INFORMATION PROCESSING SYSTEM, INFORMATION PROCESSING PROCESS AND PROGRAM

Abstract

According to one embodiment of the invention, an information processing system is provided comprising: a acquisition unit configured to acquire projection data representing a projection image of an X-ray CT scan of a measurement object, as well as an absorption model regarding the absorption of X-rays by the measurement object, wherein the projection data contain information about the projection image for each orientation with which incident X-rays strike the measurement object; a generation unit configured to generate corrected projection data for each of several candidates for hypothetically incident X-rays whose incidence on the measurement object is hypothetically assumed, wherein the corrected projection data are projection data that are corrected based on each candidate for hypothetically incident X-rays and the absorption model;a calculation unit configured to calculate a consistency indicator for each of the generated corrected projection data, indicating the degree of consistency of the corrected projection image with respect to orientation; and an output unit configured to output at least one set of corrected projection data from the generated corrected projection data, taking the consistency indicators into account.

Description

TECHNICAL AREA

[0001] The present invention relates to an information processing system, an information processing method and a program. TECHNICAL BACKGROUND

[0002] Non-Patent Document 1 discloses a method for estimating the spectrum of incident X-rays. For example, Non-Patent Document 1 discloses a method in which X-rays are incident on a structure with known line absorption coefficients, and the intensity of the transmitted X-rays is measured to estimate the spectrum of the X-rays actually incident on the object being measured. Non-Patent Document 2 serves only as a reference. PREVIOUSLY KNOWN DOCUMENTS NON-PATENT DOCUMENTS

[0003] Non-patent document 1: Duan X., Wang, et al., “CT Scanner X-Ray Spectrum E-stimation From Transmission Measurements”, Med Phys. 2011 Feb; 38(2): 993-7. Non-patent document 2: T. Würfl et al., 8th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2018) Outline of the invention; Problems to be solved from the invention

[0004] In computed tomography (CT), it is desirable to reduce negative effects on reconstructed images, such as those caused by beam hardening or scattering artifacts. However, when correcting using the spectrum of the incident X-rays estimated by the method described above, structures with known line absorption coefficients are required, and furthermore, information (e.g., absorption edges, scattering, etc.) may be present that cannot be accounted for in the model used for the estimation. Therefore, there is still room for improvement in the technology for correcting projection data in X-ray CT to reduce negative effects such as beam hardening with respect to the spectrum of the incident X-rays and the model of the object being measured. MEANS TO SOLVE THE PROBLEMS

[0005] According to one embodiment of the invention, an information processing system is provided comprising: a acquisition unit configured to acquire projection data representing a projection image of an X-ray CT scan of a measurement object, as well as an absorption model regarding the absorption of X-rays by the measurement object, wherein the projection data contain information about the projection image for each orientation with which incident X-rays strike the measurement object; a generation unit configured to generate corrected projection data for each of several candidates for hypothetically incident X-rays whose incidence on the measurement object is hypothetically assumed, wherein the corrected projection data are projection data that are corrected based on each candidate for hypothetically incident X-rays and the absorption model;a calculation unit configured to calculate a consistency indicator for each of the generated corrected projection data, indicating the degree of consistency of the corrected projection image with respect to orientation; and an output unit configured to output at least one set of corrected projection data from the generated corrected projection data, taking the consistency indicators into account.

[0006] This design allows for the flexible inclusion of information that is difficult to incorporate into existing models describing the absorption process of X-rays by measurement objects, as it can vary depending on the type of X-ray irradiation, and provides corrected projection data that reduces negative influences such as artifacts. BRIEF DESCRIPTION OF THE FIGURES Fig. Figure 1 shows an example of the system and hardware configuration of an information processing system. Fig. Figure 2 is a flowchart showing an example of the information processing sequence performed by the information processing system 1. Fig. Figure 3 shows an example of the spectrum of actually incident X-rays as a comparison object. Fig. Figure 4 shows an example of the spectrum of hypothetically incident X-rays for a case in which the convergence condition is met. Fig. Figure 5 shows an example of a tomogram of the sample reconstructed without correction. Fig. Figure 6 shows an example of a correction using the formula in Fig. 3 shown: reconstructed tomogram of the sample with the actual incident X-rays. Fig. Figure 7 shows an example of a correction using the formula in Fig. 4 hypothetically incident X-rays shown: reconstructed tomogram of the sample. FORMS OF EXECUTION OF THE INVENTION

[0007] The following section explains embodiments of the invention with reference to the figures. The features mentioned in the embodiments described below can also be combined with one another.

[0008] Programs for implementing the software presented in the embodiments can also be provided as non-transitory computer-readable media, made available for download from an external server, or provided in such a way that the programs can be started on an external computer and the functionality can be implemented on a client device (so-called "cloud computing").

[0009] Furthermore, according to one embodiment, various types of information processing can involve input and the realization of a corresponding output based on that input. There is no restriction regarding the type of information used in this information processing (hereinafter referred to as "reference information"), as long as an output is obtained as a result of the input. The reference information can be, for example, rule-based information such as databases, lookup tables, or predefined functions (including decision formulas generated by statistical methods, such as regression equations). Alternatively, it can also be a trained model that has previously learned correlations between input and output, or a large language model capable of producing a desired result upon input of a prompt.

[0010] In one embodiment, the term "unit" also includes, for example, a combination of hardware resources that can be implemented by a circuit understood in a broader sense, and information processing that can be specifically implemented by these hardware resources using software. Furthermore, in one embodiment, various types of information are processed. This information can be, for example, physical signal values ​​such as voltages or currents, signal levels as collections of binary numbers (consisting of 0s and 1s), or quantum mechanical superpositions (so-called qubits), which can be transmitted and processed by a circuit understood in a broader sense.

[0011] In a broader sense, a circuit is a circuit that is implemented in a suitable manner through at least appropriate combinations of circuits, circuit groups, processors, and memory. The processor can be a general-purpose processor or a specialized circuit. In other words, the term also encompasses application-specific integrated circuits (ASICs), programmable logic devices such as simple programmable logic devices (SPLDs), complex programmable logic devices (CPLDs), and field-programmable gate arrays (FPGAs), and the like. 1. System and hardware configuration of the information processing system 1

[0012] First, with reference to Fig. 1. The system and hardware configuration of an information processing system 1 according to the present embodiment is explained. Fig. Figure 1 shows an example of the system and hardware configuration of Information Processing System 1. Information processing system 1

[0013] The in Fig. The information processing system 1 shown in Figure 1 is capable of processing multiple projection images acquired by a CT scanner 3. The information processing system 1 comprises an information processing device 2 and a CT scanner 3. The information processing device 2 and the CT scanner 3 are configured to communicate with each other via a communication cable or a network. This allows the information processing device 2 and the CT scanner 3 to exchange various pieces of information. The system shown as an example of information processing system 1 can consist of one or more devices or structural elements. Accordingly, the information processing system 1 can also comprise only the information processing device 2 or only the CT scanner 3.The information processing device 2 and the CT device 3 are, for example, operated by a user who performs the measurement. Information processing device 2

[0014] The information processing device 2 is a PC (personal computer). However, the information processing device 2 can also be a tablet computer, smartphone, or the like. The information processing device 2 can process projection images acquired by the CT device 3. More precisely, the information processing device 2 is configured to subject projection data acquired by the CT device 3 to suitable information processing, to control the radiation generated by an X-ray generator 35, to obtain projection images captured by a detection device 36, to control the movement of a sample holding section 34, to control a rotary drive section 37, and the like.The information processing device 2 is capable of performing any information processing in connection with the CT device 3; another information processing device may also be provided between the information processing device 2 and the CT device 3. As in . Fig. As shown in Figure 1, the information processing device 2 comprises a processor 21, a storage unit 22, a communication unit 23, an input unit 24, and an output unit 25. These structural elements are electrically interconnected within the information processing device 2 via a communication bus. The information processing device 2 performs the processing according to the present embodiment.

[0015] Processor 21 performs the processing and control of all operations relating to the information processing device 2. Processor 21 can, for example, be a CPU (Central Processing Unit). The information processing by a program stored in the memory unit 22 is specifically implemented by processor 21, which is an example of hardware, and can thus be carried out through various functionalities contained within processor 21. The various functions contained within processor 21, for example, enable the functionality explained later in Fig. The processing shown in section 2 is implemented. The processor 21 is not limited to a single processor, but can also be implemented as multiple processors 21, each with one of the functionalities. A combination of these functionalities is also possible.

[0016] The memory unit 22 stores various pieces of information, which are defined in more detail below. It can be implemented, for example, as a storage device such as a solid-state drive (SSD), which stores various programs for the information processing device 2 that are executed by the processor 21, or as random-access memory (RAM), which temporarily stores the necessary information (e.g., arguments and arrays) for the program's calculations. The memory unit 22 stores various programs and variables for the information processing device 2 executed by the processor 21, as well as data and the like that the processor 21 needs when processing the programs. The memory unit 22 is an example of a storage medium.

[0017] Although a wired communication means, such as USB, IEEE 1394, Thunderbolt (registered trademark), a wired LAN network, or similar, is preferred for the communication unit 23, communication via a wireless LAN network, mobile communication via LTE, 3G, 4G, 5G, etc., Bluetooth (registered trademark), or the like is also possible depending on the circumstances. A combination of several of these communication means is even more preferable. In other words, the information processing device 2 can exchange different types of information with external devices via the communication unit 23.

[0018] The input unit 24 can be located inside the housing of the information processing device 2 or outside of it. For example, the input unit 24 can be integrated with the output unit 25 as a touch panel or touchscreen. If it is a touch panel, the user can input data by tapping, swiping, or similar actions. Of course, buttons, a mouse, a keyboard, or similar devices can also be used instead of a touch panel. In other words, the input unit 24 receives input based on the user's actions. Such input is transmitted as command signals via the communication bus to the processor 21, whereupon the processor 21 can perform a predetermined control or calculation as needed.

[0019] The output unit 25 can serve as a display for the information processing device 2. The output unit 25 can be located, for example, inside the housing of the information processing device 2 or outside of it. The output unit 25 can display a screen of a graphical user interface (GUI) with which the user can interact. This GUI can preferably be implemented as a CRT display, liquid crystal display, organic electroluminescent display, or plasma display, depending on the type of information processing device 2. CT scanner 3

[0020] The CT device 3 is a device capable of emitting X-rays onto a sample and obtaining a projection image of the sample based on the transmitted or penetrating X-rays. The CT device 3 can be a sample rotation CT device, in which a sample holding section 34 is rotated, or a gantry CT device, in which an X-ray generator 35 and the detection device 36 rotate relative to the sample holding section 34 – however, it is not limited to these configurations. The CT device 3 comprises a processor 31, a storage unit 32, a communication unit 33, a sample holding section 34, an X-ray generator 35, a detection device 36, and a rotation drive unit 37. These components are electrically interconnected within the CT device 3 via a communication bus.For the processor 31, the storage unit 32 and the communication unit 33 of the CT device 3, reference can be made to the processor 21, the storage unit 22 and the communication unit 23 of the information processing device 2.

[0021] The sample holding section 34 is designed to hold a sample table. The sample holding section 34 can be configured to move the sample table in any direction based on motion commands generated by processor 21 or processor 31. The sample table is configured to allow a sample serving as a measurement object to be placed on it.

[0022] The X-ray generator 35 emits incident X-rays onto an area containing a sample arranged on the sample holding section 34. The incident X-rays can be continuous X-rays or monochromatic X-rays.

[0023] The detection device 36 is configured to detect X-rays that have penetrated a sample located in the sample holding section 34. For the sake of simplicity, these X-rays detected by the detection device 36 will hereinafter also be referred to as "detection X-rays". The detection device 36 is, for example, a two-dimensional detection device using CCDs, image plates, or the like. The detection X-rays are transmitted as projection data to the information processing device 2 or the like.

[0024] The projection data are data obtained through CT measurements with CT device 3 and represent projection images of an X-ray CT scan (or X-ray CT projection images) of the sample. The projection data contain information about the projection images for each orientation relative to the X-rays incident on the sample. The orientation can be defined, for example, as the angle θ between the direction of incidence of the X-rays and a reference direction of the sample. The orientation (or, in other words, the angle θ) indicates the degree of rotation of a coordinate system in the projection images. This angle θ can be set, for example, in a range from 0 degrees to less than 360 degrees. The projection data can be represented, for example, as a data set of a distribution I(x, y) of the intensity I of the X-rays I(x, y) for each angle θ, where the position coordinates on the two-dimensional detection device are defined as (x, y).The projection data, in the form of a dataset of the intensity distribution I(x, y) of the detected X-rays for the angle θ for each measured orientation characterized by the angle θ, are also referred to as projection data I(x, y, θ). If the projection data are obtained using a fan-beam projection, the coordinate system (x, y, θ) can be subjected to a Fan2para transformation and converted into a parallel-beam coordinate system. For a cone-beam optical system, only the detection results in the region near the central cross-section (the center with respect to the y-direction) of the detection device, where the incident X-ray beam can be considered a fan beam, can be used.

[0025] The rotary drive unit 37 is configured to control the direction of incidence of the X-rays incident on the sample. Thus, the rotary drive unit 37 can change the angle θ (i.e., the orientation) of the direction of incidence of the X-rays with respect to the reference direction of the sample. For example, if the CT device 3 is a sample rotation CT device, the rotary drive unit 37 is configured to rotate the sample holding section 34 relative to the X-ray generator 35 and the detection device 36. If the CT device 3 is a gantry CT device, the rotary drive unit 37 is configured to rotate the X-ray generator 35 and the detection device 36 relative to the sample holding section 34. The rotary drive unit 37 may include a mechanism for adjusting the magnification factor of the projected image during acquisition (e.g.,a movement device for adjusting the distance between the X-ray generator 35 or the detection device 36 and the sample holding section 34). 2. Information processing

[0026] This section explains the information processing that is carried out using the information processing system 1 described above. Fig. Figure 2 is a flowchart illustrating an example of the information processing sequence performed by information processing system 1. This information processing can also include any number of exception handling operations, which are not shown. Exception handling includes pausing the information processing operation and skipping individual processing steps. Selections or inputs made during information processing can be based on user actions or occur automatically without user intervention. Step S1

[0027] First, in step S1, processor 21 obtains projection data I (x, y, θ) from the CT device 3 or the like. Processor 21 can also obtain radiation information.

[0028] Exposure information is information about the X-rays actually incident on the sample. The X-rays actually incident on the sample can be either the X-rays actually detected by a detection device 36 or the like, which are emitted by the X-ray generator 35, or spectra that were guaranteed in advance as standard values ​​by the manufacturer of the CT device 3. The X-rays actually incident can also be spectra that were recalculated based on measurement results in order to reproduce the X-rays actually incident. For example, the exposure information can include information about the energy range contained in the X-rays actually incident on the sample.Information about the relevant energy range can be expressed, for example, as the lower and upper limits (in other words, the energy cutoff) of the energy contained in the actual incident X-rays. The irradiation information can also include any information characterizing the spectrum, such as the peak position (especially the position of the maximum peak) of the actual incident X-rays, peak intensity, the full width at half maximum (FWHM) of peaks, and the weighted average energy. The irradiation information can also be the spectrum of the actual incident X-rays themselves. Furthermore, the irradiation information can include information about the energy range of the incident X-rays. Information about the energy range of the incident X-rays includes, for example, the upper and lower limits of the energy of the incident X-rays.The upper limit should preferably correspond to the value of the tube voltage, and the lower limit should be determined taking into account the lower limit of the detection energy of the detection device and the influence of absorption by the atmosphere. Step S2

[0029] Next, in step S2, processor 21 obtains an absorption model. The absorption model contains information about the absorption of the X-rays by the sample and can, for example, be represented as a spatial distribution of the sample's absorption coefficient f. Steps S1 and S2 are examples of steps for obtaining this model in this embodiment.

[0030] The absorption model can, for example, be represented as a model of line absorption coefficients. This model describes a correlation between the incident X-rays and the X-rays penetrating the sample as detected by the detector 36. The line absorption coefficient model is a function chosen to approximate the energy dependence of the distribution of line absorption coefficients and can, for example, be described by equation (1) according to the Lambert-Beer law. Equation (1): I=∑bDb exp(−∫dl f(Eb))

[0031] In this model, the discretized energy is denoted with the index b as E b shown. In equation (1), I on the left-hand side represents the intensity of the X-rays detected by the detection device 36. D bon the right side of equation (1) stands the intensity of the b-th energy E b , 1 represents the penetration distance of the incident X-rays in the sample, and the integral over 1 represents the line integral along the penetration path of the incident X-rays. For simplicity, the incident X-rays are considered here as continuous X-rays and modeled as a superposition of several monochromatic X-rays discretized in the energy domain. In equation (1), the penetration distance of the X-rays and the nonlinearity of the attenuation of the X-rays are expressed or modeled by adding the attenuation of the respective monochromatic X-rays over the entire energy.

[0032] As a more concrete example, the model of line absorption coefficients described above can be represented as the product of an energy-dependent scaling factor s and a line absorption coefficient f(E0) that depends only on a specific reference energy E0, as follows. Equation (2): I=∑bDb exp(−s(Eb)∫dl f(E0))

[0033] The scaling factor s(E b The scaling factor s describes the energy dependence of the line absorption coefficient and is a non-negative function of the energy E, whose value is equal to 1 at the reference energy E0. The scaling factor s can, for example, be expressed as a power function of the energy as follows. Equation (3): s(Eb)=(EbE0)α

[0034] The exponent α in equation (3) is a suitable parameter to be defined. The specific form of the scaling factor s is not limited to the form above, but can be arbitrarily defined as long as it is a function with which the energy dependence of the line absorption coefficient can be approximated, such as an exponential function or a logarithmic function. Step S3

[0035] Next, in step S3, processor 21 sets the search conditions and convergence conditions. Step S3 is an example of a search condition setting step and a convergence condition setting step, and processor 21, which performs the processing in step S3, can be viewed as the search condition setting unit and the convergence condition setting unit.

[0036] The search conditions specify the search range for hypothetical incident X-rays that are entered into the obtained correction model. These hypothetical incident X-rays are those assumed to be incident on the sample when calculating the line integrals along the penetration path of the incident X-rays with the line absorption coefficient f, based on the correction model. For the sake of simplicity, the X-rays actually incident on the sample will be referred to as "actual incident X-rays" in the following text, to distinguish them from the aforementioned hypothetical incident X-rays. The hypothetical incident X-rays can, for example, be represented as a spectrum consisting of a series of intensities D. b with the aforementioned energies E bexists. Here, the search conditions for the hypothetical incident X-rays are defined, for example, based on the aforementioned irradiation information. As an example, the processor 21 defines search conditions such that the energy range contained in the hypothetical incident X-rays is limited in consideration of the energy range contained in the actually incident X-rays (i.e., the actual incident X-rays). With such a design, the time required for correction can be reduced, and at the same time, the possibility of over-considering influences that cannot occur in reality can be limited, thus enabling a more appropriate correction. For example, the processor 21 can define the search conditions such that the range of discrete energies E b with finite intensity D bThe hypothetical incident X-rays, defined in step S4 described later, are contained within the range specified by the lower and upper limits of the actual incident X-rays. Processor 21 can also define the search conditions such that the position of the maximum peak in the hypothetical incident X-rays is limited by the position of the maximum peak in the actual incident X-rays (e.g., so that the distance between the positions of the two peaks lies within a predefined range). The search conditions can also be defined independently of the actual incident X-rays.

[0037] Convergence conditions are the criteria used to assess whether the consistency indicator described below is converging. These conditions can be defined in various ways, such as whether the consistency indicator value is below a defined threshold indicating convergence, or whether the magnitude of the change in the consistency indicator is below a defined threshold. Step S4

[0038] Next, in step S4, processor 21 determines the spectrum of the hypothetical incident X-rays. Step S4 is an example of a candidate determination step, and processor 21, which performs the processing in step S4, can be considered a candidate determination unit. The spectrum of the hypothetical incident X-rays determined in step S4 is an example of a candidate for hypothetical incident X-rays that are hypothetically assumed to be incident on the object being measured. For example, processor 21 determines the candidate for hypothetical incident X-rays such that it satisfies the search conditions determined in step S3. Such a design allows projection data to be obtained that are appropriately corrected, resulting in fewer discrepancies with the actual measurement results.Furthermore, some of the candidates for hypothetical incident X-rays can be generated based on the spectrum of the X-rays actually incident on the object being measured. This design allows the correction range to be appropriately limited in light of the hypothetical model and reduces the time required for correction. In this embodiment, the processor 21, in step S4 executed for the first time, establishes a spectrum of the hypothetical incident X-rays (i.e., an initial model of the hypothetical incident X-rays) that matches the spectrum of the actually incident X-rays. Step S5

[0039] Next, in step S5, processor 21 corrects the projection data obtained in step S1 based on the candidates for the corresponding hypothetical incident X-rays and the absorption model defined in step S4. Thus, processor 21 generates corrected projection data. For the sake of simplicity, the projection data that has undergone such a correction will subsequently be referred to as "corrected projection data".

[0040] This will be explained using an example of processing in the case of beam hardening correction. Beam hardening correction is a correction that uses a model of line absorption coefficients in which the energy dependence of the line absorption coefficients is expressed by the scale factor s, which contains a parameter. An example of beam hardening correction is a correction performed using the value of the line integral of the line absorption coefficients for a given reference energy E0. For example, as beam hardening correction, processor 21 calculates the line integrals of the line absorption coefficients f from the detection results of the detection X-rays (i.e., the projection data) using the absorption model shown in formula (2), based on the reference energy E0 specified in step S2 in the absorption model and the spectrum (E) specified in step S4.b , D b ) of the hypothetical incident X-rays. Here, processor 21 optimizes the integral ∫dlf(E0) such that the intensity distribution I(x, y, θ) of the detected X-rays is reproduced. For example, processor 21 calculates the integral ∫dlf(E0) using Newton's method, in which, for example, the scaling factor s (more precisely, the power index a contained in the scaling factor) is used as a parameter. The specific algorithm for determining ∫dlf(E0) is not limited to Newton's method, but can also be, for example, the steepest descent method. Processor 21 can calculate the line integrals of the line absorption coefficients f of energy E. b determine by multiplying the line integrals of the line absorption coefficients of the reference energy E0 by the scale factor s, which is expressed by equation (3).

[0041] Processor 21 corrects the projection data obtained in step S1 based on the calculated line integrals of the line absorption coefficients f. This yields corrected projection data. That is, the corrected projection data are projection data that have been corrected with respect to the corresponding hypothetical incident X-rays and the absorption model. The corrected projection data can contain variables (x, y, θ) corresponding to the uncorrected projection data, as well as an intensity distribution I(x, y, θ) corresponding to these variables. Step S6

[0042] Next, in step S6, processor 21 calculates a consistency indicator using the corrected projection data obtained in step S5. Step S6 is an example of a computation step, where processor 21, which performs the processing in step S6, can be considered the computation unit.

[0043] The consistency indicator is a value that indicates the degree of consistency of a corrected projection image with respect to its orientation. In this embodiment, the consistency indicator serves as an evaluation function for assessing the spectrum of the hypothetically incident X-rays used for correction. The consistency indicator can be configured to increase when the corrected projection image has low consistency with respect to its orientation and decrease when it has high consistency. The consistency indicator can, for example, be defined as NRMSD (normalized root mean square deviation) as follows. Equation (4): NRMSD=∑k(MkAveragei(Mi)−1)2

[0044] The term M k in equation (4) is defined as follows: Equation (5): Mk=∫m(k,s) ds Equation (6): m(k,s)=∫dlk,sf(r,E0)

[0045] In equations (5) and (6), s is a parameter that specifies the position of the detection and can be expressed, for example, as s = (x, y). Furthermore, k is a parameter that specifies the orientation of the incident X-rays and can be expressed, for example, as k = θ. In equation (6), r is a parameter that specifies the spatial distribution of the line absorption coefficient f in the coordinate system that specifies the position of the sample. m(k, s) in equation (6) is the line integral of the line absorption coefficient f of the reference energy E0 along a straight path of penetration of the incident X-rays in the form of a parallel beam from the position at an angle k to the detection position s. k In equation (5), M is a value that gives the value m(k, s) defined by equation (6) as the integral over all detection positions s (i.e., as the sum of the discretely obtained values). kThis value represents the total line absorption coefficient of the incident X-rays (i.e., the absorption of the incident X-rays) from an orientation characterized by an angle k as a single sum. The value of equation (6) can be used as the line integral of the line absorption coefficient f of the reference energy E0, obtained as a result of the optimization in step S5.

[0046] Processor 21 calculates the value of M using the result of the correction of the projection data according to formulas (5) and (6). k for each orientation corresponding to one of the angles k. The processor then calculates 21 according to formula (4) based on the calculated value M. k The consistency indicator (NRMSD) is used for each orientation. When the consistency for that orientation is highest, all values ​​are M. kThe orientations are the same, so that the consistency indicator then assumes the minimum value (here 0). The consistency indicator is not limited to this, but can also be a parameter that describes the dispersion of the absorption of the incident X-rays for the respective angle k, such as the dispersion or standard deviation of M. k , expresses. The consistency indicator can therefore be appropriately chosen as long as it indicates the degree of consistency of the corrected projection images with respect to orientation. Step S7

[0047] Next, in a convergence condition evaluation step in step S7, processor 21 assesses whether the consistency indicator calculated in step S6 satisfies the convergence condition. Step S7 is an example of a convergence condition evaluation step, and processor 21, executing step S7, can be considered the convergence condition evaluation unit. The convergence condition set in step S3 can be used. For example, if it is determined that the consistency indicator calculated in step S6 does not satisfy the convergence condition, processor 21 returns to step S4 and sets a new spectrum of hypothetical incident X-rays.Subsequently, processing steps S5 to S7 are executed based on the redefined spectrum of hypothetical incident X-rays, and iteratively corrected projection data for individual spectra of hypothetical incident X-rays are generated until the consistency indicator satisfies the convergence condition. The corresponding processing for this (e.g., step S5) is an example of a generation step, and processor 21, which performs such processing, can be considered a generation unit. The hypothetical incident X-rays iteratively defined in this way in step S4 are also examples of combinations of hypothetical incident X-rays, as are the hypothetical incident X-rays defined during the initial execution of step S4.In this way, Processor 21 generates corrected projection data for individual candidates for hypothetical incident X-rays, which are assumed to be hypothetically incident on the sample, and calculates a consistency indicator for each set of generated corrected projection data. For example, in step S7, if the consistency indicator does not satisfy the convergence condition, Processor 21 uses a different candidate for hypothetical incident X-rays than the previous candidates for hypothetical incident X-rays, thus iteratively performing the generation of corrected projection data and the calculation of the consistency indicator in step S6. For example, Processor 21 uses previously determined candidates for hypothetical incident X-rays (e.g.,The processor 21 determines the hypothetical incident X-rays in the next step S4 (based on the candidates for hypothetical incident X-rays defined in the immediately preceding step S4). More precisely, in the next step S4, processor 21 defines hypothetical incident X-rays that further optimize the evaluation function described above, such as the consistency indicator. The algorithm for searching for these next hypothetical incident X-rays can be chosen arbitrarily; for example, local search methods, successive improvement methods, or neighborhood search methods can be used. Furthermore, such algorithms can also be metaheuristic search methods, such as cuckoo search, genetic algorithms, or particle swarm optimization.Processor 21 can also randomly or in a specific order determine spectra of hypothetical incident X-rays from a predefined pool of candidates. These candidates can be selected based on search criteria. At least one of the candidates can be selected for the hypothetical X-ray spectrum regardless of its similarity to the actual incident X-rays.

[0048] Furthermore, processor 21 can determine the hypothetical incident X-rays based on the consistency indicator, regardless of whether they approximate the actual incident X-rays. This design makes it easier to account for the effects of factors causing more complex artifacts in the sample (e.g., the sample structure or higher-order scattering processes) in the hypothetical incident X-rays, thus reducing artifacts that cannot be reduced by correcting using the actual incident X-rays. The similarity of two X-rays can be determined by the distance between vectors of variables that define these X-rays (e.g., the intensities D). b the respective energies E b). This distance can be expressed using any indicators such as the Manhattan distance, the Euclidean distance, or the cosine similarity degree. Step S8

[0049] If processor 21 determines in step S7 that the consistency indicator meets the convergence condition, processor 21 receives a specification of parameters in step S8 that are used for the correction described below. These parameters can contain information (E b , D b ) about the spectrum of the hypothetically incident X-rays. The parameters can also include parameters for optimization based on a model of line absorption coefficients, such as the reference energy E0 or the scaling factor s(E). b) (Potential index α, etc.). This specification can be made by the user, for example. In this case, the processor 21 can reconstruct a tomogram or layer image of the sample based on the corrected projection data and display it on the output unit 25. With such a configuration, the user can be prompted to compare and evaluate the reduction of artifacts achieved by a correction selected based on the consistency indicator with the tomogram of the sample obtained from the correction. The parameter settings can also be determined automatically by the processor 21 or similar device. Step S9

[0050] Next, in step S9, processor 21 performs the actual correction of the projection data based on the parameters defined in step S8. This actual correction can be performed in the same way as the correction of the projection data in step S5, whereby the optimization of the line integration values ​​of the line absorption coefficients f can also be repeated using the spectra of the same hypothetically incident X-rays. In this case, the optimization in step S9 can also be performed with a higher number of repetitions than in step S5. Processor 21 can thus generate corrected projection data. Therefore, step S9 can also be considered a generation step. Step S10

[0051] Next, in step S10, processor 21 outputs the corrected projection data obtained through this actual correction, as an example of corrected projection data that satisfies the convergence condition. The corrected projection data can serve as the final corrected projection data. Step S10 is an example of an output step in this embodiment, and processor 21, which performs the processing in step S10, is an example of an output unit. In other words, based on the consistency indicator, processor 21 outputs at least one set of corrected projection data from the sets of corrected projection data generated in step S5. For example, processor 21 can output, from the generated corrected projection data, those corrected projection data that satisfy the convergence condition.If there are multiple corrected sets of projection data that satisfy the convergence condition, processor 21 can output at least one of the sets of corrected projection data. Step S11

[0052] Next, in step S11, processor 21 reconstructs a tomogram or cross-sectional image of the sample based on the corrected projection data output in step S10. Processor 21 presents the reconstructed tomogram of the sample to the user via output unit 25.

[0053] The processor 21 then terminates the information processing. With the configuration described above, information that was difficult to incorporate into existing models for representing the absorption of X-rays by measurement objects can be flexibly included, as it can vary depending on the type of X-ray irradiation. Corrected projection data can be obtained, reducing negative influences such as artifacts. In the embodiment described above, the line integration of the line absorption coefficient f of the sample is used as an optimization parameter, and the consistency of the absorption ratios for different orientations is evaluated based on the line integration for each orientation. This ensures that even in the case of insufficient information about the structure (shape) of the sample (e.g.,(if the structure of the sample is unknown), the influence of the structure on the distribution of the line absorption coefficient (see, for example, non-patent document 2) in hypothetically incident X-rays can be included, and a correction can be proposed that can reduce artifacts. 3. Examples of the results of this information processing

[0054] The following are examples of the information processing described above. Fig. Figure 3 shows an example of the spectrum of actually incident X-rays as a comparison object. Fig. Figure 4 shows an example of the spectrum of hypothetically incident X-rays for a case where the convergence conditions are met. This section discusses the... Fig. The hypothetical X-rays shown in Figure 4 are simply referred to as "hypothetical X-rays".

[0055] How Fig. Figure 3 shows that the spectrum of the actually incident X-rays has an intensity D b greater than 0 in the energy range E b from 10 keV to 80 keV and contains a single, maximum peak at 10 keV (or in the energy range below). The spectrum of the actually incident X-rays is the calibration value (that is, the value actually measured according to the standard) of the X-rays emitted by X-ray generator 35.

[0056] How Fig. As shown in Figure 4, the hypothetically incident X-rays in this embodiment can be represented as a discrete line-shaped spectrum, with intensity D values ​​in the range from 10 keV to 140 keV in steps of 10 keV. b exhibits. As in Fig. As shown in Figure 4, the spectrum of the hypothetical incident X-rays in the range of 10 keV to 80 keV has a finite value greater than 0 and three peaks at 10 keV or less, 50 keV, and 80 keV. The energy range contained in the spectrum of the hypothetical incident X-rays lies within the energy range contained in the spectrum of the actual incident X-rays. Of the three peaks, the peak at 50 keV has the greatest intensity. As shown in Fig. 3 and Fig. As shown in Figure 4, the hypothetical incident X-rays, which in this embodiment correspond to a consistency indicator that satisfies the convergence conditions, can have a spectrum that differs completely from the spectrum of the actually incident X-rays in various respects, such as the peak position and the ratio of the peak intensities to each other.

[0057] Next, an example of the effect of the beam hardening correction described above using these incident X-rays will be explained using a reconstructed image. Fig. Figure 5 shows an example of a tomogram of the sample reconstructed without correction. Fig. Figure 6 shows an example of a correction using the formula in Fig. 3 shown: reconstructed tomogram of the sample with the actual incident X-rays. Fig. Figure 7 shows an example of a correction using the formula in Fig. The tomogram of the sample reconstructed using hypothetical X-rays is shown in Figure 4. A multilayer ceramic capacitor (MLCC) was used as the sample. The exponent of the exponential function in the correction for generating the in Fig. The tomogram shown in Figure 6 is -3.5, and the exponent of the exponential function used to generate the tomogram shown in Figure 6 is -3.5. Fig. The value of the tomography image shown in section 7 is -4.0. For the sake of simplicity, the following explanation will be based on the value shown in the image. Fig. 5 tomograms shown as IM1, which is in Fig. The 6 tomograms shown are IM2 and the one in Fig. The tomogram shown is labeled IM3. The white or gray square shadows in the center of these tomograms IM1 to IM3 correspond to sections of the sample.

[0058] As in Fig. As shown in Figure 5, in the uncorrected tomogram IM1, the outer edges of the sample and the vertical lines within the sample appear white and blurred. This is presumably due to the influence of artifacts during CT reconstruction. In the projection data underlying these tomograms, tomogram IM2, created using the actual incident X-rays, highlights the vertical line regions in the center, while the remaining areas become darker, forming bright, X-shaped areas radiating obliquely outwards from the center of the sample. Therefore, tomogram IM2 may even have lower visibility and accuracy than the uncorrected tomogram IM1. Thus, with this information processing, the quality of the corrected tomogram IM2 may actually be degraded compared to the uncorrected tomogram IM1 by using the actual incident X-rays.

[0059] In contrast, as in Fig. Figure 7 shows that, when corrected using hypothetical incident X-rays that meet the convergence conditions, the outer edge of the sample is more distinct in tomogram IM3 than in the uncorrected tomogram IM1, and there are fewer (or no) patterns that affect the accuracy as in tomogram IM2.

[0060] In the information processing described above, hypothetical incident X-rays are determined based on a consistency indicator, independent of their similarity to the actual incident X-rays (e.g., peak position, peak intensity ratio, full width at half maximum, etc.). By incorporating various sample factors requiring correction (e.g., shape factors, higher scattering processes, etc.) into the hypothetical incident X-rays, it is possible to reduce artifacts more effectively than, for example, in the case of correction based on hypothetical incident X-rays that merely approximate the actual incident X-rays. 4. Another example of absorption model and correction

[0061] The following section explains another example of the absorption model obtained in step S2, as well as another example of the correction performed using this absorption model in step S5. The following section describes those parts of information processing that were already mentioned above with reference to Fig. The sections 2 that were explained have been omitted.

[0062] The absorption model can be designed to include components relating to other absorption or scattering processes, such as the Klein-Nishina factor f. KN A correction model that, for example, includes a component based on the Klein-Nishina factor f. KN This can be represented as follows. Equation (7): I=∑bDbexp(−s(Eb) ∫dl f(E0)−fKN(Eb)∫dlρ)

[0063] In equation (7), ρ is a function representing the charge density distribution. The Klein-Nishina factor f KN (Eb ) is determined in a suitable manner. In equation (7), with respect to the spectrum D b the incident X-rays, the scaling factor s, the reference energy E0 and the Klein-Nishina factor f KN Two variables are optimized with respect to the intensity I of the detected X-rays, namely the line integrals of the line absorption coefficients f(E0) at the reference energy E0 and the charge density distribution along the penetration path of the X-rays. Thus, the number of variables is twice as high compared to the beam hardening correction described above.

[0064] Therefore, in this embodiment, the processor 21 can be placed in step S1 of the process described in Fig. The solution of the following nonlinear systems of equations, as shown in the flowchart 2, is to be treated as a task, specifically for the case where the incident X-rays with two different spectra are incident as projection data, using the intensity distributions I Low (x, y, θ) and I High (x, y, θ) of the respective detected X-rays. Equation (8): ILow=∑bDLow,b exp(−s(Eb) ∫ dl f(E0)−fKN(Eb) ∫ dl ρ)=:F1(∫dl f(E0),∫ dl ρ) Equation (9): IHigh=∑bDHigh,b exp(−s(Eb) ∫ dl f(E0)−fKN(Eb) ∫ dl ρ)=:F2(∫dl f(E0),∫ dl ρ)

[0065] Processor 21 can calculate the solutions for both variables according to equations (8) and (9) above using various numerical analysis algorithms, such as the multi-variable Newton method. Processor 21 can then calculate the consistency indicator described above from the calculated variables, based on the line integrals of the line absorption coefficient f(E0) at the reference energy E0, and then perform the processing in step S7. If the consistency indicator satisfies the convergence condition, the process continues from step S8 and the tomogram of the sample is reconstructed. The correction, which is performed based on multiple sets of projection data if a CT scan is performed with incident X-rays with several (especially two) different energy spectra, is called dual-energy correction.The correction can therefore be a beam hardening correction or a dual-energy correction. This approach allows for the acquisition of corrected projection data that better reduces artifacts and the like. The specific implementations of the correction are not limited to those mentioned above. 5. Further considerations

[0066] The embodiments described above can also be modified as follows.

[0067] In the above embodiments, hypothetically incident X-rays were represented by discrete energies E. b with a respective intensity D bThe spectrum of hypothetical incident X-rays can be described using histogram-like degrees of freedom, but the methods for determining the hypothetical incident X-rays are not limited to this. For example, the hypothetical incident X-rays can also be described as a superposition of continuous peak distributions, such as Gaussian distributions. In this case, candidates for the spectrum of hypothetical incident X-rays can be obtained, for example, by varying the peak positions, peak intensities, full widths at half maximum (FWHM), and the like of the individual Gaussian distributions.

[0068] In the embodiment described above, processor 21 sequentially identifies a candidate for hypothetical incident X-rays by repeatedly executing step S4 and searches for hypothetical incident X-rays that satisfy the convergence condition. However, the method for identifying candidates for hypothetical incident X-rays is not limited to this. For example, processor 21 can also identify a predetermined number of candidates for hypothetical incident X-rays within a predefined search range (e.g., a range defined by search conditions), either rule-based or randomly, and calculate a consistency indicator for each of these extracted candidates, either individually or in parallel.

[0069] Processor 21 does not need to define a convergence condition. In this case, Processor 21 corrects the projection image data and calculates the consistency indicator based on the defined candidates for hypothetical incident X-rays. Processor 21 can then determine the corrected projection data to be output based on the calculated consistency indicators.

[0070] The processor 21 can also handle processing in step S8 and step S9 in Fig. Omit step 2. For example, processor 21 can output the result of the correction in step S5 as corrected projection data in step S10, which was performed using parameters for which the consistency indicator was found to satisfy the convergence condition in step S7.

[0071] The processor 21 does not need to define candidates for hypothetical incident X-rays itself, but can perform the correction of the projection image data and the calculation of the consistency indicator for each candidate by obtaining candidates for hypothetical incident X-rays that were previously defined by other devices.

[0072] The correction model is not limited to the line absorption coefficient model; any model representing the distribution of the sample's absorption coefficients as a function of the incident and penetrating X-rays can be used. For example, the correction model could also be a mass absorption coefficient model representing the distribution of these coefficients.

[0073] Information processing device 2 can be installed locally or deployed as a cloud solution. As a cloud solution, information processing device 2 can, for example, provide the aforementioned functions and processing capabilities in the form of SaaS (software as a service) or cloud computing.

[0074] In the embodiment described above, the information processing device 2 performs various storage and control functions, but instead of the information processing device 2, several external devices can also be used. That is, different information and programs can be stored distributed across multiple external devices using blockchain technology or the like.

[0075] The embodiment described above is not limited to information processing system 1, but can also be an information processing method or a program. The information processing method comprises the steps of information processing system 1. The program executes the individual steps of information processing system 1 on at least one computer.

[0076] The information processing system 1 described above can also be provided in the following configurations.

[0077] (1) An information processing system comprising: an acquisition unit configured to acquire projection data representing a projection image of an X-ray CT scan of a measurement object and an absorption model relating to the absorption of X-rays by the measurement object, wherein the projection data contain information about the projection image for each orientation in which incident X-rays strike the measurement object; a generation unit configured to generate corrected projection data for each of several candidates for hypothetically incident X-rays whose incidence on the measurement object is hypothetically assumed, wherein the corrected projection data are projection data that have been corrected on the basis of each candidate for hypothetically incident X-rays and the absorption model;a calculation unit configured to calculate a consistency indicator for each of the generated corrected projection data, indicating the degree of consistency of the corrected projection image with respect to orientation; and an output unit configured to output at least one set of corrected projection data from the generated corrected projection data, taking the consistency indicators into account.

[0078] This design also allows for the flexible inclusion of information that was difficult to consider in existing models, e.g., of the process of X-ray absorption by measurement objects, as it can vary depending on the type of X-ray irradiation, and allows for the obtaining of corrected projection data that reduces negative influences such as artifacts.

[0079] (2) Information processing system according to (1), wherein the correction is a beam hardening correction or a dual-energy correction.

[0080] This design allows for the acquisition of corrected projection data, in which the influence of artifacts and the like is appropriately reduced.

[0081] (3) Information processing system according to (1) or (2), wherein the information processing system further comprises a candidate selection unit configured to select candidates for the hypothetical incident X-rays that satisfy a search condition determined on the basis of irradiation information about the X-rays actually incident on the object being measured.

[0082] This design allows projection data to be obtained in which discrepancies with the actual measurement results are appropriately corrected.

[0083] (4) Information processing system according to (3) wherein a portion of the candidates for hypothetical incident X-rays is generated on the basis of a spectrum that actually occurs on the object being measured.

[0084] With such a design, the correction area underlying the hypothetical model can be appropriately limited, and the time required for correction can be reduced.

[0085] (5) Information processing system according to (3) or (4), wherein the irradiation information contains information about an energy range of the incident X-rays, and the information processing system further comprises a search condition setting unit for setting the search condition such that the energy range of the hypothetical incident X-rays is limited with respect to the energy range of the incident X-rays.

[0086] This design can shorten the time required for correction while simultaneously limiting the possibility of over-considering influences that cannot occur in reality, thus enabling a more appropriate correction.

[0087] (6) Information processing system according to one of (1) to (5), further comprising a convergence condition setting unit for setting a convergence condition, wherein the convergence condition setting unit assesses whether the consistency indicator satisfies the convergence condition, if it is assessed that the convergence condition is not satisfied, using another of the candidates for hypothetical incident X-rays, iteratively generates corrected projection data with the generating unit and calculates the respective consistency indicator with the computation unit, if it is assessed that the convergence condition is satisfied, and outputs the corrected projection data that satisfies the convergence condition using the output unit.

[0088] (7) Information processing system according to one of (1) to (6), further comprising a reconstruction unit for reconstructing a tomogram of the object of measurement from a projection image of an X-ray CT of the object of measurement on the basis of the output corrected projection data.

[0089] (8) Information processing method comprising the following steps: a obtaining step for obtaining projection data representing a projection image of an X-ray CT of a measurement object and an absorption model relating to the absorption of X-rays by the measurement object, wherein the projection data contain information about the projection image for each orientation in which incident X-rays strike the measurement object; a generating step for generating corrected projection data for each of several candidates for hypothetical incident X-rays whose incidence on the measurement object is hypothetically assumed, wherein the corrected projection data are projection data that have been corrected on the basis of each candidate for hypothetical incident X-rays and the absorption model;and a calculation step for calculating, for each of the generated corrected projection data, a consistency indicator that indicates the degree of consistency of the corrected projection image with respect to the orientation; and an output step for outputting at least one set of corrected projection data from the generated corrected projection data, taking the consistency indicators into account.

[0090] (9) A program which, when executed on at least one computer, causes the computer to perform the following steps: an acquisition step to obtain projection data representing a projection image of an X-ray CT of a measurement object and an absorption model relating to the absorption of X-rays by the measurement object, wherein the projection data contain information about the projection image for each orientation in which incident X-rays strike the measurement object; a generation step to generate corrected projection data for each of several candidates for hypothetical incident X-rays whose incidence on the measurement object is hypothetically assumed, wherein the corrected projection data are projection data which are corrected on the basis of each respective candidate for hypothetical incident X-rays and the absorption model;and a calculation step for calculating, for each of the generated corrected projection data, a consistency indicator that indicates the degree of consistency of the corrected projection image with respect to the orientation; and an output step for outputting at least one set of corrected projection data from the generated corrected projection data, taking the consistency indicators into account.

[0091] Of course, there are no restrictions on this.

[0092] Finally, it should be noted that various embodiments of the present invention have been described, but these serve only as examples and are not intended to limit the scope of the invention. These embodiments can also be implemented in various other forms, and within a framework that does not exceed the scope of the invention, various omissions, substitutions, and modifications can also be made. Such embodiments, as well as their variations, also fall within the scope of the invention as defined by the claims, as do their equivalents. REFERENCE MARK LIST 1 Information processing system 2 Information processing device 21 processor 22 storage units 23 Communication unit 24 Input unit 25 output units 3 Device 31 processor 32 storage units 33 Communication unit 34 Sample holding section 35 X-ray generator 36 Detection device 37 Rotary drive unit IM1 Tomogram IM2 tomogram IM3 tomogram QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited non-patent literature

[0000] Duan X., Wang, et al., “CT Scanner X-Ray Spectrum E-stimulation From Transmission Measurements,” Med Phys. 2011 Feb; 38(2): 993-7

[0003] T. Würfl et al., 8th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2018

[0003]

Claims

[1] Information processing system comprising the following: a acquisition unit that is set up to obtain projection data representing a projection image of an X-ray CT scan of a measurement object, as well as an absorption model regarding the absorption of X-rays by the measurement object, wherein the projection data contain information about the projection image for each orientation with which incident X-rays hit the measurement object; a generating unit which is set up to generate corrected projection data for each of several candidates for hypothetically incident X-rays whose incidence on the object of measurement is hypothetically assumed, wherein the corrected projection data are projection data which are subjected to correction on the basis of a respective candidate for hypothetically incident X-rays and the absorption model; a computing unit that is set up to calculate a consistency indicator for each of the generated corrected projection data, indicating the degree of consistency of the corrected projection image with respect to orientation; and an output unit that is set up to output at least one set of corrected projection data from the generated corrected projection data, taking into account the consistency indicators. [2] Information processing system according to claim 1, wherein the correction is a beam hardening correction or a dual-energy correction. [3] Information processing system according to claim 1 or 2, further comprising a candidate selection unit configured to select candidates for the hypothetical incident X-rays that meet a search condition determined on the basis of irradiation information about the X-rays actually incident on the object being measured. [4] Information processing system according to claim 3, wherein a part of the candidates for hypothetical incident X-rays is generated on the basis of a spectrum that actually occurs on the object being measured. [5] Information processing system according to claim 3 or 4, wherein the irradiation information contains information about an energy range of the incident X-rays, and The information processing system further comprises a search condition definition unit for defining the search condition such that the energy range of the hypothetically incident X-rays is limited with respect to the energy range of the incident X-rays. [6] Information processing system according to any one of claims 1 to 5, furthermore comprising a convergence condition specification unit for specifying a convergence condition, where the convergence condition definition unit is: assesses whether the consistency indicator meets the convergence condition, and If it is determined that the convergence condition is not met, projection data corrected iteratively using another of the candidates for hypothetical incident X-rays is generated with the generating unit, and the respective consistency indicator is calculated with the computational unit. If it is determined that the convergence condition is met, the output unit outputs the corrected projection data that meets the convergence condition. [7] Information processing system according to one of claims 1 to 6, further comprising a reconstruction unit for reconstructing a tomogram of the object being measured from a projection image of an X-ray CT of the object being measured on the basis of the output corrected projection data. [8] Information processing procedures with the following steps: a acquisition step to obtain projection data representing a projection image of an X-ray CT scan of a measurement object, and an absorption model regarding the absorption of X-rays by the measurement object, wherein the projection data contain information about the projection image for each orientation with which incident X-rays hit the measurement object; a generation step for generating corrected projection data for each of several candidates for hypothetically incident X-rays whose incidence on the measurement object is hypothetically assumed, wherein the corrected projection data are projection data that are subjected to correction based on a respective candidate for hypothetically incident X-rays and the absorption model; and a calculation step to calculate, for the generated corrected projection data, a consistency indicator for each, which indicates the degree of consistency of the corrected projection image with respect to the orientation; and an output step to output at least one set of corrected projection data from the generated corrected projection data, taking into account the consistency indicators. [9] A program which, when executed on at least one computer, causes the computer to perform the following steps: a acquisition step to obtain projection data representing a projection image of an X-ray CT scan of a measurement object, and an absorption model regarding the absorption of X-rays by the measurement object, wherein the projection data contain information about the projection image for each orientation with which incident X-rays hit the measurement object; a generation step for generating corrected projection data for each of several candidates for hypothetically incident X-rays whose incidence on the measurement object is hypothetically assumed, wherein the corrected projection data are projection data that are subjected to correction based on a respective candidate for hypothetically incident X-rays and the absorption model; and a calculation step to calculate, for the generated corrected projection data, a consistency indicator for each, which indicates the degree of consistency of the corrected projection image with respect to the orientation; and an output step to output at least one set of corrected projection data from the generated corrected projection data, taking into account the consistency indicators.

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