A method for improving MPI image resolution based on a physical model

Abstract

This application belongs to the field of signal imaging technology. It provides a method for generating high-resolution MPI images based on a physical model. The embodiments disclosed herein use an adaptive compensation method to cancel feedthrough interference signals, preserving the fundamental frequency of the particle signal. Therefore, complete magnetic particle nonlinear response signals can be obtained without filtering and fundamental frequency recovery, thereby improving the quality and resolution of the X-space reconstructed image. Furthermore, based on the recovered X-space reconstructed image, an X-space imaging physical model is established. Based on this model, a spatial iterative deconvolution algorithm is used to solve for the magnetic particle concentration distribution. TV regularization is used to constrain noise, and L1 sparse prior is used to reduce the iterative error of the model and increase its generalization ability. Based on this method, the MPI reconstruction resolution can be improved by several times, and even in low signal-to-noise ratio environments, a spatial resolution better than 1 mm can be achieved.

Description

Technical Field

[0001] This disclosure relates to the field of signal imaging technology, and in particular to a method for improving the resolution of MPI images based on a physical model. Background Technology

[0002] Magnetic particle imaging (MPI) is an emerging medical imaging technique that can image the distribution of superparamagnetic iron oxide nanoparticles (SPIO). Since its introduction in 2005, MPI has been widely used in bioimaging. MPI images exhibit positive contrast and good depth penetration, with no background tissue signal. Furthermore, MPI does not involve ionizing radiation, and SPIO tracers are biocompatible and renal safe; therefore, MPI is well-suited for clinical molecular imaging applications.

[0003] MPI utilizes field-free points (FFPs) or field-free lines to scan the entire field of view (FOV) along a specific trajectory, and uses receiving coils to collect the nonlinear response signal of the MNPS during the scan. Then, a reconstruction algorithm is used to map the voltage signal to the MNP concentration distribution. Currently, commonly used MPI reconstruction methods are system matrix reconstruction and X-space reconstruction. First, system matrix-based image reconstruction has higher image resolution than X-space-based methods, but SM calibration measurements are very time-consuming. Furthermore, if the tracer characteristics or magnetic field environment change, SM needs to be remeasured and recalibrated, further increasing the complexity of the method. Moreover, in large-field-of-view MPI devices, the system matrix measurement time becomes immeasurable, and system matrix storage also presents challenges. Although many sparse methods exist to reduce the number of system matrix measurements and alleviate storage pressure, they also result in a loss of reconstruction quality.

[0004] X-space reconstruction is a physical model-based method. The X-space reconstruction algorithm maps the time-domain signal of the nonlinear response of magnetic particles to the spatial domain according to the FFP position for image representation. It features real-time image reconstruction and omits the complex system function calibration measurement process. The X-reconstructed image is shown below. Figure 1 (h) and Figure 1 As shown in (b). However, severe feedthrough interference exists in MPI systems, which reduces the system's signal-to-noise ratio and causes a decrease in X-space reconstruction resolution, such as... Figure 1 (f) and Figure 1As shown in (c). Currently, a high-pass filter is used to remove feedthrough interference signals. However, this leads to the loss of the fundamental frequency of the particle signal, thereby compromising the shift invariance of the system and causing errors in X-space reconstruction, such as... Figure 1 (g) and Figure 1 As shown in (d), to address the fundamental frequency loss problem, Kuan Lu estimated the lost fundamental frequency signal by maximizing the continuity between the p-th FOV scan and its previous scans in the overlapping region. Semih Kurt reduced reconstruction artifacts caused by fundamental frequency loss by employing pFOV center imaging technology and improved the reconstruction quality of X-space based on deconvolution methods. Although fundamental frequency recovery methods are relatively mature, filtering and recovery always lead to the loss of fundamental frequency signal, resulting in compromised X-space reconstruction quality and resolution. More importantly, the physical model of X-space reconstruction can be represented as the magnetic particle concentration distribution convolved with the point spread function of the MPI system. The blurring effect of the point spread function leads to a reduction in the resolution of the X-space reconstructed image, as shown in [example missing]. Figure 1 As shown in (b), the X-space reconstructed image cannot distinguish... Figure 1 (a) Line pair phantom.

[0005] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0006] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0007] The purpose of this disclosure is to provide a method for improving the resolution of MPI images based on a physical model, thereby overcoming, at least to some extent, one or more problems caused by the limitations and defects of related technologies.

[0008] According to embodiments of this disclosure, a method for improving the resolution of MPI images based on a physical model is provided, the method comprising:

[0009] The feedthrough interference signal is acquired, and the feedthrough interference signal is canceled using an adaptive compensation method to obtain the complete magnetic particle nonlinear response signal.

[0010] The nonlinear response signal of the magnetic particles is processed using an MPI system to obtain an X-space reconstructed image;

[0011] An X-space imaging physical model is constructed based on a dual Richardson-Lucy deconvolution algorithm with TV regularization and a spatial iterative deconvolution algorithm. The X-space reconstructed image is then processed using the X-space imaging physical model to obtain an MPI image.

[0012] Furthermore, the step of acquiring the feedthrough interference signal and using an adaptive compensation method to cancel the feedthrough interference signal to obtain the complete magnetic particle nonlinear response signal includes:

[0013] The feedthrough interference signal was collected under no-load conditions. amplitude and phase ;

[0014] Based on the amplitude of the feedthrough interference signal and phase Obtain compensation signal ;

[0015] The compensation signal With feedthrough interference signal The signals are subtracted in the LNA and the phase of the compensated signal is compensated according to an adaptive compensation method to obtain the optimal low-noise signal.

[0016] Based on the optimal low-noise signal, the magnetic particle response signal is acquired to obtain the magnetic particle nonlinear response signal.

[0017] Furthermore, the step of compensating the phase of the compensated signal according to the adaptive compensation method to obtain the optimal low-noise signal includes:

[0018] The compensation signal is compensated, and the step size of the phase compensation for each compensation is... ;

[0019] Determine the compensated signal after compensation. With feedthrough interference signal Whether the low-noise signal subtracted in the LNA is stable;

[0020] If stable, output the phase change of the adaptively compensated signal. And the corresponding low-noise signal; among which, , where n represents the number of adaptive compensations;

[0021] If it is unstable, continue to compensate the compensation signal.

[0022] Furthermore, the feedthrough interference signal The expression is:

[0023]

[0024] in, The magnetic field frequency, For low noise in MPI systems, For time;

[0025] The expression for the low-noise signal is:

[0026]

[0027]

[0028]

[0029] in, ;

[0030] The expression for the nonlinear response signal of the magnetic particles is:

[0031]

[0032] in, This is the response signal of magnetic particles.

[0033] Furthermore, the expression for the X-space reconstructed image is:

[0034]

[0035] in, This represents an X-space reconstructed image. Indicates the spatial concentration distribution of magnetic particles. Represents the spatial convolution kernel of the MPI system. The spatial distribution function of noise.

[0036] Furthermore, the step of constructing an X-space imaging physical model based on a TV-regularized dual Richardson-Lucy deconvolution algorithm and a spatial iterative deconvolution algorithm, and then processing the X-space reconstructed image using the X-space imaging physical model to obtain an MPI image, includes:

[0037] An X-space imaging physical model is constructed based on a TV-regularized dual Richardson-Lucy deconvolution algorithm and a spatial iterative deconvolution algorithm.

[0038] The spatial convolution kernel of the MPI system is estimated using the TV-regularized dual Richardson-Lucy deconvolution algorithm.

[0039] The spatial concentration distribution of magnetic particles is solved using a spatial iterative deconvolution algorithm to obtain the MPI image.

[0040] Furthermore, the expression for the TV-regularized dual Richardson-Lucy deconvolution algorithm is as follows:

[0041]

[0042]

[0043] in, For the first Spatial concentration distribution of magnetic particles in the next iteration. For the first Spatial concentration distribution of magnetic particles in the next iteration. for, First regularization parameter, This is the second regularization parameter. For the convolution kernel estimated in one iteration, As the input for one iteration, () represents the divergence calculation function.

[0044] Furthermore, the spatial iterative deconvolution algorithm includes:

[0045] Based on the sparsity and smoothness characteristics of MPI images, the cost function to be minimized is established as follows:

[0046]

[0047] in, This is a weighting factor for fidelity. , representing the spatial distribution of magnetic particle concentration; , represents the spatial convolution kernel of the MPI system; , representing the X-space reconstructed image; For TV regularization, For TV regularization parameters; For L1 regularization, The regularization parameter for sparse priors;

[0048] beg The derivative is obtained as follows:

[0049]

[0050] in, .

[0051] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects:

[0052] In the embodiments of this disclosure, the method for improving MPI image resolution based on the physical model described above achieves several advantages. Firstly, by using an adaptive compensation method to cancel feedthrough interference signals and preserve the fundamental frequency of the particle signal, the complete magnetic particle nonlinear response signal can be obtained without filtering and fundamental frequency recovery, thereby improving the quality and resolution of the X-space reconstructed image. Furthermore, based on the recovered X-space reconstructed image, an X-space imaging physical model is established. Based on this model, a spatial iterative deconvolution algorithm is used to solve for the magnetic particle concentration distribution. TV regularization is used to constrain noise, and L1 sparse priors are used to reduce the model's iterative error and increase its generalization ability. Secondly, based on this method, the MPI reconstruction resolution can be improved by several times, and even in low signal-to-noise ratio environments, a spatial resolution better than 1 mm can be achieved. Simultaneously, this method achieves high-resolution magnetic particle concentration distribution reconstruction without complex system function acquisition and calibration processes. Attached Figure Description

[0053] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0054] Figure 1 This diagram illustrates a 1D MPI signal link in the prior art, simulated using a two-point phantom.

[0055] Figure 2 The diagram illustrates the steps of a method for improving the resolution of an MPI image based on a physical model, as shown in an exemplary embodiment of this disclosure.

[0056] Figure 3 This diagram illustrates a flowchart of the adaptive compensation method for signal processing in an exemplary embodiment of this disclosure.

[0057] Figure 4 This diagram illustrates a single-receive-channel MPI device in an exemplary embodiment of this disclosure.

[0058] Figure 5 The diagram illustrates the effect of using point spreads with different full width at half maximum (FWHM) for MPI image deconvolution in an exemplary embodiment of this disclosure.

[0059] Figure 6 The diagram shows a comparison of the results of two-dimensional image reconstruction of line pairs phantoms with spacing of 0.5 mm, 1 mm, 1.5 mm and 2 mm in the X direction using the RL method and the spatial iterative deconvolution method in an exemplary embodiment of this disclosure.

[0060] Figure 7 This embodiment of the present disclosure illustrates the use of the RL method and the spatial iterative deconvolution method to reconstruct two-dimensional images of line pairs phantoms with spacing of 0.5 mm, 1 mm, 1.5 mm, and 2 mm in the Y direction. Detailed Implementation

[0061] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0062] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0063] X-space reconstruction is a physical model-based method. The X-space reconstruction algorithm maps the time-domain signal of the nonlinear response of magnetic particles to the spatial domain according to the FFP position for image representation. It features real-time image reconstruction and omits complex system function calibration and measurement processes. The X-reconstructed image is shown below. Figure 1 (h) and Figure 1 As shown in (b). However, severe feedthrough interference exists in MPI systems, which reduces the system's signal-to-noise ratio and causes a decrease in X-space reconstruction resolution, such as... Figure 1 (f) and Figure 1 As shown in (c). Currently, a high-pass filter is used to remove feedthrough interference signals. However, this leads to the loss of the fundamental frequency of the particle signal, thereby compromising the shift invariance of the system and causing errors in X-space reconstruction, such as... Figure 1 (g) and Figure 1As shown in (d), to address the fundamental frequency loss problem, Kuan Lu estimated the lost fundamental frequency signal by maximizing the continuity between the pFOV scan and its previous scans in the overlapping region. Semih Kurt reduced reconstruction artifacts caused by fundamental frequency loss by employing pFOV center imaging and improved the reconstruction quality of X-space based on deconvolution methods. Although fundamental frequency recovery methods are relatively mature, filtering and recovery always lead to the loss of fundamental frequency signal, resulting in compromised X-space reconstruction quality and resolution. More importantly, the physical model of X-space reconstruction can be represented as the magnetic particle concentration distribution convolved with the point spread function of the MPI system. The blurring effect of the point spread function leads to a reduction in the resolution of the X-space reconstructed image, such as... Figure 1 As shown in (b), the X-space reconstructed image cannot distinguish... Figure 1 (a) Line pair phantom.

[0064] Figure 1 middle, Figure 1 (a) represents the excitation magnetic field. Figure 1 (b) indicates the 1D MPI received signal. Including feedthrough interference signals and nonlinear response signal of magnetic particles . Figure 1 Paths 1, 2, and 3 on the right represent the received signals. Three different processing procedures:

[0065] Path 1 indicates that the received signal is used directly. X-space reconstruction was performed, and the reconstructed image is shown in Figure (e). Physical model analysis showed that IMG1 could not be deconvolved. Path 2 indicates the use of a high-pass filter to remove feedthrough interference. The fundamental frequency component of the magnetic particle signal is shown in Figure (c). The X-space reconstruction result using the signal in Figure (c) is as follows: Figure 1 As shown in (f), physical model analysis shows that IMG1 cannot undergo deconvolution processing. Path 3 indicates the use of a feedthrough interference suppression method to obtain the nonlinear response signal of magnetic particles. ,like Figure 1 As shown in (d), the following is adopted: Figure 1 (d) The signal X-space reconstruction results are as follows Figure 1 As shown in (g), Figure 1 (h) indicates according to Figure 1 (g) The IMG3 convolutional physics model uses deconvolution to solve for the magnetic particle concentration distribution. .

[0066] This example implementation provides a method for improving the resolution of MPI images based on a physical model. (Reference) Figure 2 As shown, the method for improving the resolution of MPI images based on a physical model may include steps S101 to S103.

[0067] Step S101: Obtain the feedthrough interference signal and use an adaptive compensation method to cancel the feedthrough interference signal to obtain the complete magnetic particle nonlinear response signal;

[0068] Step S102: Process the nonlinear response signal of the magnetic particles using the MPI system to obtain the X-space reconstructed image;

[0069] Step S103: Construct an X-space imaging physical model based on the dual Richardson-Lucy deconvolution algorithm with TV regularization and the spatial iterative deconvolution algorithm. Use the X-space imaging physical model to process the X-space reconstructed image to obtain an MPI image.

[0070] The method described above for improving MPI image resolution based on a physical model achieves several advantages. Firstly, by using an adaptive compensation method to cancel feedthrough interference signals and preserve the fundamental frequency of the particle signal, the complete magnetic particle nonlinear response signal can be obtained without filtering and fundamental frequency recovery, thus improving the quality and resolution of the X-space reconstructed image. Furthermore, based on the recovered X-space reconstructed image, an X-space imaging physical model is established. This model employs a spatial iterative deconvolution algorithm to solve for the magnetic particle concentration distribution, uses TV regularization to constrain noise, and employs L1 sparse priors to reduce iterative errors and increase generalization ability. Secondly, this method can improve MPI reconstruction resolution by several times, and even in low signal-to-noise ratio environments, it can achieve a spatial resolution better than 1 mm. Moreover, this method achieves high-resolution magnetic particle concentration distribution reconstruction without complex system function acquisition and calibration processes.

[0071] Below, we will refer to Figures 2 to 7 The steps of the physical model-based method for improving MPI image resolution described in this example embodiment will be explained in more detail.

[0072] In step S101, this application employs an FPGA-based adaptive compensation system to cancel feedthrough interference signals and obtain complete particle signals. As shown in equation (1), the signal collected by the receiving coil consists of the particle nonlinear response signal and the feedthrough interference signal.

[0073] (1)

[0074]

[0075] in: For the sensitivity of the receiving coil, The permeability of free space, Indicates the applied magnetic field strength. This represents the total magnetization of all magnetic particles within the field of view. This represents the nonlinear response signal of magnetic particles. Indicates a direct feedthrough signal. This represents white noise in the system.

[0076] Feedthrough interference signal As an interference signal, its amplitude is the magnetic particle response signal. Several orders of magnitude higher, assuming the magnetic field lines inside the excitation coil are parallel and uniformly distributed, and the sensitivity distribution of the receiving coil is uniform. ,but:

[0077]

[0078] (2)

[0079]

[0080] in, Indicates the magnetic field strength through the plane of the coil , Indicates the amplitude of the magnetic field. Indicates the frequency of the magnetic field. Indicates the phase of the magnetic field. S Represents the area vector of the coil. This indicates the amplitude of the direct feedthrough signal.

[0081] Electromagnetic coupling between the MPI excitation coil and the receiving coil contaminates the fundamental frequency of the received signal. Currently, there are three methods for suppressing feedthrough interference: filtering, passive compensation, and active compensation. The filtering method uses a filter to remove the fundamental frequency of the magnetic particle response signal and the feedthrough interference signal, and then uses a fundamental frequency recovery method to restore the fundamental frequency of the particle signal. The passive compensation method is based on the electromagnetic mutual inductance theory and usually uses two- or three-segment gradient probe coils to suppress the feedthrough interference signal. However, in MPI, the passive compensation effect is limited because there is a phase difference between the coupling signals of the receiving and compensation coils to the excitation field (Supplementary Note 2). The active compensation method cancels the feedthrough interference signal by outputting the compensation signal through a subtractor, thereby preserving the complete particle nonlinear response signal. In this application, an FPGA-based adaptive compensation system is proposed to cancel the feedthrough interference signal and obtain the complete particle signal. As shown in Equation (1), the signal collected by the receiving coil consists of the particle nonlinear response signal and the feedthrough interference signal. As shown in equation (2), the feedthrough interference is a single-frequency sinusoidal signal. Therefore, a compensation signal can be generated by obtaining the amplitude and phase information of the feedthrough interference signal. The adaptive compensation method of this application is as follows: Figure 3 As shown. The method proposed in this application can cancel feedthrough interference signals in real time, ensuring real-time X-space reconstruction.

[0082] The FPGA-based adaptive compensation feedthrough interference suppression process consists of three steps, such as... Figure 3 The diagram shown is a flowchart of adaptive compensation signal processing. It consists of three parts: 1) controlling the output of the excitation signal and acquiring the feedthrough interference signal; 2) adaptive compensation; and 3) acquiring the magnetic particle signal.

[0083] 1) Acquiring feedthrough interference signals under background measurement conditions amplitude and phase .

[0084] (7)

[0085] 2) Adaptive compensation. Based on the amplitude obtained in 1). and phase Output compensation signal = ,in express n Phase change of the compensated signal after adaptive compensation , This indicates the step size for phase compensation. Compensation signal. With feedthrough interference signal Subtract from the LNA. As shown in equation (8), by adjusting make Less than the custom threshold voltage Lower noise than MPI systems .

[0086]

[0087]

[0088] (8)

[0089] in .

[0090] 3) Acquire magnetic particle response signals. Adaptive compensation feedthrough interference suppression is used when... Magnetic particle samples are placed in the sample and the magnetic particle response signal is collected.

[0091] (9)

[0092] The adaptive compensation method can suppress feedthrough interference signals, obtain complete magnetic particle nonlinear response signals, preserve the LSI characteristics of MPI scanning, and improve the quality and resolution of X-space reconstructed images. The adaptive compensation algorithm is shown in Algorithm 1.

[0093]

[0094] In a specific embodiment, this application implements an adaptive compensation method. An adaptive compensation system suitable for MPI systems was developed based on an FPGA. Using an Artix@7 XC7A35T FPGA chip, functions such as 4-channel synchronous acquisition, 4-channel asynchronous signal output, adaptive compensation, and system control were implemented. The system's ADC has a maximum sampling rate of 4 MSPS (Sample / second), and the MAX5719 can achieve a single-channel sampling rate of 10 MSPS in 20-bit mode, with a maximum output frequency of 500kHz. Based on this hardware foundation, the phase and amplitude of the feedthrough interference signal are obtained within the FPGA via FFT. The MAX5719 can stably output a 25kHz active compensation signal with the same frequency as the feedthrough interference. The output compensation signal and the feedthrough interference are then canceled out in an LNA SR560. Finally, the amplitude of the subtracted feedthrough interference signal is used as a judgment condition; adaptive compensation is completed when the amplitude of the subtracted feedthrough interference signal is lower than a set threshold voltage. The integrated MPI system is as follows: Figure 4 As shown, this adaptive compensation system can achieve device integration without increasing system complexity and improve device robustness.

[0095] like Figure 4 The image shows a self-developed single-receiver channel MPI device. Figure 4 (a) represents an FPGA-based MPI adaptive compensation system. The AD7380 is a 4-channel 18-bit synchronous ADC chip that acquires the XY drive current signal, excitation current signal, and single-channel receiving coil signal. The MAX5719 is a 20-bit single-channel DAC chip; three MAX5719 DACs output the XY drive signal and excitation signal respectively. The AD3541R is a 16-bit single-channel DAC chip that outputs a compensation signal to cancel feedthrough interference signals. Figure 4 (b) represents the MPI system architecture, including the MPI power supply module, scanning equipment, and acquisition control system.

[0096] In steps S102 and S103, based on the magnetic particle response signal The magnetic particles and their concentration distribution were obtained. The relationship between the response signal and the response signal is shown in equation (3).

[0097] (3)

[0098] in, The nonlinear response process of magnetic particles can be represented by convolution:

[0099] (4)

[0100] in The derivative of the excitation field can be represented in equation (4) as the velocity of the FFP point. This indicates the magnetic particle concentration distribution. This represents the point spread function (convolution kernel) of the MPI system. This represents the position of the FFP point at time t. After normalizing the FFP's movement velocity and mapping the particle's nonlinear response signal to the image domain based on the FFP's position, a reconstructed X-space image can be obtained.

[0101] (5)

[0102] From equation (5), it can be seen that the x-space reconstruction can be expressed as the convolution of the magnetic particle concentration distribution and the point spread function of the MPI system. Therefore, the FWHM can be used to represent the imaging resolution of the X-space, and the FWHM of the point spread function of the MPI imaging system can be expressed as:

[0103] (6)

[0104] in, Related to the properties of magnetic particles, This indicates the selection of the field gradient.

[0105] MPI imaging is used to image the concentration distribution of magnetic particles, but the X-space resolution is reduced due to the presence of convolution kernels (blur kernels). To improve the resolution of MPI imaging, deconvolution operations can be used.

[0106] According to Equation (9), the signal after feedthrough interference suppression consists of the nonlinear response signal of magnetic particles and noise. Equation (5) represents the one-dimensional X-space imaging convolution model.

[0107] According to equation (5), X-space reconstruction can be expressed as the convolution of the magnetic particle concentration distribution and the point spread function of the MPI system. Moreover, the resolution of the X-space reconstructed image is limited by the point spread function, as shown in equation (6). In the MPI system, to more clearly express the X-space imaging properties, we adopt a more intuitive mathematical analytical expression. The X-space imaging process can be modeled as the convolution of the blur function and the magnetic particle concentration distribution, and then a noise term is added, as shown in equation (10).

[0108] (10)

[0109] in, This represents an X-space reconstructed image. The spatial concentration distribution of magnetic particles is to be solved. Represents the spatial convolution kernel of the MPI system, and the unknowns. Let represent the spatial distribution function of the noise. In equation (10), is used to solve... Therefore, a deconvolution method is needed.

[0110] (1) Estimating the spatial convolution kernel of the MPI system

[0111] When solving for the spatial concentration distribution of magnetic particles, it is necessary to know... and , The point spread function of the MPI system can be solved by x-space reconstruction. Unknown. Currently, point phantoms are used to measure the spatial convolution kernel in MPI systems, but the measurement result is the convolution of the actual point spread function of the MPI system with the point phantom, which cannot be used as the system's spatial convolution kernel to solve for the spatial concentration distribution of magnetic particles. Therefore, this application adopts a blind deconvolution method (TV-regularized double Richardson-Lucy deconvolution) to estimate the spatial convolution kernel of the MPI system.

[0112] (11)

[0113] (12)

[0114] The spatial convolution kernel estimation for the MPI system is shown in Algorithm 2. This method requires X-space images of point phantom measurements as initialization for the algorithm, thereby accelerating its convergence.

[0115]

[0116] (2) Estimation of spatial concentration distribution of magnetic particles (spatial iterative deconvolution)

[0117] Based on the estimation of the spatial convolution kernel, the spatial concentration distribution of magnetic particles can be estimated. In this application, the deconvolution model of the spatial concentration distribution of magnetic particles can be solved by an optimization problem, and based on the sparsity and smoothness characteristics of MPI images, a minimized cost function is established as follows:

[0118] (13)

[0119] The first term is the fidelity term, representing the estimated fidelity. The convolution result and the input image The distance, of which The first term is a fidelity weighting factor used to balance image fidelity during iteration. The second term is TV regularization, which suppresses more noise and preserves better edge information. The third term... The l1 regularization term provides sparse prior information about the MPI image. The regularization parameter for the sparse prior is used to balance the sparse features of the image during the iteration process.

[0120] beg The derivative is shown in equation (14):

[0121] (14)

[0122] in The first term in equation (14) is consistent with the derivative of the likelihood estimate under the standard Richardson-Lucy deconvolution Gaussian distribution. This application uses AdamW to solve this convolution model. AdamW is an adaptive solution method with smaller generalization error compared to Adam. The spatial iterative deconvolution method proposed in this application is shown in Algorithm 3.

[0123]

[0124] In this application, the point spread function of the MPI system is estimated based on the X-space reconstructed image after adaptive compensation, using a TV-regularized dual Richardson-Lucy deconvolution method. Finally, the spatial deconvolution model proposed in this application is used to solve for the spatial distribution of magnetic particles. .

[0125] In a specific embodiment, accurately estimating the point spread function (PSF) of the MPI system is required to solve for the magnetic particle concentration distribution using the deconvolution method based on the X-space reconstructed image. A 1mm point phantom was used for testing. First, the X-space reconstruction method was used to obtain a reconstructed image of the 1mm phantom. Then, the dual Richardson-Lucy deconvolution method was used to predict the system's point spread. Based on the different prediction results of the PSF, the deconvolution method of this application (γ=0.0011, α=0.0022, β=0.002) was used to test the influence of the PSF on the deconvolution. The results are as follows: Figure 5 As shown.

[0126] To further illustrate the effectiveness of the spatial iterative deconvolution method in improving resolution, experiments were conducted using line-pair phantoms. Four line-pair distances were used: 0.5 mm, 1 mm, 1.5 mm, and 2 mm. Figure 5 The estimated PSF-2 improves the resolution in the Y direction by using Figure 5 The estimated PSF-3 improves the resolution in the X direction. Experiments show that this method significantly improves the resolution compared to the RL (Richardson-Lucy) deconvolution method, achieving a 4-fold improvement in spatial resolution compared to the X-space reconstructed image.

[0127] like Figure 5 As shown, Figure 5 MPI image deconvolution is performed using point spread with different full width at half maximum (FWHM). Figure 5 (a) Point spread function estimated by a double RL+TV iterative method based on measurement of point spread (1 mm point phantom, SNR=3dB) (iteration numbers are (5, 10, 15, 20) respectively). Figure 5 (b) The figure shows the 1mm point-to-phantom in the X and Y directions. Figure 5 (c) The figure shows that different point spread functions are used for deconvolution based on the spatial iterative deconvolution method.

[0128] like Figure 6 As shown, Figure 6 Two-dimensional image reconstruction of line pairs with spacing of 0.5 mm, 1 mm, 1.5 mm, and 2 mm in the X direction was performed using RL and spatial iterative deconvolution methods. The signal-to-noise ratio was set to 3 dB, and the gradient value in the X direction was set to 1.25 mT / mm. Figure 6 As shown, the spatial iterative deconvolution method is better at distinguishing line pair phantoms than RL.

[0129] like Figure 7 As shown, Figure 7Two-dimensional image reconstruction of line pairs with spacing of 0.5mm, 1mm, 1.5mm, and 2mm in the Y direction was performed using RL and spatial iterative deconvolution methods. The signal-to-noise ratio was set to 3dB, and the gradient value in the Y direction was set to 2.5mT / mm. Figure 7 As shown, the spatial iterative deconvolution method is better at distinguishing line pair phantoms than RL.

[0130] The method described above for improving MPI image resolution based on a physical model achieves several advantages. Firstly, by using an adaptive compensation method to cancel feedthrough interference signals and preserve the fundamental frequency of the particle signal, the complete magnetic particle nonlinear response signal can be obtained without filtering and fundamental frequency recovery, thus improving the quality and resolution of the X-space reconstructed image. Furthermore, based on the recovered X-space reconstructed image, an X-space imaging physical model is established. This model employs a spatial iterative deconvolution algorithm to solve for the magnetic particle concentration distribution, uses TV regularization to constrain noise, and employs L1 sparse priors to reduce iterative errors and increase generalization ability. Secondly, this method can improve MPI reconstruction resolution by several times, and even in low signal-to-noise ratio environments, it can achieve a spatial resolution better than 1 mm. Moreover, this method achieves high-resolution magnetic particle concentration distribution reconstruction without complex system function acquisition and calibration processes.

[0131] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.

[0132] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0133] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A method for generating high-resolution MPI images based on a physical model, characterized in that, The method includes: The feedthrough interference signal is acquired, and the feedthrough interference signal is canceled using an adaptive compensation method to obtain the complete magnetic particle nonlinear response signal. The nonlinear response signal of the magnetic particles is processed using an MPI system to obtain an X-space reconstructed image; An X-space imaging physical model is constructed based on a dual Richardson-Lucy deconvolution algorithm with TV regularization and a spatial iterative deconvolution algorithm. The X-space reconstructed image is then processed using the X-space imaging physical model to obtain an MPI image. The step of acquiring the feedthrough interference signal and using an adaptive compensation method to cancel the feedthrough interference signal to obtain the complete magnetic particle nonlinear response signal includes: The feedthrough interference signal was collected under no-load conditions. amplitude and phase ; Based on the amplitude of the feedthrough interference signal and phase Obtain compensation signal ; The compensation signal With feedthrough interference signal The signals are subtracted in the LNA and the phase of the compensated signal is compensated according to an adaptive compensation method to obtain the optimal low-noise signal. Based on the optimal low-noise signal, the magnetic particle response signal is acquired to obtain the magnetic particle nonlinear response signal; The step of compensating the phase of the compensated signal according to the adaptive compensation method to obtain the optimal low-noise signal includes: The compensation signal is compensated, and the step size of the phase compensation for each compensation is... ; Determine the compensated signal after compensation. With feedthrough interference signal Whether the low-noise signal subtracted in the LNA is stable; If stable, output the phase change of the adaptively compensated signal. And the corresponding low-noise signal; among which, , where n represents the number of adaptive compensations; If it is unstable, continue to compensate the compensation signal; The step of constructing an X-space imaging physical model based on a TV-regularized dual Richardson-Lucy deconvolution algorithm and a spatial iterative deconvolution algorithm, and then processing the X-space reconstructed image using the X-space imaging physical model to obtain an MPI image, includes: An X-space imaging physical model is constructed based on a TV-regularized dual Richardson-Lucy deconvolution algorithm and a spatial iterative deconvolution algorithm. The spatial convolution kernel of the MPI system is estimated using the TV-regularized dual Richardson-Lucy deconvolution algorithm. The spatial concentration distribution of magnetic particles is solved using a spatial iterative deconvolution algorithm to obtain the MPI image; The expression for the TV-regularized dual Richardson-Lucy deconvolution algorithm is as follows: in, This represents an X-space reconstructed image. Indicates the spatial concentration distribution of magnetic particles. Represents the spatial convolution kernel of the MPI system. For the first Spatial concentration distribution of magnetic particles in the next iteration. For the first Spatial concentration distribution of magnetic particles in the next iteration. for The inverse transform about the origin, First regularization parameter, This is the second regularization parameter. For the convolution kernel estimated in one iteration, For the input of one iteration, () represents the divergence calculation function; The spatial iterative deconvolution algorithm includes: Based on the sparsity and smoothness characteristics of MPI images, the cost function to be minimized is established as follows: in, This is a weighting factor for fidelity. , representing the spatial distribution of magnetic particle concentration; , represents the spatial convolution kernel of the MPI system; , representing the X-space reconstructed image; For TV regularization, For TV regularization parameters; For L1 regularization, The regularization parameter for sparse priors; beg The derivative is obtained as follows: in, .

2. The method for improving MPI image resolution based on a physical model according to claim 1, characterized in that, The feedthrough interference signal The expression is: in, The magnetic field frequency, For low noise in MPI systems, For time; The expression for the low-noise signal is: in, ; The expression for the nonlinear response signal of the magnetic particles is: in, This is the response signal of magnetic particles.

3. The method for improving MPI image resolution based on a physical model according to claim 2, characterized in that, The expression for the X-space reconstructed image is: in, This represents an X-space reconstructed image. Indicates the spatial concentration distribution of magnetic particles. Represents the spatial convolution kernel of the MPI system. The spatial distribution function of noise.

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