Ultrasonic imaging phase distortion correction calculation method and system based on time delay estimation
By calculating the phase error evaluation index and correction delay in ultrasound imaging based on time delay estimation, the complex problem of phase distortion correction calculation in the prior art is solved, and efficient correction of real-time ultrasound imaging is achieved.
Patent Information
- Application Number
- CN202411727813.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-28
- Publication Date
- 2025-02-28
- Estimated Expiration
- 2044-11-28
AI Technical Summary
In the prior art, phase distortion correction technology has complex calculations and is difficult to meet the calculation efficiency requirements of real-time ultrasound imaging.
The ultrasonic imaging phase distortion correction calculation method based on time delay estimation is used to calculate the phase error evaluation index through relative delay and exclusive-OR operations, obtain the relative delay, and calculate the correction delay and accumulated phase distortion delay, and finally perform ultrasonic imaging phase distortion correction with the weighted average phase distortion delay.
It effectively improves the accuracy of time delay estimation, reduces phase distortion between signals of each channel, meets the requirements of real-time ultrasonic imaging in industry, has low computational complexity, and improves computing efficiency.
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Figure CN119534650A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of ultrasonic imaging correction, and relates to a method and system for calculating ultrasonic imaging phase distortion correction based on time delay estimation. Background Art
[0002] In the field of industrial imaging, especially in ultrasonic imaging, phase distortion correction technology has been widely used. For non-uniform deformation layers, as long as the reference standard is clear, phase distortion correction technology can be applied. In addition, for uniform deformation layers, if the prior information of the layer thickness is mastered, phase distortion correction can also be performed. At the same time, for non-uniform deformation structures, especially structures with random reflector distribution, there are corresponding phase distortion correction methods. However, the existing phase distortion correction technology involves a lot of calculations and is more suitable for offline phase correction. It is difficult to meet the computational efficiency requirements of the correction algorithm for real-time ultrasonic imaging.
[0003] For example, prior art document 1 (CN200810105756.7) discloses a phase distortion correction method based on the lumped correlation method in phased array ultrasonic detection. When the signal-to-noise ratio of the echo signal received by the array element is relatively low, it can effectively improve the accuracy of time delay estimation and reduce the phase distortion between the signals of each channel. The lumped correlation phase correction method is that the reference signal is selected as the sum of the direct superposition of the signals received by all array elements, and each array element is correlated with the reference signal to obtain the time delay of each array element relative to the reference signal. However, this method involves a lot of calculations and is not very suitable for real-time imaging of ultrasonic phased arrays. Summary of the invention
[0004] In order to solve the deficiencies in the prior art, the present invention provides a method and system for calculating the phase distortion correction of ultrasonic imaging based on time delay estimation, which effectively improves the accuracy of time delay estimation and reduces the phase distortion between channel signals, thereby meeting the requirements of industrial real-time ultrasonic imaging.
[0005] The present invention adopts the following technical solution.
[0006] A first aspect of the present invention provides a method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation, comprising:
[0007] For each array element and each scanning angle of the ultrasound imaging, a phase error evaluation index is calculated based on the relative delay and an XOR operation, and a relative delay when the evaluation index is lower than a set threshold is obtained;
[0008] Calculating a corresponding correction delay according to the acquired relative delay, and calculating a cumulative phase distortion delay according to the correction delay;
[0009] Calculating the weight coefficient of each array element and each scanning angle in phase distortion correction, and calculating the weighted average phase distortion delay of each array element in combination with the accumulated phase distortion delay;
[0010] The weighted average phase distortion delay is used as an estimated value of array element delay time to perform ultrasound imaging phase distortion correction.
[0011] Preferably, the calculation formula of the phase error evaluation index is:
[0012]
[0013] in, is the phase error evaluation index;
[0014] M is the length of the time window;
[0015] and RF echo samples and Shift representation of ;
[0016] is the signal value of the kth sample of the nth array element at the i-th scanning angle;
[0017] is the n-1th array element at the i-th scanning angle. The signal value of each sample;
[0018] is the relative delay of the nth array element at the i-th scanning angle;
[0019] Indicates a bit-by-bit XOR operation.
[0020] Preferably, the calculation formula for the correction delay is:
[0021]
[0022] Where: is the correction delay of the nth array element at the i-th scanning angle;
[0023] is the relative delay of the nth array element at the i-th scanning angle;
[0024] T s is the sampling period of the RF echo signal sample; is the relative focus delay.
[0025] Preferably, the calculation formula for the cumulative phase distortion delay is:
[0026]
[0027] in, is the accumulated phase distortion delay of the nth array element at the i-th scanning angle;
[0028] is the correction delay of the jth array element at the i-th scanning angle.
[0029] Preferably, the calculation formula of the weight coefficient is:
[0030]
[0031] in, is the weight coefficient of the nth array element at the i-th scanning angle;
[0032] is the signal value of the kth sample of the nth array element at the i-th scanning angle;
[0033] M is the length of the time window.
[0034] Preferably, the calculation formula of the weighted average phase distortion delay is:
[0035]
[0036] in, is the weighted average phase distortion delay of the nth array element;
[0037] is the weight coefficient of the nth array element at the i-th scanning angle;
[0038] is the accumulated phase distortion delay of the nth array element at the i-th scanning angle;
[0039] K is the scan angle.
[0040] Preferably, the method of performing ultrasound imaging phase distortion correction using the weighted average phase distortion delay as an estimated value of array element delay time comprises:
[0041] The delay time of the corresponding array element is set according to the weighted average phase distortion delay of each array element, the corresponding echo amplitude signal is collected, and imaging is performed according to the collected signal.
[0042] A second aspect of the present invention provides an ultrasonic imaging phase distortion correction calculation system based on time delay estimation, comprising:
[0043] An evaluation index calculation module, used for calculating a phase error evaluation index based on relative delay and XOR operation for each array element and each scanning angle of ultrasonic imaging, and obtaining a relative delay when the evaluation index is lower than a set threshold;
[0044] A cumulative phase distortion delay calculation module, used to calculate the corresponding correction delay according to the acquired relative delay, and calculate the cumulative phase distortion delay according to the correction delay;
[0045] A weighted average phase distortion delay calculation module, used to calculate the weight coefficient of each array element and each scanning angle in phase distortion correction, and calculate the weighted average phase distortion delay of each array element in combination with the accumulated phase distortion delay;
[0046] The phase distortion correction module is used to perform phase distortion correction for ultrasonic imaging by using the weighted average phase distortion delay as an estimated value of array element delay time.
[0047] A third aspect of the present invention provides a terminal, comprising a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the method.
[0048] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method when executed by a processor.
[0049] Compared with the prior art, the beneficial effects of the present invention include at least:
[0050] The present invention uses the absolute difference and SAD between two radio frequency samples as phase error evaluation indicators to estimate the distortion mode of the echo signal reflected by the line target and / or diffuse reflector, and only involves addition operations, so the calculation complexity is relatively low; the phase error evaluation indicator is calculated based on relative delay and XOR operation, and utilizes the sensitivity of XOR operation to the phase difference of the signal. When the two signals are aligned, the result of the XOR operation will be the smallest, indicating that the phase distortion has been effectively corrected, and the phase error can be accurately evaluated; and a single-bit word length is used to perform bit-by-bit XOR operation, and the word length is truncated to 1b to further improve the calculation efficiency; by evaluating the indicator and setting the threshold, the relative delay of adjacent array channels is effectively estimated;
[0051] The present invention takes into account that an array element can only have one delay time, but for inhomogeneous media, the optimal delay times at multiple angles may be different, so a weight coefficient is introduced to calculate the weighted average phase distortion delay. The weight coefficient of each angle takes the average amplitude of the echo signal received at that angle, and the delay time of each array element is adjusted according to the signal strength, which can improve the phase distortion correction accuracy and convergence performance of ultrasonic imaging. BRIEF DESCRIPTION OF THE DRAWINGS
[0052] Figure 1 It is a flow chart of a method for calculating ultrasound imaging phase distortion correction based on time delay estimation provided by the present invention. DETAILED DESCRIPTION
[0053] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in this application are only part of the embodiments of the present invention, not all of them. Based on the spirit of the present invention, other embodiments obtained by ordinary technicians in this field without creative work are all within the scope of protection of the present invention.
[0054] Embodiment 1 of the present invention provides a method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation, such as Figure 1 As shown, including:
[0055] Step 1: For each array element and each scanning angle of the ultrasound imaging, a phase error evaluation index is calculated based on the relative delay and the XOR operation, and the relative delay when the evaluation index is lower than a set threshold is obtained;
[0056] Further preferably, the radio frequency echo signal samples obtained by sampling the ultrasonic imaging are quantized to a single bit, and the absolute difference and SAD of the ultrasonic imaging in the lateral window and the time window are calculated using the radio frequency echo signal samples represented by the single bit;
[0057] First, a SAD (Sum of Absolute Differences) function is defined to evaluate the relative phase difference between two sampled signals.
[0058] The SAD of the RF echo samples received by adjacent array channels in a time window of length M is expressed as the relative delay The function of is:
[0059]
[0060] in is the kth sample of the signal of the nth element at the ith scanning angle;
[0061] and are approximately shifted versions of each other.
[0062] Further preferably, in order to process the phase error caused by multipath and scattering, the present invention is specifically as follows:
[0063] Estimation is performed on lateral windows and time (axial) windows, and the error is reduced by minimizing the SAD over the two-dimensional window;
[0064] In order to improve the computational efficiency, the RF signal samples are quantized to a single bit, that is, only the zero-crossing information of the signal is retained; the SAD calculation is performed using the echo samples represented by a single bit, where each absolute difference operation is reduced to a bit-by-bit EXCLUSIVE-OR operate;
[0065] Using shorter word lengths can further improve the computational efficiency of the SAD technique.
[0066] The phase information of the RF signal can be fully represented by the zero crossing point of the carrier.
[0067] Therefore, the relative phase difference between two RF signals can be easily detected from the offset of their zero crossing points.
[0068] A single-bit word length is sufficient to represent the zero crossings of the sampled signal.
[0069] Therefore, the SAD technique can properly quantize the RF samples to a single bit, where each absolute difference operation is reduced to a bit-by-bit exclusive-OR.
[0070] in this case, Given by:
[0071]
[0072] in The absolute difference and SAD of ultrasound imaging in the lateral window and time window are used as phase error evaluation indicators to evaluate the quality of phase error estimation;
[0073] M is the length of the time window, which indicates the number of samples considered when calculating the sum of the XOR operation results;
[0074] and They are RF echo samples and Shift representation of ;
[0075] is the signal value of the kth sample of the nth array element at the i-th scanning angle;
[0076] is the n-1th array element at the i-th scanning angle. The signal value of each sample;
[0077] is the relative delay of the nth array element at the i-th scanning angle;
[0078] Indicates a bit-by-bit absolute difference operation.
[0079] When single-bit quantization is used, the convergence of the speckle noise phase estimation may deteriorate. This effect can be alleviated by increasing the number of averaging times or using other optimization methods.
[0080] Step 2: Calculate the corresponding correction delay according to the relative delay obtained in step 1, and calculate the cumulative phase distortion delay according to the correction delay;
[0081] The correction delay calculation method is:
[0082] For each n and i, find the expression that is minimized by minimizing the SAD function. After the value is found, Value, calculate the nth element at the i-th scanning angle, The correction delay at is given by:
[0083]
[0084] Where: is the phase distortion delay (correction delay) of the nth array element at the i-th scanning angle, which indicates the time delay required for the signal of the nth array element in order to correct the phase distortion;
[0085] is the relative delay corresponding to the minimum SAD;
[0086] T s is the sampling period of the RF echo signal sample (the time interval between two consecutive samples), is the relative focus delay;
[0087] It is calculated assuming that the speed of sound is constant in the medium and there is no phase distortion, and can be obtained using simple geometric relationships.
[0088] The accumulated phase distortion delay of the nth array element at the i-th scanning angle is the cumulative sum of the correction delays:
[0089]
[0090] in, is the accumulated phase distortion delay of the nth array element at the i-th scanning angle;
[0091] is the phase distortion delay of the j-th array element at the i-th scanning angle, which indicates the time delay required for the signal of the j-th element in order to correct the phase distortion.
[0092] In specific implementation, each It only corresponds to one This value represents the total delay from the 1st array element to the nth array element. For example, if we want to find the total delay of the 4th array element at the 3rd scanning angle, then The n in formula (4) Obtained by formula (3).
[0093] Step 3: Calculate the weight coefficient of each array element and each scanning angle in the phase distortion correction, and calculate the weighted average phase distortion delay of each array element in combination with the accumulated phase distortion delay;
[0094] Further preferably, in order to process the phase error caused by multipath and scattering, the present invention minimizes SAD while averaging the weighted estimated values at multiple scanning angles to reduce the impact of multipath and scattering. The weight coefficient is defined as the average amplitude of the echo signal received from each array element, which is used for weighted average phase distortion delay calculation. Specifically as follows:
[0095] Since the echo signal is angularly non-uniform, the average of the estimated aberration delay over a two-dimensional window requires appropriate weighting;
[0096] For the i-th scanning angle, the weight coefficient of the n-th array element is defined as the average amplitude of the echo signal received from the array element, that is:
[0097]
[0098] in, is the weight coefficient of the nth array element at the i-th scanning angle. This formula determines the weight of the angle in phase distortion correction by calculating the average amplitude of the signal received by each array element at a specific angle. The larger the weight coefficient, the stronger the signal at that angle, and the more attention should be paid to it during the correction process;
[0099] is the signal value of the kth sample of the nth array element at the i-th scanning angle;
[0100] M is the length of the time window, which indicates the number of samples considered when calculating the average amplitude;
[0101] For each array element n, the weighted aberration delay at different scanning angles i is and weight coefficient Calculate the weighted average phase distortion delay The formula is:
[0102]
[0103] in, is the weighted average phase distortion delay of the nth array element, which represents the average delay weighted by the weight coefficient of each angle at multiple scanning angles;
[0104] is the phase distortion delay of the nth array element at the i-th scanning angle;
[0105] K is the number of scan angles used for averaging.
[0106] Step 4: Use the weighted average phase distortion delay as the array element delay time estimate to perform ultrasound imaging phase distortion correction.
[0107] Further preferably, the weighted average phase distortion delay estimated in step 3 is The ultrasonic imaging phase distortion correction is performed, including: setting the corresponding array element delay time according to the weighted average phase distortion delay of each array element, collecting the corresponding echo amplitude signal, and imaging according to the collected signal.
[0108] The purpose of phase distortion correction calculation is to correct the phase error caused by the difference in sound speed in inhomogeneous media. Correcting this error requires correcting the delay time.
[0109] By considering the phase distortion delay of each array element at different scanning angles And the corresponding weight coefficient To calculate a comprehensive delay value. This comprehensive delay value can more accurately reflect the actual phase distortion of each array element at different scanning angles. The signal of each array element will be advanced or delayed in time according to its weighted average phase distortion delay to ensure that the signals of all array elements can be correctly aligned when synthesizing the ultrasonic beam. The imaging quality can be improved on the basis of optimizing beamforming.
[0110] Embodiment 2 of the present invention provides an ultrasonic imaging phase distortion correction calculation system based on time delay estimation, comprising:
[0111] An evaluation index calculation module, used for calculating a phase error evaluation index based on relative delay and XOR operation for each array element and each scanning angle of ultrasonic imaging, and obtaining a relative delay when the evaluation index is lower than a set threshold;
[0112] A cumulative phase distortion delay calculation module, used to calculate the corresponding correction delay according to the acquired relative delay, and calculate the cumulative phase distortion delay according to the correction delay;
[0113] A weighted average phase distortion delay calculation module, used to calculate the weight coefficient of each array element and each scanning angle in phase distortion correction, and calculate the weighted average phase distortion delay of each array element in combination with the accumulated phase distortion delay;
[0114] The phase distortion correction module is used to perform phase distortion correction for ultrasonic imaging by using the weighted average phase distortion delay as an estimated value of array element delay time.
[0115] Embodiment 3 of the present invention provides a terminal, including a processor and a storage medium; the storage medium is used to store instructions;
[0116] The processor is configured to operate according to the instructions to execute the steps of the method.
[0117] Embodiment 4 of the present invention provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method when executed by a processor.
[0118] Compared with the prior art, the beneficial effects of the present invention include at least:
[0119] The present invention estimates the distortion mode of the echo signal reflected by the line target and / or diffuse reflector based on the absolute difference and SAD between two radio frequency samples, and only involves addition operation, so the calculation complexity is relatively low; the present invention uses a single-bit word length for SAD calculation, and the word length is truncated to 1b to further improve the calculation efficiency; the present invention effectively estimates the relative phase error of adjacent array channels by minimizing the absolute difference sum between two radio frequency samples;
[0120] The present invention performs weighted averaging on the estimated modes at multiple scanning angles, and the weighted coefficient of each angle is the average amplitude of the echo signal received at the angle, thereby improving the accuracy and convergence performance of the SAD technology.
[0121] The present disclosure may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.
[0122] A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples of computer-readable storage media (a non-exhaustive list) include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination of the foregoing. As used herein, a computer-readable storage medium is not to be interpreted as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through a wire.
[0123] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.
[0124] The computer program instructions for performing the operation of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed completely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be customized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.
[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.
Claims
1. A method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation, characterized in that: include: For each array element and each scanning angle of the ultrasound imaging, a phase error evaluation index is calculated based on the relative delay and an XOR operation, and a relative delay when the evaluation index is lower than a set threshold is obtained; Calculating a corresponding correction delay according to the acquired relative delay, and calculating a cumulative phase distortion delay according to the correction delay; Calculating the weight coefficient of each array element and each scanning angle in phase distortion correction, and calculating the weighted average phase distortion delay of each array element in combination with the accumulated phase distortion delay; The weighted average phase distortion delay is used as an estimated value of array element delay time to perform ultrasound imaging phase distortion correction.
2. The method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation according to claim 1, characterized in that: The calculation formula of the phase error evaluation index is: in, is the phase error evaluation index; M is the length of the time window; and RF echo samples and Shift representation of ; is the signal value of the kth sample of the nth array element at the i-th scanning angle; is the n-1th array element at the i-th scanning angle. The signal value of each sample; is the relative delay of the nth array element at the i-th scanning angle; Indicates a bit-by-bit XOR operation.
3. The method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation according to claim 1, characterized in that: The calculation formula for the correction delay is: Where: is the correction delay of the nth array element at the i-th scanning angle; is the relative delay of the nth array element at the i-th scanning angle; T s is the sampling period of the RF echo signal sample; is the relative focus delay.
4. The method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation according to claim 1, characterized in that: The calculation formula of the cumulative phase distortion delay is: in, is the accumulated phase distortion delay of the nth array element at the i-th scanning angle; is the correction delay of the jth array element at the i-th scanning angle.
5. The method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation according to claim 1, characterized in that: The calculation formula of the weight coefficient is: in, is the weight coefficient of the nth array element at the i-th scanning angle; is the signal value of the kth sample of the nth array element at the i-th scanning angle; M is the length of the time window.
6. The method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation according to claim 1, characterized in that: The calculation formula of the weighted average phase distortion delay is: in, is the weighted average phase distortion delay of the nth array element; is the weight coefficient of the nth array element at the i-th scanning angle; is the accumulated phase distortion delay of the nth array element at the i-th scanning angle; K is the scan angle.
7. The method for calculating phase distortion correction of ultrasonic imaging based on time delay estimation according to claim 1, characterized in that: The method of using the weighted average phase distortion delay as an estimated value of array element delay time to perform ultrasound imaging phase distortion correction includes: The delay time of the corresponding array element is set according to the weighted average phase distortion delay of each array element, the corresponding echo amplitude signal is collected, and imaging is performed according to the collected signal.
8. An ultrasonic imaging phase distortion correction calculation system based on time delay estimation, using the method according to any one of claims 1 to 7, characterized in that: The system comprises: An evaluation index calculation module, used for calculating a phase error evaluation index based on relative delay and XOR operation for each array element and each scanning angle of ultrasonic imaging, and obtaining a relative delay when the evaluation index is lower than a set threshold; A cumulative phase distortion delay calculation module, used to calculate the corresponding correction delay according to the acquired relative delay, and calculate the cumulative phase distortion delay according to the correction delay; A weighted average phase distortion delay calculation module, used to calculate the weight coefficient of each array element and each scanning angle in phase distortion correction, and calculate the weighted average phase distortion delay of each array element in combination with the accumulated phase distortion delay; The phase distortion correction module is used to perform ultrasound imaging phase distortion correction using the weighted average phase distortion delay as an array element delay time estimation value.
9. A terminal comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1-7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program 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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