CT image generation method using quantum algorithms

Abstract

The present invention relates to a CT image generation method using a quantum algorithm, and more specifically, to an excellent CT image generation method that can easily and reliably reconstruct and acquire a CT image by quantizing the CT image using a quantum algorithm and matching it with an actual projection image using a projection transformation method.

Description

Technical Field

[0001] The present invention relates to a method for generating a CT image using a quantum algorithm. More specifically, the present invention relates to an excellent CT image generation method capable of simply and reliably reconstructing and obtaining a CT image by quantizing a CT image using a quantum algorithm and using a projection conversion method that matches the actual projection image.

Background Art

[0002] Computed tomography (CT) is a very useful medical device known for obtaining an image of a cross-section of the human body and confirming the state information of the human body by photographing a subject placed in a large machine equipped with a circular X-ray generator.

[0003] Such a CT image shows an image in which, compared to simple X-ray photography, there is no overlap of structures and the actual form can be inferred and confirmed through a dense cross-sectional image, and thus has the advantage that at least structures and lesions can be seen more clearly. Therefore, such CT images are widely used for precise examinations of most organs and diseases.

[0004] However, a CT image may not be able to sufficiently show a clear image, and it can be said that the contrast of a CT image is a very important factor in accurate diagnosis of lesions. Therefore, along with the development of CT examination methods, efforts have continued to obtain images with high contrast in CT images.

[0005] To date, an examination method has been used to obtain an image further improved by the difference in attenuation between a lesion and surrounding tissue by injecting a contrast agent that increases the X-ray attenuation degree of blood vessels. However, the injection of such a contrast agent is not only inconvenient for the patient but also raises concerns about side effects, so its use is minimized.

[0006] Thus, computed tomography (CT) is a powerful non-destructive method for analyzing the internal structure of objects and is a very useful diagnostic tool because it allows for precise examinations without damaging the object. However, it is still difficult to obtain clear CT images, making accurate diagnosis of lesions and other conditions challenging.

[0007] As a prior art studied by the present inventors, WO2017 / 188559A proposes a CT image reconstruction method for computed tomography, which includes determining at least one fixed point of the object, making the fixed point a virtual axis of rotation such that the fixed point corresponds to a straight line across the center of the sinogram, and calculating the relative positions of points other than the fixed part of the object with respect to the fixed point in the sinogram, and reconstructing the image based on the calculation of the relative positions of the points.

[0008] However, in this case, despite considerable progress in CT image reconstruction methods, there were aspects where the technical level was not sufficiently complete. [Overview of the project] [Problems that the invention aims to solve]

[0009] To solve the problems of the prior art, this invention aims to generate extremely clear CT images using a quantum-based algorithm.

[0010] Therefore, the object of the present invention is to provide a method for generating clear CT images using a quantum algorithm.

[0011] Another object of the present invention is to provide a novel QUBO (quadratic unconstrained binary optimization) model that can be applied as a quantum-based algorithm for quantizing the CT image and matching it with the actual projection image.

[0012] Another object of the present invention is to provide CT images with excellent resolution by applying the quantum-based algorithm and optimizing the superimposed sinogram and the experimentally obtained sinogram. [Means for solving the problem]

[0013] To solve the problems of the present invention described above, the present invention provides a method for generating segmented CT images from projection data by minimizing the discrepancy between an experimentally obtained sinogram and a quantized sinogram derived from a CT image using the projection used in the experiment.

[0014] According to a preferred embodiment of the present invention, the segmented CT images may be obtained by a process that includes a superimposed sinogram and an optimization step of an experimentally obtained sinogram.

[0015] According to a preferred embodiment of the present invention, the divided CT images are A step to obtain known mass decay for the sample, The steps include multiplying the mass decay by the qubit for each pixel of the CT image, The process involves using a mass attenuation coefficient to apply the same mathematical algorithm used for the beam shape obtained from the projection image to the superimposed CT image to obtain superimposed projection data, and The steps include defining the difference between the superimposed projection image and the actual projection image for each pixel in the form of an optimization problem, The steps involve calculations using the QUBO model, It is possible to generate segmented CT images by reconstructing CT images using an algorithm that includes [specific algorithm / method].

[0016] According to a preferred embodiment of the present invention, the QUBO model can be formulated by summing up the QUBO format for each pixel of all projected images.

[0017] According to a preferred embodiment of the present invention, the global minimum energy of the QUBO model can be calculated using the hybrid solver of the D-Wave system.

[0018] According to a preferred embodiment of the present invention, the QUBO model is obtained by the following Equation 1.

[0019]

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[0020] Here,

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[0028] According to a preferred embodiment of the present invention, the superimposed projection image can be obtained by a mathematical projection method used for CT images, which includes projection transformation.

[0029] According to a preferred embodiment of the present invention, the X-rays can be selected from equilibrium beams, cone beams, and fan beams, and can also be used for electrons or other transmission modes.

[0030] Furthermore, the present invention includes a QUBO model that is utilized as an image reconstruction means applied to quantum computing for the reconstruction of CT images and is characterized by being represented by formula 1 or an equation that yields the same result.

[0031] Furthermore, the present invention includes the step of obtaining a known mass decay for a sample, The steps include multiplying the mass decay by the qubit for each pixel of the acquired projection image, The process involves applying the same mathematical algorithm used for the beam shape obtained from the projection image to the superimposed image to obtain superimposed projection data, and The difference between the superimposed projection image and the projected image for each pixel provides a QUBO model design method, which includes the step of realizing the QUBO model in the form of a least squares problem. [Effects of the Invention]

[0032] As described above, the method for generating CT images according to the present invention has the effect of generating CT images with excellent resolution in a simple manner. [Brief explanation of the drawing]

[0033] [Figure 1]This document illustrates a quantum annealer using the D-Wave system employed in this invention. [Figure 2] This demonstrates the random transformation according to the present invention. [Figure 3] This example illustrates a state in which each pixel of the CT image to be realized is treated as a quantum superposition state, and a superposition sinogram is created in accordance with the light source. [Figure 4] This diagram visualizes the process by which a quantum annealer generates a CT image using qubits that satisfy the global minimum energy for the QUBO model, using a superimposed sinogram and an experimental sinogram to compute the QUBO model according to the present invention. [Figure 5] This is a conceptual diagram illustrating the Radon transform in equilibrium light according to the present invention. [Figure 6] This is a conceptual diagram illustrating the Radon transform in equilibrium light according to the present invention. [Figure 7] To compute the QUBO model according to the present invention, each pixel of the superimposed sinogram

[0034]

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[0035]

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[0036] The present invention will be described in more detail below as one embodiment.

[0037] The present invention relates to a method for producing high-resolution computed tomography (CT) images that can be read more accurately.

[0038] CT is a crucial imaging technique used for the medical analysis of the internal structure of the human body, and therefore is widely used in the medical field.

[0039] Normally, obtaining segmented CT images requires an image segmentation method after acquiring reconstructed CT images. However, errors can occur in both the reconstruction and segmentation algorithms, resulting in CT images with low resolution or that are difficult to read.

[0040] In order to solve these problems, the present invention is characterized by applying a novel method that essentially uses a high-level quantum optimization algorithm called QUBO (Quadratic Unconstrained Binary Optimization).

[0041] In this invention, CT images can be defined as tomography images, which include X-ray images but essentially refer to tomography images to which a series of tomographic imaging techniques that visualize invisible information are applied. Therefore, it includes images generated by electrons, synchrotrons, and other means in addition to X-rays.

[0042] In this invention, "represented by projection transformation" is defined identically to many projection transformations, including Radon transformations, and includes, for example, the use of cone-beam projection transformation in the medical field.

[0043] In this invention, the mass attenuation coefficient is defined as a physical value that appears when a projected beam passes through the interior of an object, and includes concepts such as the scattering coefficient and the absorption coefficient. One of the features of this invention is that it can show a CT image generated by superimposing with such a mass attenuation coefficient, and can show a CT image in a superimposed state that can complement, for example, X-ray coherence.

[0044] This invention includes a method that can utilize quantum optimization algorithms designed using quantum computing techniques.

[0045] According to a preferred embodiment of the present invention, a method is proposed for designing a new QUBO (quadratic unconstrained binary optimization) model specifically designed for such algorithms and for utilizing it.

[0046] In this invention, the QUBO model can be designed in various mathematical ways. However, the QUBO model exemplified in this invention is designed to be computed using the simplest mathematical formula. Therefore, this invention should be understood to include QUBO models for the same purpose, including those designed using a variety of mathematical design methods. Accordingly, the QUBO model expressed mathematically in this invention can be included as an equation computed for the same purpose.

[0047] Furthermore, in the present invention, the QUBO model is a model applied to quantize CT images and match them with actual projection images, where the difference between the superimposed projection image and the actual projection image for each pixel is defined in the form of an optimization equation, and can be defined as an application technique of an important algorithm used to generate improved images.

[0048] According to a preferred embodiment of the present invention, the QUBO model is particularly well suited for use when coupled with gate-model-based quantum computers, especially QAOA (Quantum Approximate Optimization Algorithm). To maximize performance when working with the QUBO model, it is preferable to use a quantum annealer instead of a gate-model quantum computer. This is based on the advantages of quantum annealers, which offer superior performance compared to gate-model quantum computers. D-Wave's Advantage quantum annealer currently has impressive specifications, including more than 5,000 qubits and more than 35,000 couplers. Thus, it is possible to use 180 logical qubits, along with interconnection. In particular, D-Wave also offers hybrid models that support up to 1 million variables and 200 million biases. Therefore, the present invention uses a newly designed QUBO model that applies such technology.

[0049] According to a preferred embodiment of the present invention, the QUBO algorithm can acquire segmented CT images from X-ray projection data while minimizing the discrepancy between experimentally obtained sinograms and quantized sinograms derived from segmented CT images quantized using Radon transforms.

[0050] According to a preferred embodiment of the present invention, D-Wave's hybrid solver system can be utilized for verification against actual X-ray data.

[0051] Computed tomography (CT), which aims to improve its usability and image reading information in this invention, is essentially a powerful means of non-destructively analyzing the internal structure of an object, and is characterized by its ability to perform precise inspections without damaging the object.

[0052] Generally, obtaining segmented CT images from projection data requires two steps. First, a back projection algorithm is applied to the projection data to reconstruct the CT image. Then, a segmentation algorithm is applied to the reconstructed CT image to obtain segmented images. The resulting CT images are then used with a back projection algorithm to reconstruct the internal structure of the object based on projection images taken at different angles. Back projection uses a variety of algorithms, including iterative methods, fast Fourier transforms, artificial intelligence, and optimization, among others. If the optimization algorithm used here leverages a complete sinogram pattern, it is possible to generate more accurate images that closely resemble the actual internal structure.

[0053] According to a preferred embodiment of the present invention, the present invention has designed an algorithm that minimizes the parallax between a reconstructed CT image and an actual sinogram by repeatedly updating the sinogram through a Radon transform on randomly generated CT images on such a technical basis.

[0054] However, conventional computer-based calculations often interfere with the quality of acquired CT images. This invention proposes a novel QUBO model to solve this problem.

[0055] According to a preferred embodiment of the present invention, the QUBO modeling method includes comparing each pixel of the superimposed sinogram with each pixel of the experimental sinogram. However, the present invention is essentially characterized by the optimization of the superimposed sinogram and the experimental sinogram.

[0056] The QUBO model proposed by this invention can be implemented on a quantum computer by leveraging its computational efficiency and similarity to optimization algorithms. Nevertheless, improving CT image quality remains an obstacle within the QUBO model due to the limited number of logical qubits and the low probability of finding the minimum energy state on a quantum computer.

[0057] According to a preferred embodiment of the present invention, when calculating a QUBO model for CT image reconstruction using the method of the present invention with a D-Wave hybrid solver, it is expected that very good results can be obtained even when using approximately 10,000 logical qubits.

[0058] In this invention, we propose the following novel QUBO model for quantum partitioning that can perform both CT image reconstruction and CT image partitioning based on the theoretical basis described above.

[0059] As one embodiment of the present invention, for example, assume that the X-ray mass decay of the sample is already known. The new algorithm multiplies the X-ray mass decay by the qubit for each pixel of the CT image. Each pixel is a quantum superposition state that can represent all values ​​for the sample and space. The new algorithm then calculates superposition projection data by applying the same mathematical algorithm to the superposition state CT image as the X-ray beam shape obtained from the X-ray projection image. For each pixel, the difference between the superposition projection image and the X-ray projection image is calculated as a QUBO in the form of a least-squares problem. Finally, the QUBO model can be formalized by summing the QUBO forms for each pixel of all projected images as shown in Equation 1 below.

[0060]

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[0061] Here, each of the aforementioned elements is as defined above.

[0062] According to the present invention, each term of the QUBO model derived through this formalization process can be expressed in the following equation 2.

[0063]

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[0064] In the above formula, each element is as defined above.

[0065] According to a preferred embodiment of the present invention, the novel algorithm can be validated using a parallel beam X-ray source, with an image size of, for example, 50 × 50, and a total of 2,500 logical qubits available. The mathematical projection method used for the superimposed CT image is the Radon transform. The total minimum energy of the QUBO model can be calculated using the hybrid solver of the D-Wave system.

[0066] In one embodiment of the present invention, verification was performed using a parallel beam X-ray source, but the new algorithm can be used for all types of X-ray sources. For example, an X-ray source can be selected from equilibrium beam, cone beam, or fan beam. In the case of medical CT, a cone beam is preferably used. Furthermore, it can also be used in synchrotron accelerators or cryogenic electron microscopes.

[0067] On the other hand, the fundamental technologies for projection transformations, such as radon transformations, that are utilized in this invention will be described.

[0068] The Radon transformation mathematically explains how to obtain projection data for parallel beam type X-ray sources.

[0069] According to a preferred embodiment of the present invention, the radon transformation can be calculated as follows:

[0070]

number

[0071] Here, p represents the slope of the line, τ represents the intercept, and δ(x) represents the delta function.

[0072] According to a preferred embodiment of the present invention, the sinogram is generated by accumulating Radon transforms with respect to angles. For example, when using the same sample at different positions, the projected position changes due to the Radon transform. The shape of the projected object in a sinogram free of motion artifacts constitutes an ideal sinogram pattern, which is an important factor when reconstructing CT images.

[0073] In relation to the reconstruction of CT images using such radon transforms, an example of an optimization algorithm is that it can be constructed in the following way.

[0074] In other words, this is an alignment method for correcting motion artifacts in the overall projection image during scanning, which, unlike previous approximation methods, calculates points within the sample in virtual space to satisfy the Helgason-Ludwig consistency condition. Therefore, high-quality CT images can be obtained even if the center of rotation in space changes.

[0075] Based on this, an algorithm can be introduced to reconstruct CT images based on sinogram patterns. In particular, this algorithm can manipulate the sinogram pattern to control the reconstructed position of the sample within the CT image.

[0076] According to a preferred embodiment of the present invention, by randomly reconstructing CT images within a specific region of interest, the algorithm minimizes the discrepancy between the sinogram generated in the initial CT image via the Radon transform and the actual sinogram. Furthermore, because it uses the complete sinogram pattern of the sample, it exhibits robustness against artifacts at specific angles.

[0077] Based on this method, the CT image reconstruction algorithm can be mathematically formulated in a form that allows for the following optimizations.

[0078]

number

[0079] In the above equation, T is one of the CT images, S is the given sinogram, and R is the Radon transform. Here, the Radon transform calculation is performed using PyTorch (1.9.0 + cu111), and the optimization calculation can be performed using the Adam optimizer from the PyTorch library.

[0080] According to the present invention, the following approach is proposed for the QUBO formula for CT image reconstruction.

[0081] The quantum analyzer and gate-model quantum computer provide the QUBO and Ising models as quantum optimization algorithms. Quantum annealing calculates the minimum value of the model, while the gate-model quantum computer calculates the maximum value using QAOA. This invention describes the use of QUBO modeling for minimization.

[0082] Generally, the pixel values ​​of a projected image correlate with the X-ray intensity passing through the thickness of the sample. The Beer-Lambert law applies to specific axial levels in regions where it is applicable.

[0083]

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[0085] Here, S(x,y) is the X-ray mass attenuation coefficient with respect to the (x,y) position of the sample, and the l-axis is defined perpendicular to the X-ray direction. This equation can be expressed as a discrete sum, as shown in equation (5) below.

[0086]

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[0087] Here,

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[0089]

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[0099] The QUBO model for each pixel of the sinogram is calculated as follows:

[0100]

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[0101] Therefore, the QUBO model for CT image reconstruction is calculated as follows:

[0102]

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[0103] One embodiment of a method for reconstructing CT images using the QUBO model for quantum CT fabrication designed in the manner described above can be summarized as follows. (1) A quantum annealer using the D-Wave system can be used as shown in Figure 1. (2) Random transformation can be performed as shown in Figure 2. (3) Each pixel of the CT image to be realized is in a quantum superposition state, and a superposition sinogram can be created in accordance with the X-ray light source (Figure 3). (4) To calculate equation (9)(QUBO), a superposed sinogram and an X-ray sinogram are used, and thereafter the quantum annealer can create CT images with qubits that satisfy the global minimum energy for the QUBO model (Figure 4). (5) An example of the Radon transform in equilibrium light can be seen in Figures 5 and 6. (6) To calculate equation (9) each pixel of the superimposed sinogram

[0104]

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[0107] The QUBO model obtained through the above process can be used to reconstruct CT images.

[0108] In the following, an embodiment of the process of acquiring CT images using the method of the present invention described above will be presented and explained. However, the present invention is not limited to such an embodiment.

[0109] <Embodiment>

[0110] 1) Data collection X-ray microcomputed tomography (μCT) was performed at beamline 6C Biomedical Imaging of the Pohang light source-II16.

[0111] Figure 8 shows images illustrating the acquisition and transformation of X-ray projection images, where (a) is the original X-ray projection image with a resolution of 2560 × 2160 pixels, (b) is a binned X-ray projection image with a resolution of 50 × 45 pixels, and (c) is an X-ray projection image with the spatial projection area set to 0.

[0112] The projection image in Figure 8(a) was obtained at a resolution of 2560 × 2160 pixels, and for experimental purposes, it was converted to a resolution of 60 × 45 pixels in Figure 8(b). 50 × 50 binning was performed with respect to the rotation center (binning is a method of aligning pixels and calculating the average value). Each set of projection images was measured at 0.5° intervals, and a total of 360 projection images were measured per set.

[0113] Here, the center of rotation is calculated and binning is performed for image preprocessing, but only the center of rotation is calculated for convenience. However, according to this embodiment, the center of rotation can also be calculated when QUBO modeling without having to calculate it separately. Depending on the performance of the quantum computer, image preprocessing may not be necessary.

[0114]

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[0115]

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[0116] 2) Quantum partitioning algorithm for X-ray data Assume the sample exists in three-dimensional space. Define α = μ / ρ as the X-ray mass attenuation coefficient and a natural number. If the number of distinct X-ray mass attenuation coefficients that each grid space may have is m+1, then each pixel of the reconstructed image can be represented by one of the combinations of a qubit and a binary number in equation (10) below, or in a form that can represent any natural number (if it is not a natural number, it can be linearly converted to a natural number).

[0117]

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[0118] Here,

[0119]

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[0120]

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[0121]

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[0122] To apply an optimization algorithm to parallel beam morphological X-ray projection data, a Radon transform is used on the superimposed CT image. The IP is defined as the superimposed sinogram transformed by the CT image I. The s-th position of the IP with respect to the projection angle θ is calculated as shown in equation (11) below.

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[0124] Here,

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[0126]

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[0127]

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[0128]

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[0129] Applying the least squares equation for the difference between p(θ,s) and IP(θ,s), the QUBO model is calculated as shown in equation (12) below.

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[0131] In equation (14) above, the second term is the linear term in the QUBO model, and the third term represents a portion of the optimized value.

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[0134] In order to derive equation (16) from equation (15) above,

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[0139] At this point, we can compare the two sinograms P and IP, and in order to calculate the energy minimization model, we subtract the pixel values ​​of the two sinograms and square them.

[0140]

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[0141] Here, θ is the projection angle, s is the sensor position, and dθ is the change in the projection angle. Also, F(θ,s) is expressed as a linear term, which is a quadratic term with the constant term removed. In the QUBO model, the constant term is excluded. The minimum value of the QUBO model is the opposite sign of the sum of the constant terms.

[0142] 3) Data acquisition and preprocessing of X-ray projection images The above equation (1)

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[0148] 4) Conclusion In this embodiment, segmented images obtained from classical CT images are compared with segmented images generated using a quantum annealer.

[0149] Figure 9 shows a conventional segmentation of a CT image, where (a) shows the axis levels used for CT image reconstruction in red on the X-ray projection image, (b) is a sinogram obtained at axis level 16, and (c) to (e) are CT images and segmented images reconstructed using a classical algorithm.

[0150] In the case of classical segmented images, sinograms corresponding to the axis levels shown by the red lines in Figure 9(a) were generated (see Figure 9(b)). The CT image shown in Figure 9(c) was reconstructed using the Fast Fourier Transform algorithm provided by MATLAB. Subsequently, the MATLAB binarization algorithm was applied to the CT image as shown in Figure 9(d) to identify the interior of the tooth.

[0151] Finally, axial-level 16 segmented images were obtained for the tooth sample (see Figure 9(e)).

[0152] We utilized the hybrid solver of the D-Wave system to execute the quantum partitioning algorithm. This new quantum algorithm allows us to compute partitioned images directly from X-ray data in a single step.

[0153] Figure 10 shows a photograph illustrating CT image segmentation using a quantum optimization algorithm, where (a) the axis levels used for CT image reconstruction are shown in red on the X-ray projection image. (b) is a sinogram obtained at axis level 16. This sinogram was constructed to be proportional to the X-ray mass decay coefficient. (c) is the image segmented by the quantum optimization algorithm. Image (d) compares the two segmented images obtained by the classical and quantum algorithms.

[0154] As shown in Figure 10(b), the sinogram can be derived from the projection image, which is proportional to the X-ray mass attenuation coefficient shown in Figure 10(a). The goal is to represent all values ​​via superimposed CT images by formulating the QUBO model and calculating the pixel values ​​of the sinogram using equation (17). The theoretically calculated minimum energy across the entire region is determined by the negative sum of the squared values ​​of each pixel in the sinogram, which is -821370.3333333333 in the dataset. Three seconds were allocated to obtain the three minimum energy values ​​-817517.07239, -817516.349165, and -817517.950592 using the solver for the QUBO model. Figure 10(c) shows the segmented images corresponding to the last energy value. Furthermore, Figure 10(d) shows a comparative analysis of the segmented image derived from the classical algorithm in Figure 9(e) and the segmented image obtained via the quantum optimization algorithm in Figure 10(c).

[0155] Based on the experimental results described above, we reached the following conclusion.

[0156] Quantum algorithms for CT image reconstruction require the same number of qubits as the number of bits in each pixel. For example, reconstructing a 50x50 CT image with 64-bit resolution requires a total of 160,000 logical qubits.

[0157] In contrast, the quantum partitioning algorithm can reconstruct and partition CT images with 2,500 logical qubits, provided the X-ray mass decay coefficient of the sample is known. Furthermore, this new algorithm can generate more precisely partitioned CT images using even fewer logical qubits.

[0158] Figure 10(b) shows the sinogram derived using MATLAB, which was subsequently converted to integer values ​​from Python. To calculate the X-ray mass decay coefficient of the sample, the Python sinogram values ​​and Radon transform applied to the segmented images in Figure 9(e) were utilized.

[0159] In this invention, approximate coefficient values ​​were used, but it has been confirmed that more accurate results can be obtained by acquiring the coefficients through experimental means using this method of the present invention. Furthermore, it is expected that even better results can be obtained by setting the values ​​of each column in the sinogram to a constant and applying uniform normalization to the entire dataset.

[0160] Furthermore, according to the present invention, because the new algorithm uses the X-ray mass decay coefficient, it is impossible to achieve the theoretically achievable minimum energy across the entire range. This is because the sample and surrounding space are mixed in the pixels surrounding the sample shell, and it is impractical to represent each pixel based solely on the X-ray mass decay coefficient of that pixel. However, during the splitting process, such pixels are converted to binary values ​​of 0 or 1, and the new algorithm can effectively solve this problem. In the embodiments of the present invention, the results were calculated by running the hybrid solver of the D-Wave system three times for three seconds each. The energy obtained differed with each iteration, and even better results could be obtained by providing more annealing time.

Claims

1. A CT image generation method using a quantum algorithm, characterized by obtaining a reconstructed and segmented CT image from projection data using a quantum algorithm that minimizes the discrepancy between an experimentally obtained sinogram and a quantized sinogram derived from a CT image quantized with a mass attenuation coefficient using projection transformation.

2. A method for generating a CT image using a quantum algorithm according to claim 1, characterized in that the CT image is obtained by a process including an optimization step of a superimposed sinogram and an experimental sinogram.

3. The reconstructed CT image is A step to obtain known mass decay for the sample, The steps include multiplying the mass decay by the qubit for each pixel of the CT image, The process involves applying the same mathematical algorithm used for the beam shape obtained from the projection image to the superimposed CT image to obtain superimposed projection data, and The first step is to implement the QUBO (quadratic unconstrained binary optimization) model in the form of an optimization problem, where the difference between the superimposed projection image and the projected image is calculated for each pixel. A method for generating a CT image using a quantum algorithm according to claim 1, characterized by reconstructing a CT image using an algorithm that includes the step of performing calculations using a QUBO model.

4. The CT image generation method using the quantum algorithm according to claim 3, characterized in that the QUBO model is a formula obtained by summing up the QUBO formats for each pixel of all projected images.

5. A method for generating CT images using the quantum algorithm described in claim 3, characterized in that it is calculated using the minimum energy across the entire range of the QUBO model.

6. A method for generating a CT image using a quantum algorithm according to claim 3, characterized in that the superimposed projection image is obtained by a mathematical projection method used for CT images that include projection transformations.

7. A method for generating CT images using a quantum algorithm according to any one of claims 3 to 6, characterized in that the QUBO model is represented by the following formula 1 or an equation that yields the same result. [Math 1] (Here, [Math 2] These are, [Math 3] These are the pixel positions and ratios of the CT images that affect the result. [Math 4] teeth, [Math 5] Location of CT images that affects the outcome [Math 6] This represents the average mass damping coefficient for . Here, [Number 7] Without knowing the value, in order to formalize the QUBO model, [Number 8] is a qubit variable [Number 9] (It is expressed as the sum of.)

8. A method for generating CT images using a quantum algorithm according to claim 3, characterized in that the projection beam is selected from equilibrium beams, cone beams, and fan beams, and can also be used in synchrotron radiation accelerators or cryogenic electron microscopes.

9. The QUBO (quadratic unconstructed binary optimization) model is used as an image reconstruction method applied to quantum computing for the reconstruction of CT images, and is characterized by being represented by the following equation 1 or an equation that yields the same result. [Number 10] (Here, [Math 11] These are, [Math 12] These are the pixel positions and ratios of the CT images that affect the result. [Number 13] teeth, [Number 14] Location of CT images that affects the outcome [Number 15] This represents the average mass damping coefficient for . Here, [Number 16] Without knowing the value, in order to formalize the QUBO model, [Number 17] is a qubit variable [Number 18] (It is expressed as the sum of.)

10. A step to obtain the known X-ray mass decay for the sample, The steps include multiplying the mass decay by the qubit for each pixel of the acquired projection image, The process involves applying the same mathematical algorithm used for the beam shape obtained from the projection image to the superimposed image to obtain superimposed projection data, and A QUBO model design method, which includes the step of realizing a QUBO (quadratic unconstrained binary optimization) model in the form of a least squares problem, where the difference between the superimposed projection image and the X-ray projection image for each pixel.

11. The QUBO model design method according to claim 10, characterized by designing using the method shown in Formula 2 below. [Number 19] (Here, [Number 20] These are, [Math 21] These are the pixel positions and ratios of the CT images that affect the result. [Number 22] teeth, [Number 23] Location of CT images that affects the outcome [Number 24] This represents the average mass damping coefficient for . Here, [Number 25] Without knowing the value, in order to formalize the QUBO model, [Number 26] is a qubit variable [Number 27] (It is expressed as the sum of.)

Images