data are acquired, and the raw projection data in this embodiment is shown in fig. 3.
In this embodiment, in step 3, an SART reconstruction algorithm is used to perform primary reconstruction on the acquired original projection data. The SART algorithm solves for x by iterating through a class of equations:
Ax＝b (1)
in formula (1), a is an M × N matrix, which is a projection transformed system matrix during image reconstruction, X is an N-dimensional column vector composed of values of voxels to be reconstructed, which represents an attenuation coefficient of each voxel in a target tissue to an X-ray, N is the number of reconstructed voxels, b is an M-dimensional column vector, which represents a projection value, and M is the total number of acquired projection pixels. In limited angle CT imaging, the value of M is typically much smaller than N, so there are numerous sets of solutions to this equation. The SART algorithm firstly gives an initial estimated value x 'to x, then the estimated value is projected to obtain an estimated value b' of a projection vector b, and then a projection value b measured under a first angle is used for obtaining1Difference b between b' and b1-b 'is corrected as a correction value x'. One correction of x 'is done for all 21 sets of projection values as an iteration, and finally x' converges to make
Figure BDA0003508870560000061
The minimum x, the least squares solution. According to the theory of the SART algorithm, the introduction of the weighting matrix W can effectively reduce artifacts.
Therefore, the value of x is required to minimize the following loss function l (x), as shown in equation (2):
Figure BDA0003508870560000062
obtaining the x which minimizes L (x) by using a gradient descent method to obtain an iterative formula of the SART algorithm:
Figure BDA0003508870560000063
wherein the content of the first and second substances,
Figure BDA0003508870560000064
and (3) representing the value of the jth voxel after the (k + 1) th iteration, wherein i is the serial number of the taken projection value, and lambda is a relaxation factor, and the convergence speed and the reconstruction result are influenced by changing lambda. J denotes each X-ray passing throughJ is more than or equal to 1 and less than or equal to J; m represents the number of times that the jth voxel is updated during the iteration, MiM is more than or equal to 1 and less than or equal to M and represents the total times of updating the jth element in the iteration processi，Amj,iAnd when the serial number of the projection value is i, the weight of the jth voxel during the mth update in the iteration process is represented. To ensure convergence, λ is taken to be 0.1 in this example and iterated 5 times. To speed up the operation, the original projection data is scaled down to 480 × 576 resolution.
As shown in fig. 4, the primary reconstruction result is obtained, the size of the reconstruction result in this example is 480 × 576 × 100, the reconstructed image is a three-dimensional image, and the three-dimensional image is divided into 100 two-dimensional image processes. Fig. 4 can see that there is a significant truncated projection artifact at the edges.
In this embodiment, in step 4, a projection transformation is performed on the primary reconstruction result to obtain a complete projection data diagram, as shown in fig. 5. The projection transformation of the primary reconstruction result is calculated using prior art techniques known to those skilled in the art and can be done by a computer, so that the complete projection data is obtained without limitation of the receiver size compared to the scanning phase in step 2, and thus the relative position of the original projection data and the projection data of the reconstructed image is known. Aligning the new projection drawing with the original projection data center, extracting a required part for the projection data of the reconstructed image, wherein the part is composed of a left block and a right block, and taking x-direction gradient information for the part from the cut-off position of the original projection drawing relative to the reconstructed projection drawing to the non-zero positions on two sides of the reconstructed projection drawing. As shown in fig. 6. The gradient is calculated by subtracting the pixel value of the right point from the pixel value of a certain pixel point. Left reconstructed projection data fLMiddle, point (x)l,yn) The gradient values in the x-direction are:
gL(xl,yn)＝fL(xl+1,yn)-fL(xl,yn) (4)
g in formula (4)LThe gradient information, which represents the pixels in the left region, is a scalar quantity, and the subscript L represents the left region.
For right reconstructed projection data fRPoint (x)r,yn) The gradient values in the x-direction are:
gR(xr,yn)＝fR(xr,yn)-fR(xr-1,yn) (5)
g in formula (5)RThe gradient information, which represents the pixels in the right region, is a scalar quantity, and the subscript R is indicated in the right region.
In this embodiment, in step 5, after obtaining the gradient information, the original projection data is complemented from the middle to the two sides. Reconstruction region f0In the middle, the original projection data is in the center, and the following iteration is respectively carried out on the parts which need to be completed at the two sides:
for the left region ynLine data, there are:
f0(xl+1,yn)＝f0(xl,yn)+gL(xl,yn) (6)
wherein l ═ l0The original projection data is processed to obtain a complementary value according to the formula (6)
Figure BDA0003508870560000071
Then according to the formula (6) to obtain
Figure BDA0003508870560000072
And so on until the iteration ends.
For the right region ynLine data, there are:
f0(xr-1,yn)＝f0(xr,yn)-gR(xr,yn) (7)
wherein r is r0The original projection data is processed to obtain a complementary value according to the formula (7)
Figure BDA0003508870560000073
Then according to the formula (7) to obtain
Figure BDA0003508870560000074
And so on until the iteration ends.
Reconstruction region f0The iteration is performed on each line of the projection data to complete the completion of the original projection data. In this example, the projection view after completion is shown in fig. 7.
In this embodiment, step 6, SART algorithm reconstruction is performed on the completed projection data to obtain a new reconstructed image.
In this embodiment, the method further includes step 7, which is to perform multiple cycles on the above steps 4 to 6 to reduce truncation artifacts of the high-layer portion picture and make the contour of the internal tissue clearer. The SART reconstructed image input in the step 4 in the loop process is the limited angle CT reconstructed image which is obtained in the step 6 in the previous loop and eliminates the truncation artifact. According to the residual situation of the truncated artifact, when a slice with a higher position is concerned, the present embodiment loops for 3 times, and finally a limited view angle CT reconstruction result with the truncated projection artifact at the edge removed is obtained, as shown in fig. 8.
The present invention provides a method for eliminating truncation artifacts in limited view tomography, and a plurality of methods and approaches for implementing the technical solution, and the above description is only a specific embodiment of the present invention, and it should be noted that, for those skilled in the art, a plurality of modifications and amendments can be made without departing from the principle of the present invention, and these modifications and amendments should also be regarded as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (9)

1. A method for removing truncation artifacts in limited view tomography, comprising the steps of:
step 1, respectively placing an X-ray emitter and a receiver on the upper part and the lower part of a target tissue;
step 2, using an X-ray emitter to move around the tissue and emit X-rays within a limited angle, and simultaneously collecting original projection data by a receiver;
step 3, reconstructing the original projection data to obtain a reconstructed image;
step 4, carrying out projection transformation on the reconstructed image to obtain complete projection data; obtaining gradient information of the complete projection data;
step 5, complementing the original projection data by using the gradient information to obtain complemented projection data;
and 6, reconstructing the supplemented projection data to obtain a limited-angle CT reconstructed image with truncated artifacts eliminated.
2. The method of claim 1, wherein the step 4 of obtaining gradient information for the complete projection data comprises:
aligning the complete projection data with the original projection data according to the relative position of the complete projection data and the original projection data, and extracting a required part of the complete projection data, wherein the part consists of a left block and a right block, and the parts are respectively a cut-off part of the original projection data relative to the complete projection data to non-zero parts of two sides of the complete projection data and are recorded as left-side reconstructed projection data fLAnd right reconstructed projection data fR；
Reconstructing projection data f to the leftLAnd right reconstructed projection data fRTaking gradient information in the x direction and reconstructing projection data f on the left sideLMiddle, pixel (x)l，yn) Gradient value g in x-directionL(xl，yn) Comprises the following steps:
gL(xl，yn)＝fL(xl+1，yn)-fL(xl，yn)
reconstructing projection data f to the rightRPixel point (x)r，yn) The gradient values in the x-direction are:
gR(xr，yn)＝fR(xr，yn)-fR(xr-1，yn)
where l denotes the left reconstructed projection data fLPosition index in the middle x-direction, r represents the right reconstructed projection data fRIn the x direction, n represents the y directionA position index.
3. The method of claim 2, wherein in step 5, the projection data f is reconstructed from the left sideLAnd right reconstructed projection data fRThe missing part of the original projection data is completed from the inner side to the two sides by the gradient information of the projection data, and the completed projection data is obtained.
4. A method for eliminating truncation artifacts in limited view tomography according to claim 3, wherein said step 5 comprises:
the projection data after the completion of the recording is f0Compensated projection data f0In the middle, original projection data are in the middle; and (3) completing the original projection data from the middle to two sides, and respectively iterating the parts needing to be completed at the two sides as follows:
for the left region ynLine data, there are:
f0(xl+1，yn)＝f0(xl，yn)+gL(xl，yn)
wherein, l ═ l0Processing the projection data to obtain a compensation value according to the formula
Figure FDA0003508870550000021
Then obtaining the result according to the formula
Figure FDA0003508870550000022
Until the iteration is finished;
for the right region ynLine data, there are:
f0(xr-1，yn)＝f0(xr，yn)-gR(xr，yn)
wherein r is r0Processing the projection data to obtain a compensation value according to the formula
Figure FDA0003508870550000023
Then obtaining the product according to the formula
Figure FDA0003508870550000024
Until the iteration is over;
and (4) performing iteration of the left area and the right area on each row to complete the completion of the original projection data.
5. The method of claim 4, further comprising a step 7 of performing more than one loop of steps 4 to 6 to obtain a truncated-artifact-removed finite-angle CT reconstructed image, wherein the reconstructed image input in step 4 in the loop is the truncated-artifact-removed finite-angle CT reconstructed image obtained in step 6 in the previous loop.
6. The method of claim 5, wherein in step 1 the X-ray emitter is positioned above the receiver such that the X-rays emitted by the emitter cover substantially the entire target tissue.
7. The method of claim 6, wherein in step 2, the X-ray emitter moves in an arc around the receiver in a plane perpendicular to the receiver, and emits X-rays at regular intervals in a limited angle range while the receiver receives the X-rays to obtain the original projection data.
8. The method of claim 7, wherein the step 3 performs three-dimensional reconstruction on the acquired original projection data by using SART reconstruction algorithm to obtain a primary SART reconstructed image.
9. The method of claim 8, wherein in step 6, the supplemented projection data is reconstructed by using an SART algorithm to obtain a limited angle CT reconstructed image with the truncated artifacts removed.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117078784A (en) * 2023-08-17 2023-11-17 北京朗视仪器股份有限公司 Image reconstruction method, device and equipment

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117078784A (en) * 2023-08-17 2023-11-17 北京朗视仪器股份有限公司 Image reconstruction method, device and equipment

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