Information extraction method based on dose distribution and X-ray phase contrast imaging system
阅读说明：本技术 基于剂量分布的信息提取方法及x射线相衬成像系统 (Information extraction method based on dose distribution and X-ray phase contrast imaging system ) 是由 张丽 吴承鹏 高河伟 邢宇翔 于 2019-11-11 设计创作，主要内容包括：一种基于剂量分布的信息提取方法及X射线相衬成像系统,所述信息提取方法包括：以机械步进方式或等同于机械步进的方式在设置物体和不设置物体的情况下分别进行曝光；X射线探测器在曝光后进行探测,获取背景位移曲线和物体位移曲线；采用一信息提取算法分析背景位移曲线和物体位移曲线,以提取出物体的相衬或暗场信息；其中,机械步进方式或等同于机械步进的方式中,各步的X射线剂量不是均匀的,各步的X射线剂量遵循一特定剂量分布,所述特定剂量分布使得总剂量保持固定的情况下相衬或者暗场信息的方差最小且均值不变。该分布降低了数据的噪声,可以在相同总剂量下得到更低噪声水平的对比度信息或者在相同的噪声水平下降低采集需要的总剂量。(An information extraction method based on dose distribution and an X-ray phase contrast imaging system are provided, wherein the information extraction method comprises the following steps: respectively carrying out exposure under the conditions of setting an object and not setting the object in a mechanical stepping mode or a mode equivalent to the mechanical stepping mode; detecting by an X-ray detector after exposure to obtain a background displacement curve and an object displacement curve; analyzing the background displacement curve and the object displacement curve by adopting an information extraction algorithm to extract phase contrast or dark field information of the object; wherein, in the mechanical stepping mode or the mode equivalent to the mechanical stepping mode, the X-ray dose of each step is not uniform, and the X-ray dose of each step follows a specific dose distribution, wherein the specific dose distribution enables the variance of phase contrast or dark field information to be minimum and the mean value to be unchanged under the condition that the total dose is kept fixed. This distribution reduces the noise of the data, allowing for lower noise level contrast information at the same total dose or reducing the total dose required for acquisition at the same noise level.)
1. An information extraction method based on dose distribution, which is used for an X-ray phase contrast imaging system, and is characterized in that the information extraction method comprises the following steps:
respectively carrying out exposure under the conditions of setting an object and not setting the object in a mechanical stepping mode or a mode equivalent to the mechanical stepping mode;
detecting by an X-ray detector after exposure to obtain a background displacement curve without an object and an object displacement curve with the object;
analyzing the background displacement curve and the object displacement curve by adopting an information extraction algorithm to extract phase contrast or dark field information of the object;
wherein in the mechanical stepping mode or the mode equivalent to mechanical stepping, the X-ray dose of each step is not uniform, and the X-ray dose of each step follows a specific dose distribution, wherein the specific dose distribution enables the variance of phase contrast or dark field information to be minimum and the mean value to be unchanged under the condition that the total dose is kept fixed.
2. The information extraction method of claim 1, wherein the information extraction algorithm comprises one or more of the following algorithms: D-MMA, GD-MMA, TA-MMA and DB-MMA.
3. The information extraction method of claim 2, wherein when the information extraction algorithm is D-MMA, GD-MMA, TA-MMA, or DB-MMA, the specific dose distribution is related to a kernel function in the information extraction algorithm.
4. The information extraction method according to claim 3, wherein when the information extraction algorithm is D-MMA, GD-MMA, or TA-MMA, the X-ray dose of each step in the specific dose distribution is proportional to a kernel function in the information extraction algorithm, and the specific dose distribution is weighted by the kernel function.
5. The information extraction method according to claim 3, wherein when the information extraction algorithm is DB-MMA, the specific dose distribution satisfies:
x＝eiRF-1＝[x0，x1，...，xN-1]
Wherein t (n) represents the dose for each step; n is 1,.. and N is the total number of steps; e.g. of the typeiRepresents a three-dimensional unit vector of 0 at the i-th position, otherwise; r represents a Jacobian matrix in a matrix expression of three kinds of contrast information, and each element in the Jacobian matrix is a kernel function corresponding to the contrast information; f is a circulant matrix with the elements of the circulant matrix being background displacement curves.
6. The information extraction method according to claim 1, wherein the X-ray dose of each step is controlled by adjusting one or more of a current of the X-ray source, an exposure time, a voltage of the X-ray source, or an intensity of the X-ray source of each step so that the X-ray dose of each step follows a specific dose distribution.
7. The information extraction method according to claim 1,
the X-ray source providing the X-rays is one of the following light sources: an X-ray source, a microfocus X-ray source, and a synchrotron radiation X-ray source;
the X-ray detector comprises one of the following detectors: an energy integrating type detector or a photon counting type detector.
8. The information extraction method of claim 1, wherein the X-ray phase contrast imaging system comprises one of the following imaging systems: an analytical crystal-based imaging system, a grating-based imaging system, and an edge-illuminated imaging system;
wherein the grating-based imaging system comprises one of a Talbot-Lau type, a geometric projection type, and a bi-phase grating type.
9. An X-ray phase contrast imaging system is characterized in that a background displacement curve and an object displacement curve are obtained in a mechanical stepping mode or a mode equivalent to the mechanical stepping mode; analyzing the background displacement curve and the object displacement curve by adopting an information extraction algorithm to extract phase contrast or dark field information of the object; wherein in the mechanical stepping mode or the mode equivalent to mechanical stepping, the X-ray dose of each step is not uniform, and the X-ray dose of each step follows a specific dose distribution, wherein the specific dose distribution enables the variance of phase contrast or dark field information to be minimum and the mean value to be unchanged under the condition that the total dose is kept fixed.
10. The X-ray phase contrast imaging system of claim 9, wherein the information extraction algorithm comprises one or more of the following algorithms: D-MMA, GD-MMA, TA-MMA and DB-MMA;
optionally, when the information extraction algorithm is D-MMA, GD-MMA, TA-MMA or DB-MMA, the specific dose distribution is related to a kernel function in the information extraction algorithm;
further optionally, when the information extraction algorithm is D-MMA, GD-MMA, or TA-MMA, the X-ray dose of each step in the specific dose distribution is proportional to a kernel function in the information extraction algorithm, and the specific dose distribution takes the kernel function as a weight;
further optionally, when the information extraction algorithm is DB-MMA, the specific dose distribution satisfies:
x＝eiRF-1＝[x0，x1，...，xN-1]
Wherein t (n) represents the dose for each step; n is 1,.. and N is the total number of steps; e.g. of the typeiRepresents a three-dimensional unit vector of 0 at the i-th position, otherwise; r represents a Jacobian matrix in a matrix expression of three kinds of contrast information, and each element in the Jacobian matrix is a kernel function corresponding to the contrast information; f is a circulant matrix with the elements of the circulant matrix being background displacement curves.
Technical Field
The disclosure belongs to the technical field of X-ray imaging, and relates to an information extraction method based on dose distribution and an X-ray phase contrast imaging system.
Background
The X-ray phase contrast imaging technology can realize local structure resolution on a micron or even submicron level, and is a good supplement to the traditional X-ray attenuation imaging technology. The technology can simultaneously extract three kinds of contrast information of absorption, phase contrast and dark field, and is suitable for low atomic number and low density substances, in particular to biological soft tissue structures including mammary glands.
Depending on the Imaging principle, the X-ray phase contrast Imaging currently implemented on conventional X-ray sources mainly includes analytical crystal-based Imaging (ABI), Grating-based Imaging (GI), Speckle-based Imaging (SI), and Edge-Illumination Imaging (EI). In order to obtain information contained due to micro refraction and scattering of radiation in a substance, the above three other X-ray phase contrast imaging systems usually obtain a displacement curve on each detector pixel by a step-and-scan method, such as a phase-stepping method in an X-ray grating phase contrast imaging technique, wherein the displacement curve is approximated by a cosine curve, and a gaussian curve in an edge-illuminated imaging. The method comprises the steps of obtaining a background displacement curve and an object displacement curve under the conditions that an object exists and the object does not exist respectively, and then obtaining attenuation information, refraction information and small-angle scattering information corresponding to the object from the difference of the two curves through an information extraction method, wherein the attenuation information, the refraction information and the small-angle scattering information correspond to three image contrasts of absorption, phase contrast and a dark field respectively.
Most of the existing analysis methods reduce the noise of data by optimizing information extraction algorithms. There is still a need to further improve the noise problem.
Disclosure of Invention
Technical problem to be solved
The invention provides an information extraction method based on dose distribution and an X-ray phase contrast imaging system, wherein the X-ray dose of each step in a step scanning mode is changed, so that the dose of X-rays is distributed regularly, the distribution reduces the noise of data, and the contrast information with lower noise level can be obtained under the condition of the same total dose or less total dose needs to be acquired when the contrast information with the same noise level is obtained.
(II) technical scheme
According to an aspect of the present disclosure, there is provided a dose distribution-based information extraction method for an X-ray phase contrast imaging system, the information extraction method including: respectively carrying out exposure under the conditions of setting an object and not setting the object in a mechanical stepping mode or a mode equivalent to the mechanical stepping mode; detecting by an X-ray detector after exposure to obtain a background displacement curve without an object and an object displacement curve with the object; analyzing the background displacement curve and the object displacement curve by adopting an information extraction algorithm to extract phase contrast or dark field information of the object; wherein in the mechanical stepping mode or the mode equivalent to mechanical stepping, the X-ray dose of each step is not uniform, and the X-ray dose of each step follows a specific dose distribution, wherein the specific dose distribution enables the variance of phase contrast or dark field information to be minimum and the mean value to be unchanged under the condition that the total dose is kept fixed.
The information extraction algorithm comprises one or more of the following algorithms: D-MMA, GD-MMA, TA-MMA and DB-MMA.
In an embodiment of the present disclosure, when the information extraction algorithm is D-MMA, GD-MMA, TA-MMA, or DB-MMA, the particular dose distribution is related to a kernel function in the information extraction algorithm.
In an embodiment of the present disclosure, when the information extraction algorithm is D-MMA, GD-MMA or TA-MMA, the X-ray dose of each step in the specific dose distribution is proportional to a kernel function in the information extraction algorithm, and the specific dose distribution takes the kernel function as a weight.
When the information extraction algorithm is DB-MMA, the specific dose distribution satisfies:
t is a constant
x＝eiRF-1＝[x0，x1，...，xN-1]
Wherein t (n) represents the dose for each step; n is 1,.. and N is the total number of steps; e.g. of the typeiRepresents a three-dimensional unit vector of 0 at the i-th position, otherwise; r represents a Jacobian matrix in a matrix expression of three kinds of contrast information, and each element in the Jacobian matrix is a kernel function corresponding to the contrast information; f is a circulant matrix with the elements of the circulant matrix being background displacement curves.
In an embodiment of the present disclosure, the X-ray dose of each step is controlled by adjusting one or more of a current of the X-ray source, an exposure time, a voltage of the X-ray source, or an intensity of the X-ray source of each step, such that the X-ray dose of each step follows a specific dose distribution.
In an embodiment of the present disclosure, the X-ray source providing the X-rays is one of the following light sources: an X-ray source, a microfocus X-ray source, and a synchrotron radiation X-ray source;
the X-ray detector comprises one of the following detectors: an energy integrating type detector or a photon counting type detector.
In an embodiment of the present disclosure, the X-ray phase contrast imaging system comprises one of the following imaging systems: an analytical crystal-based imaging system, a grating-based imaging system, and an edge-illuminated imaging system;
wherein the grating-based imaging system comprises one of a Talbot-Lau type, a geometric projection type, and a bi-phase grating type.
According to another aspect of the present disclosure, there is provided an X-ray phase contrast imaging system that obtains a background displacement curve and an object displacement curve in a mechanical step-by-step manner or equivalent to the mechanical step-by-step manner; analyzing the background displacement curve and the object displacement curve by adopting an information extraction algorithm to extract phase contrast or dark field information of the object; wherein in the mechanical stepping mode or the mode equivalent to mechanical stepping, the X-ray dose of each step is not uniform, and the X-ray dose of each step follows a specific dose distribution, wherein the specific dose distribution enables the variance of phase contrast or dark field information to be minimum and the mean value to be unchanged under the condition that the total dose is kept fixed.
In an embodiment of the present disclosure, the information extraction algorithm includes one or more of the following algorithms: D-MMA, GD-MMA, TA-MMA and DB-MMA.
In an embodiment of the present disclosure, when the information extraction algorithm is D-MMA, GD-MMA, TA-MMA, or DB-MMA, the particular dose distribution is related to a kernel function in the information extraction algorithm.
In an embodiment of the present disclosure, when the information extraction algorithm is D-MMA, GD-MMA or TA-MMA, the X-ray dose of each step in the specific dose distribution is proportional to a kernel function in the information extraction algorithm, and the specific dose distribution takes the kernel function as a weight.
When the information extraction algorithm is DB-MMA, the specific dose distribution satisfies:
x＝eiRF-1＝[x0，x1，...，xN-1]
Wherein t (n) represents the dose for each step; n is 1,.. and N is the total number of steps; e.g. of the typeiRepresents a three-dimensional unit vector of 0 at the i-th position, otherwise; r represents a Jacobian matrix in a matrix expression of three kinds of contrast information, the JacobianIn the comparable matrix, each element is a kernel function corresponding to the contrast information; f is a circulant matrix with the elements of the circulant matrix being background displacement curves.
(III) advantageous effects
According to the technical scheme, the information extraction method based on the dose distribution and the X-ray phase contrast imaging system have the following beneficial effects:
(1) the X-ray dose of each step in a step scanning mode is changed, so that the X-ray dose of each step is distributed in a certain rule, the variance and the mean of phase contrast or dark field information are minimum and the extracted phase contrast or dark field information is minimum under the condition that the total dose is kept fixed due to the specific dose distribution, the noise of data is reduced due to the distribution, and the contrast information with lower noise level can be obtained under the condition of the same total dose; reducing the overall dose level in the data acquisition process under the condition of ensuring the contrast information with the same noise level;
(2) the solution method of the variable dose distribution is suitable for various X-ray phase contrast imaging systems, such as ABI, EI and GI, and the GI system is not limited in category, namely various systems including Talbot-Lau type, geometric projection type, bi-phase grating type and the like, and the application range is wide.
Drawings
Fig. 1 is a flowchart illustrating a method for extracting information based on dose distribution according to an embodiment of the present disclosure.
Fig. 2 is a schematic diagram of (a) an X-ray phase contrast imaging system and (b) two displacement curves according to an embodiment of the present disclosure.
Fig. 3 is a schematic diagram of a process of acquiring image information by using the information extraction method shown in fig. 1.
Fig. 4 is a diagram illustrating a result of comparing an optimal exposure time distribution in the information extraction method according to an embodiment of the present disclosure with a conventional method.
FIG. 5 is a cross-sectional comparison graph of phase contrast information extracted by the optimized weighted distribution exposure time acquisition mode and (a) uniformly distributed exposure time in the case of processing simulation data by using the D-MMA algorithm.
FIG. 6 is a comparison graph of noise levels of phase contrast information extracted using the D-MMA algorithm for processing simulation data, uniformly distributed exposure times, and optimized weighted distribution exposure time acquisition modes according to one embodiment of the present disclosure.
Detailed Description
The existing methods for acquiring both background displacement curves and object displacement curves are usually based on uniformly spaced mechanical structure steps, while the X-ray dose of each step is the same, i.e. the X-ray source voltage, current, exposure time, etc. remain unchanged.
The method is based on the characteristics of an MMA data analysis method, and provides an information extraction method based on dose distribution and an X-ray phase contrast imaging system. In other words, the overall dose level during data acquisition can be reduced under contrast information conditions that guarantee the same noise level, which is of great significance for many practical applications of X-ray phase contrast imaging.
The disclosed dose distribution method and system of an X-ray phase contrast imaging system are directed to an imaging system based on a mechanical stepping mode, or other imaging modes or systems capable of obtaining a similar background displacement curve and an object displacement curve, such as a distributed incoherent X-ray source sequential exposure mode based on a direction perpendicular to a grating stripe in the publication number "WO 2016070771a 1" and the invention name "X-ray phase contrast imaging system and imaging method", or an X-ray phase contrast imaging system capable of forming a background displacement curve and an object displacement curve similar to a mechanical stepping mode in a staggered grating or inclined grating and distributed incoherent X-ray source sequential exposure mode parallel to a grating stripe direction in chinese patent application number 201910439158.1. The types of systems to which the dose distribution method of the present application is applicable include ABI, EI, and GI, and the GI system category is not limited, i.e., includes various types of systems such as Talbot-Lau type, geometric projection type, and bi-phase grating type. In addition, the object position can be placed between the light source and the first grating or between the two gratings. In addition, the X-ray source can be a conventional X-ray source, a microfocus X-ray source or a synchrotron X-ray source. Furthermore, the X-ray detector may be either an energy integration type detector or a photon counting type detector.
For the purpose of promoting a better understanding of the objects, aspects and advantages of the present disclosure, reference is made to the following detailed description taken in conjunction with the accompanying drawings.
First embodiment
In a first exemplary embodiment of the present disclosure, a dose distribution method of an X-ray phase contrast imaging system is provided.
Under the condition that other conditions are not changed, the dosage of the X-ray is in direct proportion to the current and the exposure time of the X-ray source, has a certain relation with the voltage of the X-ray source, and is in direct proportion to the light intensity of the X-ray source, so that the dosage of the X-ray is in direct proportion to the light intensity received by the detector according to the beer's law. In this embodiment, in order to adjust the X-ray dose of each step more clearly, the X-ray dose control is realized by changing the current of the X-ray source or the exposure time. It is clear that changing the dose size of each step can cause problems in the original information extraction method, and dose distribution control needs to overcome adverse effects on the information extraction method and also needs to assist the information extraction method in reducing data noise.
Fig. 1 is a flowchart illustrating a dose distribution method of an X-ray phase contrast imaging system according to an embodiment of the present disclosure.
Referring to fig. 1, the information extraction method based on dose distribution of the present disclosure includes:
step S11: respectively carrying out exposure under the conditions of setting an object and not setting the object in a mechanical stepping mode or a mode equivalent to the mechanical stepping mode; wherein in the mechanical stepping mode or the mode equivalent to mechanical stepping, the X-ray dose of each step is not uniform, and the X-ray dose of each step follows a specific dose distribution, wherein the specific dose distribution enables the variance of phase contrast or dark field information to be minimum and the mean value to be unchanged under the condition that the total dose is kept fixed;
in an embodiment of the present disclosure, the information extraction algorithm includes one or more of the following algorithms: D-MMA, GD-MMA, TA-MMA and DB-MMA.
In an embodiment of the present disclosure, when the information extraction algorithm is D-MMA, GD-MMA, TA-MMA, or DB-MMA, the particular dose distribution is related to a kernel function in the information extraction algorithm.
In an embodiment of the present disclosure, when the information extraction algorithm is D-MMA, GD-MMA or TA-MMA, the X-ray dose of each step in the specific dose distribution is proportional to a kernel function in the information extraction algorithm, and the specific dose distribution takes the kernel function as a weight.
In an embodiment of the present disclosure, when the information extraction algorithm is DB-MMA, the specific dose distribution satisfies:
x＝eiRF-1＝[x0，x1，...，xN-1]
Wherein t (n) represents the dose for each step; n is 1,.. and N is the total number of steps; e.g. of the typeiRepresents a three-dimensional unit vector of 0 at the i-th position, otherwise; r represents a Jacobian matrix in a matrix expression of three kinds of contrast information, and each element in the Jacobian matrix is a kernel function corresponding to the contrast information; f is a circulant matrix with the elements of the circulant matrix being background displacement curves.
The derivation of the specific dose distribution is described in the following with specific examples.
Step S12: detecting by an X-ray detector after exposure to obtain a background displacement curve without an object and an object displacement curve with the object;
in an embodiment of the present disclosure, the X-ray imaging system comprises one of the following imaging systems: an analytical crystal-based imaging system (ABI), a grating-based imaging system (GI), and an edge-illuminated imaging system (EI);
wherein the grating-based imaging system (GI) comprises one of a Talbot-Lau type, a geometric projection type, and a bi-phase grating type.
Fig. 2 is a schematic diagram of (a) an X-ray phase contrast imaging system and (b) two displacement curves according to an embodiment of the present disclosure.
In the present embodiment, taking a Talbot-Lau type GI system as an example, referring to (a) in fig. 2, the X-ray phase contrast imaging system mainly includes an X-ray source S, a source grating G0, a phase grating G1, an analyzer grating G2, and an X-ray detector.
The X-ray source providing X-rays is one of the following sources: x-ray sources (conventional X-ray sources), microfocus X-ray sources, and synchrotron radiation X-ray sources.
The source grating G0, the phase grating G1 and the analyzer grating G2 form a fixed grating module P, the distance between the source grating G0 and the phase grating G1 is L, and the distance between the phase grating G1 and the analyzer grating G2 is D. The position of the object W to be scanned may be between the light source and the first grating or between two gratings.
The X-ray detector comprises one of the following detectors: an energy integrating type detector or a photon counting type detector.
Referring to fig. 2 (b), the step position is an abscissa, the signal intensity detected by the X-ray detector is an ordinate, the background displacement curve corresponding to the non-placed object is indicated by a circle, and the object displacement curve corresponding to the placed object is indicated by a square. Hereinafter, f (φ) and S (φ) are used to respectively represent the background displacement curve and the object displacement curve, where φ represents the position during the stepping process, in this embodiment, step S11 is used to adjust the X-ray dose at each step during the stepping process, and the dose is not shown in (b) of FIG. 2.
Step S13: analyzing the background displacement curve and the object displacement curve by adopting an information extraction algorithm to extract phase contrast or dark field information of the object;
in this embodiment, the information extraction algorithm includes one or more of the following algorithms: D-MMA, GD-MMA, TA-MMA and DB-MMA. The D-MMA method is not suitable for the X-ray grating integrated imaging system, and the applicant has found that if the background displacement curve is translated so that the maximum value is located at the center position, and the corresponding object displacement curve is translated by the same distance, the method can be applied to the GI system. On the basis of the above, the applicant's prior patent, chinese patent application No. 201910593224.0, found that both displacement curves satisfy an integral characteristic, namely: the inner product of the displacement curve and any one function only contains the zeroth order term and the first order term in the Fourier series, so that a generalized D-MMA method, namely GD-MMA, is established, the range of the kernel function is widened, and the patent application provides an optimized kernel function form. Another analytical MMA-like information extraction algorithm is proposed in applicant's patent application No. 201910207542.9, which is described in the original document as: the ASAXS (analytical small angle X-ray scattering) method, which is referred to as TA-MMA herein, is applicable to the information extraction algorithm in the above three patents.
Fig. 3 is a schematic diagram of a process of acquiring image information by using the information extraction method shown in fig. 1.
The following method for extracting information of D-MMA, DB-MMA, GD-MMA and TA-MMA will be specifically described, and then referring to fig. 3, it will be described that the X-ray dose determined at each step in the information extraction method based on dose distribution follows a specific dose distribution and the derivation process of the expression form of the specific dose distribution, by taking an example of extracting specific information (for example, phase contrast information, but of course, dark field information) by using a specific information extraction algorithm (for example, GD-MMA information extraction algorithm) under one specific imaging system (for example, a Talbot-Lau type GI system).
In this example, under a GI system of Talbot-Lau type, phase contrast information is extracted using a GD-MMA information extraction algorithm, the X-ray dose for each step is not uniform, and the X-ray dose for each step follows a specific dose distribution.
Introduction of MMA information extraction algorithm
1. MMA Process
Multi-moment Analysis (MMA) based on Small Angle Scattering (SAXS, Small Angle X-ray Scattering) is a convolution-based data Analysis method. The basic assumptions for MMA-like processes are: the object displacement curve s (φ) may be expressed as a convolution of the background displacement curve f (φ) and the small angle scattering distribution g (φ), with the expression:
2. DB-MMA Process
In DB-MMA, DB-MMA is based on Deconvolution-based MMA method (DB-MMA, Deconvolution-based MMA), firstly, Deconvolution is carried out from a background displacement curve f (phi) and an object displacement curve s (phi) on each acquired X-ray detector pixel by a Lucy-Richardson iteration method to obtain small-angle scattering distribution, here, in order to highlight the key point, the parameter inside brackets, the position phi in the stepping process is omitted, the full-text omission mode is the same, and the k-th iteration calculation formula in the Deconvolution process is as follows:
wherein the content of the first and second substances,
A→M0(g)＝∫g(φ)dφ (3)
Wherein M isn(g) Representing the original n-order moment of g (phi),
The DB-MMA has the advantages that model assumption is not needed to be carried out on a displacement curve, the noise level of an acquired image is low, the problem of phase wrapping does not occur, more information of third moment and above can be calculated, but the limiting factors are that the calculation time of a deconvolution iterative process is long, the optimal iteration times need to be set manually, and the iteration possibly causes loss of part of structural details.
3. D-MMA method
On the basis of DB-MMA, D-MMA also starts from the convolution relation in the formula (1), and can be obtained according to the Fourier transform property of the convolution:
wherein the content of the first and second substances,and
from the formula (6), it can be obtained
the reduction and normalization of equations (8) to (10) in equation (7) can obtain the multi-order moment expressions corresponding to absorption, phase contrast, and dark field as:
the greatest advantage of D-MMA over DB-MMA is that the complex and time-consuming deconvolution iterative process is avoided, and the same multi-moment information can be obtained without introducing more model assumptions.
4. GD-MMA process
In particular, in X-ray phase contrast imaging (GI) based on gratings, from theories such as fresnel diffraction in wave optics and moire bias in geometric optics, researchers have found that when only ± 1 st order diffraction is considered, the background displacement curve can be regarded as a cosine function model, and in practical experiments, the model is found to fit well with actual data, so in the GI system, the background displacement curve can be expressed as:
based on the above expression and the orthogonality of the trigonometric function, the applicant's chinese patent application No. 201910593224.0 found that both displacement curves satisfy an integral characteristic, namely: the inner product of the displacement curve and any one function only contains the zeroth order term and the first order term in the Fourier series. From the D-MMA method described above, it was found that D-MMA is mainly calculated from f (φ) or s (φ) and another kernel function h (φ) (e.g., h for phase contrast)P(phi) is phi, h for dark fieldD(φ)＝φ2) The inner product of (d). Applying this integral characteristic of the displacement curve to the displacement curve, chinese patent application No. 201910593224.0 established a generalized D-MMA method, namely GD-MMA. In GD-MMA, the kernel functions in the computation corresponding to phase contrast and dark field information, respectively, are:
further, chinese patent application No. 201910593224.0 also finds an optimal GD-MMA kernel function for noise suppression, namely:
5. TA-MMA method
The applicant's chinese patent application No. 201910207542.9 proposes another algorithm for extracting MMA-like information, TA-MMA, whose information extraction method is as follows:
wherein M is0Zero order moment for small angle scattering distribution (scattering angle distribution); m1Is the first moment of the small angle scattering distribution; m2The second moment of the angular scattering distribution.
Wherein, SinM1(. o.) and CosM1(. cndot.) is defined as follows,
SinM1(y)＝∫sin(φ)y(φ)dφ (22)
CosM1(y)＝∫cos(φ)y(φ)dφ (23)
(II) dose distribution followed by X-ray dose in each step in MMA information extraction algorithm
The MMA method is based on the premise that a background displacement curve and an object displacement curve are acquired, a general acquisition mode is to perform mechanical stepping at uniform intervals and ensure that the X-ray dose of each step is the same (i.e., the X-ray source voltage, current, exposure time, etc. remain unchanged).
From the viewpoint of dose research, under the condition that other conditions are not changed, the dose of the X-ray is proportional to the current and the exposure time of the X-ray source, has a certain relation with the voltage of the X-ray source, and is certainly proportional to the light intensity of the X-ray source, so that the dose is proportional to the light intensity received by the detector according to the beer's law. Thus, in order to adjust the X-ray dose per step relatively unambiguously, the current of the X-ray source or the exposure time can be varied.
1. GD-MMA information extraction algorithm and D-MMA information extraction algorithm
In the following, under a Talbot-Lau type GI system, a GD-MMA information extraction algorithm is adopted to extract phase contrast information for analysis, and discussion is made to optimize the noise level of the finally extracted phase contrast information by changing the dose of each step under the condition that the total dose is not changed in the data acquisition process. Of course, in this example, the kernel function in GD-MMA is a broadened version of the kernel function in D-MMA, and the derivation is equally applicable to the D-MMA method.
For practical simplicity, the dose is changed by only changing the exposure time of each step, but of course, it is also possible to change the exposure time or other factors as long as the dose of X-rays can be adjusted. Assuming that the total number of steps is N and the exposure time of each step is t (N), where N is 1. The specific dose distribution is such that in the case where the total dose remains fixed (corresponding to the constraint of equation (25)), the phase contrast (corresponding to the phase contrast information expression in equation (24) in the present embodiment) or the variance of the dark field information is minimal (corresponding to equation (24)) and the mean value is unchanged (corresponding to equation (26)), since there is no object when the background displacement curve f (Φ) is acquired, there is no need to consider the dose caused to the scanned object in this portion, and the second term may not be considered in equation (12). The above optimization problem can therefore be expressed in the form:
wherein Var (·) represents the variance of the variable; min represents a minimum function;
Wherein
On the other hand, according to the existing data acquisition scheme, the doses corresponding to the steps are equal and are equal to the total dose divided by the total number of steps, i.e. t0(N) is equal to delta T and T/N, and an object displacement curve s under the condition of equal dosage in each step is obtained according to the (N) is equal to delta T0(n) and is generally regarded as s0(n) satisfies the cosine model as well as the background displacement curve, and s is known by referring to the form of equation (14)0(n) may be expressed as:
according to the fact that the dosage is proportional to the exposure time and the light intensity received by the detector, an object displacement curve expression s (n) under any exposure time distribution t (n) can be obtained, namely:
for the denominator in equation (24)In other words, it can be considered as
furthermore, considering the statistical noise of the detector, the noise in s (n) is generally considered to satisfy the poisson distribution, and thus can be expressed as:
wherein the content of the first and second substances,
in order for the constraint/constraint (25) to be satisfied, i.e., the mean value is constant, the kernel function needs to be removed from the exposure time distribution t (n), so as to obtain the objective function as follows:
from equation (32) above, it can be seen that the first term in parentheses is the mean, which remains unchanged regardless of t (n), and the second term is the source of variance, so the final optimization problem can be expressed as:
carrying out optimization solution by using a Lagrange multiplier method, and firstly obtaining a Lagrange function as follows:
wherein λ is a constant. Then, the partial derivatives are calculated for t (N), N ═ 1,.., N, and λ, and are set to 0:
from the first equation (36) we can derive:
thereby, it is possible to obtain:
substituting equation (39) into the second equation (37) results in the final optimal exposure time distribution expression:
the optimal exposure time distribution or the optimal dose distribution optimized according to the phase contrast information of the D-MMA and GD-MMA information extraction algorithms is the specific dose distribution introduced above.
As can be seen from equation (40) above, in this example, the particular dose distribution is associated with a kernel function in the information extraction algorithm.
In some application scenarios, s0(n) is not readily available, s can be approximated as0(n) is constant, giving the following approximate distribution: in one example, the X-ray dose for each step in the specific dose distribution is proportional to a kernel function in the information extraction algorithm, and the specific dose distribution takes the kernel function as a weight. The exposure time at data acquisition can be determined only by the kernel function in the algorithm:
2. TA-MMA information extraction algorithm
Furthermore, for the dose distribution optimization of the TA-MMA algorithm, the conclusion can also be drawn using equation (40) except that its kernel functions corresponding to the phase contrast information and the dark field information are obtained according to equations (20) and (21), for example, the kernel functions for the phase contrast information can be expressed as follows:
hP(φ)＝CosM1(f)sin(φ)-SinM1(f)cos(φ) (42)
as can be seen from the above, when the information extraction algorithm is D-MMA, GD-MMA, or TA-MMA, the particular dose distribution is related to the kernel function in the information extraction algorithm.
In one example, when the information extraction algorithm is D-MMA, GD-MMA, or TA-MMA, the X-ray dose for each step in the particular dose distribution is proportional to a kernel function in the information extraction algorithm, with the particular dose distribution weighted by the kernel function.
3. DB-MMA information extraction algorithm
In addition, the DB-MMA algorithm is less efficient but has wider application range, so the optimal form of the dose distribution is deduced by a noise propagation method in the following. In the following formulas, the matrix parameters are represented in bold font unless otherwise defined, for example,
Firstly, the convolution assumption relation formula (1) of DB-MMA can be expressed as follows in a matrix form:
wherein s represents a matrix form of an object displacement curve s (phi); fg represents a matrix form of convolution of the background displacement curve f (phi) and the small-angle scattering distribution g (phi); g represents a matrix form of the small-angle scattering distribution g (phi);
s＝[s(0)，s(1)，...，s(N-1)]T，g＝[g(0)，g(1)，...，g(N-1)]Tto do so
Wherein, VsA covariance matrix representing s; (matrix)TRepresents the transpose of the matrix (matrix)-1Representing an inverse matrix;
then, the DB-MMA information extraction formulas (3) to (5) are also expressed in matrix form as:
where M represents three kinds of contrast information: zero order moment M of small angle scattering distribution0Normalized first moment
M＝[M0(g)，M1(g)，M2(g)]Tjacobian matrix
In the jacobian matrix, each element in the first row, the second row and the third row is a kernel function corresponding to contrast information; from this relationship, the covariance matrix V of M can be obtained by the least square noise propagation relationship as wellM：
When the ith information of the three kinds of contrast information is optimized, the variance of one of the three kinds of contrast information can be expressed as:
wherein e isiRF-1Abbreviated as x, i.e. x-eiRF-1＝[x0，x1，...，xN-1]. In general, the noise at each step satisfies the poisson distribution, and thus is proportional to the exposure time, which results in:
according to the formulas (48) (49), it is possible to obtain:
therefore, the optimal distribution of DB-MMA is the dose distribution as long as equation (50) is satisfied, where t (n) satisfies equation (25). As can be seen from equation (50), the dose distribution is related to R, i.e., to the kernel function in the information extraction algorithm, and in equation (50), x is eiRF-1＝[x0，x1，...，xN-1]It is also stated that the dose distribution is also related to the value of the background displacement curve, and the dose distribution obtained based on equation (50) can achieve the extracted phase contrast or dark field information with unchanged value and minimum noise under the condition of non-uniformity.
As can be seen from the above, when the information extraction algorithm is DB-MMA, the specific dose distribution is related to the kernel function in the information extraction algorithm.
In order to more intuitively compare the difference between the optimal exposure time distribution and the conventional distribution derived above,
fig. 4 is a diagram illustrating a result of comparing an optimal exposure time distribution in the information extraction method according to an embodiment of the present disclosure with a conventional method. In FIG. 4, the optimized distribution of exposure times for both kernel functions D-MMA and GD-MMA is compared to the conventional uniform distribution, and the overall dose remains unchanged. D-MMA medium employing hPUsing h in optimal form of GD-MMA noiseP(phi) is optimized to sin (phi), and is obtained according to the formula (40)The exposure time distributions are compared.
FIG. 5 is a cross-sectional comparison graph of phase contrast information extracted by the optimized weighted distribution exposure time acquisition mode and (a) uniformly distributed exposure time in the case of processing simulation data by using the D-MMA algorithm.
With h in D-MMAPFor example, the distributions (a) and (b) in fig. 5 show phase contrast information cross-hatching for uniformly distributed exposure times and weighted distribution exposure times in the case of processing simulation data, and it is evident that the exposure times weighted with kernel functions at the same dose produce lower noise levels compared to (a) and (b) in fig. 5.
For further quantitative comparison, the objective function in equation (33) is calculated under the condition that the simulation data N is 19, and the exposure time values after the conventional uniform distribution and D-MMA kernel function weight optimization are respectively calculated, so as to calculate the theoretically reducible noise ratio as:
then, by changing different photon numbers, the noise level actually generated by two data acquisition modes under different poisson noise levels and the noise ratio reduced by weighted distribution are simulated, as shown in fig. 6, it can be seen that the noise ratio is basically near the theoretical value given by formula (51), and the rationality of the derivation process is proved.
Second embodiment
In a second exemplary embodiment of the present disclosure, an X-ray phase contrast imaging system is provided. The X-ray dose of each step in the X-ray phase contrast imaging system of the present embodiment follows a certain dose distribution. The X-ray phase contrast imaging system of the present disclosure can also implement three kinds of contrast information extraction using the information extraction method based on dose distribution mentioned in the present disclosure.
The X-ray phase contrast imaging system obtains a background displacement curve and an object displacement curve in a mechanical stepping mode or a mode equivalent to the mechanical stepping mode; analyzing the background displacement curve and the object displacement curve by adopting an information extraction algorithm to extract phase contrast or dark field information of the object; wherein in the mechanical stepping mode or the mode equivalent to mechanical stepping, the X-ray dose of each step is not uniform, and the X-ray dose of each step follows a specific dose distribution, wherein the specific dose distribution enables the variance of phase contrast or dark field information to be minimum and the mean value to be unchanged under the condition that the total dose is kept fixed.
In an embodiment of the present disclosure, the specific dose distribution is associated with a kernel function in an information extraction algorithm. For example, the information extraction algorithm is D-MMA, GD-MMA, TA-MMA, or GB-MMA.
In an embodiment of the present disclosure, the specific dose distribution is proportional to a kernel function in an information extraction algorithm. The information extraction algorithm is D-MMA, GD-MMA or TA-MMA.
In an embodiment of the present disclosure, when the information extraction algorithm is DB-MMA, the specific dose distribution satisfies:
t is a constant
x＝eiRF-1＝[x0，x1，...，xN-1]
Wherein t (n) represents the dose for each step; n is 1,.. and N is the total number of steps; e.g. of the typeiRepresents a three-dimensional unit vector of 0 at the i-th position, otherwise; r represents a Jacobian matrix in a matrix expression of three kinds of contrast information, and each element in the Jacobian matrix is a kernel function corresponding to the contrast information; f is a circulant matrix with the elements of the circulant matrix being background displacement curves.
In summary, the present disclosure provides an information extraction method based on dose distribution and an X-ray phase contrast imaging system, which first proposes that the dose of X-rays in each step is distributed regularly by changing the dose of X-rays in each step in a step-by-step scanning manner, and the specific dose distribution makes the variance of phase contrast or dark field information minimum and mean value unchanged under the condition that the total dose is kept fixed, so that the distribution reduces the noise of data, and can obtain contrast information with a lower noise level under the condition of the same total dose; the overall dose level in the data acquisition process can be reduced under the condition of ensuring the contrast information with the same noise level; the solution method of the variable dose distribution is suitable for various X-ray phase contrast imaging systems, such as ABI, EI and GI, and the GI system is not limited in category, namely various systems including Talbot-Lau type, geometric projection type, bi-phase grating type and the like, and the application range is wide.
The word "comprising" or "comprises" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. In addition, unless steps are specifically described or must occur in sequence, the order of the steps is not limited to that listed above and may be changed or rearranged as desired by the desired design. The embodiments described above may be mixed and matched with each other or with other embodiments based on design and reliability considerations, i.e., technical features in different embodiments may be freely combined to form further embodiments.
The above-mentioned embodiments are intended to illustrate the objects, aspects and advantages of the present disclosure in further detail, and it should be understood that the above-mentioned embodiments are only illustrative of the present disclosure and are not intended to limit the present disclosure, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present disclosure should be included in the scope of the present disclosure.
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