CN114081517A - Static dual-energy tomosynthesis imaging system and method - Google Patents

Static dual-energy tomosynthesis imaging system and method Download PDF

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CN114081517A
CN114081517A CN202111201682.9A CN202111201682A CN114081517A CN 114081517 A CN114081517 A CN 114081517A CN 202111201682 A CN202111201682 A CN 202111201682A CN 114081517 A CN114081517 A CN 114081517A
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赵生捷
张桐
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Tongji University
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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
    • A61B6/02—Devices for diagnosis sequentially in different planes; Stereoscopic radiation diagnosis
    • A61B6/03—Computerised tomographs
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
    • A61B6/50—Clinical applications
    • A61B6/502—Clinical applications involving diagnosis of breast, i.e. mammography
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
    • A61B6/52—Devices using data or image processing specially adapted for radiation diagnosis
    • A61B6/5211—Devices using data or image processing specially adapted for radiation diagnosis involving processing of medical diagnostic data
    • A61B6/5229—Devices using data or image processing specially adapted for radiation diagnosis involving processing of medical diagnostic data combining image data of a patient, e.g. combining a functional image with an anatomical image
    • A61B6/5235—Devices using data or image processing specially adapted for radiation diagnosis involving processing of medical diagnostic data combining image data of a patient, e.g. combining a functional image with an anatomical image combining images from the same or different ionising radiation imaging techniques, e.g. PET and CT

Abstract

The invention relates to a static dual-energy tomosynthesis camera system and a method, wherein the system comprises a fixed frame, one end of the fixed frame is fixed with a distributed carbon nano tube array light source, the other end of the fixed frame is fixed with a double-layer detector, the distributed carbon nano tube array light source comprises a plurality of field emission light sources which are distributed and arranged, the double-layer detector comprises two scintillation detectors which are mutually overlapped and respectively used for absorbing low-energy X-ray photons and high-energy X-ray photons. Compared with the prior art, the distributed carbon nanotube array light source is used for replacing a single-ray source + rotating frame framework in the traditional BDT, so that the scanning process in multi-angle measurement is avoided; the double-layer detector is adopted to receive the measurement information of the two energy spectrum regions respectively, so that a multi-energy spectrum tomographic image containing the motif material component information can be reconstructed, small lesions hidden in a two-dimensional image can be found, and unnecessary biopsy, measurement time and potential motion artifacts are reduced.

Description

Static dual-energy tomosynthesis imaging system and method
Technical Field
The invention relates to the field of three-dimensional tomosynthesis imaging, in particular to a static dual-energy tomosynthesis imaging system and a static dual-energy tomosynthesis imaging method.
Background
Three-dimensional tomosynthesis imaging is a new tomographic imaging mode, and can acquire a few two-dimensional projections of an object from a limited angle range, so that tomographic images of different depths reflecting three-dimensional information of the object can be reconstructed. Compared with the traditional computed tomography technology, the X-ray radiation device has the advantages of small X-ray radiation dose and low economic cost. As a potential screening tool, it has been used clinically for the detection of lung and breast cancer lesions.
A typical application of the three-dimensional Tomosynthesis imaging technology is Digital Breast Tomosynthesis imaging (DBT), which is composed of a high-pressure X-ray source, a rotating gantry, and an energy integrating detector, and collects the intensity of X-rays projected by the whole energy spectrum section as measurement data, and then uses the negative logarithm of the measurement data for filtered back-projection reconstruction.
However, such conventional DBTs have two drawbacks:
first, the system does not allow for the acquisition of measurements containing spectral attenuation information that can be used to identify the material composition of the object and reduce beam hardening artifacts. One existing prototype of a spectral three-dimensional tomosynthesis imaging system utilizes photon counting detectors, which allow both high and low energy measurements to be obtained. However, it is currently costly and pulse pile-up phenomena occur at high X-ray fluxes, which affect its use in routine clinical examinations;
secondly, the projection data of a plurality of projection angles acquired by the system are acquired by stepping or continuous rotation of the frame, so that the measurement time is long, and the scanned organ can move due to physiological movement of the patient, such as respiration, and the like, so that the final reconstructed image has artifacts.
Disclosure of Invention
The invention aims to provide a static dual-energy tomosynthesis imaging system and method for overcoming the defects of high cost and long measurement time of acquiring projection data of a plurality of projection angles by stepping or continuously rotating of a photon counting detector in the prior art.
The purpose of the invention can be realized by the following technical scheme:
a static dual-energy tomosynthesis camera system comprises a fixed frame, wherein a distributed carbon nanotube array light source is fixed at one end of the fixed frame, a double-layer detector is fixed at the other end of the fixed frame, the distributed carbon nanotube array light source comprises a plurality of field emission light sources which are distributed and arranged, the double-layer detector comprises two scintillation detectors which are overlapped with each other and are respectively used for absorbing low-energy X-ray photons and high-energy X-ray photons.
Furthermore, the distributed carbon nanotube array light source comprises a field emission anode and a plurality of field emission cathodes arranged in a distributed manner, each field emission cathode is connected with a corresponding control circuit, and the field emission cathodes are carbon nanotube-based field emission cathodes.
Further, the control circuit is an MOS tube, and a grid electrode of the MOS tube is pre-programmed with a pulse signal.
Furthermore, the static dual-energy tomosynthesis camera system also comprises a pressing plate, wherein the pressing plate is arranged on the fixed rack, is positioned between the distributed carbon nanotube array light source and the double-layer detector and is used for matching with the double-layer detector to fix the die body.
The invention also provides a tomosynthesis imaging method of the static dual-energy tomosynthesis imaging system, which comprises the following steps:
installing a die body to be photographed in front of the double-layer detector, transmitting X rays through a distributed carbon nanotube array light source according to a preset pulse signal, synchronously triggering and controlling the exposure of the double-layer detector through an electric signal, and simultaneously obtaining measurement data of two spectral bands of low energy and high energy;
and combining the pre-constructed detector measurement value calculation formula with the obtained measurement data of the low-energy spectrum and the high-energy spectrum to construct an optimization problem of the reconstructed image, obtaining an optimal solution of the reconstructed image through continuous iterative optimization, and multiplying the optimal solution by the attenuation coefficient of the base material to obtain the energy spectrum tomographic image of the die body to be photographed.
Further, the construction process of the detector measurement value calculation formula comprises the following steps:
respectively constructing low-energy and high-energy measurement value calculation formulas of the double-layer detector;
acquiring linear attenuation coefficients of the die body to be shot according to the components of the die body to be shot, and substituting the linear attenuation coefficients into the low-energy and high-energy measurement value calculation formulas;
and converting the low-energy and high-energy measurement value calculation formula into a discretization form, and constructing the low-energy and high-energy measurement value calculation formula containing all the field emission light sources.
Further, the calculation formula of the low-energy and high-energy measured values of the double-layer detector is as follows:
Figure RE-GDA0003458674090000031
Figure RE-GDA0003458674090000032
in the formula I0(E) Is the energy spectrum of the field emission light source, d (e) is the spectral response of the double layer detector,
Figure RE-GDA0003458674090000033
as a die body point
Figure RE-GDA0003458674090000034
The linear attenuation coefficient of (a) is,
Figure RE-GDA0003458674090000035
a projection path for X-rays, EthTo distinguish the threshold for high and low energy, IlowFor low energy measurement, IhighFor high energy measurement, EminAs energy minimum, EmaxIs the energy maximum;
the components of the die body to be shot comprise fat and glands, and the linear attenuation coefficient of the die body to be shot has an expression formula as follows:
Figure RE-GDA0003458674090000036
wherein τ (E) represents the linear attenuation coefficient of the component,
Figure RE-GDA0003458674090000037
indicating that the component is at the point
Figure RE-GDA0003458674090000038
Specific gravity ofSubscripts 1 and 2 correspond to the components fat and gland, respectively;
after substituting the linear attenuation coefficient of the die body to be shot, the calculation formula of the low-energy and high-energy measured values is as follows:
Figure RE-GDA0003458674090000039
Figure RE-GDA00034586740900000310
the low and high energy measurements comprising all field emission light sources are calculated as:
yliw＝exp(-HXT)·wlow
yhigh＝exp(-HXT)·whigh
in the formula, ylowFor low energy measurements involving all field emission light sources, yhighTo contain high energy measurements of all field emission light sources,
Figure RE-GDA00034586740900000311
Mx×Myis the detection dimension of the double-layer detector,
Figure RE-GDA00034586740900000312
indicating the high and low energy spectral response of the dual-energy detector,
Figure RE-GDA00034586740900000313
representing the weight of the ith base material in each voxel in a phantom that is discrete by N voxels,
Figure RE-GDA00034586740900000314
the spectral attenuation of 2 materials in a total of K spectral intervals is shown, and H is the intersection of each projection path and each voxel in the phantom.
Further, the expression of the optimization problem of the reconstructed image is as follows:
Figure RE-GDA00034586740900000315
in the formula, X is a reconstructed image.
Further, a three-dimensional total variation regularization is added to the optimization problem of the reconstructed image, and an expression of the optimization problem of the reconstructed image is as follows:
Figure RE-GDA0003458674090000041
s.t.ylow＝exp(-HXT)·wlow
yhigh＝exp(-HXT)·whigh
in the formula, X*In order to add a reconstructed image obtained after three-dimensional total variation regularization,
Figure RE-GDA0003458674090000042
represents X:,lIs used in the form of a three-dimensional tensor.
Further, in the iterative optimization process, an intermediate variable Z is introduced, and X and Z are alternately updated through iteration until a preset stop condition is met, so that an optimal solution of a reconstructed image is obtained;
the optimized expression for iteratively and alternately updating X and Z is as follows:
Figure RE-GDA0003458674090000043
s.t.ylow＝exp(-HXT)·wlow,yhigh＝exp(-HXT)·whigh
in the formula, λ is a regular term weight, and t is an iteration step number.
Compared with the prior art, the invention has the following advantages:
(1) according to the static dual-energy tomosynthesis camera system provided by the invention, firstly, a distributed carbon nanotube array light source is used for replacing a single-ray source and a rotating frame framework in the traditional BDT, so that the scanning process in multi-angle measurement is avoided; and secondly, a double-layer detector is adopted to receive the measurement information of the two energy spectrum regions respectively, so that a multi-energy spectrum tomographic image containing the material component information of the phantom can be reconstructed.
(2) The invention also provides a corresponding tomosynthesis imaging method for the static dual-energy tomosynthesis imaging system, which divides the measurement value calculation formula of the detector into high energy and low energy, constructs the measurement value calculation formula containing all the sub-light sources in a discrete form and realizes the three-dimensional image reconstruction of the static dual-energy tomosynthesis imaging system.
(3) In the iterative optimization process of obtaining the three-dimensional image X, the three-dimensional total variation regularization is added to improve the quality of a reconstructed image, an intermediate variable Z is introduced, X and Z are iteratively and alternately updated, and the matching precision of the obtained three-dimensional image X and the convergence speed in the iterative process are further improved.
(4) The static dual-energy tomosynthesis camera system provided by the invention can obtain three-dimensional chromatographic images reflecting breast structure and component information, and can discover tiny lesions hidden in a two-dimensional image by utilizing the three-dimensional chromatographic images; eliminating false positives and false negatives caused by the two-dimensional projection images; judging disease information by using the structure and component information of the tumor reflected by the energy spectrum three-dimensional chromatographic image, and reducing unnecessary biopsy; meanwhile, due to the fact that no scanning process exists, measuring time and potential motion artifacts are reduced.
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Fig. 1 is a schematic structural diagram of a distributed carbon nanotube X-ray source array according to an embodiment of the present invention, which is composed of a plurality of field emission light sources;
FIG. 2 is a schematic structural diagram of a dual-layer detector according to an embodiment of the present invention, which is composed of two conventional scintillation detectors stacked on each other;
fig. 3 is a schematic structural diagram of a static dual-energy tomosynthesis imaging system provided in an embodiment of the present disclosure, which mainly includes a distributed carbon nanotube X-ray source array, a dual-layer detector, a fixed frame, and a pressing plate;
FIG. 4 is a 2-dimensional projection of a phantom used in experiments in accordance with embodiments of the present invention at an angle of 0, including two materials: fat and glands (soft tissue);
fig. 5 is a three-dimensional tomosynthesis image of two basic materials contained in the phantom in the embodiment of the present invention, wherein Z is 2 to 10, which represents a tomosynthesis image of an even number layer of the phantom, and for convenience of comparison, fig. 5 also provides a real value corresponding to each image and a reconstructed image of a conventional digital breast three-dimensional tomosynthesis at the same time, and it can be seen that a decomposed breast three-dimensional tomosynthesis image of a material can be obtained by using the proposed static dual-energy digital breast three-dimensional imaging apparatus.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
Example 1
The embodiment provides a static dual-energy tomosynthesis camera system, including fixed frame, the one end of this fixed frame is fixed with distributed carbon nanotube array light source, and the other end is fixed with double-deck detector, and distributed carbon nanotube array light source includes a plurality of field emission light sources that the distributing type was arranged, and double-deck detector includes two scintillation detectors that superpose each other, is used for absorbing low energy X ray photon and high energy X ray photon respectively.
Specifically, the distributed carbon nanotube array light source comprises a field emission anode and a plurality of field emission cathodes arranged in a distributed mode, each field emission cathode is connected with a corresponding control circuit, each field emission cathode is a carbon nanotube-based field emission cathode, each control circuit is an MOS (metal oxide semiconductor) tube, and a grid of each MOS tube is pre-programmed with a pulse signal.
In this embodiment, the static dual-energy tomosynthesis imaging system further includes a pressing plate, which is installed on the fixed frame, is located between the distributed carbon nanotube array light source and the double-layer detector, and is used to cooperate with the double-layer detector to fix the mold body.
The working principle is as follows:
a distributed carbon nanotube X-ray source array is shown in fig. 1 and is comprised of a plurality of field emission light sources. A field emission X-ray source uses a field emission cathode as an electron source to generate an electron beam by means of field electron emission. Under the action of an external electric field, the height and the width of the surface potential barrier of the cathode are reduced, and a large number of electrons in the emitter penetrate through the surface potential barrier to escape due to quantum tunneling effect. The field emission cathode has low working temperature and low power consumption, so that the integration of a plurality of cathodes by a single X-ray source is easy to realize, and the array distribution is realized; second, field emission X-ray sources can achieve high time resolution, programmable X-ray emission, since field electron emission is not time-delayed. The programmable emission of X-rays in time and space can be realized by providing pre-programmed pulse signals for MOS tube grids corresponding to different electron emission sources, and the acquisition of X-ray transmission images with different viewing angles can be realized by applying the array light source to a DBT system.
The double-layer detector is shown in fig. 2 and consists of two conventional scintillation detectors stacked on top of each other. In a dual layer detector, the top layer absorbs mainly low energy X-ray photons, while the bottom layer absorbs mainly the remaining high energy X-ray photons. Since the double-layer detector can simultaneously obtain the measurement data of two spectral bands of low energy and high energy, the problem of registration or the problem of motion artifact does not exist. Furthermore, the data obtained from the dual layer detector is not affected by cross scatter radiation, relative to a high energy, low energy dual light source system.
As shown in fig. 3, the static dual-energy digital mammary gland tomosynthesis imaging device constructed by using the distributed carbon nanotube X-ray array and the double-layer detector can realize programmable emission of X-rays by providing pre-programmed pulse signals to MOS tube gates corresponding to electron emission sources at different angular positions, synchronously trigger and control exposure of the double-layer detector through electric signals, and simultaneously obtain measurement data of two spectral bands of low energy and high energy.
The present embodiment further provides a tomosynthesis imaging method of the static dual-energy tomosynthesis imaging system, including the following steps:
installing a die body to be photographed in front of a double-layer detector, transmitting X rays through a distributed carbon nanotube array light source according to a preset pulse signal, synchronously triggering and controlling the exposure of the double-layer detector through an electric signal, and simultaneously obtaining measurement data of two spectral bands of low energy and high energy;
the method includes the steps of combining a pre-constructed detector measurement value calculation formula with obtained measurement data of two spectral bands of low energy and high energy to construct an optimization problem of a reconstructed image, obtaining an optimal solution of the reconstructed image through continuous iterative optimization, and multiplying the optimal solution by an attenuation coefficient of a base material to obtain an energy spectrum tomographic image of a phantom to be photographed, wherein the phantom to be photographed is a breast in the embodiment, and the phantom to be photographed comprises fat and glands as shown in fig. 4.
The construction process of the calculation formula of the measured value of the detector comprises the following steps:
respectively constructing low-energy and high-energy measurement value calculation formulas of the double-layer detector;
acquiring linear attenuation coefficients of the die body to be shot according to the components of the die body to be shot, and substituting the linear attenuation coefficients into a low-energy and high-energy measurement value calculation formula;
the low and high energy measurement calculation formulas are converted to discretized form and constructed to contain all the field emission light sources.
The specific implementation process comprises the following steps:
double-layer probeThe high and low energy discrimination threshold of the detector is EthThen the low and high energy measurements from the top and bottom layers, respectively, are:
Figure RE-GDA0003458674090000071
Figure RE-GDA0003458674090000072
wherein I0(E) Is the energy spectrum of the X-ray source, d (e) is the energy spectral response of the detector,
Figure RE-GDA0003458674090000073
as a die body point
Figure RE-GDA0003458674090000074
The linear attenuation coefficient of (a) is,
Figure RE-GDA0003458674090000075
is the projection path of the X-ray.
Material decomposition is one of the important applications of spectral X-ray tomography, and for three-dimensional synthetic tomography for breast scanning, the phantom components scanned typically include fat and glands, and therefore their linear attenuation coefficients can be divided into linear combinations of these two components:
Figure RE-GDA0003458674090000076
where τ (E) represents the linear attenuation coefficient of the component,
Figure RE-GDA0003458674090000077
indicating that the component is at the point
Figure RE-GDA0003458674090000078
Specific gravity of (a). Bringing (3) into (1) and (2) gives:
Figure RE-GDA0003458674090000079
Figure RE-GDA00034586740900000710
using dimension Mx×MyThe projection process for obtaining measurements from a distributed carbon nanotube X-ray array containing a total of P sub-light sources can be represented in discrete form:
ylow＝exp(-HXT)·wlow (6)
yhigh＝exp(-HXT)·whigh (7)
wherein the content of the first and second substances,
Figure RE-GDA0003458674090000081
Figure RE-GDA0003458674090000082
representing the high and low energy spectral response of the dual-energy detector;
Figure RE-GDA0003458674090000083
representing the weight of the ith base material in each voxel in a phantom that is discrete by N voxels.
Figure RE-GDA0003458674090000084
The spectral attenuation of 2 materials in a total of K spectral intervals is shown, and H is the intersection of each projection path and each voxel in the phantom.
The reconstruction of two base material images X from low and high dual energy measurements can be represented as an optimization problem as follows:
Figure RE-GDA0003458674090000085
in consideration of similarity between different depth tomographic images, the invention introduces three-dimensional total variation (3DTV) regularization to each base material tomographic image to promote a reconstructed imageQuality, given three-dimensional images
Figure RE-GDA0003458674090000086
It is defined as:
Figure RE-GDA0003458674090000087
wherein
Figure RE-GDA0003458674090000088
For adapting the resolution in the different modes. Using equation (9) as the regularization term for the reconstruction, an optimization problem can be obtained:
Figure RE-GDA0003458674090000089
s.t.ylow＝exp(-HXT)·wlow
yhigh＝exp(-HXT)·whigh (10)
in the formula, X*In order to add a reconstructed image obtained after three-dimensional total variation regularization,
Figure RE-GDA00034586740900000810
represents X:,lIn the form of a three-dimensional tensor,
to solve the reconstruction problem, an intermediate variable Z is introduced and X, Z are iteratively updated alternately:
Figure RE-GDA00034586740900000811
s.t.ylow＝exp(-HXT)·wlow,yhigh＝exp(-HXT)·whigh (11)
in the formula, λ is a regular term weight, and t is an iteration step number. Updating X can be carried out by adopting a Gauss Newton method; and updating Z may employ an iterative clipping algorithm. Multiple iterations until a preset stop condition (iteration number, relative error, or error reduction) is metX is obtained as X*. And the energy spectrum tomography image can be composed of X*And the base material attenuation coefficient T, as shown in fig. 5.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. The static dual-energy tomosynthesis camera system is characterized by comprising a fixed frame, wherein one end of the fixed frame is fixed with a distributed carbon nanotube array light source, the other end of the fixed frame is fixed with a double-layer detector, the distributed carbon nanotube array light source comprises a plurality of field emission light sources which are distributed and arranged, the double-layer detector comprises two scintillation detectors which are mutually overlapped and respectively used for absorbing low-energy X-ray photons and high-energy X-ray photons.
2. The static dual-energy tomosynthesis imaging system of claim 1, wherein the distributed carbon nanotube array light source comprises a field emission anode and a plurality of field emission cathodes arranged in a distributed manner, each field emission cathode is connected with a corresponding control circuit, and the field emission cathodes are carbon nanotube-based field emission cathodes.
3. The static dual-energy tomosynthesis imaging system of claim 2, wherein the control circuit is a MOS transistor whose gate is pre-programmed with a pulse signal.
4. The static dual-energy tomosynthesis camera system of claim 1, further comprising a pressing plate installed on the fixed frame and located between the distributed carbon nanotube array light source and the double-layer detector for cooperating with the double-layer detector to fix the mold body.
5. A tomosynthesis imaging method of a static dual-energy tomosynthesis imaging system according to any one of claims 1 to 4, comprising the steps of:
installing a die body to be photographed in front of the double-layer detector, transmitting X rays through a distributed carbon nanotube array light source according to a preset pulse signal, synchronously triggering and controlling the exposure of the double-layer detector through an electric signal, and simultaneously obtaining measurement data of two spectral bands of low energy and high energy;
and combining the pre-constructed detector measurement value calculation formula with the obtained measurement data of the low-energy spectrum and the high-energy spectrum to construct an optimization problem of the reconstructed image, obtaining an optimal solution of the reconstructed image through continuous iterative optimization, and multiplying the optimal solution by the attenuation coefficient of the base material to obtain the energy spectrum tomographic image of the die body to be photographed.
6. The method of claim 5, wherein the construction of the detector measurement calculation formula comprises:
respectively constructing low-energy and high-energy measurement value calculation formulas of the double-layer detector;
acquiring linear attenuation coefficients of the die body to be shot according to the components of the die body to be shot, and substituting the linear attenuation coefficients into the low-energy and high-energy measurement value calculation formulas;
and converting the low-energy and high-energy measurement value calculation formula into a discretization form, and constructing the low-energy and high-energy measurement value calculation formula containing all the field emission light sources.
7. The method of claim 5, wherein the low and high energy measurements of the double layer detector are calculated by the formula:
Figure RE-FDA0003458674080000021
Figure RE-FDA0003458674080000022
in the formula I0(E) Is the energy spectrum of the field emission light source, d (e) is the spectral response of the double layer detector,
Figure RE-FDA0003458674080000023
as a die body point
Figure RE-FDA00034586740800000214
The linear attenuation coefficient of (a) is,
Figure RE-FDA0003458674080000024
a projection path for X-rays, EthTo distinguish the threshold for high and low energy, IlowFor low energy measurement, IhighFor high energy measurement, EminAs energy minimum, EmaxIs the energy maximum;
the components of the die body to be shot comprise fat and glands, and the linear attenuation coefficient of the die body to be shot has an expression formula as follows:
Figure RE-FDA0003458674080000025
wherein τ (E) represents the linear attenuation coefficient of the component,
Figure RE-FDA0003458674080000026
indicating that the component is at the point
Figure RE-FDA00034586740800000215
Subscripts 1 and 2 correspond to the components fat and gland, respectively;
after substituting the linear attenuation coefficient of the die body to be shot, the calculation formula of the low-energy and high-energy measured values is as follows:
Figure RE-FDA0003458674080000027
Figure RE-FDA0003458674080000028
the low and high energy measurements comprising all field emission light sources are calculated as:
ylow＝exp(-HXT)·wlow
yhigh＝exp(-HXT)·whigh
in the formula, ylowFor low energy measurements involving all field emission light sources, yhighTo contain all high-energy measurements of the field emission light source, ylow，
Figure RE-FDA0003458674080000029
Mx×MyIs the detection dimension of a double-layer detector, wlow，
Figure RE-FDA00034586740800000210
Indicating the high and low energy spectral response of the dual-energy detector,
Figure RE-FDA00034586740800000211
representing the weight of the ith base material in each voxel in a phantom that is discrete by N voxels,
Figure RE-FDA00034586740800000212
the spectral attenuation of 2 materials in a total of K spectral intervals is shown, and H is the intersection of each projection path and each voxel in the phantom.
8. The method of claim 7, wherein the optimization problem for the reconstructed image is expressed by:
Figure RE-FDA00034586740800000213
in the formula, X is a reconstructed image.
9. The method according to claim 7, wherein the optimization problem of the reconstructed image is further added with a three-dimensional total variation regularization, and the expression of the optimization problem of the reconstructed image is as follows:
Figure RE-FDA0003458674080000031
s.t.ylow＝exp(-HXT)·wlow
yhigh＝exp(-HXT)·whigh
in the formula, X*In order to add a reconstructed image obtained after three-dimensional total variation regularization,
Figure RE-FDA0003458674080000032
represents X：，lIs used in the form of a three-dimensional tensor.
10. The method according to claim 9, wherein in the iterative optimization process, an intermediate variable Z is introduced, and X and Z are alternately updated through iteration until a preset stop condition is met to obtain an optimal solution of a reconstructed image;
the optimized expression for iteratively and alternately updating X and Z is as follows:
Figure RE-FDA0003458674080000033
s.t.ylow＝exp(-HXT)·wlow，yhigh＝exp(-HXT)·whigh
in the formula, λ is a regular term weight, and t is an iteration step number.
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