Ultrasonic tomography sound velocity imaging method based on implicit neural representation network

Abstract

The invention belongs to the technical field of ultrasonic sound velocity image reconstruction, and particularly relates to an implicit neural representation network-based ultrasonic fault sound velocity imaging method, which comprises the following steps of: dividing grids in a fault plane imaging region, performing block division on all grids, determining two-dimensional coordinates of any grid in each grid block, and determining a two-dimensional coordinate of any grid in each grid block; converting the two-dimensional coordinate into a high-dimensional feature vector; all the high-dimensional feature vectors are input into a pre-trained implicit neural representation network, output values serve as sound velocity distribution values of corresponding grid blocks, space arrangement is conducted on the sound velocity distribution values of all the grid blocks, the sound velocity distribution values of all the grid blocks in the arrangement result are mapped to the actual sound velocity value range, and a sound velocity image of a fault plane imaging area is obtained; and performing forward modeling on the sound velocity image to obtain sound field data generated by simulation, comparing the sound field data with actually observed sound field data, optimizing network parameters, and taking the final sound velocity image as a reconstruction result. According to the method, the ultrasonic fault sound velocity imaging precision can be ensured without an accurate initial sound velocity model.

Description

Technical Field

[0001] The present invention belongs to the technical field of ultrasonic sound velocity image reconstruction, and more specifically, relates to an ultrasonic tomographic sound velocity imaging method based on an implicit neural representation network. Background Art

[0002] Ultrasonic tomography is an emerging ultrasound imaging technology. It is developed based on the theory of CT and has the advantages of ultrasound imaging. Therefore, it has become a widely anticipated technological innovation. This technology uses a set of ultrasonic transducer arrays surrounding the object to transmit and receive ultrasound signals, and reconstructs and calculates the collected data, so as to obtain three modalities of two-dimensional or three-dimensional sound velocity images, attenuation images and reflection images of the target body. Compared with traditional ultrasound imaging and CT, ultrasound tomography has the advantages of being non-invasive, non-ionizing radiation, high resolution, and multi-modality, and has shown great potential in clinical application fields such as musculoskeletal imaging, breast cancer screening, and cranial imaging.

[0003] Full waveform inversion is a high-resolution sound velocity image reconstruction algorithm widely used in ultrasonic tomography. This method is based on the optimization technology under the constraint of wave equation. It establishes a connection between tissue acoustic parameters and received sound pressure signals, and minimizes the difference between actual observation data and prediction model by iteratively updating the model, thereby restoring the acoustic parameters of the internal structure or properties of the system and reconstructing the sound velocity image. Compared with other methods, full waveform inversion takes into account the full wave field information of the sound field, including rich wave phenomena (such as single and multiple reflections, transmission, scattering, etc.), which is closer to the actual situation of sound wave propagation, so the reconstructed image has better quality and higher resolution.

[0004] Although the full waveform inversion algorithm can provide high-resolution imaging results, it needs to solve nonlinear partial differential equations, which makes the whole method quite complicated. Therefore, the method has high computational overhead and relatively high computing power requirements, resulting in relatively long reconstruction time.

[0005] At the same time, from a mathematical point of view, full waveform inversion is an ill-conditioned non-convex nonlinear inverse problem. In the actual solution process, it is often easy to encounter multiple solutions, and the final result is easy to converge to the local optimal solution. Therefore, the initial sound velocity model provided in the application process has a great influence on the inversion result. This is also a common problem faced by major domestic and foreign ultrasonic tomography equipment manufacturers in the process of sound velocity image reconstruction. In the actual application of ultrasonic tomography, especially in high-frequency conditions, it is difficult to obtain an accurate initial sound velocity model, which not only has a great impact on the solution results, but also seriously restricts the further development of full waveform inversion technology in this field. Summary of the invention

[0006] In view of the defects of the prior art and the need for improvement, the present invention provides an ultrasonic tomography sound velocity imaging method based on an implicit neural representation network, the purpose of which is to ensure the accuracy of ultrasonic tomography sound velocity imaging without requiring an accurate initial sound velocity model.

[0007] To achieve the above object, according to one aspect of the present invention, there is provided an ultrasonic tomographic sound velocity imaging method based on an implicit neural representation network, comprising:

[0008] S1. Divide the tomographic plane imaging area into grids, and divide all grids into blocks to obtain multiple grid blocks, determine the two-dimensional coordinates of any grid in each grid block, and convert each two-dimensional coordinate into a high-dimensional feature vector; wherein the size of each grid block is n*n, n represents the number of grids on any side, and n≥1;

[0009] S2. Input all the converted high-dimensional feature vectors into a pre-trained implicit neural representation network, and use the output value as the sound velocity distribution value of the corresponding grid block. According to the distribution of the tomographic plane imaging area, the sound velocity distribution values ​​at each grid block are spatially arranged, and the sound velocity distribution value at each grid block in the arrangement result is mapped to the actual sound velocity value range through a mapping function to obtain a sound velocity image of the tomographic plane imaging area.

[0010] S3, forward modeling the sound velocity image to obtain simulated sound field data, with the goal of minimizing the deviation between the sound field data and the actually observed sound field data, optimizing the parameters of the implicit neural representation network, re-executing S2 until a preset termination condition is reached, and using the current sound velocity image as the final reconstructed ultrasonic tomography sound velocity image.

[0011] Furthermore, Fourier feature mapping is used to transform each two-dimensional coordinate into a high-dimensional feature vector.

[0012] Furthermore, the implicit neural representation network is a multi-layer perceptron network.

[0013] Furthermore, by minimizing the loss function including the data consistency term and the regularization term, the deviation between the simulated sound field data and the actually observed sound field data is minimized.

[0014] Furthermore, n is greater than 1.

[0015] Furthermore, the pre-trained implicit neural representation network is used as an initial sound speed model for network training, which satisfies the following conditions: it can output a uniform known background sound speed image.

[0016] The present invention also provides an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0017] The present invention also provides a computer-readable storage medium, which includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to execute the steps of the method described above.

[0018] The present invention also provides a computer program product, comprising a computer program or instructions, which implement the steps of the method described above when executed by a processor.

[0019] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0020] (1) The present invention uses an implicit neural representation network (structure) to reconstruct the sound velocity image. This method transforms the image reconstruction problem into a process of constructing a neural network that maps input coordinates to sound velocity values. Among them, the traditional image representation is usually a set of discrete pixel values, while the implicit neural representation parameterizes the image into a continuous function that maps the coordinates to the attribute value of the image at that position (i.e., the sound velocity value). This method can achieve effective storage and high-resolution reconstruction of the image. In addition, the use of the implicit neural representation network can introduce regularization terms in the network optimization process, thereby alleviating the pathological nature of the full waveform inversion and ensuring the accuracy of ultrasonic tomography sound velocity imaging without the need for an accurate initial sound velocity model.

[0021] (2) The traditional implicit neural representation network directly uses the spatial coordinates of pixels in the image as the input of the multi-layer perceptron. However, this processing method has a weak ability to represent complex signals. Therefore, in this method, the two-dimensional coordinates (x, y) are converted into high-dimensional features through Fourier feature mapping, so that the high-frequency information in the signal can be better learned.

[0022] (3) In the present invention, n is preferably greater than 1. In this case, the two-dimensional coordinate information of a certain grid in each grid block is mapped through the network and output as the sound speed distribution information of the grid block. There is no need to input the two-dimensional coordinates of all grids in the grid block into the network for mapping. This improves the calculation efficiency without sacrificing accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A flowchart of an ultrasonic tomographic sound velocity imaging method based on an implicit neural representation network provided by an embodiment of the present invention;

[0024] Figure 2 A specific flow chart of the ultrasonic tomography sound velocity imaging method provided by an embodiment of the present invention;

[0025] Figure 3 A schematic diagram of network input and output provided by an embodiment of the present invention;

[0026] Figure 4 A comparison diagram of sound velocity imaging provided in an embodiment of the present invention, wherein (a) is a true value image, (b) is a reconstruction result of a traditional full waveform inversion algorithm, (c) is a reconstruction result of the algorithm proposed in the present invention, (d) is an error diagram between the reconstruction result of the traditional method and the true value, and (e) is an error diagram between the reconstruction result of the present invention and the true value. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0028] Embodiment 1

[0029] An ultrasonic tomographic sound velocity imaging method based on implicit neural representation network, such as Figure 1 As shown, including:

[0030] S1. Divide the tomographic plane imaging area into grids, and divide all grids into blocks to obtain multiple grid blocks, determine the two-dimensional coordinates of any grid in each grid block, and convert each two-dimensional coordinate into a high-dimensional feature vector; wherein the size of each grid block is n*n, n represents the number of grids on any side, and n≥1;

[0031] S2. Input all the converted high-dimensional feature vectors into an implicit neural representation network, and use the output value as the sound velocity distribution value of the corresponding grid block. The sound velocity distribution values ​​at each grid block are spatially arranged according to the distribution of the tomographic plane imaging area, and the sound velocity distribution value at each grid block in the arrangement result is mapped to the actual sound velocity value range through a mapping function to obtain a sound velocity image of the tomographic plane imaging area;

[0032] S3, forward modeling the sound velocity image to obtain simulated sound field data, with the goal of minimizing the deviation between the sound field data and the actually observed sound field data, optimizing the parameters of the implicit neural representation network, re-executing S2 until a preset termination condition is reached, and using the current sound velocity image as the final reconstructed ultrasonic tomography sound velocity image.

[0033] The full waveform inversion algorithm is based on the wave equation, and the basic form of the wave equation is:

[0034]

[0035] Among them, f is the sound source term, u is the sound field data, and c is the sound speed, which corresponds to the sound speed image to be reconstructed in this embodiment.

[0036] The full waveform inversion problem can be defined as an optimization problem satisfying the above wave equation:

[0037]

[0038] in, is the reconstructed sound velocity image, u(c) is the sound field data of the prediction model, and u obs It is the actual observed sound field data.

[0039] The optimization problem of full waveform inversion is essentially a non-convex nonlinear problem under the constraints of partial differential equations. The algorithm has a high dependence on the set initial model (i.e., the initial sound velocity image). Under the influence of partial differential terms, this problem is different from other traditional medical imaging technologies (such as CT, MRI, PET, etc.). Its non-convex nonlinear characteristics make the solution process extremely complex and unstable. If the starting model is not selected properly, it may cause the solution result to fall into a local minimum, thereby producing a sound velocity image reconstruction result that does not conform to physiological characteristics. In addition, as the frequency of ultrasound increases, the non-convexity of the problem will continue to intensify, which poses a great challenge to problem solving.

[0040] In order to solve the above problems, this embodiment uses an implicit neural representation network (structure) to reconstruct the sound speed image. This method transforms the image reconstruction problem into a process of building a neural network that maps from input coordinates to sound speed values, and alleviates the pathological nature of full waveform inversion by adding regularization terms in the optimization process. Traditional image representation is usually a set of discrete pixel values, while implicit neural representation parameterizes the image as a continuous function that maps coordinates to the attribute value of the image at that position (here, the sound speed value). This method can achieve efficient storage and high-resolution reconstruction of images.

[0041] Based on this idea, this embodiment proposes to use an implicit neural representation network as a generator to generate a sound velocity image. The network receives image coordinate information as input, and performs iterative optimization by comparing the difference between the sound field data calculated (forward modeled) by the sound velocity image output by the implicit neural representation network and the actual observed sound field data. Specifically, the network represents its output signal as a continuous function of two-dimensional coordinates (x, y). The function is represented as f θ , it can be preferably parameterized by a multi-layer perceptron (MLP) with parameter θ, thereby being able to transform the sound speed image It is expressed as:

[0042]

[0043] Different from the traditional full waveform inversion method, this method does not directly optimize the sound velocity value, but optimizes the parameters in the generator network to effectively reconstruct the problem, thereby realizing the parameterization conversion of the full waveform inversion problem. Preferably, it is defined as follows:

[0044]

[0045] Among them, (x, y) represents the spatial coordinates of the input, φ(·) represents the Fourier feature map, and by performing a series of sine and cosine transforms on the two-dimensional coordinates, a high-dimensional feature vector φ(x, y) is obtained as the network input to capture more complex features. θ is the network parameter to be optimized, N θ is a multilayer perceptron network structure, M is a mapping function, which maps the network output to the actual sound velocity value range, and NR is a forward operator (forward operator), which converts the sound velocity distribution image to an ultrasonic signal, thereby realizing a comparison with the actual measurement signal. The mapping function is used to convert the network output N θ (φ(x,y)) is mapped to the sound velocity value in the preset range of the area of ​​interest. Assume that the sound velocity in this area is [c 1 ,c 2 ], the mapping function can be defined as:

[0046] M 1 (z)=(c 2 -c 1 )z+c 1

[0047] M 2 (z)=(c 2 -c 1 ) z +c 1

[0048] Among them, M 1 is a linear transformation, which is suitable for tissues with little change in sound velocity, such as soft tissue areas (such as breasts, etc.); while M 2 An exponential function is used for mapping, which is suitable for areas with significant changes in sound speed, such as the brain or limbs containing bones (whose sound speed is much higher than the surrounding soft tissue). By applying these conversion operators, it is easier for network parameters to reach a convergence state. In the above formula, z represents the sound speed distribution value.

[0049] In general, an unsupervised algorithm for ultrasonic tomography sound velocity imaging using implicit neural representation in an embodiment of the present invention represents the required sound velocity map as a continuous function of spatial coordinates, and reconstructs the sound velocity image based on the original observation signal collected by the ultrasonic tomography system. A given spatial coordinate value is input, and a fully connected neural network is used for parameterization. The reconstructed sound velocity image is generated through the network, and the image is forward-calculated through a recurrent neural network operator to generate an ultrasonic signal. The generated result is compared with the actual observation signal, and the loss function containing the data consistency term and the regularization term is minimized and continuously iterated and optimized to learn the network parameters. The purpose is to minimize the difference between the ultrasonic signal calculated by the sound velocity image generated by the network and the actual observation signal, and reconstruct a sound velocity image that is closest to the actual situation.

[0050] The specific implementation process can be found in Figure 2 , wherein, when collecting signals (i.e., sound field data), the ultrasonic tomography system may be composed of a group of ultrasonic transducer arrays surrounding the object to be inspected, and a single-shot all-receive mode is used to collect data, wherein the transmitting array elements sequentially transmit ultrasonic signals, and all array elements receive signals at the same time, and the received signals can be represented by a three-dimensional matrix [N s ,N r ,T] indicates that the three dimensions correspond to the transmitting array element, the receiving array element and the time sampling point respectively.

[0051] In addition, during the simulation process, it is necessary to properly discretize the physical parameters in the region of interest to obtain the coordinate distribution (image). Considering that the ultrasonic tomography system has a fixed sampling frequency, it is equivalent to knowing that the time step Δt is the inverse of the sampling frequency. In this way, the main focus is on the spatial discretization scale, that is, the size of the image. In order to simplify the problem, a square grid is chosen here for spatial discretization, which means that there are the same number of discrete points in two spatial dimensions. The number of discrete points is determined by the main transmission frequency of the system, and the number of discrete points is determined based on the stability and dispersion conditions of the finite difference method:

[0052]

[0053]

[0054] Among them, f represents the main frequency of the emitted sound source, L is the actual space size, and N represents the number of discrete points in space, which also corresponds to the size of the image. In practical applications, it is preferred to select the smallest possible N value while satisfying the above stability and dispersion conditions, so as to reduce the computational overhead and improve the computational efficiency.

[0055] Furthermore, the main part of the reconstruction algorithm network (i.e., implicit neural representation network) is a multi-layer perceptron, i.e., a fully connected neural network. Before using the multi-layer perceptron, the coordinate distribution needs to be transformed first. Specifically, the two-dimensional coordinates (x, y) are converted into high-dimensional features through Fourier feature mapping. For example, a frequency matrix b that satisfies the normal distribution is first randomly generated with a shape of (2,200), and the 2 rows of the matrix correspond to the frequency vectors of the x and y coordinates, respectively. Each element in the frequency matrix is ​​used as the frequency of the sine and cosine functions for feature mapping calculation to obtain the corresponding frequency features, and finally each coordinate is converted into the corresponding 400 features as the input layer of the network. Based on the above description, the Fourier feature mapping process can be expressed by the following formula:

[0056]

[0057] Among them, j is the index of the input coordinate, i is the index of the frequency parameter pair, and k corresponds to the index of the Fourier feature, which determines whether to calculate the sine or cosine feature. Finally, the input feature matrix is ​​obtained, with a dimension of (n, 400), where n is the number of input coordinates and each row corresponds to a Fourier feature obtained by mapping a coordinate.

[0058] In order to reduce the amount of calculation, it can be preferred that the network output is designed as a 4×4 image block in this embodiment. This operation can reduce the number of input coordinates. Only one coordinate point in the middle area of ​​the image block is input to generate the value of the corresponding image block. Finally, each image block is spliced ​​into a complete sound speed map according to the position relationship. The specific process can be seen in Figure 3 The mapped feature vectors are input into a multi-layer fully connected neural network, and the network learns the mapping relationship from these features to the sound speed distribution image through training.

[0059] The loss function including data consistency term and regularization term can be specifically defined as:

[0060]

[0061] Among them, Loss DC Indicates data consistency item, Loss TV is the total variation regularization term, and λ is the coefficient of the regularization term, which is determined by experiments.

[0062] The formula for the data consistency term is:

[0063]

[0064] This loss value is the L2 norm value between the simulated sound field data and the actual observed sound field data, which is used to measure the error between the two.

[0065] The formula for the total variation regularization term is:

[0066]

[0067] in, and are the gradient values ​​of the image in the x and y directions, respectively. The total variation regularization term is added to promote the smoothness of the solution to reduce artifacts and noise in the sound velocity image.

[0068] During the training process, a pre-training is first performed to map the output of the total network architecture to a uniform sound speed image, whose sound speed constant is the background sound speed, so as to provide a stable initial state for the network, so that it can converge to the correct solution faster. After that, the generator network is trained based on the network parameters obtained by pre-training. The input features are passed through the generator network N θ After the prediction sound speed image is obtained by the mapping function M, the sound speed image is input into the forward operator network N R Calculate the sound field distribution signal corresponding to the sound velocity distribution field. Then, according to the actual spatial position of the receiving sensor of the ultrasonic tomography system, extract the signal of a specific point from the calculated sound pressure distribution to obtain a set of simulated ultrasonic signal data (predicted sound field data). Calculate the loss between the ultrasonic signal and the actual observed signal, and gradually optimize the network parameters. In this process, a predefined loss function is used to quantify the difference between the two, and the automatic differentiation technology of the deep learning framework is used to calculate the gradient of the loss value with respect to the generator network parameters. These gradients are then passed to the optimizer (such as Adam or L-BFGS) to update the network parameters. The network with updated parameters will be able to generate a sound velocity image that is closer to the actual situation. This process continues to iterate until the predetermined maximum number of iterations is reached or the value of the loss function drops below the preset threshold, completing the training of the generator network.

[0069] according to Figure 4 As shown in the sound velocity imaging comparison diagram, the algorithm of the present invention can reconstruct a sound velocity image with higher accuracy, which is demonstrated here by numerical simulation experimental results. Under the same initial sound velocity model conditions, the breast sound velocity image reconstructed by the algorithm of the present invention is closer to the real image, and can also better determine the shape and position of the tumor, with a smaller error from the true value. It should be noted that the traditional full waveform inversion algorithm and the algorithm of the present invention use the same number of iterations.

[0070] Embodiment 2

[0071] The present application also relates to an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0072] The electronic device may be a computing device such as a desktop computer, a notebook, a PDA, a cloud server, etc. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. The memory may be used to store computer programs and / or modules, and the processor may perform various functions of the electronic device by running or executing computer programs and / or modules stored in the memory, and calling data stored in the memory.

[0073] The relevant technical solution is the same as that in Embodiment 1 and will not be described in detail here.

[0074] Embodiment 3

[0075] The present application also relates to a computer-readable storage medium having a computer program stored thereon, and the steps of the above method are implemented when the computer program is executed by a processor.

[0076] Specifically, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, an internal memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0077] The relevant technical solution is the same as that in Embodiment 1 and will not be described in detail here.

[0078] Embodiment 4

[0079] The embodiment of the present application provides a computer program product or a computer program, which includes computer instructions stored in a computer-readable storage medium. The processor of a computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device performs the steps of the method of the above embodiment of the present application.

[0080] The relevant technical solution is the same as that in Embodiment 1 and will not be described in detail here.

[0081] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An ultrasonic tomographic sound velocity imaging method based on an implicit neural representation network, characterized in that: include: S1. Divide the tomographic plane imaging area into grids, and divide all grids into blocks to obtain multiple grid blocks, determine the two-dimensional coordinates of any grid in each grid block, and convert each two-dimensional coordinate into a high-dimensional feature vector; wherein the size of each grid block is n*n, n represents the number of grids on any side, and n≥1; S2. Input all the converted high-dimensional feature vectors into a pre-trained implicit neural representation network, and use the output value as the sound velocity distribution value of the corresponding grid block. According to the distribution of the tomographic plane imaging area, the sound velocity distribution values ​​at each grid block are spatially arranged, and the sound velocity distribution value at each grid block in the arrangement result is mapped to the actual sound velocity value range through a mapping function to obtain a sound velocity image of the tomographic plane imaging area. S3, forward modeling the sound velocity image to obtain simulated sound field data, with the goal of minimizing the deviation between the sound field data and the actually observed sound field data, optimizing the parameters of the implicit neural representation network, re-executing S2 until a preset termination condition is reached, and using the current sound velocity image as the final reconstructed ultrasonic tomography sound velocity image.

2. The ultrasonic tomography sound velocity imaging method based on implicit neural representation network according to claim 1, characterized in that: Each two-dimensional coordinate is converted into a high-dimensional feature vector by Fourier feature mapping.

3. The ultrasonic tomography sound velocity imaging method based on implicit neural representation network according to claim 1, characterized in that: The implicit neural representation network is a multi-layer perceptron network.

4. The ultrasonic tomography sound velocity imaging method based on implicit neural representation network according to claim 1, characterized in that: By minimizing the loss function including data consistency term and regularization term, the deviation between the simulated sound field data and the actually observed sound field data is minimized.

5. The ultrasonic tomography sound velocity imaging method based on implicit neural representation network according to claim 1, characterized in that: n is greater than 1.

6. The ultrasonic tomography sound velocity imaging method based on implicit neural representation network according to claim 1, characterized in that: A recurrent neural network is used to perform the forward calculation operation.

7. The ultrasonic tomography sound velocity imaging method based on implicit neural representation network according to any one of claims 1 to 6, characterized in that: The pre-trained implicit neural representation network is used as an initial sound speed model for network training, which meets the following conditions: it can output a uniform known background sound speed image.

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed by a processor, the device where the storage medium is located is controlled to perform the steps of any one of the methods according to claims 1 to 7.

10. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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