CN113223112B - Generalized equiangular detector CT image analysis reconstruction method - Google Patents

Generalized equiangular detector CT image analysis reconstruction method Download PDF

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CN113223112B
CN113223112B CN202110691377.6A CN202110691377A CN113223112B CN 113223112 B CN113223112 B CN 113223112B CN 202110691377 A CN202110691377 A CN 202110691377A CN 113223112 B CN113223112 B CN 113223112B
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CN113223112A (en
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高河伟
邢宇翔
张丽
陈志强
李亮
邓智
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Tsinghua University
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
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    • G06T2207/10072—Tomographic images
    • G06T2207/10081—Computed x-ray tomography [CT]
    • G—PHYSICS
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    • G06T2207/20068—Projection on vertical or horizontal image axis

Abstract

The application discloses an image analysis reconstruction method of a generalized equiangular detector CT, which comprises the following steps: acquiring projection data of an object to be reconstructed, and performing weighting processing on the projection data; approximating a convolution kernel function used in the reconstruction; and reconstructing the object to be reconstructed by using the projection data after the weighting processing and the approximated convolution kernel function. The method and the device have the advantages that the projection data are pre-weighted, corrected and reconstructed by using the FBP method, and accurate reconstruction of the projection data is achieved within a certain range of deviation.

Description

Generalized equiangular detector CT image analysis reconstruction method
Technical Field
The application relates to the technical field of radiation imaging, in particular to an image analysis reconstruction method of a generalized equiangular detector CT.
Background
In a conventional fan-beam equiangular detector CT, the radiation source is located at the center of the circular arc of the detector, so that the field angle of each detector unit to the radiation source is equal, and the image reconstruction thereof can also be implemented by using an FBP algorithm. However, when the source is not located at the center of the detector arc, i.e. a generalized equiangular detector architecture such as the fourth generation CT and the compact coplanar CT/PET imaging architecture, as shown in fig. 1 and 2, since the opening angle of each detector unit with respect to the source is not equal, the FBP cannot be used to realize accurate reconstruction.
Disclosure of Invention
The present application is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, the present application aims to provide an image analysis reconstruction method for a generalized equiangular detector CT, which performs pre-weighting correction on Projection data and then performs reconstruction by using an FBP (filtered Back-Projection reconstruction) method, so as to achieve accurate reconstruction of the Projection data within a certain range of deviation.
In order to achieve the above object, an embodiment of the present application provides an image analysis reconstruction method for a generalized equiangular detector CT, including:
acquiring projection data of an object to be reconstructed, and performing weighting processing on the projection data;
performing approximate transformation on a convolution kernel function used in reconstruction;
and reconstructing the object to be reconstructed by using the projection data after the weighting processing and the convolution kernel function after the approximate transformation.
According to the image analysis reconstruction method of the generalized equiangular detector CT, the projection data do not need to be rearranged into equiangular data or equidistant data when the non-equiangular projection data of the generalized equiangular detector are faced, and the spatial resolution is higher. A reconstruction algorithm which firstly carries out weighting correction and then uses an FBP method is obtained by derivation and approximation for projection data with unequal ray source opening angles, and an accurate reconstructed image can be obtained within a certain deviation range.
Additional aspects and advantages of the present application will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the present application.
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The foregoing and/or additional aspects and advantages of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic diagram illustrating an architecture of a fourth generation CT and a third generation equiangular fan beam CT;
FIG. 2 is a schematic diagram of a compact co-planar PET/CT imaging configuration according to one embodiment of the present application;
FIG. 3 is a three-dimensional schematic diagram of a generalized equiangular detector CT imaging architecture in accordance with one embodiment of the present application;
FIG. 4 is a schematic diagram of a generalized equiangular CT imaging architecture, in accordance with one embodiment of the present application;
FIG. 5 is a generalized isometric CT imaging architecture in accordance with an embodiment of the present application;
FIG. 6 is a flowchart of a method for image-resolved reconstruction of generalized equiangular detector CT according to one embodiment of the present application;
FIG. 7 is a cross-sectional view of a reconstruction result under a generalized equiangular detector CT for a water cylinder according to one embodiment of the present application.
Detailed Description
Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.
An image analysis reconstruction method of a generalized equiangular detector CT proposed according to an embodiment of the present application is described with reference to the accompanying drawings.
It will be appreciated that the present application is based on a generalized equiangular detector CT system for reconstruction.
Generalized equiangular detectors have a different geometry from conventional equiangular CT architectures in CT imaging. On one hand, the circle center of the circle where the detector circular arc is located is neither the ray source nor the rotation center. On the other hand, the radiation source is not necessarily on the circle of the detector, i.e. the distance from the rotation center is not necessarily equal to the distance from the detector to the rotation center, as shown in fig. 3, 4 and 5, which is a different structure from the conventional equiangular detector CT.
When the circle center of the detector arc is at the rotation center or the ray source, each detector unit has the same field angle relative to the ray source, and the image can be accurately reconstructed by directly using the reconstruction formula of the equiangular detector CT. When the center of the detector arc is near the rotation center or near the radiation source, i.e. in this case, it is a generalized equiangular structure, as shown in fig. 3, 4, and 5. At this time, because the opening angles of each detector unit relative to the ray source are not equal, an accurate real-invariant FBP-form reconstruction formula cannot be obtained. The invention provides a reconstruction algorithm of a generalized equiangular detector CT geometric framework aiming at two conditions that the circle center of a detector circular arc is near a ray source and the circle center of the detector circular arc is near a rotation center.
FIG. 6 is a flowchart of a generalized equiangular detector CT image-resolving reconstruction method, according to one embodiment of the present application.
As shown in fig. 6, the method for image analysis and reconstruction of generalized equiangular detector CT includes the following steps:
and step S1, acquiring projection data of the object to be reconstructed, and performing weighting processing on the projection data.
In step S2, the convolution kernel used for reconstruction is subjected to approximate transformation.
And step S3, reconstructing the object to be reconstructed by using the projection data after the weighting processing and the convolution kernel function after the approximate transformation.
For fan beam equiangular CT, there is a basic reconstruction formula:
Figure BDA0003126888190000031
wherein:
L2＝(D+xcosβ+ysinβ)2+(-xsinβ+ycosβ)2 (2)
Figure BDA0003126888190000032
α is the fan angle of the detector unit with respect to the source, β is the rotation angle, D is the source-to-origin distance, and f (x, y) is the function of the reconstruction point. The data p (α, β) are projection data values representing the fan angle α of the fan beam detector at a rotation angle β. h is a convolution kernel function, theoretically
Figure BDA0003126888190000033
S-L filters are commonly used, the basic discrete form of which is:
Figure BDA0003126888190000034
for the generalized equiangular detector CT imaging structure proposed by the system, as shown in FIG. 3, where S is a ray source, O is a rotation center, and the circle center of the detector arc has two possible positions: d1Coincident with the center of rotation, D2Coinciding with the centre of rotation. Because the circle center of the arc where the detector is located is not the radiation source but is near the radiation source or the rotation center, the field angle of each detector unit to the radiation source is not necessarily equal, the imaging formula of the equiangular fan-beam CT cannot be directly used, and the following relationship between the field angle γ of the detector to the circle center of the detector arc and the field angle α to the radiation source can be obtained through the attached fig. 4 and 5:
Figure BDA0003126888190000035
wherein k is the distance D from the ray source to the circular arc center of the detector1And the ratio of the distance R from the detector to the circular arc center of the detector:
D1＝kR (6)
for the structure I shown in the attached figure 4, S is a ray source, O is a rotation center, the circle center of a detector arc is superposed with the rotation center, namely the circle center of the detector arc is at the rotation center, and the value of k is about 1; for the second configuration shown in fig. 5, S is the radiation source, O is the rotation center, the center of the detector arc is near the radiation source, that is, the center of the detector arc is near the radiation source, and at this time, the value of k is about 0.
The relation of α and γ is directly substituted into the basic imaging equation (1) of fan-beam CT:
Figure BDA0003126888190000036
from equation (7), it can be seen that the kernel function is due to convolution
Figure BDA0003126888190000037
It is no longer in a real form and cannot be implemented using the FBP method. To implement FBP, in a real invariant form, it is reconstructed using a pre-weighted approximation.
Figure BDA0003126888190000041
Wherein:
Figure BDA0003126888190000042
it can be seen that m is actually the average of g' (), and the average is used instead of g′And ζ, the original formula is converted into a real invariant form at this time, and the convolution operation can be realized. However, in this approximation, since the detector units at different positions have different beam angles, the reconstruction results have inconsistency, and in order to correct the inconsistency, the projection data needs to be pre-weighted before the filtering convolution. One factor used for pre-weighting is:
Figure BDA0003126888190000043
it can be seen that the weighting factor w includes the inconsistency between γ and α, and is used to correct the projection data, where n is a parameter and a typical value of n is 4.
Further, the method of the present application can also realize the reconstruction of the three-dimensional framework based on the FDK algorithm for the pre-weighting algorithm proposed by the generalized equiangular detector CT. For a conventional equiangular detector CT, the reconstruction formula of the FDK algorithm:
Figure BDA0003126888190000044
wherein:
Figure BDA0003126888190000045
the three-dimensional FDK reconstruction method is varied from the two-dimensional case in that it is projected onto a central plane, i.e., cos η, for projection data of a non-central plane. b (z) is the z-direction coordinate on the detector of the ray passing through point (x, y, z).
The generalized equiangular detector CT three-dimensional situation differs in that the distance from each detector cell in the middle tier to the source is not equal (conventional equiangular detectors are R). Then the three-dimensional FDK reconstruction formula of the generalized FDK algorithm:
Figure BDA0003126888190000046
wherein:
Figure BDA0003126888190000047
Figure BDA0003126888190000048
finishing to obtain:
Figure BDA0003126888190000049
in summary, the algorithm of the present application includes the following steps:
1) firstly, projection data are subjected to pre-weighting correction:
Figure BDA0003126888190000051
w is a weighting factor used, and a typical weighting factor is the one shown in equation (10).
2) Multiplying the pre-weighted projection data by a geometric weighting factor required by fan beam CT:
Figure BDA0003126888190000052
3) calculating g' (x) at [ - γ [ ]m,γm]And solving the convolution kernel function under the corresponding conditions:
Figure BDA0003126888190000053
4) for the projection data p after geometric correction1(γ, β) convolution is performed using a convolution kernel:
Figure BDA0003126888190000054
5) to the projection data after filter convolution
Figure BDA0003126888190000055
Carrying out back projection reconstruction:
Figure BDA0003126888190000056
wherein:
Figure BDA0003126888190000057
Figure BDA0003126888190000058
specifically, the projection data is first pre-weighted, and the pre-weighting factor can be the factor shown in equation (10), or can be a weighting factor obtained by other methods, so as to compensate for the disparity deviation caused by the convolution kernel approximation. Secondly, the mean value of g' (gamma) is approximated to realize a real invariant structure, namely, the convolution kernel function is written as (gamma)0- γ). The weighting factors used for pre-weighting are not limited to be performed before filtering, but can also be performed after filtering to weight the projection data, and the key point is the approximate compensation used for the subsequent convolution kernel. And finally, calculating corresponding geometric weight for the three-dimensional non-central layer.
In the embodiments of the present application, as shown in fig. 3, 4 and 5, for the first imaging architecture, the center of the circle where the arc of the detector is located is the rotation center, and the source of radiation does not necessarily have a certain deviation, i.e., "loose", from the common circle of the detector. The magnitude of the ratio k is then around 1.
For the second imaging architecture, the center of the circle where the arc of the detector is located is near the source of radiation, and when the value of the ratio k is near 0, a negative value may exist, and the distance should be regarded as a directed distance.
To achieve accurate reconstruction results, the imaging system should be able to accurately calibrate the following parameters before using the imaging algorithm: the distance from the detector to the rotation center, the distance from the ray source to the rotation center, the rotation angle of the detector and the ray source in each rotation, the physical size of a single detector, the overall size of the detector arc array and the like.
As shown in fig. 7, a cross-sectional view of the reconstruction of a water cylinder under a generalized equiangular detector CT is shown. Fig. 7(a) shows the case where k is 0.9, and fig. 7(b) shows the case where k is-0.1. The group channel represents the result of the accurate algorithm reconstruction of the traditional equiangular detector under the same parameters; using only
Figure BDA0003126888190000061
And using only m without using the pre-weighting coefficients w in the reconstruction; final correct result represents the final result after correction reconstruction using the method.
According to the image analytic reconstruction method of the generalized equiangular detector CT, the non-equiangular projection data facing the generalized equiangular detector do not need to be rearranged into equiangular data or equidistant data, and the spatial resolution is higher. A reconstruction algorithm which firstly carries out weighting correction and then uses an FBP method is obtained by derivation and approximation for projection data with unequal ray source opening angles, and an accurate reconstructed image can be obtained within a certain deviation range.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to implicitly indicate the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless explicitly specified otherwise.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Moreover, various embodiments or examples and features of various embodiments or examples described in this specification can be combined and combined by one skilled in the art without being mutually inconsistent.
While embodiments of the present application have been shown and described above, it will be understood that the above embodiments are exemplary and should not be construed as limiting the present application and that changes, modifications, substitutions and alterations in the above embodiments may be made by those of ordinary skill in the art within the scope of the present application.

Claims (3)

1. An image analysis reconstruction method of generalized equiangular detector CT is characterized by comprising the following steps:
acquiring projection data of an object to be reconstructed, and performing weighting processing on the projection data;
performing approximate transformation on a convolution kernel function used in reconstruction;
reconstructing the object to be reconstructed by using the projection data after weighting processing and the convolution kernel function after approximate transformation;
the weighting processing of the projection data includes:
Figure FDA0003638941620000011
wherein the content of the first and second substances,
Figure FDA0003638941620000012
for the weighted projection data, p (gamma, beta) is the projection data, weThe weight factor is beta, the rotation angle is beta, and the fan angle of the detector unit relative to the circle center of the detector arc is gamma; the weighting factors are:
Figure FDA0003638941620000013
wherein alpha is the fan angle of the detector unit to the ray source, gamma is the fan angle of the detector unit to the circular arc center of the detector, and n is a parameter;
the approximately transforming the convolution kernel function used in the reconstruction includes:
h(sin(g(γ0)-g(γ)))≈h(sin(m(γ0-γ)))
Figure FDA0003638941620000014
wherein gamma is the fan angle of the detector unit relative to the circle center of the detector arc, and gamma is0The fan angle gamma of the detector unit corresponding to the ray passing through the reconstructed pixel point relative to the circular center of the detector arcmIs the maximum fan angle of the detector unit relative to the circle center of the detector arc,
Figure FDA0003638941620000015
for the fan angle of the detector unit to the ray source, g' (x) is the derivative of a function g (x), and k is the ratio of the distance from the ray source to the center of the detector arc to the distance from the detector to the center of the detector arc;
the reconstructing the object to be reconstructed by using the projection data after the weighting processing and the convolution kernel function after the approximate transformation comprises the following steps:
Figure FDA0003638941620000021
wherein f (x, y, z) is the reconstruction value of the object to be reconstructed, L2＝(D+xcosβ+ysinβ)2+(-xsinβ+ycosβ)2，
Figure FDA0003638941620000022
Figure FDA0003638941620000023
D is the distance from the ray source to the original point, and R is the distance from the detector to the circle center of the detector arc.
2. The method of claim 1,
and weighting the projection data before or after filtering.
3. The method of claim 1, wherein the reconstructing the object to be reconstructed comprises two-dimensional reconstruction and three-dimensional reconstruction.
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