An electrode detection type magnetoacoustic electromagnetic particle concentration image reconstruction method based on compressed sensing

Abstract

This invention discloses a method for reconstructing magnetoacoustic electromagnetic particle concentration images based on compressed sensing, belonging to the field of medical imaging technology. The method includes: acquiring voltage signals, reciprocal current density data, and vibration velocity data of the reconstructed region from the detection electrode based on a simulation model; constructing a linear equation between the voltage signal and the magnetic particle concentration distribution, and finding the optimal sparse basis; introducing a compressed sensing reconstruction method, constraining the magnetic particle concentration distribution through sparse priors, transforming the concentration distribution reconstruction problem into an optimization problem with regularization terms; solving the magnetic particle concentration distribution under the condition of consistent voltage measurement data; and plotting the solution based on the results. This invention enables rapid reconstruction of magnetoacoustic electromagnetic particle concentration images based on compressed sensing.

Description

Technical Field

[0001] This invention belongs to the field of concentration distribution image reconstruction, and particularly relates to a method for reconstructing magnetoacoustic electromagnetic particle concentration images based on compressed sensing electrode detection. Background Technology

[0002] Magnetic particles, due to their excellent biocompatibility and magnetic response characteristics, have significant application value in fields such as tumor diagnosis and targeted drug delivery. In 2025, Yan Xiaoheng's team published an electrode-detection-based magnetoacoustic electromagnetic particle concentration image method (Hou X, Yan X, Chen W, et al. Magneto-Acousto-Electrical Tomography of Magnetic Nanoparticles with Electrode Detection[J]. IEEE Transactions on Instrumentation and Measurement, 2025.). This method uses the method of moments for discretization, solves the virtual wave source matrix, and reconstructs the magnetic particle concentration by receiving voltage signals and acoustic field data from electrodes. They proposed an electrode-detection-based magnetoacoustic electromagnetic particle concentration image reconstruction method based on projective gradient descent-least squares. This method achieves magnetic particle concentration image reconstruction by solving the virtual wave source matrix equation using projective gradient descent-least squares. Although it has high reconstruction accuracy, it suffers from problems such as large data storage requirements, numerous iterations, and high computational complexity. Therefore, further research is needed on the reconstruction of electrode-detection-based magnetoacoustic electromagnetic particle concentration images.

[0003] The compressed sensing theory proposed in this invention provides a new approach to image reconstruction. Through sparse sampling and linear reconstruction, it achieves high-quality signal recovery at a rate far lower than the Nyquist sampling rate, thereby achieving the goals of high-quality image reconstruction and reduced reconstruction time. Currently, compressed sensing is widely used in medical imaging such as MRI and CT, but its application in electrode-detection magnetoacoustic electromagnetic particle concentration reconstruction has not yet been developed. Summary of the Invention

[0004] To fill the aforementioned technological gap, this invention proposes a rapid reconstruction method for magnetoacoustic electromagnetic particle concentration based on compressed sensing electrode detection. This method utilizes compressed sensing theory to achieve rapid, stable, and high-quality reconstruction of magnetic particle concentration distribution, and has promising application prospects.

[0005] The present invention adopts the following technical solution: Step 1: Establish a physical model of the concentration distribution of magnetoacoustic and electromagnetic particles using simulation software. The model includes an ultrasonic excitation module, a static magnetic field module, an electrode detection module, as well as water area, biological tissue, magnetic particle region and absorption layer. By setting different parameters, obtain the corresponding voltage signal, vibration velocity of the reconstructed region and reciprocal current density. Step 2: Based on the magnetoacoustic-electromagnetic effect and the reciprocity theorem, establish the formula for reconstructing the concentration of magnetoacoustic-electromagnetic particles, construct the linear equation between the voltage signal and the magnetic particle concentration distribution, and discretize the original data; Step 3: Based on the fact that the magnetic particle region is constant and small, and the simulation model determines that the dimension of the measurement data is smaller than the dimension of the variable to be reconstructed, the reconstruction problem is determined to be an underdetermined problem, and a sparse basis with a suitable magnetic particle concentration is found. Step 4: Introduce the compressed sensing reconstruction method. Constrain the magnetic particle concentration distribution through sparse priors, transforming the concentration distribution reconstruction problem into an optimization problem with regularization terms. Under the condition of ensuring the consistency of voltage measurement data, solve the magnetic particle concentration distribution problem and reconstruct the magnetic particle concentration distribution image based on the solution results, thereby obtaining the electrode detection magneto-acoustic electromagnetic particle concentration image based on compressed sensing.

[0006] As an optional embodiment of the present invention, in step one, a simulation model of magnetoacoustic electromagnetic particle concentration imaging is established, and the initial conditions of the simulation are set. The simulation model is a mosaic model, with an absorption layer set on the outer layer of the water area to meet the theoretical boundary conditions and prevent sound wave reflection. Biological tissue and ultrasonic excitation are set inside the water area. The detection electrodes are placed on both sides of the biological tissue perpendicular to the ultrasonic excitation direction. A magnetic particle region is set inside the biological tissue. The ultrasonic excitation is uniformly set outside the biological tissue and inside the water area, with a total of [number missing] magnetic particles set. One incentive, one sound source Excitation signals are sequentially emitted into the magnetic particle region, positive and negative unit currents are passed through the detection electrodes, and the static magnetic field is set to... The axis is orthogonal to the sound field and electric field, and then multiphysics simulation is performed on the reconstructed region to obtain the point sound source. Voltage signal at the lower detection electrode Vibration velocity in the reconstructed area and the reciprocal current density at the detection electrode ,in =1, 2, ..., .

[0007] As an optional embodiment of the present invention, in step two, the corresponding signals obtained from each ultrasonic excitation emission simulation model are discretized: a voltage matrix is ​​constructed from the voltage signal, a sound field matrix is ​​constructed from the vibration velocity data, and a reciprocal matrix is ​​constructed from the reciprocal current density data. A magnetoacoustic-electric reconstruction formula is then established using the magnetoacoustic-electric formula. The magnetoacoustic-electric formula is as follows:

[0008] In equation (1), It is a voltage signal. The permeability of free space, The vibrational velocity of the magnetic particles. For the magnetic moment of magnetic particles, For magnetic particle concentration, To represent the reciprocal current density, the formula is simplified as follows:

[0009] In equation (2), The Z component of the magnetic moment of the magnetic particle. Vibration velocity data Quantity, These are the reciprocal current densities. Quantity, For the first One ultrasonic excitation; let the reconstructed kernel function be... :

[0010] In equation (3), To reconstruct a point in the discretized region, To obtain the discretized grid area, substituting equation (3) into equation (2) yields:

[0011] In equation (4), The total number of discretization points. For voltage matrix, The kernel function matrix, This is the magnetic particle concentration matrix.

[0012] As an optional embodiment of the present invention, in step three, the search for the sparse domain and sparse constraint term that satisfy the reconstruction of magnetic particle concentration adopts transform domain sparse constraint, the magnetic particle concentration is expressed as the product of the transform domain and the sparse coefficients, and sparse reconstruction is achieved by applying sparse constraints to the sparse coefficients:

[0013] In equation (5), It is a transform domain. It is the sparsity coefficient.

[0014] As an optional embodiment of the present invention, in step four, the sparsity constraint term adopts a total variational constraint to represent the gradient sparsity characteristics of the magnetic particle concentration in space, thereby enhancing the reconstruction accuracy of the segmented uniform region and suppressing noise; a total variational constraint is applied to the magnetic particle concentration:

[0015] In equation (6), For a first-order horizontal operator, It is a vertical first-order operator. This is a sparse constraint term on the magnetic particle concentration.

[0016] As an optional embodiment of the present invention, in step four, the optimization problem includes a data fitting term and a regularization term, wherein the data fitting term is used to constrain the consistency between the reconstruction result and the measured voltage, and the regularization term is used to introduce sparse constraints, thereby achieving a balance between reconstruction accuracy and stability by adjusting the regularization parameter.

[0017] Compared with the prior art, the present invention has the following advantages: (1) The present invention is to solve the problems of slow reconstruction speed and large data volume in the existing magnetoacoustic electromagnetic particle concentration imaging methods. The present invention is based on compressed sensing to solve the magnetoacoustic electromagnetic particle concentration, thereby effectively reducing the data volume and shortening the reconstruction time, and is suitable for reconstructing magnetic particle concentration images with multiple excitations. (2) The present invention divides the reconstruction area into finite element meshes according to the finite element method, and constructs equations by acquiring voltage signals, vibration velocity of the reconstruction area, and reciprocal current density, and uses compressed sensing to solve for the magnetic particle concentration distribution, without the need for a secondary solution process of virtual wave field source. Attached Figure Description

[0018] Figure 1 This is a flowchart of the electrode detection-based magneto-acoustic-electromagnetic particle concentration reconstruction method based on compressed sensing of the present invention.

[0019] Figure 2 This is a simulation model of the electrode-detection-based magnetoacoustic electromagnetic particle concentration image reconstruction method of the present invention;

[0020] Figure 3 Theoretical diagram of magnetoacoustic and electromagnetic particle concentration;

[0021] Figure 4 This is a diagram showing the reconstruction results of magnetoacoustic electromagnetic particles. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Please see Figure 1 The above is a flowchart of an electrode detection-based magneto-acoustic electromagnetic particle concentration reconstruction method based on compressed sensing, provided by an embodiment of the present invention. A simulation model needs to be established before executing the method.

[0024] Please see Figure 2 This is a simulation model of the electrode-detection type magnetoacoustic electromagnetic particle concentration image reconstruction method of the present invention. A finite element simulation software is used to build the electrode-detection type magnetoacoustic electromagnetic particle concentration model. A two-dimensional model is established and numerical simulation analysis is performed. The water area is a square with a side length of 50mm; biological tissue is a circle with a radius of 15mm; and magnetic particles are a circle with a radius of 10mm. The origin of the coordinate system is set as the center for all three regions. The ultrasonic excitation is a circle with a radius of 1mm, and the center of the circle is set on a circle with a radius of 20mm for circular scanning. The default material for the water area model is water, and the materials for the biological tissue and magnetic particle regions are set as ideal homogeneous media with fixed parameters. Pressure acoustics is set, and a time-domain explicit module is used as the acoustic simulation module. The ultrasonic excitation emitted sound pressure is... Sound waves are analytic functions Set the saturation magnetic field in the magnetic particle region, with the direction being... An electric field is set to create a pair of levitation potentials, namely levitation potential 1 and levitation potential 2, above and below the biological tissue. Levitation potential 1 is fed into a 1-axis... The current, the floating potential 2 is passed into -1 The current is such that the floating potential 2 is grounded; the reconstructed area is meshed, with the maximum element parameter being one-third of the wavelength and the minimum element parameter being one-fifth of the wavelength.

[0025] This invention is achieved through the following technical solution: This invention provides a method for reconstructing magnetoacoustic electromagnetic particle concentration images based on compressed sensing electrode detection, specifically including the following steps:

[0026] Step 1: Establish a physical model of the concentration distribution of magnetoacoustic and electromagnetic particles using simulation software. The model includes an ultrasonic excitation module, a static magnetic field module, an electrode detection module, as well as water area, biological tissue, magnetic particle region and absorption layer. Obtain corresponding voltage data, vibration velocity data and reciprocal current density data by setting ultrasonic excitation at different locations.

[0027] (1) Simulation parameters

[0028] The simulation model parameters of this invention are shown in Table 1.

[0029] Table 1 Simulation Parameters name expression value Particle diameter d(nm) 30 concentration <![CDATA[N(particles / m 3 )]]> <![CDATA[1.05*10 22 ]]> Volume fraction φ 0.148 Saturation magnetic field strength H(kA / m) 800 Saturation magnetization M(A / m) <![CDATA[1.544*10 5 ]]> Magnetic moment <![CDATA[m(A*m 2 )]]> <![CDATA[2.184×10 -18 ]]> temperature T(K) 300 Boltzmann constant k(J / K) <![CDATA[1.38×10 -23 ]]> Vacuum permeability <![CDATA[μ0]]> <![CDATA[4π*10 -7 ]]> Particle volume <![CDATA[S(m 3 )]]> <![CDATA[9π / 2*10 -24 ]]> frequency f(MHz) 1 sound pressure P(MPa) 0.1 cycle T0(s) <![CDATA[1*10 -6 ]]> angular frequency ω <![CDATA[6.2832*10 6 ]]>

[0030] (2) Simulation operation

[0031] A model was established for simulation. The ultrasonic excitation was performed in a 15° step rotation. Ultrasonic waves were emitted sequentially, for a total of 24 excitations. Suspension potential 1 was used as the detection electrode, and suspension potential 2 was used as the zero potential point. Therefore, the voltage value of suspension potential 1 can be regarded as the potential difference. The voltage signal at a certain point of suspension potential 1 was collected with a step size of one-twentieth of a cycle and a total time of 30 cycles. A total of 601 time points were collected. The simulation model can directly export the data, including vibration velocity data at each time point in the reconstructed area, reciprocal current density data of the biological tissue area, and voltage data at all time points of a certain point of suspension potential 1.

[0032] Step 2: Assuming biological tissue and magnetic particles are ideal fluids, and the sound field adopts the sound pressure wave equation, the magnetic particles vibrate and are subjected to Lorentz force, resulting in charge separation. Based on the generalized Ohm's law and the current continuity equation, the Poisson equation for the scalar potential and the boundary conditions are obtained:

[0033] (7)

[0034] In equation (7), For scalar potential, The vibrational velocity of the magnetic particles. The magnetization intensity of magnetic particles, It is a static magnetic field. Let be the magnetic particle concentration distribution function. The conductivity of the medium, It is the entire solution domain. It is a boundary. It is a boundary outward normal direction, This represents the directional derivative along the direction of the outward normal.

[0035] Based on the reciprocity theorem and considering only a pair of electrodes with a unit current injected, the voltage equation is obtained: (8)

[0036] In equation (8), It is a voltage signal. To obtain the reciprocal current density, simplifying equation (2) yields the final magnetoacoustic-electric equation: (9)

[0037] In equation (9), For the magnetic moment of magnetic particles, To obtain the free permeability, the voltage data is discretized into a voltage matrix. Expanding the formula according to the vector product rule yields: (10)

[0038] In equation (10), The Z component of the magnetic moment of the magnetic particle. Vibration velocity data Quantity, These are the reciprocal current densities. Quantity, For the first One ultrasonic excitation; let the reconstructed kernel function be... : (11)

[0039] In equation (11), To reconstruct a point in the discretized region, To obtain the discretized grid area, substituting equation (9) into equation (8) yields: (12)

[0040] In equation (12), The total number of discretization points. For voltage matrix, The kernel function matrix, This is the magnetic particle concentration distribution matrix.

[0041] Step 3: Based on the equation in Step 2, and combining it with Step 1... The matrix has dimensions (601×24, 1). The matrix has dimensions (201×201, 1). The matrix has dimensions of (601×24, 201×201). Since the measurement dimension is smaller than the dimension to be reconstructed, the reconstruction problem is determined to be underdetermined. Common sparse bases for imaging reconstruction in compressed sensing include orthogonal transformation bases and gradient sparse domains. Each sparse base can be represented as: (13)

[0042] In equation (13), It is a sparse base. It is a sparse signal;

[0043] The sparsity performance of the constructed gradient sparse domain for reconstructing magnetoacoustic and electromagnetic particle concentrations was calculated on a simulation dataset. Based on the comparison, the gradient sparse domain constructed in this case study exhibits the best performance index. Therefore, it was adopted as the sparse basis in subsequent reconstruction steps. And establish a compressed sensing model.

[0044] Step 4: After determining a suitable sparse basis for the target signal, this embodiment transforms the problem of reconstructing the magnetic particle concentration distribution into an optimization problem with a regularization term. The specific process is as follows:

[0045] In this embodiment, the measured voltage vector is U, the measurement matrix is ​​K, and the vector to be reconstructed is N. Since this embodiment is an underdetermined problem, a compressed sensing reconstruction framework is introduced, and the following optimization problem is constructed: (14)

[0046] In equation (14), the first term The first term is the data fitting term, used to constrain the consistency between the reconstructed results and the measured voltage; the second term... This is a sparse constraint term (regular term) used to represent the sparse characteristics of the magnetic particle concentration in space; This is a regularization parameter used to balance the weights between data fitting and sparse priors;

[0047] Regarding the sparse constraint term, the gradient sparse region has already been selected in step three: (15)

[0048] In equation (15), For a first-order horizontal operator, The operator is a vertical first-order operator. This constraint utilizes the property that the gradient of magnetic particle concentration is zero in a uniform region and non-zero only at the boundary, thus possessing optimal sparse representation capability for piecewise constant distributions. In this embodiment, the solution algorithm used is the L-BFGS-B optimization algorithm for iterative solution. The solution data is obtained, the concentration distribution in the reconstructed region is constructed, and finally, an electrode-detected magnetoacoustic electromagnetic particle concentration image based on compressed sensing is obtained.

[0049] Through the above description of the embodiments, those skilled in the art will clearly understand that the methods of the above embodiments can be implemented by means of software, and of course, they can also be implemented by hardware, but in many cases the former is a better implementation method.

[0050] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A method for image reconstruction of magnetoacoustic electromagnetic particle concentration based on compressed sensing electrode detection, characterized in that, Includes the following steps: Step 1: Use simulation software to establish a physical model of the concentration distribution of magnetoacoustic and electromagnetic particles, and set different parameters to obtain corresponding data; Step 2: Establish the formula for reconstructing the concentration of magnetoacoustic and electromagnetic particles, construct a linear equation between the voltage signal and the magnetic particle concentration distribution, and discretize the original data; Step 3: Based on the fact that the magnetic particle region is constant and small, and the dimension of the measurement data is smaller than the dimension of the variable to be reconstructed, the reconstruction problem is determined to be an underdetermined problem, and a suitable sparse basis is found. Step 4: Introduce the compressed sensing reconstruction method. Constrain the magnetic particle concentration distribution through sparse priors, transforming the concentration distribution reconstruction problem into an optimization problem with regularization terms. Under the condition of satisfying the consistency of voltage measurement data, solve the magnetic particle concentration distribution to obtain the magnetic particle concentration image.

2. The method for image reconstruction of magnetoacoustic electromagnetic particle concentration based on compressed sensing electrode detection according to claim 1, characterized in that, In step one, a simulation model for magnetoacoustic electromagnetic particle concentration imaging is established, and the initial conditions for the simulation are set. The simulation model is a mosaic model, with an absorption layer set on the outer layer of the water area to meet the theoretical boundary conditions and prevent sound wave reflection. Biological tissue and ultrasonic excitation are set inside the water area. The detection electrodes are placed on both sides of the biological tissue perpendicular to the direction of ultrasonic excitation. A magnetic particle region is set inside the biological tissue. The ultrasonic excitation is uniformly set outside the biological tissue and inside the water area. A total of [number missing] magnetic particle regions are set. One incentive, one sound source Excitation signals are sequentially emitted into the magnetic particle region, positive and negative unit currents are passed through the detection electrodes, and the static magnetic field is set to... The axis is orthogonal to the sound field and electric field, and then multiphysics simulation is performed on the reconstructed region to obtain the point sound source. Voltage signal at the lower detection electrode Vibration velocity in the reconstructed area and the reciprocal current density at the detection electrode ,in =1, 2, ..., .

3. The method for image reconstruction of magnetoacoustic electromagnetic particle concentration based on compressed sensing using electrode detection according to claim 1, characterized in that, In step two, the corresponding signals obtained from each ultrasonic excitation emission simulation model are discretized, such as constructing a voltage matrix from voltage signal data, a sound field matrix from vibration velocity data, and a reciprocal matrix from reciprocal current density data. A magnetoacoustic-electric reconstruction formula is then established using the magnetoacoustic-electric formula. The magnetoacoustic-electric formula is as follows: In equation (1), It is a voltage signal. The permeability of free space, The vibrational velocity of the magnetic particles. For the magnetic moment of magnetic particles, For magnetic particle concentration, To represent the reciprocal current density, the formula is simplified as follows: In equation (2), The Z component of the magnetic moment of the magnetic particle. Vibration velocity data Quantity, These are the reciprocal current densities. Quantity, For the first One ultrasonic excitation; let the reconstructed kernel function be... : In equation (3), To reconstruct a point in the discretized region, To obtain the discretized grid area, substituting equation (3) into equation (2) yields: In equation (4), The total number of discretization points. For voltage matrix, The kernel function matrix, This is the magnetic particle concentration distribution matrix.

4. The method for image reconstruction of magnetoacoustic electromagnetic particle concentration based on compressed sensing electrode detection according to claim 1, characterized in that, In step three, the sparse domain that satisfies the magnetic particle concentration reconstruction and the sparse constraint term are found using transform domain sparse constraints. The magnetic particle concentration is expressed as a product of the transform domain and the sparse coefficients, and sparse reconstruction is achieved by applying sparse constraints to the sparse coefficients. In equation (5), It is a transform domain. It is the sparsity coefficient.

5. The method for image reconstruction of magnetoacoustic electromagnetic particle concentration based on compressed sensing electrode detection according to claim 1, characterized in that, In step four, the sparsity constraint term employs a total variational constraint to represent the spatial gradient sparsity of the magnetic particle concentration, thereby enhancing the reconstruction accuracy of the segmented uniform region and suppressing noise; a total variational constraint is applied to the magnetic particle concentration: In equation (6), For a first-order horizontal operator, It is a vertical first-order operator. This is a sparse constraint term on the magnetic particle concentration.

6. The method for image reconstruction of magnetoacoustic electromagnetic particle concentration based on compressed sensing electrode detection according to claim 1, characterized in that, In step four, the optimization problem includes a data fitting term and a regularization term. The data fitting term is used to constrain the consistency between the reconstruction result and the measured voltage, while the regularization term is used to introduce sparse constraints. By adjusting the regularization parameter, a balance between reconstruction accuracy and stability can be achieved.

Images