NeRF-based magnetic nanoparticle image reconstruction method and system

Abstract

The invention relates to the field of magnetic nanoparticle (MPI) image reconstruction, in particular to a neural radiation field (NeRF)-based magnetic nanoparticle image reconstruction method and system, and aims to solve the widely existing problems of limited training data and poor model generalization in the existing deep learning-based MPI image reconstruction algorithm. The method comprises the following steps: acquiring a response voltage signal of to-be-detected superparamagnetic nanoparticles (MNPs) as a truth value of model learning; acquiring a system matrix; setting a grid point coordinate matrix as the input of the network; the MPI reconstruction image is output by the network, a predicted response voltage signal is obtained after downsampling and system matrix processing, loss is calculated according to the predicted response voltage signal and the measured voltage signal and returned, and the high-quality MPI reconstruction image is output after iteration is finished. According to the method, the problem of scarcity of MPI data is effectively relieved, and the adaptability and generalization ability of the model to different data sets are remarkably enhanced.

Description

Technical Field

[0001] The present invention relates to the field of magnetic nanoparticle image reconstruction, and in particular to a NeRF-based magnetic nanoparticle image reconstruction method and system. Background Art

[0002] Magnetic Particle Imaging (MPI) is a cutting-edge medical imaging technology that has attracted attention for its excellent imaging speed, high sensitivity, and no radiation exposure. The technology relies on the nonlinear response of magnetic nanoparticles (MNPs) in a specific magnetic field to accurately depict the distribution of these tracers in vivo. The application scope of MPI has expanded to multiple fields, including cell tracing, vascular imaging, functional neuroimaging, etc., showing its broad potential in medical diagnosis.

[0003] Image reconstruction is a core research area in MPI technology. Due to the inherent ill-posedness of the inverse problem of MPI reconstruction, traditional iterative reconstruction methods often lead to large noise and severe artifacts in the reconstructed image. In recent years, with the development of deep learning technology, MPI image reconstruction methods based on this technology have gradually emerged. These methods effectively circumvent the ill-posed problem by directly mapping the input magnetic nanoparticle response signal to the spatial three-dimensional distribution in the body, significantly improving image quality and reconstruction speed.

[0004] Nevertheless, the scarcity of real MPI data remains the main obstacle that limits deep learning from further improving the quality and generalization ability of MPI images. Although a variety of simulation methods have been proposed to expand the training data set of deep learning models, studies have shown that there are significant differences between the magnetic nanoparticle signals generated by these simulation methods and the signals collected by actual devices. This difference may affect the effect of model training, thereby limiting the application potential of deep learning in MPI image reconstruction.

[0005] In general, the application of deep learning in the field of MPI image reconstruction shows great potential, but it also faces the dual challenges of data acquisition limitations and model generalization. At present, this field urgently needs to develop a deep learning method that can provide high-quality image reconstruction results without relying on large-scale training datasets. Such a method will effectively alleviate the problem of data scarcity and significantly enhance the model's adaptability and generalization ability to different datasets. Summary of the invention

[0006] In order to solve the above problems in the prior art, namely, the problems of limited training data acquisition and model generalization faced by the prior art, the present invention provides a magnetic nanoparticle image reconstruction method based on NeRF, the method comprising:

[0007] Step S11: Select a type of MNPs as the sample to be tested, and obtain the response voltage signal of the MNPs sample based on the MPI device represents the complex data form, M represents the number of frequencies of the signal;

[0008] Step S12: Acquire the system matrix of the length, width and height (w1, w2, w3) of the undersampling grid grid1 set according to the MPI imaging N represents the number of all grid points in the undersampling grid, that is, N = w1 × w2 × w3;

[0009] Step S13: Construct a fully connected network model MLP. The model input is the spatial coordinate matrix transformed according to the full sampling grid grid2, and the model output is the image reconstructed by MPI Where D is the size of the full sampling grid, that is, D = d1 × d2 × d3, d1, d2, d3 represent the length, width, and height of the full sampling grid grid2 respectively;

[0010] Step S14: Downsample the MPI image generated in the above steps to obtain a downsampled image. Then Φ d Multiplying with the system matrix S, we get the predicted response voltage signal

[0011] Step S15: Iteratively calculate the loss function and return it to continuously optimize the weight coefficients in the MLP. After the iteration is completed, the optimal MPI high-quality image Φ is obtained.

[0012] The present invention does not need to train the model through a large amount of training data, but uses the neural network itself to continuously iterate and learn to update the network parameters, and directly maps the three-dimensional position coordinates in the scene to the MPI image. The above-mentioned spatial grid is converted into three-dimensional spatial position coordinates through position encoding as the input of the network, and the coordinate range is normalized to [-1,1], which is convenient for network learning and processing. In addition, by setting the grid size and downsampling operations, the MPI image reconstruction resolution is expanded by ρ times. The cleverness of the present invention is that while completing the MPI image reconstruction task, the image resolution can also be improved at the same time.

[0013] As a further optimization of the NeRF-based magnetic nanoparticle image reconstruction method.

[0014] Preferably, in step S11, the response voltage signal of the MNPs sample is obtained by:

[0015] Prepare a MNPs standard sample with an iron concentration of 0.5 mg / mL and a volume of 0.5 mL;

[0016] Place the MNPs standard sample in the center of the imaging field of view of the MPI device;

[0017] The scanning is completed by continuously moving the exciting magnetic field in the field of view, and the response voltage signal y of the MNPs standard sample is obtained. meas .

[0018] Preferably, step S12 obtains the system matrix by:

[0019] According to the size of the undersampling grid grid1 set during MPI imaging, that is, the length, width, and height are w1, w2, and w3 respectively, a small sample (size 1 mm3) filled with MNPs standard sample is automatically placed at each grid position under the imaging field of view by a robot or a mechanical arm, and then the MPI device is scanned to obtain the corresponding response voltage signal. The number of frequency points contained in the response signal is M. After all grid positions are scanned, the corresponding system matrix is ​​obtained.

[0020] Preferably, the grid2 coordinate matrix setting method of the model input in step S13 is:

[0021] Each pixel in the grid is encoded with a unique coordinate based on the position information. Δd1, Δd2, Δd3 are the grid point spacing sizes along the x, y, and z directions, respectively, and d1, d2, d3 are the number of all grid points in the x, y, and z directions, respectively. We normalize the grid point coordinate range to [-1, 1], where the grid point spacing sizes are: Δd1 = 2 / (d1-1), Δd2 = 2 / (d2-1), Δd3 = 2 / (d3-1). These grid point coordinates are stacked along the x direction to obtain a D×3 matrix, and D is defined as D = d1×d2×d3.

[0022] The spatial grid is converted into three-dimensional spatial position coordinates through position encoding as the input of the network, and the coordinate range is normalized to [-1,1] to facilitate network learning and processing. This is one of the key contents of the present invention.

[0023] Preferably, the MPI image generated by the model in step S14 Perform uniform downsampling according to the size of grid1, and get Among them, the downsampling rate By combining the system matrix S, the predicted response voltage signal y is obtained pre is: y pre =S×Φ d .

[0024] Through this operation, the MPI image reconstruction resolution is expanded by ρ times. The cleverness of the present invention lies in that while completing the MPI image reconstruction task, the image resolution can also be improved at the same time, which is also one of the key contents of the present invention.

[0025] Preferably, the loss function calculation formula in step S15 is:

[0026] loss = ‖y pre -y meas ‖2⑵

[0027] Through continuous iterative calculation, the loss function is minimized and the weight coefficients in the MLP network are optimized. When the number of iterations reaches the preset maximum value, the iteration is stopped and the reconstructed MPI image Φ is output.

[0028] Another aspect of the present invention provides a magnetic nanoparticle image reconstruction system based on NeRF, which includes the following modules:

[0029] The response voltage signal acquisition module is configured to obtain the response voltage signal y collected by the MNPs standard sample (sample to be tested) under the MPI device excitation system. meas ;

[0030] The system matrix acquisition module is configured to set the size of the sampling grid grid1 according to the imaging field of view requirements in the task, that is, the length, width and height are w1, w2, and w3 respectively. A small sample (size of 1 mm3) filled with MNPs standard sample is automatically placed at each grid position under the imaging field of view by a robot or a mechanical arm, and then the MPI device is scanned to obtain the corresponding response voltage signal. The number of frequency points contained in the response signal is M. After all grid positions are scanned, the corresponding system matrix is ​​obtained. Where N = w1×w2×w3 is the number of all grid points;

[0031] The MPI image reconstruction module is configured to stack the calculated grid point coordinates of the full sampling grid grid2 along the x direction to obtain a D×3 coordinate matrix as the input of the MLP model. The model output is the reconstructed MPI image Φ. After uniformly downsampling Φ, Φ is obtained. d , by multiplying it with the system matrix S, we get the predicted response voltage signal y pre , by calculating y pre and meas The L2 loss between them (as shown in Formula 1) is continuously iterated to optimize the model. When the preset number of iterations is reached, the model training is stopped and the MPI high-quality reconstructed image Φ is output.

[0032] This method does not require a large amount of training data to train the model. Instead, it uses the Neural Radiance Field (NeRF) technology to continuously iterate and learn the neural network to update the network parameters, and directly maps the three-dimensional position coordinates in the scene to the MPI image. In terms of system design, the training data set construction module, model training module, model verification module, etc. are omitted, which greatly simplifies the system composition while ensuring the quality of the task.

[0033] Beneficial effects of the present invention:

[0034] (1) The deep learning method is used to solve the inverse problem, which avoids the complex parameter adjustment problems faced in the traditional MPI image reconstruction process and greatly improves the efficiency and stability of the inverse problem solution.

[0035] (2) The present invention does not need to train the model with a large amount of training data. Instead, the neural network is regarded as a field function through the Neural Radiance Field (NeRF) technology, which directly maps the three-dimensional position coordinates in the scene to the MPI image. Through the continuous iterative learning and updating of network parameters by the neural network itself, NeRF can learn continuous three-dimensional MPI reconstructed images from a set of sparse three-dimensional coordinates.

[0036] (3) This method solves the problems of insufficient image resolution and weak model generalization caused by scarce training data when processing MPI image reconstruction based on deep learning. It improves the stability and accuracy of MPI image reconstruction, expands the potential of MPI imaging, and meets the development needs and direction of precision medicine. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Other features, objects and advantages of the present application will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings:

[0038] Figure 1 It is a schematic flow chart of a magnetic nanoparticle image reconstruction method based on NeRF according to an embodiment of the present invention;

[0039] Figure 2 It is a schematic diagram of the framework of a magnetic nanoparticle image reconstruction system based on NeRF according to an embodiment of the present invention;

[0040] Figure 3 is a schematic diagram of generating a spatial grid coordinate matrix according to an embodiment of the present invention;

[0041] Figure 4 is a schematic diagram of reconstruction results of a magnetic nanoparticle image reconstruction method based on NeRF according to an embodiment of the present invention;

[0042] Figure 5It is a schematic diagram of the training process of a NeRF-based magnetic nanoparticle image reconstruction method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The present application will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the relevant invention, rather than to limit the invention. It is also necessary to explain that, for ease of description, only the parts related to the relevant invention are shown in the accompanying drawings.

[0044] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0045] The NeRF-based magnetic nanoparticle image reconstruction method of the present invention comprises the following steps:

[0046] Step S11: Select a type of MNPs as the sample to be tested, and obtain the response voltage signal of the MNPs sample based on the MPI device represents the complex data form, M represents the number of frequencies of the signal;

[0047] Step S12: Acquire the system matrix of the length, width and height (w1, w2, w3) of the undersampling grid grid1 set by MPI imaging N represents the number of all grid points in the undersampling grid, that is, N = w1 × w2 × w3;

[0048] Step S13: Construct a fully connected network model MLP. The model input is the spatial coordinate matrix transformed according to the full sampling grid grid2, and the model output is the image reconstructed by MPI Where D is the size of the full sampling grid, that is, D = d1 × d2 × d3, d1, d2, d3 represent the length, width, and height of the full sampling grid grid2 respectively;

[0049] Step S14: Downsample the MPI image generated in the above step to obtain a downsampled image. Then Φ d Multiplying with the system matrix S, we get the predicted response voltage signal

[0050] Step S15: Iteratively calculate the loss function and return it to continuously optimize the weight coefficients in the MLP. After the iteration is completed, the optimal MPI high-quality image Φ is obtained.

[0051] In order to more clearly illustrate the NeRF magnetic nanoparticle image reconstruction method of the present invention, the following is combined with Figure 1 Each step in the embodiment of the present invention is described in detail.

[0052] The NeRF magnetic nanoparticle image reconstruction method of the first embodiment of the present invention includes steps S11 to S12, each of which is described in detail as follows:

[0053] Step S11, select a type of MNPs as a sample to be detected, and obtain the response voltage signal of the MNPs sample based on the MPI device represents the complex data form, M represents the number of frequencies of the signal;

[0054] The magnetic nanoparticle imaging system includes a gradient scanning integrated unit, an excitation scanning integrated unit, a low-frequency scanning unit, and a signal receiving unit:

[0055] The gradient scanning integrated unit constructs a magnetic field free point (FFP) by passing a DC current through a symmetrical coil, and then passes a low-frequency cosine current so that the FFP area can move along the z direction of the field of view (FOV), thereby completing the z-direction scanning of the field of view.

[0056] The excitation scanning integrated unit generates an excitation magnetic field by passing a high-frequency alternating current through the axial coil to excite the MNPs in the FFP to produce a nonlinear response signal. At the same time, by controlling the excitation voltage, the FFP can be moved along the x-direction of the field of view, thereby completing the x-direction scanning of the field of view.

[0057] The low-frequency scanning unit passes a low-frequency cosine current through a symmetrical coil, so that the FFP moves along the y direction of the field of view, thereby completing the y-direction scanning of the field of view.

[0058] The signal receiving unit, which integrates the receiving coil and the data acquisition circuit, is responsible for collecting the response signals generated by the MNPs and storing them.

[0059] The method for obtaining the response voltage signal of the MNPs sample is as follows:

[0060] Prepare a MNPs standard sample with an iron concentration of 0.5 mg / mL and a volume of 0.5 mL;

[0061] Place the MNPs standard sample in the center of the imaging field of view of the MPI device;

[0062] The excitation magnetic field and the scanning magnetic field are continuously moved in the field of view to complete the scanning, and the response voltage signal y of the MNPs standard sample is obtained. meas .

[0063] Step S12, collecting the system matrix of the length, width and height (w1, w2, w3) of the undersampling grid grid1 set by MPI imaging N represents the number of all grid points in the under-sampling grid, that is, N=w1×w2×w3.

[0064] The method for obtaining the system matrix is ​​as follows:

[0065] According to the size of the undersampling grid grid1 set during MPI imaging, that is, the length, width, and height are w1, w2, and w3 respectively, a small sample (size 1mm3) filled with MNPs standard sample is automatically placed at each grid position under the imaging field of view using a robot or a mechanical arm, and then the MPI device is scanned to obtain the corresponding response voltage signal. The voltage signal collected at each position is used as a column of the system matrix, and the number of frequency points contained in the response signal is M. After all grid positions are scanned, the corresponding system matrix is ​​obtained.

[0066] Step S13, construct a fully connected network model MLP, the model input is the spatial coordinate matrix transformed according to the full sampling grid grid2, and the model output is the image reconstructed by MPI Wherein, D is the full sampling grid size, that is, D = d1×d2×d3, d1, d2, d3 represent the length, width, and height of the full sampling grid grid2 respectively.

[0067] The fully connected network model MLP includes 8 fully connected layers, and the number of nodes in each layer is 256.

[0068] like Figure 3 As shown, the grid2 coordinate matrix setting method of the model input is:

[0069] Each pixel in the grid is encoded with a unique coordinate based on the position information. Δd1, Δd2, Δd3 are the grid point spacing sizes along the x, y, and z directions, respectively, and d1, d2, d3 are the number of all grid points in the x, y, and z directions, respectively. We normalize the grid point coordinate range to [-1, 1], so the grid point spacing sizes are: Δd1 = 2 / (d1-1), Δd2 = 2 / (d2-1), Δd3 = 2 / (d3-1). These grid point coordinates are stacked along the x direction to obtain a D×3 matrix, and D is defined as D = d1×d2×d3.

[0070] Step S14, downsampling the MPI image generated in step S13 to obtain a downsampled image Then Φ d Multiplying with the system matrix S, we get the predicted response voltage signal

[0071] In the downsampling operation, the downsampling rate is set to ρ is an integer. The larger the ρ is set, the higher the final MPI image resolution will be. By combining the system matrix S, the predicted response voltage signal y is obtained. pre is: y pre =S×Φ d .

[0072] Step S15, iteratively calculate the loss function and return it to continuously optimize the weight coefficients in the MLP. After the iteration is completed, the optimal MPI high-quality image Φ is obtained.

[0073] The process of iterative calculation and optimization of the model is as follows Figure 5 As shown in the figure, first, the grid point coordinates are set as the input of the network model. Secondly, the network model outputs the MPI reconstructed image. Then, after downsampling and system matrix multiplication operations, the predicted response voltage signal is obtained. The measured response voltage signal is used as the true value, and the loss function is calculated with the predicted value and returned to continuously optimize the parameters of the network. Finally, the preset maximum number of iterations is reached, the calculation stops, and a high-quality MPI reconstructed image is output.

[0074] The loss function calculation method is:

[0075] loss = ‖y pre -y meas ‖2⑶

[0076] Through continuous iterative calculation, the loss function is minimized and the weight coefficients in the MLP network are optimized. When the number of iterations reaches the preset maximum value, the iteration is stopped and the reconstructed MPI image Φ is output.

[0077] The maximum number of iterations is set to 1500. Figure 4 As shown in the figure, the number of iterations will affect the image reconstruction quality. After the number of iterations reaches 1500, the image quality does not improve significantly as the number of iterations increases. Therefore, 1500 is set as the final number of iterations.

[0078] A magnetic nanoparticle image reconstruction system based on NeRF according to a second embodiment of the present invention is as follows: Figure 2 As shown, it includes: a response voltage acquisition module, a system matrix acquisition module, and an image reconstruction module;

[0079] The response voltage acquisition module is configured to acquire the response voltage signal y collected by the MNPs standard sample (sample to be tested) under the MPI device excitation system. meas ;

[0080] The system matrix acquisition module is configured to set the size of the sampling grid grid1 according to the imaging field of view requirements in the task, that is, the length, width, and height are w1, w2, and w3 respectively. A small sample (size 1mm3) filled with MNPs standard sample is automatically placed at each grid position under the imaging field of view by a robot or a mechanical arm, and then the MPI device is scanned to obtain the corresponding response voltage signal. The number of frequency points contained in the response signal is M. After all grid positions are scanned, the corresponding system matrix is ​​obtained. Where N = w1×w2×w3 is the number of all grid points;

[0081] The MPI image reconstruction module is configured to stack the calculated grid point coordinates of the full sampling grid grid2 along the x direction to obtain a D×3 coordinate matrix as the input of the MLP model. The model output is the reconstructed MPI image Φ. After uniformly downsampling Φ, Φ is obtained. d By multiplying it with the system matrix S, the predicted response voltage signal y is obtained. pre By calculating y pre and meas The L2 loss between them (as shown in Formula 1) is continuously iterated to optimize the model. When the preset number of iterations is reached, the model training is stopped and the MPI high-quality reconstructed image Φ is output.

[0082] It should be noted that the NeRF-based magnetic nanoparticle image reconstruction system provided in the above embodiment is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the modules or steps in the embodiments of the present invention can be decomposed or combined. For example, the modules in the above embodiments can be combined into one module, or further divided into multiple sub-modules to complete all or part of the functions described above. The names of the modules and steps involved in the embodiments of the present invention are only for distinguishing the modules or steps, and are not regarded as improper limitations of the present invention.

[0083] An electronic device according to the third embodiment of the present invention comprises: at least one processor; and a memory communicatively connected to at least one of the processors; wherein the memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the above-mentioned NeRF-based magnetic nanoparticle image reconstruction method.

[0084] A computer-readable storage medium according to a fourth embodiment of the present invention stores computer instructions, and the computer instructions are used to be executed by the computer to implement the above-mentioned NeRF-based magnetic nanoparticle image reconstruction method. A person skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process and related instructions of the storage device and the processing device described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0085] The terms "first", "second", etc. are used to distinguish similar objects rather than to describe or indicate a particular order or sequence.

[0086] The term "comprise" or any other similar term is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus / device that includes a list of elements includes not only those elements but also other elements not expressly listed, or also includes elements inherent to such process, method, article, or apparatus / device.

[0087] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A magnetic nanoparticle image reconstruction method based on NeRF, characterized in that: The method comprises the following steps: Step S11: Select a type of MNPs as the sample to be tested, and obtain the response voltage signal of the MNPs sample based on the MPI device represents the complex data form, M represents the number of frequencies of the signal; Step S12: Acquire the system matrix of the length, width and height (w1, w2, w3) of the undersampling grid grid1 set by MPI imaging N represents the number of all grid points in the undersampling grid, that is, N = w1×w2×w3; Step S13: Construct a fully connected network model MLP. The model input is the spatial coordinate matrix transformed according to the full sampling grid grid2, and the model output is the image reconstructed by MPI Where D is the size of the full sampling grid, that is, D = d1 × d2 × d3, d1, d2, d3 represent the length, width, and height of the full sampling grid grid2 respectively; Step S14: Downsample the MPI image generated in the above step to obtain a downsampled image. Then Φ d Multiplying with the system matrix S, we get the predicted response voltage signal Step S15: Iteratively calculate the loss function and return it to continuously optimize the weight coefficients in the MLP. After the iteration is completed, the optimal MPI high-quality image Φ is obtained.

2. The NeRF-based magnetic nanoparticle image reconstruction method according to claim 1, characterized in that: In step S11, the response voltage signal of the sample MNPs to be detected is obtained by: Prepare a MNPs standard sample with an iron concentration of 0.5 mg / mL and a volume of 0.5 mL; Place the MNPs standard sample in the center of the imaging field of view of the MPI device; The scanning is completed by continuously moving the exciting magnetic field in the field of view, and the response voltage signal y of the MNPs standard sample is obtained. meas .

3. The NeRF-based magnetic nanoparticle image reconstruction method according to claim 1, characterized in that: In step S12, the system matrix S is obtained by: According to the size of the undersampling grid grid1 set during MPI imaging, that is, the length, width, and height are w1, w2, and w3 respectively, a small sample (size 1 mm3) filled with MNPs standard sample is automatically placed at each grid position under the imaging field of view by a robot or a mechanical arm, and then the MPI device is scanned to obtain the corresponding response voltage signal. The number of frequency points contained in the response signal is M. After all grid positions are scanned, the corresponding system matrix is ​​obtained.

4. The NeRF-based magnetic nanoparticle image reconstruction method according to claim 1, characterized in that: The method for setting the grid2 coordinate matrix of the model input in step S13 is: Each pixel in the grid is encoded with a unique coordinate based on the position information. Δd1, Δd2, and Δd3 are the grid point spacing sizes along the x, y, and z directions, respectively. d1, d2, and d3 are the number of all grid points in the x, y, and z directions, respectively. The grid point coordinate range is normalized between [-1, 1], where the grid point spacing sizes are: Δd1 = 2 / (d1-1), Δd2 = 2 / (d2-1), and Δd3 = 2 / (d3-1). These grid point coordinates are stacked along the x direction to obtain a D×3 matrix, and D is defined as D=d1×d2×d3.

5. The NeRF-based magnetic nanoparticle image reconstruction method according to claim 1, characterized in that: In step S14, the predicted response voltage signal y is obtained. pre , the method is: MPI image generated by network model Perform uniform downsampling according to the size of grid1, and get Among them, the downsampling rate By combining the system matrix S, the predicted response voltage signal y is obtained pre is: y pre =S×Φ d .

6. The NeRF-based magnetic nanoparticle image reconstruction method according to claim 1, characterized in that: The loss function calculation formula in step S15 is: loss=‖y pre -y meas ‖2⑴ Through continuous iterative calculation, the loss function is minimized and the weight coefficients in the MLP network are optimized. When the number of iterations reaches the preset maximum value, the iteration is stopped and the reconstructed MPI image Φ is output.

7. A magnetic nanoparticle image reconstruction system based on NeRF, characterized in that: The system includes the following modules: The response voltage signal acquisition module is configured to obtain the response voltage signal y collected by the MNPs standard sample (sample to be tested) under the MPI device excitation system. meas ; The system matrix acquisition module is configured to set the size of the sampling grid grid1 according to the imaging field of view requirements in the task, that is, the length, width and height are w1, w2, and w3 respectively. A small sample (size of 1 mm3) filled with MNPs standard sample is automatically placed at each grid position under the imaging field of view by a robot or a mechanical arm, and then the MPI device is scanned to obtain the corresponding response voltage signal. The number of frequency points contained in the response signal is M. After all grid positions are scanned, the corresponding system matrix is ​​obtained. Where N = w1×w2×w3 is the number of all grid points; The MPI image reconstruction module is configured to stack the calculated grid point coordinates of the full sampling grid grid2 along the x direction to obtain a D×3 coordinate matrix as the input of the MLP model. The model output is the reconstructed MPI image Φ. After uniformly downsampling Φ, Φ is obtained. d , by multiplying it with the system matrix S, the predicted response voltage signal y is obtained pre , by calculating y pre and meas The L2 loss between them (as shown in Formula 1) is continuously iterated to optimize the model. When the preset number of iterations is reached, the model training is stopped and the MPI high-quality reconstructed image Φ is output.

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