Sampling method and device using multi-nuclear magnetic resonance imaging optimal bandwidth

Abstract

The invention discloses a sampling method for optimizing bandwidth by using multi-nuclear magnetic resonance imaging. The method comprises the following steps: determining a magnetic resonance scanning track and a coding gradient; calculating a density compensation coefficient corresponding to the k value and performing normalization processing to obtain a normalized density compensation coefficient corresponding to the k value; calculating a relaxation compensation coefficient corresponding to the k value; calculating image noise power based on the sampling bandwidth, the normalized density compensation coefficient corresponding to the k value and the relaxation compensation coefficient corresponding to the k value; the sampling bandwidth is optimized based on the minimum image noise power; obtaining an optimal sampling bandwidth; and carrying out sampling by using the optimal sampling bandwidth setting, carrying out density compensation and relaxation time compensation on a sampling signal, and carrying out gridding reconstruction on the compensated sampling signal to obtain a magnetic resonance image. The invention also relates to a corresponding device. By the adoption of the sampling method and device for optimizing the bandwidth through multi-nuclear magnetic resonance imaging, the image signal-to-noise ratio of multi-nuclear magnetic resonance imaging can be increased, and the image quality is improved.

Description

Technical Field

[0001] The present invention belongs to the field of multi-nuclear magnetic resonance imaging (Magnetic Resonance Imaging, MRI) methods, and particularly relates to a sampling method and device for optimizing the bandwidth in multi-nuclear magnetic resonance imaging, which is applicable to the setting of sampling bandwidth parameters for multi-nuclear magnetic resonance imaging, improves the signal-to-noise ratio of multi-nuclear magnetic resonance imaging, and realizes the optimization of image quality. Background Art

[0002] Magnetic resonance imaging is an important tool in the field of contemporary medical imaging. With its advantages of non-invasive, non-radiative, and good soft tissue contrast, it is widely used in clinical diagnosis and scientific research. There are more than 60 elements in the human body, and the atomic nuclei with non-zero spins can all generate magnetic resonance signals. With the development of multi-nuclear magnetic resonance imaging technology, the imaging capabilities of different elements further expand the application scope of MRI, providing rich multi-element information for the detection of life activities.

[0003] In multi-nuclear magnetic resonance imaging, the T 2 or T 2 * relaxation time of multiple nuclides is relatively short (such as 23 Na, 129 Xe, etc.), the sampling time window is short, and it is difficult for conventional magnetic resonance imaging sequences to capture sufficient signals. Therefore, an ultrashort echo time (UTE) imaging sequence is usually adopted. The UTE sequence is one of the key technologies to solve the imaging problem under short T 2 or T 2 * relaxation time. When setting the sequence parameters, the sampling bandwidth is an important parameter and is closely related to the signal-to-noise ratio of the image. Theoretically, the noise power of the sampled signal is proportional to the sampling bandwidth. The larger the sampling bandwidth, the greater the noise power. On the other hand, the readout time of sampling is inversely proportional to the sampling bandwidth. The smaller the sampling bandwidth, the longer the readout time. During the signal readout period, the signal decays due to T 2 * relaxation, which will cause image blurring and thus reduce the true resolution of the image.

[0004] Therefore, how to balance the influence of the image signal-to-noise ratio and the true resolution in the setting of the sampling bandwidth and find the optimal sampling bandwidth setting is an important issue in multi-nuclear magnetic resonance imaging methods. However, there is little research on this issue, and currently, there is a lack of an efficient and reliable solution that can optimize the bandwidth setting under different imaging parameters to meet the actual application requirements. The sampling bandwidth setting is still mainly based on experience, and after collecting multiple images, a moderate sampling bandwidth is selected according to the image quality. Summary of the Invention

[0005] The object of the present invention is to provide a sampling method and device for optimizing the bandwidth using multi-nuclear magnetic resonance imaging in view of the above problems existing in the prior art.

[0006] The above object of the present invention is achieved by the following technical means:

[0007] A sampling method for optimizing the bandwidth using multi-nuclear magnetic resonance imaging, characterized by comprising the following steps:

[0008] Step 1: Determine the magnetic resonance scanning trajectory and encoding gradient;

[0009] Step 2: Perform sampling under the encoding gradient selected in Step 1, calculate the density compensation coefficient dc(k) corresponding to the k value, and perform normalization processing to obtain the normalized density compensation coefficient dcn(k) corresponding to the k value;

[0010] Step 3: Calculate the relaxation compensation coefficient rc(k) corresponding to the k value;

[0011] Step 4: Calculate the image noise power based on the sampling bandwidth BW, the normalized density compensation coefficient dcn(k) corresponding to the k value, and the relaxation compensation coefficient rc(k) corresponding to the k value;

[0012] Step 5: Optimize the sampling bandwidth based on minimizing the image noise power to obtain the optimal sampling bandwidth.

[0013] The calculation formula of the sampling bandwidth described in Step 4 is as follows,

[0014] BW = γG P FOV 1

[0015] where BW is the sampling bandwidth, γ is the gyromagnetic ratio of the imaging nucleus, G P is the intensity of the encoding gradient in the plateau period, and FOV 1 is the size of the first dimension of the sampling field of view FOV.

[0016] The calculation formula of the density compensation coefficient dc(k) corresponding to the k value in Step 2 is as follows:

[0017]

[0018] where,

[0019]

[0020] where BW is the sampling bandwidth, FOV 1 is the size of the first dimension of the sampling field of view FOV, t(k) is the sampling time corresponding to reaching the k value under the encoding gradient, and T rampis the gradient climb time, k is the k value of the k-space corresponding to the magnetic resonance image, k max is the maximum k value of the k-space corresponding to the magnetic resonance image, Matrix 1 represents the size of the first dimension of the sampling matrix Matrix, T acq is the sampling time when the k value of the k-space reaches k max at that time.

[0021] The calculation formula for the relaxation compensation coefficient rc(k) corresponding to the k value in step 3 is as follows:

[0022]

[0023] where e is the natural constant, t(k) is the sampling time corresponding to reaching the k value under the encoding gradient, T 2 * is for T 2 * The relaxation time corresponding to relaxation.

[0024] The calculation formula for the image noise power described in step 4 is as follows:

[0025]

[0026] where P σ (BW) is the image noise power, σ k is the noise of the signal in the k-space, k max is the maximum k value of the k-space corresponding to the magnetic resonance image.

[0027] The calculation formula for minimizing the image noise power in step 5 is as follows:

[0028]

[0029] where is to obtain The sampling bandwidth BW with the smallest value, P σi is the image noise power corresponding to the i-th relaxation time T 2 * N represents the number of relaxation time T 2 * values.

[0030] It also includes step 6:

[0031] Perform sampling using the optimized sampling bandwidth setting obtained in step 5, multiply the obtained sampling signal by the updated normalized density compensation coefficient dcn(k) to obtain the density-compensated sampling signal, then multiply the density-compensated sampling signal by the updated relaxation compensation coefficient rc(k) to obtain the sampling signal after compensation is completed. After the sampling signal after compensation is completed undergoes grid reconstruction, a magnetic resonance image is obtained.

[0032] A computer device includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it implements the steps of the above-mentioned sampling method using optimized bandwidth for multi-nuclear magnetic resonance imaging except step 6.

[0033] A computer-readable storage medium stores a computer program. When the computer program is executed by a processor, it implements the steps of the above-mentioned sampling method using optimized bandwidth for multi-nuclear magnetic resonance imaging except step 6.

[0034] A computer program product includes a computer program. When the computer program is executed by a processor, it implements the steps of the above-mentioned sampling method using optimized bandwidth for multi-nuclear magnetic resonance imaging except step 6.

[0035] The present invention has the following beneficial effects compared with the existing methods:

[0036] By establishing a calculation method for the image noise power under different sampling bandwidths and optimizing the sampling bandwidth setting with the goal of minimizing the image noise power, the signal-to-noise ratio of the multi-nuclear magnetic resonance imaging is enhanced, thereby improving the image quality. Description of the Drawings

[0037] Figure 1 is a flowchart of the present invention;

[0038] Figure 2 is a graph showing the relationship between the intensity of the encoding gradient and the time of the encoding gradient corresponding to different sampling bandwidths BW of the present invention; the horizontal axis is the time of the encoding gradient, and the vertical axis is the intensity of the encoding gradient;

[0039] Figure 3 is a graph showing the relationship between the k value corresponding to the signal and the sampling time under different sampling bandwidths BW of the present invention; the horizontal axis is the magnitude of the k value corresponding to the signal, and the vertical axis is the sampling time corresponding to that k value;

[0040] Figure 4 is a graph showing the relationship between the normalized density compensation coefficient and the corresponding k value of the present invention; the horizontal axis is the magnitude of the k value corresponding to the signal, and the vertical axis is the magnitude of the normalized density compensation coefficient;

[0041] Figure 5 is a graph showing the relationship between the relaxation compensation coefficient and the corresponding k value under different sampling bandwidths BW of the present invention; the horizontal axis is the magnitude of the k value corresponding to the signal, and the vertical axis is the magnitude of the density compensation coefficient;

[0042] Figure 6 is a graph showing the relationship between the image noise power and the sampling bandwidth BW of the present invention; the horizontal axis is the magnitude of the sampling bandwidth BW, and the vertical axis is the value of the logarithm of the image noise power;

[0043] Figure 7For the relaxation time T of the present invention 2 * Relationship diagram with the corresponding optimized sampling bandwidth BW value; the horizontal axis is the relaxation time T 2 * Size, and the vertical axis is the optimized sampling bandwidth BW value. Specific implementation manner

[0044] To facilitate the understanding and implementation of the present invention by those of ordinary skill in the art, the present invention will be further described in detail below in conjunction with embodiments. The embodiments described herein are only used to illustrate and explain the present invention, and are not intended to limit the present invention.

[0045] Embodiment 1:

[0046] A sampling method using the optimized bandwidth of multi-nuclear magnetic resonance imaging includes the following steps:

[0047] Step 1: Determine the magnetic resonance scanning trajectory and encoding gradient.

[0048] In magnetic resonance imaging, the setting range of the sampling bandwidth BW is related to the encoding gradient of the magnetic resonance hardware. In this embodiment, the sampling of the magnetic resonance uses a radial (radial) trajectory for radial sampling, and the encoding gradient adopts a fixed ramp time mode, that is, during a single sampling period, the intensity of the encoding gradient first ramps up with a fixed ramp time, and then enters the plateau period. During the plateau period, the intensity of the encoding gradient remains unchanged, and after the sampling ends, the intensity of the encoding gradient decreases to 0 with the same decay time as the ramp time.

[0049] In this embodiment, the sampling parameters are: the sampling field of view (FOV) is set to 32mm×32mm, the sampling matrix (Matrix) is set to 64×64, and the number of excitations for radial sampling is 202 times.

[0050] Based on the above sampling parameters, the maximum k value k of the k-space corresponding to the magnetic resonance image is calculated max as:

[0051]

[0052] wherein, FOV 1 represents the size of the first dimension of the sampling field of view FOV, and Matrix 1 represents the size of the first dimension of the sampling matrix Matrix. Since the radial sampling is a square field of view and isotropic resolution, the same result can be obtained by taking any one-dimensional value of the sampling field of view FOV and the sampling matrix Matrix. In this embodiment, k max is 1000m -1 .

[0053] The k value in k-space is the integral of the encoding gradient. The value of k(t) that changes with the sampling time t can be expressed as:

[0054]

[0055] where G(τ) is the value of the encoding gradient that changes with time τ, γ is the gyromagnetic ratio of the imaging nucleus, and T is the total sampling time.

[0056] According to the Nyquist sampling theorem, the maximum distance between adjacent sampling points in k-space should be equal to 1 / FOV 1 , that is, γG P Δt = 1 / FOV 1 , where G P is the strength of the encoding gradient during the plateau period, and Δt is the time interval between sampling points. At the same time, the sampling bandwidth BW is the reciprocal of the time interval between sampling points, that is, BW = 1 / Δt. The relationship between the sampling bandwidth BW and the strength of the encoding gradient during the plateau period can be calculated as:

[0057] BW = γG P FOV 1 (3)

[0058] In this embodiment, in the fixed ramp time mode, the ramp time is set to be fixed at 100 μs, and the maximum ramp rate does not exceed 2000 T / m / s. The maximum strength of the encoding gradient that can be achieved during the plateau period in this mode is 0.2 T / m. The maximum sampling bandwidth BW corresponding to this sampling parameter is 2.72×10 5 Hz.

[0059] The sampling time T when the k value in k-space reaches k max in this fixed ramp time mode is: acq

[0060]

[0061] where T ramp is the gradient ramp time. Sampling and the encoding gradient are turned on simultaneously. During the gradient ramp time T ramp of the encoding gradient, the encoding gradient ramps linearly. At the end of the gradient ramp time T ramp , the strength of the encoding gradient reaches G P . During the plateau period, the strength of the encoding gradient remains unchanged. After sampling is completed, the encoding gradient decays to 0 after a time equal to the gradient ramp time T ramp .

[0062] Figure 2 is a graph showing the relationship between the strength of the encoding gradient and the time of the encoding gradient corresponding to different sampling bandwidths BW.

[0063] ​Step 2: Sampling is performed under the encoding gradient selected in Step 1, the density compensation coefficient dc(k) corresponding to the k value is calculated and normalized to obtain the normalized density compensation coefficient dcn(k) corresponding to the k value.

[0064] Sampling is performed under the encoding gradient described in Step 1, and the sampling signal is filled in the k-space. In radial sampling, the sampling density at the center of the k-space is large, and the sampling density at the outer periphery of the k-space is small.

[0065] In the region with a large sampling density, the noise is small after averaging the sampling signals, while in the region with a small sampling density, the noise is large after averaging the sampling signals, and the noise power is inversely proportional to the sampling density. Therefore, after radial sampling, the sampling signals in the k-space can be density-compensated by multiplying the sampling signals by the density compensation coefficient. The density compensation coefficient is the reciprocal of the sampling density, that is, dc(k)=1 / D(k), where dc(k) is the density compensation coefficient corresponding to the k value, and D(k) is the sampling density corresponding to the k value.

[0066] In the fixed climb mode, the k value k(t) varying with the sampling time t is calculated, which is expressed as:

[0067]

[0068] The sampling time t(k) corresponding to reaching the k value under this encoding gradient can be expressed as:

[0069]

[0070] Figure 3 It is a relationship diagram of the k value corresponding to different sampling bandwidths BW and the sampling time t.

[0071] In the radial sampling mode, the sampling density is inversely proportional to the k value and also inversely proportional to the rate of change of the k value with time. Based on this, the density compensation coefficient corresponding to the radial sampling can be calculated. The density compensation coefficient is the reciprocal of the sampling density:

[0072]

[0073] In the radial sampling mode, the sampling density at the outermost periphery of the k-space is usually the lowest, and it just satisfies the Nyquist sampling law. Therefore, the density compensation coefficient at the outermost periphery is the largest. Based on this, the density compensation coefficient can be normalized, dcn(k)=dc(k) / max(dc(k)), where max represents taking the maximum value, and dcn(k) represents the normalized density compensation coefficient corresponding to the k value, which is convenient for subsequent calculations. Figure 4 It is a relationship diagram of the normalized density compensation coefficient and the signal k value.

[0074] Step 3: Calculate the relaxation compensation coefficient rc(k) corresponding to the k value.

[0075] The sampling bandwidth BW is inversely proportional to the sampling time t. During the sampling process, T 2 * Relaxation will cause signal attenuation, resulting in image blurring and reducing the true resolution of the image. Therefore, to compare images under different sampling bandwidths BW, a comparison standard needs to be established to correct for T 2 * the influence of relaxation. In this embodiment, before image reconstruction, relaxation time compensation is performed on the sampled signal, with the goal of keeping the true resolution of the magnetic resonance image consistent. The attenuation of the sampled signal caused by relaxation is compensated by multiplying by a relaxation compensation coefficient to offset the influence of relaxation, so that magnetic resonance images under different sampling bandwidths BW can be compared at the same true resolution.

[0076] During the sampling process, the signal corresponding to the k value at the relaxation time T 2 * can be expressed as:

[0077]

[0078] where SI 0 is the signal intensity corresponding to when not considering T 2 * relaxation, SI(k) is the signal intensity of the sampled signal at the k value, and e is the natural constant.

[0079] The relaxation compensation coefficient rc(k) of the k value signal is the reciprocal of the signal attenuation caused by relaxation, i.e.:

[0080]

[0081] where rc(k) is the relaxation compensation coefficient corresponding to the k value, and T 2 * is the relaxation time corresponding to T 2 * relaxation. Figure 5 is a graph of the relationship between the relaxation compensation coefficient rc(k) and the k value. It can be seen that the smaller the bandwidth, the longer the sampling time, and the larger the relaxation compensation coefficient.

[0082] Step 4: Calculate the image noise power based on the sampling bandwidth BW, the normalized density compensation coefficient dcn(k) corresponding to the k value, and the relaxation compensation coefficient rc(k) corresponding to the k value.

[0083] The noise in magnetic resonance images comes from the sampling noise in the entire k-space. During the sampling process, the noise power in the sampling signal is proportional to the sampling bandwidth BW. After passing through the density compensation coefficient and the relaxation compensation coefficient, the sampling signal is reconstructed through gridding to obtain a magnetic resonance image. During the gridding reconstruction process, the noise power is small after averaging in the area with a large sampling density, and the noise power is large after averaging in the area with a small sampling density. When the sampling density is different, the corresponding noise power distribution is corrected by the density compensation coefficient; when the sampling bandwidth BW is different, the influence of relaxation on the sampling signal is corrected by the relaxation compensation coefficient. During the correction process, the noise power is also amplified or reduced accordingly with the compensation coefficient.

[0084] In this embodiment, the image noise power P σ (BW) under the combined action of the density compensation coefficient and the relaxation compensation coefficient can be expressed as:

[0085]

[0086] Among them, σ k is the noise of the signal in the k-space, the noise is a measured value, and P σ (BW) is the power of the image noise, dcn(k) is the normalized density compensation coefficient, and rc(k) is the relaxation compensation coefficient.

[0087] Step 5: Optimize the sampling bandwidth based on minimizing the image noise power to obtain the optimal sampling bandwidth.

[0088] From the calculation method of the image noise power, it can be seen that the image noise power is a function of parameters such as the sampling bandwidth BW and the relaxation time T 2 * and so on. The relaxation time T 2 * can be determined by experimental measurement, or the approximate range of the relaxation time T 2 * can be determined according to prior knowledge, and then the value of the relaxation time T 2 * is discretized. The objective function for optimizing the sampling bandwidth is:

[0089]

[0090] In the formula, is to obtain the sampling bandwidth BW with the minimum value, and calculating the sampling bandwidth BW that makes take the minimum value is the optimized bandwidth. P σi is the image noise power corresponding to the i-th relaxation time T 2 * , and N represents the number of values of the relaxation time T 2 * values.

[0091] The value of the image noise power varies significantly with the change of the sampling bandwidth BW. Therefore, the logarithm of the image noise power P σ (BW) is taken to reduce the numerical range and determine the minimum image noise power. Figure 6 For the relaxation time T 2 * When the value of the relaxation time T is 2 ms, the relationship between the logarithm value of the noise power and the sampling bandwidth BW is shown. At this time, the sampling bandwidth corresponding to the minimum image noise power is set to 12900 Hz. When the sampling bandwidth is 12900 Hz, the noise power is 88% of the noise power when the sampling bandwidth is 8000 Hz, and 91% of the noise power when the sampling bandwidth is 20000 Hz.

[0092] According to Formula 11, the corresponding relationship between the relaxation time T 2 * and the optimal sampling bandwidth BW can be obtained ( Figure 7 ). It can be seen that the optimized sampling bandwidth BW and the relaxation time T 2 * are inversely correlated.

[0093] Step 6: Use the optimal sampling bandwidth setting to sample to obtain a magnetic resonance image.

[0094] Use the optimized sampling bandwidth setting obtained in Step 5 to sample. Multiply the obtained sampling signal by the updated normalized density compensation coefficient dcn(k) to obtain the density-compensated sampling signal. Then multiply the density-compensated sampling signal by the updated relaxation compensation coefficient rc(k) to obtain the sampling signal after compensation is completed. After the sampling signal after compensation is completed undergoes gridded reconstruction, a magnetic resonance image is obtained.

[0095] Those of ordinary skill in the art can understand that all or part of the processes in implementing the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above various methods.

[0096] Embodiment 2:

[0097] In this embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory. When the processor executes the computer program, the steps in the above various method embodiments are implemented.

[0098] Embodiment 3:

[0099] In this embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0100] Embodiment 4:

[0101] In this embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0102] It should be noted that the embodiments described in the present invention are only illustrative of the spirit of the present invention. Those skilled in the art to which the present invention pertains can make various modifications or supplements to the described embodiments or use similar ways to substitute, but will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A method for sampling using multi-nuclear magnetic resonance imaging to optimize bandwidth, characterized in that: The following steps are involved: Step 1: Determine the magnetic resonance scanning trajectory and encoding gradient; Step 2: Sampling is performed under the coding gradient selected in step 1, the density compensation coefficient dc(k) corresponding to the k value is calculated and normalized to obtain the normalized density compensation coefficient dcn(k) corresponding to the k value; Step 3: Calculate the relaxation compensation coefficient rc(k) corresponding to the k value; Step 4: Calculate the image noise power based on the sampling bandwidth BW, the normalized density compensation coefficient dcn(k) corresponding to the k value, and the relaxation compensation coefficient rc(k) corresponding to the k value; Step 5: Optimize the sampling bandwidth based on minimizing the image noise power to obtain the optimal sampling bandwidth.

2. A method for sampling using multi-nuclear magnetic resonance imaging to optimize bandwidth according to claim 1, characterized in that: The calculation formula for the sampling bandwidth described in step 4 is as follows, BW=γG P FOV1 Where BW is the sampling bandwidth, γ is the gyromagnetic ratio of the imaging nucleus, G P is the intensity of the encoding gradient during the plateau period, and FOV1 is the size of the first dimension of the sampling field of view FOV.

3. A method for sampling using multi-nuclear magnetic resonance imaging to optimize bandwidth according to claim 1, characterized in that: The calculation formula of the density compensation coefficient dc(k) corresponding to the k value in step 2 is as follows: in, Among them, BW is the sampling bandwidth, FOV1 is the size of the first dimension of the sampling field of view FOV, t(k) is the sampling time corresponding to the k value under the encoding gradient, T ramp is the gradient climbing time, k is the k value of the k space corresponding to the magnetic resonance image, k max is the maximum k value of the k-space corresponding to the magnetic resonance image, Matrix1 represents the size of the first dimension of the sampling matrix Matrix, T acq The k value of k space reaches k max The sampling time of .

4. A method for sampling using multi-nuclear magnetic resonance imaging to optimize bandwidth according to claim 1, characterized in that: The relaxation compensation coefficient rc(k) corresponding to the k value in step 3 is calculated as follows: Among them, e is a natural constant, t(k) is the sampling time corresponding to the k value under the encoded gradient, and T2* is the relaxation time corresponding to the relaxation of T2*.

5. The method for optimizing bandwidth using multi-nuclear magnetic resonance imaging according to claim 1, characterized in that: The image noise power calculation formula described in step 4 is as follows: Among them, P σ (BW) is the image noise power, σ k is the noise of the signal in k-space, k max is the maximum k value of the k-space corresponding to the magnetic resonance image.

6. A method for sampling using multi-nuclear magnetic resonance imaging to optimize bandwidth according to claim 1, characterized in that: The calculation formula for minimizing the image noise power in step 5 is as follows: in, Is to seek The minimum sampling bandwidth BW,P σi is the i-th relaxation time T2 * The corresponding image noise power is as follows, where N represents the relaxation time T2 * The number of values.

7. A method for sampling using multi-nuclear magnetic resonance imaging to optimize bandwidth according to claim 1, characterized in that: Also includes step 6: Use the optimized sampling bandwidth setting obtained in step 5 for sampling, multiply the obtained sampling signal by the updated normalized density compensation coefficient dcn(k) to obtain the density compensated sampling signal, then multiply the density compensated sampling signal by the updated relaxation compensation coefficient rc(k) to obtain the compensated sampling signal, and the compensated sampling signal is grid-reconstructed to obtain a magnetic resonance image.

8. A computer 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 a sampling method for optimizing bandwidth using multi-nuclear magnetic resonance imaging according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of a sampling method for optimizing bandwidth using multi-nuclear magnetic resonance imaging according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of a sampling method for optimizing bandwidth using multi-nuclear magnetic resonance imaging according to any one of claims 1 to 6 are implemented.

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