Acoustoelectric tomography image formation algorithm based on two-point gradient iteration method

Abstract

The application discloses a kind of acoustic-electric tomography image imaging algorithm based on two-point gradient iterative method, and the innovation is to improve the calculation efficiency by two-point gradient iterative method, and the accuracy of image reconstruction is improved by the selection of regularization term.The core of the application is to use the characteristics of acoustic-electric hybrid imaging, that is, when the boundary detection current is applied, the power density data is obtained by using ultrasonic disturbance, so as to obtain the internal data of biological tissue.At the same time, according to the different characteristics of different biological tissue conductivity, different regularization terms are introduced, two-point gradient iterative method is established, and high-resolution reconstruction of biological tissue conductivity is realized.Compared with the traditional acoustic-electric imaging method, the application reduces the calculation and storage cost of multiple observation currents, improves the imaging efficiency.And the iteration process is modified by using a special regularization term, so that the boundaries or geometric characteristics of different tissues can be accurately determined, and the imaging accuracy is improved.

Description

Technical Field

[0001] This invention belongs to the field of medical imaging technology, specifically relating to an acoustic-electrical tomography imaging algorithm based on a two-point gradient iteration method. Background Technology

[0002] Acoustic-Electric Tomography (AET) is a hybrid imaging technique. Compared to single imaging methods, hybrid imaging is not simply multimodal imaging, but rather combines the physical interactions of multiple different imaging modalities to perform imaging modeling, and then designs algorithms to reconstruct parametric images of biological tissues. AET combines Electrical Impedance Tomography (EIT) and ultrasound imaging to reconstruct the electrical conductivity within biological tissues. It is an emerging non-invasive imaging technique, well-suited for imaging biological tissues based on conductivity, and offers high resolution. Compared to traditional EIT, AET imaging utilizes the acoustic-electric effect. When biological tissue is subjected to external ultrasonic perturbation, its internal conductivity undergoes minute local changes. For a given incident current at the boundary, boundary voltage data corresponding to all ultrasonic incident directions and two perpendicular initial phases are measured. This yields power density data at various points within the tissue, which, along with the boundary current, is used to reconstruct the internal conductivity of the biological tissue. Because it utilizes information from within the biological tissue, its imaging accuracy is higher than that of traditional EIT.

[0003] Specifically, the initial phase is applied as Sound waves with frequency k and amplitude p Under the influence of this sound wave, the conductivity σ approximately becomes Where ζ is the coupling coefficient measuring the change in conductivity between the sound wave and the measured object, its magnitude depends on the specific measurement in the actual application, ε=pΓ, It is the acoustic wave amplitude, and Γ > 0 is a measure of the modulation of the acoustic signal with the constitutive parameters in the medium. For a given boundary current f, let u ε u -ε These correspond to the conductivity σ ε ,σ -ε The potential distribution, using u ε ,u -ε The satisfied EIT equation can be obtained from Green's formula.

[0004]

[0005] For σ in the above formula ε ,σ -ε ,u ε ,u -ε , and J εBy performing an asymptotic expansion and comparing the coefficients of the first-order terms of ε, we can obtain...

[0006]

[0007] Where u represents the potential distribution corresponding to the conductivity σ and the boundary current f. In the above equation, we take... And by performing a linear combination, we obtain

[0008]

[0009] For all incident frequencies The power density function of interior points can be obtained from boundary measurement data using the inverse Fourier transform.

[0010]

[0011] AET utilizes the power density function of the internal points given by the above formula and the control system.

[0012]

[0013] To reconstruct the electrical conductivity within biological tissues, this process essentially involves solving a nonlinear equation concerning σ and u, requiring the development of efficient and stable solution methods. This is the core innovation of this invention. Summary of the Invention

[0014] Objective: To ensure the unique determination of σ, we utilize power density data corresponding to three appropriately selected sets of boundary incident currents as input data for reconstructing conductivity. The invention has three core components. First, a serial method is developed for multiple sets of currents, updating them sequentially to avoid the large storage requirements of computation caused by using multiple sets of boundary incident currents simultaneously. Second, suitable regularization terms are proposed to address the different conductivity characteristics of different biological tissues, thereby enabling more accurate determination of the boundaries or geometric features of different tissues. Third, an efficient and clear method for reconstructing conductivity images is obtained using a two-point gradient iteration method.

[0015] Technical solution: The acoustic-electric tomography image reconstruction method based on the two-point gradient iteration method proposed in this patent includes the following four steps:

[0016] (a) Data collection: For three sets of appropriate incident currents applied around the object being measured, solve the control system to simulate and generate internal power density data;

[0017] (b) Selecting appropriate regularization terms: Based on the smoothness of the power density function of the biological tissue to be measured, introduce appropriate multiple regularization terms and give the weight coefficient β between the multiple regularization terms;

[0018] (c) Iterative inversion: Using the internal power density data corresponding to the three sets of incident currents as input information, the conductivity is iteratively solved using the two-point gradient iteration method.

[0019] (d) Output: Given an appropriate stopping criterion, output the reconstructed conductivity image.

[0020] Specifically, in step (a), an incident current is applied around the biological tissue, and numerical simulation is used to obtain the power density data inside the biological tissue. The current includes, but is not limited to, direct current in polynomial form and low-frequency alternating current in trigonometric function form. Regarding the data collection, since this invention mainly focuses on designing an effective method for given internal power density data, we directly solve the control system to simulate and obtain the internal power density data. In the actual AET imaging model, this data is obtained through the acoustic-electric effect, performing an inverse Fourier transform on the boundary measurement data.

[0021] Specifically, in step (b), the geometric distribution characteristics of the power density data reflect the geometric distribution characteristics of the conductivity. Therefore, some prior geometric information about the conductivity can be directly obtained from its distribution characteristics. See the detailed implementation steps for specific selection methods.

[0022] Specifically, in step (c), the internal power density data corresponding to the three sets of currents are... Add Gaussian random noise to obtain noise data. From the following minimization problem

[0023]

[0024] Solve for σ, where Θ is a pre-defined regularization term. Iteratively solve the above minimization problem using the two-point gradient method to obtain the inverse solution σ for conductivity. n , where n represents the number of iterations. For detailed solution, please refer to the specific implementation steps.

[0025] Specifically, in step (d), the stopping criteria include, but are not limited to, the deviation principle, i.e.

[0026]

[0027] Where H j σ represents the operator for the acousto-electro-optical imaging model. n,j The result of the nth iteration under the j-th current is given, where τ > 1 is a pre-selected deviation parameter and δ is the data error. When the above stopping criterion is met, the iteration stops, and the final reconstructed conductivity image is obtained.

[0028] The output results save the conductivity σ obtained from the iterative inversion. nThe image is analyzed, and evaluation metrics are calculated for it and the simulated test image, including relative error, MSE (mean squared error), and PSNR (peak signal-to-noise ratio).

[0029] Beneficial Effects: The acoustic-electric tomography image reconstruction method based on the two-point gradient iteration method proposed in this invention can quickly invert conductivity images and accurately extract structural features from them. Compared with existing traditional acoustic-electric imaging methods, this invention reduces the computational and storage costs of multiple sets of observed currents and improves imaging efficiency. Simultaneously, it utilizes a special regularization term to correct the iterative calculation process, thereby enhancing imaging accuracy. Attached Figure Description

[0030] Figure 1 This is a flowchart of the overall process of the acoustic-electric tomography imaging algorithm based on the two-point gradient iteration method of this invention.

[0031] Figure 2 This is a flowchart of the acoustic-electric tomography imaging algorithm based on the two-point gradient iteration method of the present invention.

[0032] Figure 3 This explains the acoustoelectric effect of the AET imaging model. Under the action of this initial acoustic wave, the conductivity changes. At the same time, given multiple sets of boundary currents f, the potential distribution u for different conductivity levels inside the device also changes. Thus, the power density function of the internal points can be obtained from the boundary measurement data.

[0033] Figure 4 The figures show the error and residual curves of the two-point gradient iteration method proposed in this invention under different noise levels; the first row, left: select Iterative L-term of regularization term for reconstructing brain conductivity images 1 Error; First row right: Select The iterative residuals of the brain conductivity image are reconstructed using regularization terms; second row, left: select Θ TV Iterative TV error of reconstructing brain conductivity images using regularization terms; second row right: select Θ TV The iterative residuals of brain conductivity images are reconstructed using regularization terms.

[0034] Figure 5 This is the simulation experiment design for the present invention. The first line contains δ. e After reducing the noise level to 8%, the power density data were obtained using three sets of currents; the second row shows the noise levels as δ. e =8%, 2%, 0.8%, 0.2% when using Regularization terms reconstruct brain conductivity images; the third row contains noise levels of δ. e When = 8%, 2%, 0.8%, 0.2%, use Θ TV Regularization terms reconstruct brain electrical conductivity images. Detailed Implementation

[0035] The objectives, technical solutions, and advantages of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] This invention proposes a two-point gradient iterative method for reconstructing electroacoustic tomography (ECTM) images. Specifically, based on the smoothness of biological tissues observed in the data, a suitable regularization term Θ is introduced, and dynamic correction coefficients are incorporated during the iteration process, significantly improving both the efficiency and the accuracy of image reconstruction. The flowchart of this invention is as follows: Figure 1 As shown, the specific steps are as follows.

[0037] (a) Data collection: Three sets of incident currents were applied to the boundary of the organism. In the numerical simulation, the direct currents were expressed in polynomial form as f1 = x1, f2 = x2. Or trigonometric function type low-frequency alternating current f j =sin(ω) j θ), j = 1, 2, 3. In the numerical simulation, the conductivity σ is substituted into the simulation test data. * Generate power density data Where u j Add current f to the boundary j Then, the equation of the ellipse

[0038] The solution, where Represents the gradient operator. This represents the derivative along the outward normal direction of the region boundary; three sets of noisy observation data were obtained by adding random Gaussian noise. Where e follows a standard Gaussian distribution, and records the noise level.

[0039] (b) Selecting the regularization term Θ: Based on the smoothness of the biological tissue conductivity expressed by the power density function, select an appropriate regularization term and adjust the scaling factor β between the regularization terms; the regularization term includes, but is not limited to, the following three forms:

[0040]

[0041]

[0042]

[0043] Where β > 0 is the weighting coefficient of the balance regularization term. If the power density data of the observed object varies relatively uniformly, then it is directly adopted. Perform iterative calculations; if the power density data of the observed object is sparse and discontinuous, then... Perform iterative calculations; if the observed object power density distribution data shows repeated discontinuous textures (including but not limited to brain sulci and gyri, lung textures, etc.), then Θ can be selected. TV Perform iterative calculations. Adjust the β value based on the projected area of ​​the discontinuity or the proportion of texture; typically, β = 10 is chosen.

[0044] (c) Iterative inversion: Establish a two-point gradient iterative method to perform iterative inversion.

[0045] Specifically, given an initial conjecture ξ0 (which can generally be taken as ξ0 = 0), the problem to solve the minimum problem σ0 = argmin is: σ The initial guess of conductivity is obtained from {Θ(σ)-<ξ0,σ>}. For each iteration step n, the initial guess of conductivity is obtained from (ξ0,σ>). n ,σ n Define sequence ξ n,0 =ξ n,1 =ξ n , and σ n,0 =σ n,1 =σ n .

[0046] Specifically, for a given number of outer loop steps n, the inner loop iteration is performed using three sets of incident currents j = 1, 2, 3.

[0047] ζ n,j =ξ n,j +λ n,j (ξ n,j -ξ n,j-1 ),

[0048] z n,j =argmin σ {Θ(σ)-<ζ n,j ,σ>}.

[0049]

[0050] σ n,j+1 =argmin σ {Θ(σ)-<ξ n,j+1 ,σ>},

[0051] Where the correction coefficient λ n,j You can specifically choose as

[0052] λ = 0, or or Step size parameters H j '(z n,j ) * Operator H j The conjugate form of the derivative,

[0053]

[0054] in in Let c be a set of basis functions in the finite element method, with coefficients c k Determined by the following system of linear equations

[0055]

[0056] Specifically, for a given constant τ > 1 (typically τ = 1.05), test the residuals. The relationship between the magnitudes of τ and δ, if satisfied for all three sets of currents... If 1 ≤ j ≤ 3, the iteration stops, and σ n :=σ n,4 This is denoted as the final conductivity.

[0057] (d) Output iterative image and simulation test image σ * Evaluation metrics between them. Evaluation metrics include, but are not limited to, the following relative errors.

[0058]

[0059] And MSE (mean squared error) and PSNR (peak signal-to-noise ratio). Specifically, the mean squared error is...

[0060]

[0061] Where x = {x i |i=1,2,…,N},y={y i |i=1,2,…,N} is the vector representation of the image, σ n (i), σ * (j) represents the pixel values ​​of the iterated image and the image from the simulation iteration, and N represents the total number of pixels in the reconstructed image. The peak signal-to-noise ratio is...

[0062]

[0063] Where MAX represents the maximum pixel value in the simulated test image. To more clearly illustrate the feasibility and superiority of this invention, the performance of the method of this invention in the iterative inversion of human brain conductivity images in numerical simulation is shown below, and a numerical comparison is made with the classic Landweber iterative method.

[0064] Figure 4 The two-point gradient iteration method is given in the calculation process L 1Error curves. Table 1 compares the two-point gradient iteration method with the Landweber iteration method, including the MSE, PSNR, and number of iterations for the test data. Numerical results show that the proposed method has a significant improvement in computational efficiency compared to the Landweber iteration method.

[0065] Table 1 uses Comparison of brain conductivity reconstruction results with regularization terms

[0066]

[0067] Figure 5 The simulation results of this invention under different noise levels are shown. The relative noise levels are 8%, 2%, 0.8%, and 0.2%, respectively. It can be seen that as the noise decreases, the reconstruction effect on the electrical conductivity of the human brain is significantly improved, and the outline information of the brain can still be clearly identified even under high noise conditions.

Claims

1. An acoustic-electrical computed tomography (ECT) imaging algorithm based on a two-point gradient iteration method, characterized in that, Includes the following steps: (a) Data collection: For the three sets of incident currents applied around the object being measured, solve the control system respectively to simulate and generate internal power density data; (b) Selection of regularization terms: Based on the smoothness of the power density data of the biological tissue to be measured, multiple regularization terms are introduced, and the weight coefficients between the multiple regularization terms are given. ; (c) Iterative inversion: Using the internal power density data corresponding to the three sets of incident currents as input information, the conductivity is solved iteratively using the two-point gradient iteration method; (d) Output results: Given the stopping criteria, output the reconstructed conductivity image; In step (a), an incident current is applied around the biological tissue, and power density data inside the biological tissue is obtained by numerical simulation. The current includes, but is not limited to, direct current in polynomial form and low-frequency alternating current in trigonometric function form. Direct current in polynomial form is , , Trigonometric function type low-frequency alternating current is , In numerical simulation, the conductivity of the simulation test is substituted. Generate power density data ,in Add current to the boundary Then, the equation of the ellipse The solution; in Represents the gradient operator. This represents the derivative along the outward normal direction of the region boundary; three sets of noisy observation data were obtained by adding random Gaussian noise. , ,in The noise level follows a standard Gaussian distribution. = ; In step (b), different regularization terms are selected based on the geometric characteristics and smoothness exhibited by the power density data of biological tissues; the regularization terms include, but are not limited to, the following three types: in These are the weighting coefficients between regularization terms; if the power density data of the observed object varies relatively evenly, then they are directly used. Perform iterative calculations; If the power density data of the observed object is sparse and discontinuous, then adopt... Perform iterative calculations; If the observed object's power density distribution data shows repeated discontinuous textures, then select... Perform iterative calculations; adjust based on the projected area of ​​the discontinuous surface or the proportion of texture. Values, select .

2. The acoustic-electric tomography imaging algorithm based on the two-point gradient iteration method according to claim 1, characterized in that: In step (c), the internal power density data corresponding to the three sets of incident currents collected in step (a) are used. , Gaussian random noise was added to obtain noise data. The following minimization problem Solve ,in Given a regularization term, the above minimization problem is solved using a two-point gradient iteration method to obtain the inverse solution of conductivity. ,in Indicates the number of iterations.

3. The acoustic-electric tomography imaging algorithm based on the two-point gradient iteration method according to claim 2, characterized in that: In step (d), the stopping criteria include, but are not limited to, the deviation principle, i.e. ， in This represents the operator for the acousto-electro-optical imaging model. For the first Group current under the first Step-by-step iterative calculation results For the pre-selected deviation parameters, The data error is considered; when the above stopping criterion is met, the iteration stops, and the final reconstructed conductivity image is obtained.

4. The acoustic-electric tomography imaging algorithm based on the two-point gradient iteration method according to claim 1, characterized in that: In step (d), the output is a reconstructed conductivity image, and the output image is compared with the simulation test image. Evaluation metrics between them; evaluation metrics include, but are not limited to, the following relative errors. ， ， ， In addition, the mean square error of MSE and the peak signal-to-noise ratio of PSNR.

5. The acoustic-electric tomography imaging algorithm based on the two-point gradient iteration method according to claim 4, characterized in that: The mean squared error is , in , For image vectorization representation, , The pixel values ​​of the iterative image and the simulation count image. The total number of pixels in the reconstructed image; Peak signal-to-noise ratio is ， in This represents the maximum pixel value in the simulation test image.

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