CN108051458A - A kind of X-ray energy spectrum method of estimation based on rational fraction fitting multipotency drop shadow curve - Google Patents
A kind of X-ray energy spectrum method of estimation based on rational fraction fitting multipotency drop shadow curve Download PDFInfo
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Abstract
The present invention discloses a kind of X-ray energy spectrum method of estimation based on rational fraction fitting multipotency drop shadow curve, and step is as follows：(1) X-ray machine voltage NkV is set, the die body of M group different-thickness is scanned, obtains measurement data (Hj,pj), j=1 ..., M；(2) using Quadratic Rational fraction by measure data fitting multipotency drop shadow curve P (H)；(3) intensive sampling in above-mentioned multipotency drop shadow curve, obtains sampled data (Hk,pk), k=1,2 ..., M*；(4) sampled data (H is utilizedk,pk), k=1,2 ..., M*, system of linear equations is constructed, and solves and obtains X-ray energy spectrum.Since Quadratic Rational fraction parameter is few, a small amount of measurement data can fit high-precision multipotency drop shadow curve.Therefore, the method for the present invention can substantially reduce the number of the measurement data of spectra estimation needs, effectively reduce the workload of spectra estimation.
Description
Technical Field
The invention belongs to the technical field of X-ray CT imaging, relates to an X-ray energy spectrum estimation method, and particularly relates to an X-ray energy spectrum estimation method based on rational fraction fitting multi-energy projection curves.
Background
The accuracy of X-ray CT imaging depends on the accuracy of modeling the interaction between X-rays and substances, wherein the X-ray energy spectrum is an important factor, and plays an important role in dual-energy-spectrum CT image reconstruction, CT image hardening correction, quantitative analysis of CT images and other applications.
For an X-ray CT system, because the ray flow generated by an X-ray machine is very strong, an X-ray energy spectrum is difficult to be directly measured by devices such as a spectrometer and the like. A more common approach is to estimate the energy spectrum indirectly using measurements of X-rays through known phantoms of different thicknesses. The indirect estimation methods can be divided into two categories according to different description modes of the X-ray energy spectrum: one is that according to the physical fact, an analytical formula containing unknown parameters is established to depict the X-ray energy spectrum; the other is to estimate the discrete X-ray energy spectrum, i.e. segment the energy range of the X-ray and estimate the proportion of X-ray photons to all photons in each segment. The first method has few unknown parameters and is relatively easy to solve; however, the accuracy of the method depends heavily on the accuracy of the analytical expression on the representation of the X-ray energy spectrum, and an inaccurate expression can cause systematic deviation of the X-ray energy spectrum. The second method resolves the energy spectrum estimation problem into a solution problem of a linear equation system, and the form is simple. However, typically the system of equations is severely ill-conditioned, and direct solution may result in inaccurate energy spectra.
In order to overcome the above difficulties, on one hand, people propose more stable solving methods, such as adding constraints, EM solving and the like; on the other hand, the adaptability of the problem is improved by increasing the measurement data quantity and increasing the number of equations. In engineering applications, measurement data of dozens of die bodies with different thicknesses are generally required to be measured under one scanning condition (fixed voltage, current, filter plate and the like), and the work is complicated and large.
Through searching, no patent publication related to the present patent application has been found.
Disclosure of Invention
The invention aims to solve the problems of more measurement data and large workload in the prior art, and provides an X-ray energy spectrum estimation method based on a rational fraction fitting multi-energy projection curve, which comprises the steps of firstly using the rational fraction fitting multi-energy projection curve for the measurement data; then sampling the multi-energy projection curve, and constructing a linear equation system for estimating an X-ray energy spectrum; finally, solving the equation set to estimate an X-ray energy spectrum; the method can obviously reduce the requirement on the number of the measured data and reduce the workload of energy spectrum estimation.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an X-ray energy spectrum estimation method based on rational fraction fitting multi-energy projection curve comprises the following steps:
the method includes the steps of setting the voltage N kV of an X-ray machine, scanning M groups of mold bodies with different thicknesses, and obtaining measurement data (H) j ,p j ) J =1, \ 8230, M, where j is a measurement data index;
fitting a multifunctional projection curve P (H) by using measurement data in a secondary rational division manner;
thirdly, densely sampling on the multi-energy projection curve P (H) to obtain sampling data (H) k ,p k ),k＝1,2,…,M * Wherein k is a sample data index;
fourth sample data (H) k ,p k ),k＝1,2,…,M * And constructing a linear equation system and solving to obtain an X-ray energy spectrum.
Moreover, the expression of the secondary rational fraction in the step is as follows:
wherein (alpha) 1 ,α 2 ,α 3 ) Is the undetermined coefficient.
In the step three, the number of sampling data is greater than the number of measurement data in the step, namely M * >M。
Moreover, the linear equation set constructed in step four is:
AX＝B；
whereinFor unknown X-ray spectral vectors, N * Is a matrix of discrete points and coefficients of an X-ray energy spectrum curve(Vector)
The number of rows in the coefficient matrix A is equal to or greater than the number of columns, that is, M * ≥N * 。
The method of the invention has the advantages and positive effects that:
because the secondary rational fraction parameters are few, a small amount of measurement data can be used for fitting a high-precision multifunctional projection curve, so that the method can remarkably reduce the requirement on the number of the measurement data, can estimate a high-precision X-ray energy spectrum by only needing a small amount of measurement data, and reduces the workload of energy spectrum estimation.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a graph of the results of a multi-energy projection curve fitted using M =3 measurement data by the method of the present invention;
FIG. 3 is a graph of M taken from the curve of FIG. 2 according to the method of the present invention * A result graph of =140 sample data;
FIG. 4 is a graph showing the results of the conventional method and the method of the present invention for estimating the power spectrum.
Detailed Description
For a further understanding of the contents, features and effects of the present invention, reference will now be made to the following examples, which are to be considered in conjunction with the accompanying drawings. It should be noted that the present embodiment is illustrative, not restrictive, and the scope of the invention should not be limited by the following embodiments.
The equipment used in the invention is the equipment commonly used in the field if no special provisions are made; the methods used in the present invention are those commonly used in the art, unless otherwise specified.
Example 1
An X-ray energy spectrum estimation method based on rational fraction fitting multi-energy projection curve comprises the following steps:
the method includes the steps of setting the voltage N kV of an X-ray machine, scanning M groups of mold bodies with different thicknesses, and obtaining measurement data (H) j ,p j ) J =1, \ 8230, M, where j is a measurement data index;
fitting a multifunctional projection curve P (H) by using measurement data in a secondary rational division manner;
thirdly, densely sampling on the multi-energy projection curve P (H) to obtain sampling data (H) k ,p k ),k＝1,2,…,M * Wherein k is a sample data index;
fourth, sampling data (H) is utilized k ,p k ),k＝1,2,…,M * And constructing a linear equation system and solving to obtain an X-ray energy spectrum.
Example 2
An X-ray energy spectrum estimation method based on rational fraction fitting multi-energy projection curve comprises the following steps:
the method includes the steps of setting the voltage N kV of an X-ray machine, scanning M groups of mold bodies with different thicknesses, and obtaining measurement data (H) j ,p j ) J =1, \ 8230, M, where j is a measurement data index;
fitting a multifunctional projection curve P (H) by using measurement data in a secondary rational division manner;
wherein, the expression of the quadratic rational fraction is as follows:
wherein (alpha) 1 ,α 2 ,α 3 ) Is the undetermined coefficient.
Thirdly, densely sampling on the multi-energy projection curve P (H) to obtain sampling data (H) k ,p k ),k＝1,2,…,M * Wherein k is a sample data index;
the number of sampling data is greater than the number of measuring data in the step, namely M * >M；
Fourth, sampling data (H) is utilized k ,p k ),k＝1,2,…,M * Constructing a linear equation set, and solving to obtain an X-ray energy spectrum;
wherein the constructed linear equation system is as follows:
AX＝B；
whereinFor unknown X-ray spectral vectors, N * Is a matrix of the number of discrete points and coefficients of an X-ray energy spectrum curve(Vector)
Wherein the number of rows of the coefficient matrix A is greater than or equal to the number of columns, i.e. M * ≥N * 。
Example 3
In order to better embody the advantages of the X-ray energy spectrum estimation method based on rational fraction fitting multi-energy projection curve in reducing the measurement data requirement, the algorithm of the present invention is compared with the existing typical algorithm EM in combination with a specific embodiment.
The method of the invention has the flow as shown in figure 1, and comprises the following specific steps:
1. setting up X-raysScanning M groups of die bodies with different thicknesses under the condition of the mechanical voltage of N kV to obtain measurement data (H) j ,p j ) J =1, \ 8230, M, the specific implementation method is as follows:
and simulating the energy Spectrum of a GE Maxiray 125 bulb tube passing through 0mm and 1mm Cu filters under 140kV by using open source software Spectrum GUI, and normalizing the energy Spectrum. The energy spectrum of the filter with the thickness of 1mm is added as the energy spectrum to be estimated, and the energy spectrum without the filter is used as the initial value of the iterative solution of the linear equation set. Obtaining the discretization representation S of the energy spectrum by equally spaced 1keV energy spectrum values i ,i＝1,…,N＝140。
In (0, 14.8)]M =3 thicknesses H are taken at equal intervals in cm j J =1,2,3, and the X-ray multi-color projection data corresponding to the aluminum phantom of different thicknesses is calculated according to the following formula:
wherein the linear attenuation coefficient mu of the aluminum material i Obtained from the National Institute of Standards and Technology (NIST) website. In particular, (H) 0 ,p 0 )＝(0,0)。
2. Fitting a multi-energy projection curve P (H) by using a quadratic rational fraction formula according to the measured data, wherein the specific implementation method comprises the following steps:
based on the above measured data (H) j ,p j ) J =1,2,3, coefficient of the quadratic rational equation (α) is determined 1 ,α 2 ,α 3 ) I.e. solving the following system of linear equations:
after estimating the coefficients, the multi-energy projection curve can be expressed by the following equation:
figure 2 gives the multi-energy projection curve and the rational result of fitting using 3 measurement points, the two curves substantially coinciding.
3. Densely sampling on the fitting curve to obtain sampling data (H) k ,p k ),k＝1,2,…,M * The specific implementation method is as follows:
on the multi-energy projection curve, according to the thickness, the thickness is [0,14.8 ]]Taking M at equal intervals in cm * =140 sample data (H) k ,p k ) K =1,2, \8230;, 140, as shown in fig. 3.
4. The method comprises the following steps of constructing a linear equation set by utilizing sampling data, and solving to obtain the energy spectrum distribution of the X-ray, wherein the specific implementation method comprises the following steps:
the constructed linear system of equations is:
AX＝B；
whereinFor unknown X-ray spectral vectors, N * =140 discrete points of X-ray energy spectrum curve, coefficient matrix(Vector)And solving the linear equation set to obtain the X-ray energy spectrum estimated by the method.
Fig. 4 shows the results of the conventional method for directly estimating the power spectrum using the measured data and the method of the present invention for estimating the power spectrum. It can be seen that the spectrum estimated by the method of the present invention is closer to the true spectrum than the spectrum estimated by the conventional method.
In light of the foregoing description of the preferred embodiments of the present invention, it is to be understood that various changes and modifications may be made without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.
Claims (5)
1. An X-ray energy spectrum estimation method based on rational fraction fitting multi-energy projection curve is characterized in that: the method comprises the following steps:
the method includes the steps of setting the voltage N kV of an X-ray machine, scanning M groups of mold bodies with different thicknesses, and obtaining measurement data (H) j ,p j ) J =1, \ 8230, M, where j is a measurement data index;
fitting a multifunctional projection curve P (H) by using measurement data in a secondary rational division manner;
thirdly, densely sampling on the multi-energy projection curve P (H) to obtain sampling data (H) k ,p k ),k＝1,2,…,M * Wherein k is a sample data index;
fourth, sampling data (H) is utilized k ,p k ),k＝1,2,…,M * And constructing a linear equation system and solving to obtain an X-ray energy spectrum.
2. The method of claim 1, wherein the X-ray energy spectrum estimation method based on the rational fraction fitting multi-energy projection curve comprises: the expression of the secondary rational fraction in the step is as follows:
wherein (alpha) 1 ,α 2 ,α 3 ) Is the undetermined coefficient.
3. The method of claim 1, wherein the X-ray energy spectrum estimation method based on rational fraction fitting multi-energy projection curve comprises: the number of sampling data in the step three is greater than the number of measurement data in the step, namely M * >M。
4. The method of claim 1, wherein the X-ray energy spectrum estimation method based on rational fraction fitting multi-energy projection curve comprises: the linear equation set constructed in the step four is as follows:
AX＝B；
whereinFor unknown X-ray spectral vectors, N * Is a matrix of discrete points and coefficients of an X-ray energy spectrum curve(Vector)
5. The method of claim 4, wherein the X-ray energy spectrum estimation method based on the rational fraction fitting multi-energy projection curve comprises: the number of rows of the coefficient matrix A is more than or equal to the number of columns, namely M * ≥N * 。
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Cited By (5)
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| CN108992083A (en) * | 2018-08-14 | 2018-12-14 | 广州华端科技有限公司 | Cone beam computed tomography method for correcting image and system |
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| CN112581556A (en) * | 2020-12-25 | 2021-03-30 | 上海联影医疗科技股份有限公司 | Multi-energy CT image hardening correction method and device, computer equipment and storage medium |
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| CN113392509B (en) * | 2021-05-27 | 2022-08-23 | 南方医科大学 | Accurate estimation method for actual energy spectrum of X-ray |
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