CN111487265B - Cone beam CT hardening artifact correction method combining projection consistency - Google Patents
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Abstract
The invention provides a cone beam CT hardening artifact correction method combining projection consistency. The method comprises the following steps: reconstructing the logarithmic data according to the multi-energy projection to obtain a CT image, dividing the CT image, and binarizing to obtain a binarized image model; establishing a re-projection coordinate system according to cone beam CT imaging system parameters during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-rays and the binary image model through the corresponding relation between the binary image model and the virtual detector to obtain the length of the rays passing through the object; polynomial fitting is carried out on the logarithmic data according to the length of the ray passing through the object and the multi-energy projection, so as to obtain a hardening artifact correction model; correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent single-energy projection logarithmic data; and reconstructing the logarithmic data according to the equivalent single-energy projection to obtain a corrected CT image. The invention is suitable for various types of detectors without any precondition.
Description
Technical Field
The invention relates to the technical field of flat panel detector beam hardening correction, in particular to a cone beam CT hardening artifact correction method combining projection consistency.
Background
In computed tomography (Computed Tomography, CT) technology, the energy is E 0 Intensity is I 0 According to beer's law, it is known that the intensity I after passing through an object of length l is: i=i 0 exp (- ≡u (x, y, z) dl); wherein u (x, y, z) is the position of a certain section of the measured object at E 0 In the case of a linear decay coefficient. Monoenergetic projection logarithmized data p m The method comprises the following steps:
the amount is distributed in (E max ,E min ) Within the range, let its energy spectrum distribution be S (E), and lineThe sexual attenuation coefficient is a function of energy and is then derived from beer's law
Multi-energy projection logarithmized data p p The method comprises the following steps:
from p p The expression of (2) shows that the larger l is, the p is p The larger but not the linear relationship between the two. Let p be p For the purpose of discussion of the increase and decrease of this function, it is known that g' (l) is a monotonically decreasing function with respect to l, i.e., p increases with l p The magnitude of the increase becomes smaller. Because the lower-energy photons in the ray beam attenuate faster than the higher-energy photons, the energy distribution of the ray beam is different when the ray beam passes through objects with different thicknesses, and the attenuation coefficient u corresponding to the average energy of the ray beam is not constant any more but decreases with the increase of the thickness of the passing object. True logarithmic projection data p due to radiation hardening effects p With the logarithmic projection data p assumed in reconstruction m With respect to the linear attenuation coefficient u (x, y, z, E) having a different expression, the data is not linear with the traversing length, p is used in the reconstruction process p Instead of p m Thereby causing artifacts in the reconstructed image, which are hardening artifacts due to the multi-energy X-rays, which are represented by the fact that the gray value of the center of the reconstructed image of the single-material object is smaller than the edge and takes on a cup shape. Hardening artifacts severely degrade the CT image quality and therefore require correction.
For correction of hardening artifacts, there are many correction methods, mainly polynomial fitting (Huang Kuidong, etc., cone beam CT beam hardening correction method based on slice contour re-projection [ J ]. Instrument and meter journal [ 2008.029 (009): 1873-1877), monte Carlo correction method, iterative correction method, etc. The polynomial fitting method has the advantages that polynomial coefficients are easy to calculate, thinking is simple and easy to accept, and correction effect is good under certain conditions. In view of the effectiveness and simplicity of this method, it is currently the most commonly used calibration method. However, the polynomial fitting method has the effect of amplifying noise, amplifies noise in an image while correcting beam hardening, and has a good effect on a detected object of a single material, but needs a phantom of the same material as the detected object, and lacks flexibility in practical application. The Monte Carlo method is also called a statistical simulation method, is a very important numerical calculation method guided by a probability statistical theory, and is characterized by being a random sampling method. The premise of this method application is that the material of the object to be inspected must be known. The iterative method is a process of continuously recursively using the old value of the variable. An advantage of the iterative method is that some physical effects, such as beam hardening, can be fused into the forward projection process, so that the beam hardening can be considered during reconstruction to achieve artifact removal. However, the iterative reconstruction algorithm is still in a research stage at present due to the reasons of large calculated amount, low reconstruction speed, low parallelism and the like, and is not widely applied in practice.
Disclosure of Invention
In order to solve the problems of poor flexibility and large calculation amount caused by the requirement of a precondition (for example, a body film with the same material as a detected object is required and the material of the detected object is required to be known in advance) in the existing correction method, the invention provides a cone beam CT hardening artifact correction method combining projection consistency.
The cone beam CT hardening artifact correction method combining projection consistency provided by the invention comprises the following steps:
step 1: reconstructing the logarithmic data according to the multi-energy projection to obtain a CT image, carrying out image segmentation on the CT image, and carrying out binarization on the segmented contour image to obtain a binarized image model of the object entity region;
step 2: establishing a re-projection coordinate system according to cone beam CT imaging system parameters during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-rays and the binary image model through the corresponding relation between the binary image model and a virtual detector to obtain the length of a ray passing through an object;
step 3: performing polynomial fitting on the logarithmic data according to the length of the ray passing through the object and the multi-energy projection to obtain a hardening artifact correction model;
step 4: correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent mono-energy projection logarithmic data;
step 5: and reconstructing the digitized data according to the equivalent single-energy projection to obtain a corrected CT image.
Further, the step 2 specifically comprises:
firstly, determining a projection point C of a reconstructed point (X, y, z) on a central plane, and then respectively making auxiliary lines CA and CD perpendicular to an X-axis and a central ray SO from the point C to obtain a geometric relation:
CE＝CF×cosβ＝-xsinβ+ycosβ
and because:
the horizontal position a (x, y, β) of the ray on the virtual detector is:
and then the vertical position b (x, y, z, beta) of the ray on the virtual detector is obtained as follows:
wherein O represents the rotation center position, (X, Y, z) represents the coordinate of a reconstructed point, S represents the position of an X-ray source, SO ' is the center ray of conical X-rays, SK represents one ray passing through the reconstructed point, K ' represents the projection of K point on the center layer surface of the flat panel detector, K ' is M, U is the length of SM, beta is the included angle between the center ray and the Y axis, K is the cone angle of the ray SK, gamma is the included angle between SK ' and the center ray SO ', and E, F is the intersection point of the center ray SO, CD and CA respectively; A. d are all points on the X-axis; r represents the distance of the X-ray source from the center of the object.
Further, step 4 includes:
step 4.1: giving the transmission thickness X of the experimental material corresponding to the experimental material and X-rays, and scanning the experimental material to obtain the X-ray transmission intensity I p Corresponding rays and data y:
x＝[x 1 x 2 …x n ] T
y＝ln(I 0 /I P )＝[y 1 y 2 …y n ] T
step 4.2: from the transmission thickness x and the radiation and data y, a curve y=ax is taken b Fitting the rays and the data y, and estimating parameters a 'and b' of a and b in the curve by using least square fitting to obtain:
step 4.3: calculating the equivalent transmission thickness x according to the a 'and b' obtained by fitting estimation eq ：
Step 4.4: according to the equivalent transmission thickness x eq Obtaining a fitting equation of the equivalent beam and beer's law;
step 4.5: the multi-energy projection is carried into the step 4.2 to obtainIs a fitting curve of (2)
And (3) obtaining a penetration thickness x1 corresponding to the multi-energy projection logarithmic data, and then introducing the penetration thickness x1 into a fitting equation of the equivalent beam and the beer law obtained in the step (4.4) to obtain equivalent single-energy projection logarithmic data corresponding to the multi-energy projection logarithmic data.
The invention has the beneficial effects that:
the cone beam CT hardening artifact correction method combining projection consistency provided by the invention comprises the steps of carrying out beam hardening correction on a correlation relation of fitting by utilizing a relation curve between the length of a penetrating object of rays and a multi-energy projection value, preprocessing a reconstructed image of original projection, and carrying out image segmentation to obtain image segmentation information; then, a re-projection coordinate system is established according to the cone beam CT imaging system parameters during actual scanning, and the corresponding relation between the length of the ray passing through the object and the projection gray level is obtained through intersection calculation of the ray and re-projection of the binary image model onto the flat panel detector; finally, the beam hardening curve is fitted and the beam hardening artifacts are corrected and optimized using data consistency conditions. The method does not need a precondition (for example, a body film with the same material as the detected object is not needed, and the material of the detected object is not needed to be known in advance), and the required hardening correction parameters are all obtained by calculating the projection image, so the method is applicable to various detectors, and compared with an iterative reconstruction algorithm, the method has small calculated amount, and can simply and effectively eliminate beam hardening artifacts of cone beam CT.
Drawings
FIG. 1 is a schematic flow chart of a cone beam CT hardening artifact correction method combining projection consistency according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a scanning structure according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a circumferential scan geometry provided by an embodiment of the present invention;
FIG. 4 is a diagram illustrating an image before correction of beam hardening artifacts according to an embodiment of the present invention;
fig. 5 is an image of a beam hardening artifact corrected by the method according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
As shown in fig. 1, an embodiment of the present invention provides a cone beam CT hardening artifact correction method in combination with projection consistency, the method comprising the steps of:
s101: reconstructing the logarithmic data according to the multi-energy projection to obtain a CT image, carrying out image segmentation on the CT image, and carrying out binarization on the segmented contour image to obtain a binarized image model of the object entity region;
s102: establishing a re-projection coordinate system according to cone beam CT imaging system parameters during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-rays and the binary image model through the corresponding relation between the binary image model and a virtual detector to obtain the length of a ray passing through an object;
s103: performing polynomial fitting on the logarithmic data according to the length of the ray passing through the object and the multi-energy projection to obtain a hardening artifact correction model;
s104: correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent mono-energy projection logarithmic data;
s105: and reconstructing the digitized data according to the equivalent single-energy projection to obtain a corrected CT image.
The cone beam CT hardening artifact correction method combining projection consistency provided by the embodiment of the invention does not need any preconditions (for example, a body film with the same material as a detected object is not needed, and the material of the detected object is not needed to be known in advance), and the required hardening correction parameters are all obtained by calculating projection images, so that the cone beam CT hardening artifact correction method can be suitable for various types of detectors, has small calculated amount compared with an iterative reconstruction algorithm, and can simply and effectively eliminate the cone beam CT beam hardening artifact.
Example 2
On the basis of the above embodiment 1, the embodiment of the present invention further provides a cone beam CT hardening artifact correction method in combination with projection consistency, including the following steps:
s201: reconstructing the logarithmic data according to the multi-energy projection to obtain a CT image, carrying out image segmentation on the CT image, and carrying out binarization on the segmented contour image to obtain a binarized image model of the object entity region;
specifically, when the image is segmented, the finer and better the reconstructed CT image is segmented, at least the rough contour of the measured object should be segmented. The reconstructed CT image generates a stereoscopic data, and binarization is performed to obtain information represented by each individual data, after which the information of each individual data can be clearly obtained, for example, 0 represents air and 1 represents an object. The solid area is the area where the object is located.
S202: establishing a re-projection coordinate system according to cone beam CT imaging system parameters during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-rays and the binary image model through the corresponding relation between the binary image model and a virtual detector to obtain the length of a ray passing through an object;
specifically, re-projecting the binary image model onto a flat panel detector to obtain a corresponding relationship between the binary image model and a virtual detector, including:
the scanning structure of the circular track FDK reconstruction algorithm is shown in fig. 2, wherein O represents the rotation center position, (x, y, z) represents the coordinates of the reconstructed point, a virtual detector is introduced at the point O for the convenience of representation and calculation, and the scanned object is positioned at the scanning center position. The X-ray source is positioned at S, so 'is the central ray of conical X-ray, SK represents a ray passing through the reconstructed point, K' represents the projection of K point on the central layer surface (Z=0) of the flat panel detector, the reconstructed point is M, the length of SM is U, the central ray forms a beta angle with the Y axis, K is the cone angle of the ray SK, and gamma is the included angle between SK 'and the central ray so'.
The geometric relationship of the circumferential scan is shown in fig. 3, in which C is a projection point of a reconstructed point of coordinates (X, y, z) on a central plane, SO is a central ray, and auxiliary lines CA and CD are respectively made from the point C and perpendicular to the X axis and SO, SO can obtain the following geometric relationship:
CE＝CF×cosβ＝-xsinβ+ycosβ
and because:
the horizontal position a (x, y, β) of the ray on the virtual detector is:
and then the vertical position b (x, y, z, beta) of the ray on the virtual detector is obtained as follows:
specifically, the corresponding relation between the binary image model and the virtual detector can be obtained through deduction according to the formula, so that the number of binary image model elements corresponding to single virtual detector elements can be expressed as the number of binary image models penetrated by X-rays, namely the length of rays penetrating through an object.
S203: performing polynomial fitting on the logarithmic data according to the length of the ray passing through the object and the multi-energy projection to obtain a hardening artifact correction model;
s204: correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent mono-energy projection logarithmic data;
specifically, in the correction process, a group of beams and data y of the transmission thickness X are measured through experiments, and a relation curve between the X-ray beams and the data y and the transmission thickness X, namely, the X-ray beams and the fitting curve is obtained after fitting. Then, the equivalent transmission thickness is fitted by using the X-ray beam and the fitting curve, thereby obtaining a fitting equation of the equivalent beam and beer's law. And finally, reconstructing, so that the influence of the hardening of the X-ray beam can be effectively eliminated. As an embodiment, the step comprises the sub-steps of:
s2041: giving the transmission thickness X of the experimental material corresponding to the experimental material and X-rays, and scanning the experimental material to obtain the X-ray transmission intensity I p Corresponding rays and data y:
x＝[x 1 x 2 …x n ] T
y＝ln(I 0 /I P )＝[y 1 y 2 …y n ] T
wherein n represents the number of X-ray penetrating object parts which are not 0;
s2042: from the transmission thickness x and the radiation and data y, a curve y=ax is taken b Fitting the rays and the data y, and estimating parameters a ', b' of a and b in the curve by using least square fitting to obtain:
in particular, the curve y=ax is used b The method for fitting the ray and the data y is as follows: taking the logarithm from two sides
lgy＝lga+blgx
A ', b' can be estimated using a least squares fit:
s2043: calculating the equivalent transmission thickness x according to the a 'and b' obtained by fitting estimation eq ：
Specifically, the X-ray beam and the fitted curve may be represented by the fitted equation:
fitting. Correspondingly, if the transmission thickness X of the polychromatic beam sum is to be corrected to be the equivalent transmission thickness of the monochromatic beam sum, it is necessary to ensure that the X-rays are equivalent to the attenuation coefficient and the beam sum value of the monochromatic rays, and the transmission thickness X is expressed as the equivalent transmission thickness X as known from beer's law eq I.e. equivalent beam and beer's law should be expressed as y=ux eq Thereby obtaining x eq 。
S2044: according to the equivalent transmission thickness x eq Obtaining a fitting equation of the equivalent beam and beer's law;
s2045: the multi-energy projection logarithm data is put into a fitting curve obtained in the step S2042
In (3) obtaining the logarithm of the multi-energy projectionAnd (3) converting the penetration thickness x1 corresponding to the data, and then bringing the penetration thickness x1 into a fitting equation of the equivalent beam and beer law obtained in the step S2046 to obtain equivalent monoenergetic projection logarithm data corresponding to the multipotent projection logarithm data.
S205: and reconstructing the digitized data according to the equivalent single-energy projection to obtain a corrected CT image.
In order to verify the effectiveness of the cone beam CT hardening artifact correction method provided by the invention, the invention also provides the following steps of FIG. 4 and FIG. 5: FIG. 4 is a reconstructed image that has not been corrected using the method of the present invention; fig. 5 is a reconstructed image corrected using the method of the present invention. As shown in fig. 4, it can be seen that there is a serious cup-like artifact on the image and the beam hardening phenomenon is serious. And as shown in fig. 5, after the correction by the method of the invention, the cup-shaped artifact caused by beam hardening can be removed well, and compared with the traditional correction method, the correction of the cup-shaped artifact is more thorough, and the correction effect of the hardening artifact is good.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (2)
1. A cone beam CT hardening artifact correction method in combination with projection consistency, comprising:
step 1: reconstructing the logarithmic data according to the multi-energy projection to obtain a CT image, carrying out image segmentation on the CT image, and carrying out binarization on the segmented contour image to obtain a binarized image model of the object entity region;
step 2: establishing a re-projection coordinate system according to cone beam CT imaging system parameters during actual scanning, re-projecting the binary image model onto a flat panel detector, and performing intersection calculation on the X-rays and the binary image model through the corresponding relation between the binary image model and a virtual detector to obtain the length of a ray passing through an object; the method comprises the following steps:
firstly, determining a projection point C of a reconstructed point (X, y, z) on a central plane, and then respectively making auxiliary lines CA and CD perpendicular to an X-axis and a central ray SO from the point C to obtain a geometric relation:
CE＝CF×cosβ＝-xsinβ+ycosβ
and because:
the horizontal position a (x, y, β) of the ray on the virtual detector is:
and then the vertical position b (x, y, z, beta) of the ray on the virtual detector is obtained as follows:
wherein O represents the rotation center position, (X, Y, z) represents the coordinate of a reconstructed point, S represents the position of an X-ray source, SO ' is the center ray of conical X-rays, SK represents one ray passing through the reconstructed point, K ' represents the projection of K point on the center layer surface of the flat panel detector, K ' is M, U is the length of SM, beta is the included angle between the center ray and the Y axis, K is the cone angle of the ray SK, gamma is the included angle between SK ' and the center ray SO ', and E, F is the intersection point of the center ray SO, CD and CA respectively; A. d are all points on the X-axis; r represents the distance from the X-ray source to the center of the object;
step 3: performing polynomial fitting on the logarithmic data according to the length of the ray passing through the object and the multi-energy projection to obtain a hardening artifact correction model;
step 4: correcting the multi-energy projection logarithmic data according to the hardening artifact correction model to obtain equivalent mono-energy projection logarithmic data;
step 5: and reconstructing the digitized data according to the equivalent single-energy projection to obtain a corrected CT image.
2. The method of claim 1, wherein step 4 comprises:
step 4.1: giving the transmission thickness X of the experimental material corresponding to the experimental material and X-rays, and scanning the experimental material to obtain the X-ray transmission intensity I p Corresponding rays and data y:
x＝[x 1 x 2 …x n ] T
y＝ln(I 0 /I P )＝[y 1 y 2 …y n ] T
wherein n represents the number of X-ray penetrating object parts which are not 0;
step 4.2: from the transmission thickness x and the radiation and data y, a curve y=ax is taken b Fitting the rays and the data y, and estimating parameters a ', b' of a and b in the curve by using least square fitting to obtain:
step 4.3: calculating the equivalent transmission thickness x according to the a 'and b' obtained by fitting estimation eq ：
Step 4.4: according to the equivalent transmission thickness x eq Obtaining a fitting equation of the equivalent beam and beer's law;
step 4.5: the multi-energy projection logarithm data is put into the fitting curve obtained in the step 4.2
And (3) obtaining a penetration thickness x1 corresponding to the multi-energy projection logarithmic data, and then introducing the penetration thickness x1 into a fitting equation of the equivalent beam and the beer law obtained in the step (4.4) to obtain equivalent single-energy projection logarithmic data corresponding to the multi-energy projection logarithmic data.
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