A static dual-energy tomosynthesis imaging system and method

Through a static dual-energy tomosynthesis camera system, using a distributed carbon nanotube array light source and a double-layer detector, combined with an iterative optimization algorithm, the problems of lack of energy spectrum attenuation information and motion artifacts in existing three-dimensional tomosynthesis camera technology are solved, and efficient and accurate three-dimensional image reconstruction is achieved.

CN114081517BActive Publication Date: 2025-09-19TONGJI UNIV
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Patent Information

Application Number
CN202111201682.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2021-10-15
Publication Date
2025-09-19
Estimated Expiration
2041-10-15

AI Technical Summary

Technical Problem

Existing three-dimensional tomography synthesis imaging technology cannot obtain energy spectrum attenuation information, which makes material identification difficult and causes beam hardening artifacts. At the same time, multi-angle measurement causes motion artifacts and high-cost photon counting detectors.

Method used

It adopts a distributed carbon nanotube array light source and a double-layer detector with a fixed rack structure. It acquires low-energy and high-energy measurement data through synchronous triggering, reconstructs images with an iterative optimization algorithm, and adds a three-dimensional total variation regularization to improve image quality.

Benefits of technology

It achieves low-cost and rapid acquisition of three-dimensional tomographic images reflecting breast structure and composition information, reduces motion artifacts and beam hardening artifacts, and improves image matching accuracy and the convergence speed of the iterative process.

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Abstract

The present invention relates to a static dual-energy tomosynthesis imaging system and method. The system includes a fixed frame, one end of which is fixed with a distributed carbon nanotube array light source, and the other end is fixed with a double-layer detector. The distributed carbon nanotube array light source includes multiple field emission light sources arranged in a distributed manner, and the double-layer detector includes two superimposed scintillation detectors, each for absorbing low-energy X-ray photons and high-energy X-ray photons. Compared with the existing technology, the present invention utilizes a distributed carbon nanotube array light source to replace the single-ray source + rotating frame architecture of traditional BDT, avoiding the scanning process in multi-angle measurement. The double-layer detector receives measurement information from two energy spectrum intervals respectively, thereby reconstructing a multi-energy spectrum tomographic image containing information about the material composition of the phantom. This can detect subtle lesions hidden in two-dimensional images, reducing unnecessary biopsies, measurement time, and potential motion artifacts.
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Description

Technical Field

[0001] The present invention relates to the field of three-dimensional tomosynthesis imaging, and in particular to a static dual-energy tomosynthesis imaging system and method. Background Art

[0002] 3D tomosynthesis is an emerging tomographic imaging modality that reconstructs slice images at varying depths, reflecting the object's three-dimensional information, by acquiring a small number of 2D projections from a limited range of angles. Compared to traditional computed tomography, it offers advantages over traditional computed tomography (CT) technology, such as reduced X-ray radiation dose and lower cost. As a promising screening tool, it is already being used clinically to detect lung and breast cancer lesions.

[0003] A typical application of 3D tomosynthesis imaging technology is Digital Breast Tomosynthesis (DBT), which consists of a high-voltage X-ray source, a rotating gantry, and an energy-integrating detector. It collects X-ray intensity projected across the entire energy spectrum as measurement data, and then uses the negative logarithm of the measurement data for filtered back-projection reconstruction.

[0004] However, this traditional DBT has two drawbacks:

[0005] First, the system cannot obtain measurements containing spectral attenuation information, which can be used to identify the material composition of an object and reduce beam hardening artifacts. An existing prototype spectral 3D tomosynthesis camera system utilizes a photon counting detector, which allows for simultaneous acquisition of high- and low-energy measurements. However, its current high cost and pulse pile-up at high X-ray fluxes limit its use in routine clinical examinations.

[0006] Secondly, the system obtains projection data at multiple projection angles by stepping or continuously rotating the gantry, so the measurement time is relatively long. During this period, physiological movements such as the patient's breathing will cause the scanned organs to move, resulting in artifacts in the final reconstructed image. Summary of the Invention

[0007] The purpose of the present invention is to provide a static dual-energy tomosynthesis imaging system and method in order to overcome the defects of the above-mentioned prior art, such as the high cost of obtaining high-energy and low-energy measurement values ​​of photon counting detectors and the long measurement time of obtaining projection data of multiple projection angles by stepping or continuous rotation.

[0008] The purpose of the present invention can be achieved by the following technical solutions:

[0009] A static dual-energy tomosynthesis imaging system includes a fixed frame, one end of which is fixed with a distributed carbon nanotube array light source, and the other end is fixed with a double-layer detector. The distributed carbon nanotube array light source includes multiple field emission light sources arranged in a distributed manner, and the double-layer detector includes two superimposed scintillation detectors, which are used to absorb low-energy X-ray photons and high-energy X-ray photons respectively.

[0010] Furthermore, the distributed carbon nanotube array light source includes a field emission anode and a plurality of distributedly arranged field emission cathodes, each of the field emission cathodes is connected to a corresponding control circuit, and the field emission cathodes are carbon nanotube-based field emission cathodes.

[0011] Furthermore, the control circuit is a MOS transistor, and the gate of the MOS transistor is pre-programmed with a pulse signal.

[0012] Furthermore, the static dual-energy tomosynthesis imaging system further includes a pressure plate, which is mounted on the fixed frame and 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 phantom.

[0013] The present invention further provides a tomosynthesis imaging method for the static dual-energy tomosynthesis imaging system as described above, comprising the following steps:

[0014] The phantom to be imaged is mounted in front of the double-layer detector, and X-rays are emitted by a distributed carbon nanotube array light source according to a preset pulse signal. The exposure of the double-layer detector is controlled by synchronous triggering of an electrical signal, and measurement data of both low-energy and high-energy spectral bands are obtained simultaneously.

[0015] Based on the pre-constructed detector measurement value calculation formula and the obtained measurement data of the low-energy and high-energy spectral bands, an optimization problem for reconstructing the image is constructed. Through continuous iterative optimization, the optimal solution for reconstructing the image is obtained and multiplied by the attenuation coefficient of the basic material to obtain the energy spectrum tomography image of the phantom to be imaged.

[0016] Furthermore, the process of constructing the detector measurement value calculation formula includes:

[0017] Construct calculation formulas for low-energy and high-energy measurements of the double-layer detector respectively;

[0018] Obtaining a linear attenuation coefficient of the phantom to be imaged according to the components of the phantom to be imaged, and substituting the coefficient into the calculation formula of the low-energy and high-energy measurement values;

[0019] The low-energy and high-energy measurement value calculation formulas are converted into a discretized form, and low-energy and high-energy measurement value calculation formulas containing all field emission light sources are constructed.

[0020] Furthermore, the calculation formula for the low-energy and high-energy measurement values ​​of the double-layer detector is:

[0021]

[0022]

[0023] Where I0(E) is the energy spectrum of the field emission light source, D(E) is the energy spectrum response of the double-layer detector, For the model at point The linear attenuation coefficient, is the projection path of X-rays, E th is the high and low energy distinction threshold, I low is the low energy measurement value, I high is the high energy measurement value, E min is the minimum energy, E max is the maximum energy;

[0024] The components of the phantom to be imaged include fat and glands, and the linear attenuation coefficient of the phantom to be imaged is expressed as follows:

[0025]

[0026] Where τ(E) represents the linear attenuation coefficient of the component, Indicates that the component is at point The specific gravity of the , subscripts 1 and 2 correspond to the components fat and glandular, respectively;

[0027] After substituting the linear attenuation coefficient of the phantom to be photographed, the calculation formula for the low-energy and high-energy measurement values ​​is:

[0028]

[0029]

[0030] The formula for calculating the low and high energy measurements including all field emission sources is:

[0031] y liw =exp(-HXT)·w low

[0032] y high =exp(-HXT)·w high

[0033] Where y low is the low energy measurement value including all field emission sources, y high is a high-energy measurement value that includes all field emission sources, M x ×M y is the detection dimension of the double-layer detector, represents the high and low energy spectrum response of the dual energy detector, Represents the weight of the lth basic material in each voxel in the motif discretized into N voxels, represents the spectral attenuation of two materials in a total of K energy spectrum intervals, and H is the intersection of each projection path and each voxel in the phantom.

[0034] Furthermore, the expression of the optimization problem of reconstructing the image is:

[0035]

[0036] Where X is the reconstructed image.

[0037] Furthermore, the optimization problem of reconstructing the image is further added with a three-dimensional total variation regularization, and the expression of the optimization problem of reconstructing the image is:

[0038]

[0039] sty low =exp(-HXT)·w low

[0040] y high =exp(-HXT)·w high

[0041] Where, X * is the reconstructed image obtained after adding the three-dimensional total variation regularization, Represents X :,l The three-dimensional tensor form of .

[0042] Furthermore, in the iterative optimization process, an intermediate variable Z is introduced, and X and Z are updated alternately through iteration until a preset stopping condition is met, thereby obtaining the optimal solution for reconstructing the image;

[0043] The optimization expression for iteratively updating X and Z is:

[0044]

[0045] sty low =exp(-HXT)·w low ,y high =exp(-HXT)·w high

[0046] Where λ is the regularization term weight and t is the number of iteration steps.

[0047] Compared with the prior art, the present invention has the following advantages:

[0048] (1) The static dual-energy tomosynthesis camera system provided by the present invention, firstly, uses a distributed carbon nanotube array light source to replace the single-ray source + rotating frame structure in the traditional BDT, avoiding the scanning process in multi-angle measurement; secondly, uses a double-layer detector to receive measurement information in two energy spectrum intervals respectively, thereby reconstructing a multi-energy spectrum tomography image containing the material composition information of the model.

[0049] (2) The present invention also provides a corresponding tomography imaging method for a static dual-energy tomography imaging system, divides the detector's measurement value calculation formula into high and low energy, and constructs a measurement value calculation formula containing all sub-light sources in a discrete form to achieve three-dimensional image reconstruction of the above-mentioned static dual-energy tomography imaging system.

[0050] (3) In the iterative optimization process of obtaining the three-dimensional image X, the present invention adds a three-dimensional total variation regularization to improve the quality of the reconstructed image, introduces an intermediate variable Z, and iteratively updates X and Z, further improving the matching accuracy of the obtained three-dimensional image X and the convergence speed during the iterative process.

[0051] (4) The static dual-energy tomosynthesis camera system provided by the present invention can obtain three-dimensional tomographic images reflecting breast structure and component information, which can be used to detect tiny lesions hidden in two-dimensional images; eliminate false positives and false negatives caused by two-dimensional projection images; use the structure and component information of the mass reflected in the energy spectrum three-dimensional tomographic image to judge disease information, thereby reducing unnecessary biopsies; and at the same time, since there is no scanning process, the measurement time and potential motion artifacts are reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a schematic structural diagram of a distributed carbon nanotube X-ray source array provided in an embodiment of the present invention, which is composed of multiple field emission light sources;

[0053] Figure 2 A schematic structural diagram of a double-layer detector provided in an embodiment of the present invention, which is composed of two conventional scintillation detectors superimposed on each other;

[0054] Figure 3 This is a schematic structural diagram of a static dual-energy tomosynthesis imaging system provided in an embodiment of the present invention, which mainly includes a distributed carbon nanotube X-ray source array, a double-layer detector, a fixed frame, and a pressure plate;

[0055] Figure 4 This is a 2D projection image of the phantom used in the experiment in the embodiment of the present invention at an angle of 0°, which contains two materials: fat and gland (soft tissue);

[0056] Figure 53D tomosynthesis images of two basic materials contained in the phantom according to an embodiment of the present invention, wherein Z=2 to 10 represent tomographic images of even-numbered layers of the phantom. For ease of comparison, Figure 5 The real value corresponding to each image and the reconstructed image of the traditional digital breast 3D tomosynthesis are also provided. It can be seen that the material decomposed breast 3D tomographic image can be obtained by using the proposed static dual-energy digital breast 3D camera. DETAILED DESCRIPTION

[0057] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0058] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0059] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not require further definition or explanation in subsequent drawings.

[0060] Example 1

[0061] This embodiment provides a static dual-energy tomosynthesis imaging system, including a fixed frame, one end of which is fixed with a distributed carbon nanotube array light source, and the other end of which is fixed with a double-layer detector. The distributed carbon nanotube array light source includes multiple field emission light sources arranged in a distributed manner, and the double-layer detector includes two superimposed scintillation detectors, which are used to absorb low-energy X-ray photons and high-energy X-ray photons respectively.

[0062] Specifically, the distributed carbon nanotube array light source includes a field emission anode and multiple field emission cathodes arranged in a distributed manner. Each field emission cathode is connected to a corresponding control circuit. The field emission cathode is a field emission cathode based on carbon nanotubes. The control circuit is a MOS tube, and the gate of the MOS tube is pre-programmed with a pulse signal.

[0063] In this embodiment, the static dual-energy tomosynthesis camera system further includes a pressure plate, which is mounted on a fixed frame and 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 phantom.

[0064] Working principle:

[0065] Distributed carbon nanotube X-ray source arrays such as Figure 1 As shown, it consists of multiple field emission light sources. A field emission X-ray source uses a field emission cathode as an electron source, generating an electron beam through field-induced electron emission. Under the action of an external electric field, the height and width of the cathode surface barrier decrease, and a large number of electrons in the emitter escape by penetrating the surface barrier due to the quantum tunneling effect. Because the field emission cathode has a low operating temperature and low power consumption, it is easy to integrate multiple cathodes into a single X-ray source, thereby achieving an array distribution. Secondly, because field electron emission has no time delay, the field emission X-ray source can achieve high time resolution and programmable X-ray emission. By providing pre-programmed pulse signals to the gates of the MOS tubes corresponding to different electron emission sources, temporal and spatial programmable emission of X-rays can be achieved. By using such an array light source in a DBT system, it is possible to acquire X-ray transmission images from different perspectives.

[0066] Double-layer detectors such as Figure 2 As shown in Figure 1, it consists of two conventional scintillation detectors stacked on top of each other. In a dual-layer detector, the top layer primarily absorbs low-energy X-ray photons, while the bottom layer primarily absorbs the remaining high-energy X-ray photons. Because a dual-layer detector can simultaneously acquire measurement data from both low- and high-energy spectral bands, there are no registration issues or motion artifacts. Furthermore, compared to a high- and low-energy dual-source system, data obtained from a dual-layer detector is not affected by cross-scatter radiation.

[0067] The static dual-energy digital breast tomosynthesis imaging device constructed by using the above-mentioned distributed carbon nanotube X-ray array and double-layer detector is Figure 3 As shown, by providing pre-programmed pulse signals to the gates of the MOS tubes corresponding to the electron emission sources at different angular positions, programmable X-ray emission can be achieved. The exposure of the double-layer detector is controlled by synchronous triggering of the electrical signal, and measurement data of both low-energy and high-energy spectral bands can be obtained at the same time.

[0068] This embodiment also provides a tomosynthesis imaging method for the static dual-energy tomosynthesis imaging system, comprising the following steps:

[0069] The phantom to be imaged is mounted in front of a double-layer detector. X-rays are emitted by a distributed carbon nanotube array light source according to a pre-set pulse signal. The exposure of the double-layer detector is controlled by synchronous triggering of an electrical signal, and measurement data of both low-energy and high-energy spectral bands are obtained simultaneously.

[0070] According to the pre-established detector measurement value calculation formula and the obtained measurement data of the low-energy and high-energy spectral bands, an optimization problem for reconstructing the image is constructed. Through continuous iterative optimization, the optimal solution for reconstructing the image is obtained and multiplied by the attenuation coefficient of the basic material to obtain the energy spectrum tomographic image of the phantom to be photographed. In this embodiment, the phantom to be photographed is the breast, which includes fat and glands. Figure 4 shown.

[0071] The process of constructing the detector measurement value calculation formula includes:

[0072] Construct calculation formulas for low-energy and high-energy measurements of the double-layer detector respectively;

[0073] According to the components of the phantom to be imaged, the linear attenuation coefficient of the phantom to be imaged is obtained and substituted into the calculation formula of the low-energy and high-energy measurement values;

[0074] The calculation formulas for low-energy and high-energy measurement values ​​are converted into discretized forms, and the calculation formulas for low-energy and high-energy measurement values ​​that include all field emission light sources are constructed.

[0075] The specific implementation process includes the following steps:

[0076] Assume that the high and low energy discrimination threshold of the double-layer detector is E th , then the low and high energy measurements obtained from the top and bottom layers respectively are:

[0077]

[0078]

[0079] Where I0(E) is the energy spectrum of the X-ray source, D(E) is the energy spectrum response of the detector, For the model at point The linear attenuation coefficient, is the projection path of the X-ray.

[0080] Material decomposition is one of the important applications of spectral X-ray tomography. For 3D synthetic tomography used for breast scanning, the scanned phantom components usually include fat and glands. Therefore, its linear attenuation coefficient can be decomposed into a linear combination of these two components:

[0081]

[0082] Where τ(E) represents the linear attenuation coefficient of the component, Indicates that the component is at point Substituting (3) into (1) and (2), we can get:

[0083]

[0084]

[0085] Using dimension M x ×M y The projection process of obtaining measurement values ​​from a distributed carbon nanotube X-ray array containing a total of P sub-light sources can be expressed in discrete form:

[0086] y low =exp(-HXT)·w low (6)

[0087] y high =exp(-HXT)·w high (7)

[0088] in, Represents the high and low energy spectrum response of the dual energy detector; Represents the weight of the lth basic material in each voxel in the motif discretized into N voxels. represents the spectral attenuation of two materials in a total of K energy spectrum intervals, and H is the intersection of each projection path and each voxel in the phantom.

[0089] Reconstructing two basic material images X from low and high dual energy measurements can be formulated as the following optimization problem:

[0090]

[0091] Considering the similarity between tomographic images at different depths, the present invention introduces a three-dimensional total variation (3DTV) regularization to each basic material tomographic image to improve the quality of the reconstructed image. It is defined as:

[0092]

[0093] in Used to adapt to the resolution in different modes. Using formula (9) as the regularization term for reconstruction, the optimization problem can be obtained:

[0094]

[0095] sty low =exp(-HXT)·w low

[0096] y high =exp(-HXT)·w high (10)

[0097] Where, X * is the reconstructed image obtained after adding the three-dimensional total variation regularization, Represents X :,l The three-dimensional tensor form of

[0098] In order to solve the reconstruction problem, an intermediate variable Z is introduced and X and Z are updated alternately iteratively:

[0099]

[0100] sty low =exp(-HXT)·w low ,y high =exp(-HXT)·w high (11)

[0101] Where λ is the regularization weight and t is the number of iterations. The Gauss-Newton method can be used to update X, while the iterative shearing algorithm can be used to update Z. Repeat multiple iterations until the preset stopping conditions (number of iterations, relative error, or error reduction) are met. The resulting X is X * . The energy spectrum tomography image can be obtained by X * The product of the attenuation coefficient T of the base material is obtained, such as Figure 5 shown.

[0102] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A tomosynthesis imaging method for a static dual-energy tomosynthesis imaging system, characterized in that: The static dual-energy tomosynthesis imaging system includes a fixed frame, one end of which is fixed with a distributed carbon nanotube array light source, and the other end of which is fixed with a double-layer detector, wherein the distributed carbon nanotube array light source includes a plurality of field emission light sources arranged in a distributed manner, and the double-layer detector includes two superimposed scintillation detectors for absorbing low-energy X-ray photons and high-energy X-ray photons respectively; The method comprises the following steps: The phantom to be imaged is mounted in front of the double-layer detector, and X-rays are emitted by a distributed carbon nanotube array light source according to a preset pulse signal. The exposure of the double-layer detector is controlled by synchronous triggering of an electrical signal, and measurement data of both low-energy and high-energy spectral bands are obtained simultaneously. Based on the pre-established detector measurement value calculation formula and the obtained low-energy and high-energy spectral measurement data, an optimization problem for reconstructing the image is constructed. Through continuous iterative optimization, the optimal solution for reconstructing the image is obtained and multiplied by the attenuation coefficient of the base material to obtain the energy spectrum tomographic image of the phantom to be imaged. The process of constructing the detector measurement value calculation formula includes: Construct calculation formulas for low-energy and high-energy measurements of the double-layer detector respectively; Obtaining a linear attenuation coefficient of the phantom to be imaged according to the components of the phantom to be imaged, and substituting the coefficient into the calculation formula of the low-energy and high-energy measurement values; Converting the low-energy and high-energy measurement value calculation formulas into a discretized form, and constructing low-energy and high-energy measurement value calculation formulas that include all field emission light sources; The calculation formula for the low-energy and high-energy measurement values ​​of the double-layer detector is: Where I0(E) is the energy spectrum of the field emission light source, D(E) is the energy spectrum response of the double-layer detector, For the model at point The linear attenuation coefficient, is the projection path of X-rays, E th is the high and low energy distinction threshold, I low is the low energy measurement value, I high is the high energy measurement value, E min is the minimum energy, E max is the maximum energy; The components of the phantom to be imaged include fat and glands, and the linear attenuation coefficient of the phantom to be imaged is expressed as follows: Where τ(E) represents the linear attenuation coefficient of the component, Indicates that the component is at point The specific gravity of the , subscripts 1 and 2 correspond to the components fat and glandular, respectively; After substituting the linear attenuation coefficient of the phantom to be photographed, the calculation formula for the low-energy and high-energy measurement values ​​is: The formula for calculating the low and high energy measurements including all field emission sources is: y low =exp(-HXT)·w low y high =exp(-HXT)·w high Where y low is the low energy measurement value including all field emission sources, y high is the high energy measurement value including all field emission sources, y low , M x ×M y is the detection dimension of the double-layer detector, w low , represents the high and low energy spectrum response of the dual energy detector, Represents the weight of the lth basic material in each voxel in the motif discretized into N voxels, represents the spectral attenuation of two materials in a total of K energy spectrum intervals, and H is the intersection of each projection path and each voxel in the phantom.

2. The method according to claim 1, characterized in that The distributed carbon nanotube array light source includes a field emission anode and a plurality of distributedly arranged field emission cathodes. Each of the field emission cathodes is connected to a corresponding control circuit. The field emission cathodes are carbon nanotube-based field emission cathodes.

3. The method according to claim 2, characterized in that The control circuit is a MOS transistor, and the gate of the MOS transistor is pre-programmed with a pulse signal.

4. The method according to claim 1, wherein The static dual-energy tomosynthesis camera system further includes a pressure plate, which is mounted on the fixed frame and 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 phantom.

5. The method according to claim 1, wherein The expression of the optimization problem of reconstructing the image is: Where X is the reconstructed image.

6. The method according to claim 1, characterized in that The optimization problem of reconstructing the image is further added with a three-dimensional total variation regularization. The expression of the optimization problem of reconstructing the image is: s.t.y lpw =exp(-HXT)·w low y high =exp(-HXT)·w high Where, X * is the reconstructed image obtained after adding the three-dimensional total variation regularization, Represents X :,l The three-dimensional tensor form of .

7. The method according to claim 6, characterized in that In the iterative optimization process, an intermediate variable Z is introduced, and X and Z are updated alternately through iteration until a preset stopping condition is met, thereby obtaining the optimal solution for reconstructing the image; The optimization expression for iteratively updating X and Z is: sty low =exp(-HXT)·w low ,y high =exp(-HXT)·w high Where λ is the regularization term weight and t is the number of iteration steps.

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