A regularization-based multi-parameter full-waveform inversion ultrasound imaging method

Abstract

This invention discloses a regularized multi-parameter full-waveform inversion ultrasound imaging method, comprising: acquiring full-matrix time-domain sound field data of the model to be imaged, obtaining the frequency-domain observed sound field after discrete Fourier transform; constructing the QFWI forward modeling equation to obtain the forward-modeled simulated sound field; calculating the data residual between the frequency-domain observed sound field and the forward-modeled simulated sound field to construct the objective function of QFWI; further obtaining the gradient information of the sound velocity distribution and quality factor Q distribution of the model parameters; calculating the update direction of the model parameters; and iteratively updating the initial sound velocity distribution and initial quality factor Q distribution based on the initial sound velocity distribution and initial quality factor Q distribution of the model to be imaged, as well as the gradient information and update direction of the model parameters, to obtain the final sound velocity distribution and quality factor Q distribution. This invention not only accurately simulates the propagation phenomenon of sound waves in complex media, but also effectively distinguishes the characteristics of the medium based on the reconstruction results, and has good clinical application prospects.

Description

Technical Field

[0001] This invention relates to the field of ultrasound imaging technology, and more particularly to a multi-parameter full-waveform inversion ultrasound imaging method. Background Technology

[0002] Ultrasound imaging equipment has become the preferred examination method for clinical soft tissue imaging due to its convenience and lack of radiation. However, it still faces physical challenges in high-resolution imaging. Traditional ultrasound technology mainly relies on the reflection signals from tissue interfaces for imaging, resulting in relatively low spatial resolution. Ultrasound computed tomography (CT) is an emerging imaging technology that can accurately reconstruct high-resolution images of biological tissue characteristics using the transmission of ultrasound waves in tissues. Full Waveform Inversion (FWI) is an optimized iterative quantitative imaging algorithm that directly solves the wave equation, comprehensively considering multiple acoustic wave components such as transmitted waves, reflected waves, and scattered waves, to achieve high-resolution reconstruction of the acoustic parameters of the target, reaching sub-millimeter resolution in soft tissue imaging.

[0003] As research has progressed, FWI has demonstrated its ability to reconstruct high-resolution sound velocity models, and its current application in reconstructing biological tissue parameters tends to address more complex problems. Both benign and malignant breast lesions exhibit high sound velocities with relatively small differences in their distribution; therefore, additional parameters are needed to determine the nature of the lesion. Attenuation refers to the energy loss of sound waves propagating in a medium, and the level of energy loss is quantified as a material property of viscous media. The quality factor Q is a dimensionless physical quantity that can be used as an indicator of the degree of material dissipation. Benign breast lesions exhibit low attenuation characteristics (high Q value), while malignant lesions exhibit high attenuation characteristics (low Q value). Therefore, further reconstructing the attenuation characteristics of tissues based on the reconstructed sound velocities can effectively differentiate tissue characteristics.

[0004] FWI has expanded from single velocity inversion to multi-parameter reconstruction, gradually enriching and improving the physical model of wave propagation. This allows for accurate reproduction in forward modeling of FWI, considering the more complex and realistic physical phenomena of sound wave propagation in biological tissues. However, multi-parameter inversion presents gradient imbalance issues, such as the difference between velocity and the quality factor Q. Velocity, as a first-order kinematic parameter, significantly affects the phase of the ultrasound signal; while the attenuation parameter can influence the signal phase through dispersion relations, its main role is in amplitude information. Parameter trade-offs or crosstalk are an inherent challenge in multi-parameter FWI.

[0005] Patent application number 202310805700.7 discloses a method and system for cortical bone ultrasound imaging based on frequency domain full-wave inversion, comprising: S1: setting up an acquisition environment for acquiring experimental wavefield signals of a cortical bone phantom model to be imaged; S2: acquiring experimental wavefield signals of the cortical bone phantom model to be imaged; S3: setting an initial sound velocity model, performing forward modeling on the simulated wavefield in the frequency domain, extrapolating the simulated wavefield, and recording the simulated wavefield information in the frequency domain; S4: constructing a loss function required for full-wave inversion based on the experimental wavefield signal and the simulated wavefield signal, optimizing the loss function using the conjugate gradient method to obtain an optimized sound velocity distribution model; S5: increasing the fixed center frequency, assigning the optimized sound velocity distribution model to the initial sound velocity model, repeating steps S2-S4 until all frequency points are iterated, and outputting the final sound velocity model. This invention patent, by utilizing full-waveform inversion technology, greatly alleviates the dependence on a priori sound velocity distribution models. However, the patent only reconstructs the sound velocity distribution of the model under test. Summary of the Invention

[0006] To address the technical problem that traditional single-parameter FWI forward modeling fails to accurately simulate the propagation of sound waves in complex media, and the reconstruction results cannot effectively distinguish the characteristics of the medium, this invention proposes a regularized multi-parameter full-waveform inversion ultrasound imaging method. By proposing a multi-parameter joint inversion method (QFWI) based on model parameter constraints, it effectively overcomes the limitations of traditional single-parameter FWI in handling complex media. At the same time, it can reconstruct the sound velocity and quality factor Q distribution with high accuracy, which helps to accurately identify the nature of soft tissue lesions in complex tissues and has good clinical application prospects.

[0007] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0008] A regularization-based multi-parameter full-waveform inversion ultrasound imaging method includes the following steps:

[0009] S1. Using a multi-element ring ultrasonic transducer array, full-matrix time-domain acoustic field data acquisition is performed on the model to be imaged. After discrete Fourier transform, the frequency domain observation acoustic field is obtained.

[0010] S2. Construct the QFWI forward modeling equation using the KF dissipation model, and obtain the forward modeling simulation sound field based on the QFWI forward modeling equation;

[0011] S3. Calculate the data residual between the frequency domain observed sound field and the forward modeling simulated sound field. Construct the data fitting term of the objective function of QFWI based on least squares, and add the model parameter stability function as a regularization term to obtain the objective function of QFWI.

[0012] S4. Based on the objective function of QFWI, derive the gradient expressions for the sound velocity distribution and quality factor Q distribution of the model parameters, and obtain the gradient information of the sound velocity distribution and quality factor Q distribution of the model parameters.

[0013] S5. Based on the gradient information of the sound velocity distribution and quality factor Q distribution of the model parameters, the conjugate gradient method is used to calculate the update direction of the sound velocity distribution and quality factor Q distribution of the model parameters.

[0014] S6. Based on the initial sound velocity distribution and initial quality factor Q distribution of the model to be imaged, as well as the gradient information and update direction of the model parameter sound velocity distribution and quality factor Q distribution, iteratively update the initial sound velocity distribution and initial quality factor Q distribution to obtain the final sound velocity distribution and quality factor Q distribution.

[0015] Specifically, the method for constructing the QFWI forward modeling equation using the KF dissipation model is as follows: the KF dissipation model is introduced into the Helmholtz equation in the frequency domain to describe the slowness, and the quality factor Q is explicitly embedded in the complex slowness to describe the frequency-dependent attenuation characteristics of the medium; the Helmholtz equation containing the dissipation term is spatially discretized using a nine-point finite difference scheme to obtain a discrete expression of the Helmholtz equation containing the dissipation term in matrix form, and the QFWI forward modeling equation is constructed.

[0016] Specifically, the expression for the QFWI forward modeling equation is as follows:

[0017]

[0018]

[0019] In the formula, Let be the Laplace operator, ω be the angular frequency, x be the spatial position, v(x) be the speed of sound at spatial position x, and δ(x,ω) and u(x,ω) be the source term and sound field at spatial position x at angular frequency ω, respectively. v(ω) is the speed of sound at angular frequency ω, where v is the speed of sound, ω... r Here is the reference frequency, and i is the imaginary part.

[0020] Specifically, the expression for the objective function of QFWI is:

[0021] E(ω,m)=E data (ω,m)+μE reg (ω,m)

[0022] Where μ is the regularization weight, ω is the angular frequency, and m is the unknown model parameter to be solved;

[0023] E data (ω,m) is the L2 normalized mismatch function, expressed as follows:

[0024]

[0025] Where, p i and d i It is the i-th excitation source δ on the ring ultrasonic transducer array i The forward modeling of the sound field and the observed sound field, where i ranges from 1 to N, and N is the number of elements in the ring ultrasonic transducer array;

[0026] E reg (ω,m) is the model parameter stability function, which can be mathematically expressed as the following space integral form:

[0027]

[0028] In the formula, ε is the control factor in the regularization term. This is the gradient operator.

[0029] Specifically, the gradient expressions for the model parameter sound speed distribution and the quality factor Q distribution are as follows:

[0030]

[0031] In the formula, A is the complex impedance matrix, E is the quantification index of the error, and u i δ is the i-th excitation source on the annular ultrasonic transducer array. i The sound field, v is the speed of sound, and K is the sparse sampling operator.

[0032] Specifically, the formula for calculating the update direction of the model parameter sound velocity distribution and quality factor Q distribution using the conjugate gradient method is as follows:

[0033]

[0034] d k =-g k +β k d k-1

[0035] Among them, g k-1 With g k These are the gradients of the objective function with respect to the model parameters in the (k-1)th and kth iterations, respectively, where <·,·> denote the inner product operation, and β k d is the conjugate coefficient. k-1 With d k These are the update directions of the model parameters in the (k-1)th and kth iterations, respectively; in the initial iteration, it degenerates into standard gradient descent, and the model update direction in the first iteration is d1 = -g1; the optimal step size α k Determined through line search.

[0036] Specifically, the iterative formula for iteratively updating the initial sound velocity distribution and the initial quality factor Q distribution is as follows:

[0037] m k+1 =m k +α k d k

[0038] In the formula, m k+1 For the model parameters after iteration, m k These are the model parameters before iteration.

[0039] Specifically, a two-stage simultaneous inversion strategy is adopted in the process of iteratively updating the sound velocity distribution and the quality factor Q distribution.

[0040] The two-stage simultaneous inversion strategy employs a frequency domain multi-scale inversion method in both stages, stably guiding the inversion process by gradually advancing from low frequency to high frequency, and jointly inverting the sound velocity distribution and quality factor Q distribution at each frequency point.

[0041] In the first stage, a joint inversion strategy is used to simultaneously update the initial sound velocity distribution and the initial quality factor Q distribution to obtain preliminary two-parameter imaging results.

[0042] In the second stage, the quality factor Q distribution obtained from the first-order inversion is discarded, and only the updated sound velocity distribution is retained as the basis for updating. Based on the updated sound velocity distribution and the initial quality factor Q distribution, the joint inversion is carried out again until the iteration ends, and the final sound velocity distribution and quality factor Q distribution are obtained.

[0043] Specifically, the model to be imaged is biological tissue.

[0044] Specifically, the method for obtaining the forward modeling simulation sound field is as follows: solving the computational domain sound field u = A using a nine-point finite difference and LU decomposition algorithm. -1 δ, using the sparse sampling operator K to extract the sound field p=Ku at the multi-element annular ultrasonic transducer array, and obtain the forward modeling simulation sound field.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] 1) Compared with traditional acoustic FWI, this invention introduces the Kolsky-Futterman (KF) dissipation model in the forward modeling process, thereby more accurately describing the propagation law of sound waves in biological tissues.

[0047] 2) The objective function in the full waveform inversion consists of two parts: the sound field data fitting term and the model parameter constraint term. The additional parameter constraints help suppress ill-posedness during the inversion process and promote the stable convergence of the objective function.

[0048] 3) The two-stage simultaneous inversion strategy adopted in this invention effectively alleviates the pathological and ill-posed problems in multi-parameter FWI and realizes high-resolution reconstruction of the sound velocity distribution and quality factor Q distribution of biological soft tissue. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart of the present invention.

[0051] Figure 2 This is a diagram of a ring array observation system and a realistic model of breast lesions according to an embodiment of the present invention; wherein, Figure 2 -(a) shows the true sound velocity distribution and quality factor Q distribution of the benign tumor model. Figure 2 -(b) shows the true sound velocity distribution and quality factor Q distribution of the malignant tumor model.

[0052] Figure 3 This is the reconstruction result of the sound velocity distribution and quality factor Q distribution of a single benign tumor lesion in one embodiment of the present invention.

[0053] Figure 4 This is the reconstruction result of the sound velocity distribution and quality factor Q distribution of a single malignant tumor lesion in one embodiment of the present invention.

[0054] Figure 5 This is a curve showing the decrease in sound velocity distribution and quality factor Q distribution loss for a single benign or malignant tumor lesion in one embodiment of the present invention.

[0055] Figure 6 This is a true model and reconstruction result of the sound velocity distribution and quality factor Q distribution of multiple lesions in one embodiment of the present invention; wherein, Figure 6 -(a) shows the true sound velocity distribution and quality factor Q distribution of multiple lesions. Figure 6 -(b) shows the reconstructed sound velocity distribution and quality factor Q distribution.

[0056] Figure 7 This is a true model and reconstruction result of the sound velocity distribution and quality factor Q distribution of calcified lesions in one embodiment of the present invention. Figure 7 -(a) shows the true sound velocity distribution and quality factor Q distribution of calcified lesions. Figure 7 -(b) shows the reconstructed sound velocity distribution and quality factor Q distribution. Detailed Implementation

[0057] 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 embodiments of the present invention, and not all embodiments. 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.

[0058] like Figure 1 As shown, a regularized multi-parameter full-waveform inversion ultrasound imaging method is proposed. This method utilizes a model parameter constraint-based multi-parameter joint inversion method (hereinafter referred to as QFWI) to simultaneously invert the sound velocity and quality factor Q parameters of biological tissues. The imaging model is then subjected to time-domain forward modeling, and the frequency-domain observed sound field is obtained after discrete Fourier transform. QFWI uses the KF dissipation model to construct the forward modeling equation, explicitly introducing the quality factor Q into the complex slow term, thereby accurately describing the attenuation behavior of sound waves in the forward modeling simulation. The loss function consists of a traditional data fitting term and an additional model parameter constraint term, achieving regularization constraints and enhancing the stability and convergence of the inversion. During the inversion process, the inversion proceeds sequentially from low frequency to high frequency, employing a two-stage simultaneous inversion strategy to achieve joint updates of the sound velocity and quality factor Q distributions. The specific steps are as follows:

[0059] S1. Using a multi-element ring ultrasonic transducer array, full-matrix time-domain acoustic field data acquisition is performed on the model to be imaged. After discrete Fourier transform, the frequency domain observation acoustic field d is obtained.

[0060] The model to be imaged is biological tissue; the matrix size of the frequency domain observed sound field d is (N f N r N s N f N represents the number of frequencies selected. s N represents the number of emission sources. r This represents the number of receiving sources.

[0061] In this embodiment, the time-domain acoustic field data was obtained through simulation experiments using the k-Wave toolkit, based on the actual spatial scale of biological tissue imaging and the propagation characteristics of ultrasound in the medium, such as Figure 2 As shown, the model's computational range was set to 24×24cm, and the spatial grid spacing was set to dx=dy=0.15cm. A ring-shaped ultrasonic transducer array with a diameter of 22cm and containing 512 elements was arranged around the biological tissue. To balance tissue penetration capability and interface imaging accuracy, a Ricker wavelet with a main frequency of 1MHz was selected as the excitation signal, and the time step was set to 2.87×10⁻⁶ according to the CFL condition. -2μs. To accurately simulate sound wave propagation and reduce boundary reflections, a perfectly matched layer with a thickness of 8 mm was set at the boundary of the computational domain. The complete sound field time series was recorded in full matrix acquisition mode, and after discrete Fourier transform, 25 dB of Gaussian white noise was added to simulate noise interference in the actual imaging environment, generating a frequency domain observation sound field of size 512×512.

[0062] S2. Construct the QFWI forward equation using the KF dissipation model and explicitly introduce the quality factor Q into the complex slow term; obtain the forward simulation sound field based on the QFWI forward equation.

[0063] The propagation of sound waves in the frequency domain is described by the Helmholtz equation:

[0064]

[0065] in, Let ω be the Laplace operator, x be the spatial position, v(x) be the speed of sound at spatial position x, δ(x,ω) and u(x,ω) be the source term and sound field at spatial position x at angular frequency ω, respectively, and the slowness at spatial position x is s(x) = 1 / v(x).

[0066] After spatial discretization using the nine-point finite difference scheme, the Helmholtz equation can be expressed in matrix form:

[0067] A(x,ω)u(x,ω)=δ(ω) (2)

[0068] Among them, the complex impedance matrix It is a large sparse matrix.

[0069] To characterize the dispersion and attenuation effects of the medium, a KF model is introduced into the Helmholtz equation to describe slowness, and the quality factor Q is explicitly embedded in the complex slowness:

[0070]

[0071] In the formula, v(ω) is the speed of sound at angular frequency ω, ω r Let i be the reference frequency and i be the imaginary part. Thus, the complex impedance matrix A is reconstructed, and the computational domain sound field u = A is efficiently solved using the nine-point finite difference and LU decomposition algorithms. -1 δ, the sound field p = Ku at the multi-element ring ultrasonic transducer array extracted using the sparse sampling operator K, is the forward modeling sound field.

[0072] The QFWI forward equation consists of equations (1) and (3).

[0073] In this embodiment, based on the number of elements in the annular ultrasonic transducer array, the size of the forward modeling simulation sound field is 512×512.

[0074] S3. Calculate the data residual between the frequency domain observed sound field d and the forward modeling simulated sound field p. Construct the data fitting term of the objective function of QFWI based on least squares, and add an additional model parameter stability function as a regularization term. This transforms QFWI from a least squares-based optimization process into a regularized optimization problem, suppressing ill-posedness in the multi-parameter inversion process and promoting the convergence of the objective function.

[0075] The objective function of the QFWI is shown in equation (4):

[0076] E(ω,m)=E data (ω,m)+μE reg (ω,m) (4)

[0077] Where μ is the regularization weight and m is the unknown model parameter to be solved.

[0078] E data (ω,m) is the L2 normalized mismatch function, used to measure the difference between the frequency domain observed sound field d and the forward modeled sound field p. The L2 normalized mismatch function E... data The expression for (ω,m) is as follows:

[0079]

[0080] Where, p i and d i It is the i-th excitation source δ on the ring ultrasonic transducer array i The forward modeling of the sound field and the observed sound field, where i ranges from 1 to N, and N is the number of elements in the ring ultrasonic transducer array.

[0081] E reg (ω,m) is the model parameter stability function, used as a regularization term. MGS regularization enhances the spatial smoothness and stability of the model parameters by penalizing abrupt and discontinuous changes in the speed of sound and quality factor Q. The mathematical form of the model parameter stability function is expressed as a spatial integral:

[0082]

[0083] In the formula, ε is the gradient operator, and ε is the control factor in the regularization term to prevent the denominator from approaching zero and to adjust the sparsity and edge preservation ability of the regularization term.

[0084] S4. Based on the objective function of QFWI, derive the gradient expressions for the sound velocity distribution and quality factor Q distribution of the model parameters, and obtain the gradient information of the sound velocity distribution and quality factor Q distribution of the model parameters.

[0085] To avoid numerical instability in the low-attenuation region, a parameterization scheme v is selected. -1 and Q -1 Based on the mapping relationship between the unknown model parameters to be solved and the sound field, i.e., formulas (7) and (3), the unknown model parameter m to be solved in the QFWI objective function is set as the slowness s as the transition parameter for gradient derivation. Then, the QFWI objective function has a certain relationship with the two model parameters v. -1 and Q -1 The update gradient is written as:

[0086]

[0087] In the formula, E is the quantitative index of error, and u i δ is the i-th excitation source on the annular ultrasonic transducer array. i The domain of sound field, where v is the speed of sound.

[0088] S5. Based on the gradient information of the sound velocity distribution and quality factor Q distribution of the model parameters, the conjugate gradient method is used to calculate the update direction d of the sound velocity distribution and quality factor Q distribution of the model parameters. k The calculation formula is as follows:

[0089]

[0090] d k =-g k +β k d k-1 (11)

[0091] Among them, g k-1 With g k These are the gradients of the objective function with respect to the model parameters in the (k-1)th and kth iterations, respectively, where <·,·> denote the inner product operation, and β k d is the conjugate coefficient. k-1 With d k These represent the update directions of the model parameters in the (k-1)th and kth iterations, respectively. In the initial iteration, it degenerates into standard gradient descent, meaning the model update direction in the first iteration is d1 = -g1. The optimal step size α... k Determined through line search.

[0092] S6. Based on the initial sound velocity distribution and initial quality factor Q distribution of the model to be imaged, as well as the gradient information and update direction of the model parameter sound velocity distribution and quality factor Q distribution, iteratively update the initial sound velocity distribution and initial quality factor Q distribution to obtain the final sound velocity distribution and quality factor Q distribution.

[0093] The iterative formula is shown in formula (12).

[0094] m k+1 =m k+α k d k (12)

[0095] In the formula, m k+1 For the model parameters after iteration, m k These are the model parameters before iteration.

[0096] To effectively alleviate the ill-posedness problem in multi-parameter FWI and achieve high-resolution reconstruction of the spatial distributions of sound velocity and quality factor Q, a two-stage simultaneous inversion strategy is adopted during the iterative update of the initial sound velocity distribution and the initial quality factor Q distribution. This two-stage simultaneous inversion strategy employs a frequency domain multi-scale inversion method in both stages, stably guiding the inversion process by gradually advancing from low to high frequencies, and jointly inverting the sound velocity and quality factor Q distributions at each frequency point.

[0097] In the first stage, a joint inversion strategy was used to simultaneously update the initial sound velocity distribution and the initial quality factor Q distribution, obtaining preliminary two-parameter imaging results.

[0098] In the second stage, to further improve the inversion accuracy and stability, the quality factor Q distribution obtained from the first-order inversion is discarded, and only the updated sound velocity distribution is retained as the basis for updating. Based on the updated sound velocity distribution and the initial quality factor Q distribution, the joint inversion is carried out again until the iteration ends, and the final sound velocity distribution and quality factor Q distribution are obtained, thus obtaining more accurate and robust sound velocity and quality factor Q distribution imaging results.

[0099] In this embodiment, based on the transmission frequency and energy distribution range, two frequency bands are set for the inversion: [0.3MHz, 1.25MHz] and [0.325MHz, 1.275MHz], with a step size of 50kHz for both, to ensure the continuity and stability of the inversion. The initial model is set as a homogeneous water medium, with an initial sound velocity of 1480m / s and an initial quality factor Q of 1e5 to approximate a zero-attenuation condition.

[0100] Figure 3 The reconstruction results and cross-sectional views of the sound velocity distribution and quality factor Q distribution of benign lesions according to the present invention are shown. The similarity between the calculated inversion results and the real model is calculated, with similarities of 0.9113 and 0.8630 for the sound velocity distribution and quality factor Q distribution, respectively. It can be observed that the lesion area exhibits a significantly higher sound velocity characteristic than normal tissue, and the Q value is close to the level of surrounding fat and other tissues, which is consistent with the typical acoustic characteristics of benign tumors. The tissue structure of benign lesion areas is relatively homogeneous, with weak energy attenuation, typically exhibiting the characteristics of high sound velocity and low attenuation (high Q value).

[0101] Figure 4The reconstruction results and cross-sectional images of the sound velocity distribution and quality factor Q distribution of malignant lesions presented in this invention are shown. The similarity between the calculated inversion results and the real model is calculated, with similarities of 0.9167 and 0.8925 for the sound velocity distribution and quality factor Q distribution, respectively. The lesion region also exhibits a significantly higher sound velocity characteristic than normal tissue, but its Q value is significantly lower than that of the surrounding normal tissue, which is consistent with the acoustic characteristics of malignant tumors. Malignant lesion regions have high tissue specificity, leading to increased energy dissipation during sound wave propagation, typically exhibiting a high sound velocity and high attenuation (low Q value) characteristic. Although there is some overlap in the high sound velocity distributions of the two types of lesions, QFWI, by quantifying the attenuation characteristics of tissues, explains the differences in their pathological essence, verifying the specific advantage of the quality factor Q in differentiating benign and malignant tumors.

[0102] Figure 5 The curves showing the model loss variation of the single tumor model of the present invention during the inversion process are presented. Figure 5 -(a) shows the loss curve of the sound velocity distribution of the inverted benign tumor model. During the two-stage inversion process, the loss function continues to decrease, indicating that the reconstruction result gradually approaches the real model. Figure 5 -(b) shows the loss curve of the inverted benign tumor quality factor Q distribution. Due to parameter crosstalk, the loss increases slightly in the first three iterations, and then shows a continuous downward trend. The inverted quality factor Q distribution gradually approaches the real model. Figure 5 -(c) and Figure 5 -(d) shows the loss curves of the sound velocity distribution and quality factor Q distribution of the malignant tumor model during the inversion process, exhibiting a trend consistent with the inversion results of benign tumors. This verifies that the QFWI method in this invention has good robustness and effectiveness in the joint reconstruction and property determination of acoustic parameters of soft tissue.

[0103] Furthermore, this invention is applied to multiple tumor models and calcification point models. Figure 6 The true model and reconstruction results of the sound velocity distribution and quality factor Q distribution of the multiple tumor model of the present invention are presented. Figure 6 -(a) shows the true sound velocity distribution and quality factor Q distribution of the multiple tumor model. Figure 6 -(b) presents the reconstructed sound velocity distribution and quality factor Q distribution of the multiple tumor model. The similarity between the inversion results and the real model was calculated, with similarities of 0.9284 and 0.9139 for the sound velocity distribution and quality factor Q distribution, respectively. The inverted sound velocity distribution clearly located and separated the two lesions, and the Q parameter inversion results further determined the nature of the lesions. The Q values ​​of both lesions were significantly lower than those of normal tissue, indicating that they were malignant lesions.

[0104] Figure 7The true model and reconstruction results of the sound velocity distribution and quality factor Q distribution of the calcification model of the present invention are presented. Figure 7 -(a) shows the true sound velocity distribution and quality factor Q distribution of the calcification model. Figure 7 -(b) shows the reconstruction results of the sound velocity distribution and quality factor Q distribution of the calcification model. The similarity between the inversion results and the real model was calculated, and the similarity of the sound velocity distribution and the quality factor Q distribution were 0.9066 and 0.8684, respectively. The reconstructed sound velocity distribution can accurately locate the position of calcification points, and the inversion results of the Q parameters successfully present the high attenuation characteristics of calcification points. Since the sound velocity of calcification points is significantly higher than that of soft tissue, the large difference in sound velocity can easily introduce large errors in the inversion process using pure water parameters as the initial model, thereby aggravating the parameter crosstalk effect in multi-parameter inversion. Especially in the second stage of Q parameter inversion, due to the large sound velocity error, the accumulated sound field error propagates during the inversion process, producing obvious low-Q artifact regions around calcification points. However, this artifact does not affect the nature analysis of the lesion. Combined with the joint inversion characteristics of high sound velocity and extremely low Q value, the location and physical characteristics of calcification points can still be accurately identified, further verifying the robustness and discriminative ability of the present invention in the imaging of complex lesions.

[0105] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A regularization-based multi-parameter full-waveform inversion ultrasound imaging method, characterized in that, Includes the following steps: S1. Using a multi-element ring ultrasonic transducer array, full-matrix time-domain acoustic field data acquisition is performed on the model to be imaged. After discrete Fourier transform, the frequency domain observation acoustic field is obtained. S2. Construct the QFWI forward modeling equation using the KF dissipation model, and obtain the forward modeling simulation sound field based on the QFWI forward modeling equation; S3. Calculate the data residual between the frequency domain observed sound field and the forward modeling simulated sound field. Construct the data fitting term of the objective function of QFWI based on least squares, and add the model parameter stability function as a regularization term to obtain the objective function of QFWI. S4. Based on the objective function of QFWI, derive the gradient expressions for the sound velocity distribution and quality factor Q distribution of the model parameters, and obtain the gradient information of the sound velocity distribution and quality factor Q distribution of the model parameters. S5. Based on the gradient information of the sound velocity distribution and quality factor Q distribution of the model parameters, the conjugate gradient method is used to calculate the update direction of the sound velocity distribution and quality factor Q distribution of the model parameters. S6. Based on the initial sound velocity distribution and initial quality factor Q distribution of the model to be imaged, as well as the gradient information and update direction of the model parameter sound velocity distribution and quality factor Q distribution, iteratively update the initial sound velocity distribution and initial quality factor Q distribution to obtain the final sound velocity distribution and quality factor Q distribution. The method for constructing the QFWI forward modeling equation using the KF dissipation model is as follows: the KF dissipation model is introduced into the Helmholtz equation in the frequency domain to describe the slowness, and the quality factor Q is explicitly embedded in the complex slowness to describe the frequency-dependent attenuation characteristics of the medium; the Helmholtz equation containing the dissipation term is spatially discretized using a nine-point finite difference scheme to obtain a discrete expression of the Helmholtz equation containing the dissipation term in matrix form, and the QFWI forward modeling equation is constructed. The objective function of QFWI is expressed as follows: ； in, For regularization weights, Angular frequency, These are the unknown model parameters that need to be solved; It is the L2 normalized mismatch function, expressed as follows: ； in, and It is the first on the ring ultrasonic transducer array One source of motivation The forward modeling of the sound field and the observed sound field, The value ranges from 1 to N, where N is the number of elements in the ring ultrasonic transducer array. It is the model parameter stability function, mathematically expressed as the following space integral form: ； In the formula, This is the control factor in the regularization term. For gradient operators; Spatial location; The gradient expressions for the sound velocity distribution and the quality factor Q distribution of the model parameters are: ； ； In the formula, It is a complex impedance matrix. As a quantitative indicator of error, The first on the ring ultrasonic transducer array One source of motivation The sound field, For the speed of sound, It is a sparse sampling operator; This is the reference frequency.

2. The regularization-based multi-parameter full-waveform inversion ultrasound imaging method according to claim 1, characterized in that, The expression for the QFWI forward equation is: ； ； In the formula, For the Laplace operator, Angular frequency, Spatial location The speed of sound at that location and They are at angular frequency Below, spatial location The source term and sound field at the location; Angular frequency The speed of sound at that time This is the imaginary part.

3. The regularization-based multi-parameter full-waveform inversion ultrasound imaging method according to claim 2, characterized in that, The formula for calculating the update direction of the sound velocity distribution and quality factor Q distribution of the model parameters using the conjugate gradient method is as follows: ； ； in, and They are the first The iteration and the The gradient of the objective function with respect to the model parameters in the next iteration. This represents the inner product operation. The conjugate coefficient, and They are the first The iteration and the The update direction of the model parameters in the next iteration; in the initial iteration, it degenerates into standard gradient descent, and the update direction of the model in the first iteration is... Optimal step size Determined through line search.

4. The regularization-based multi-parameter full-waveform inversion ultrasound imaging method according to claim 3, characterized in that, The iterative formula for updating the initial sound velocity distribution and the initial quality factor Q distribution is as follows: ； In the formula, These are the model parameters after iteration. These are the model parameters before iteration.

5. The regularization-based multi-parameter full-waveform inversion ultrasound imaging method according to claim 4, characterized in that, A two-stage simultaneous inversion strategy is adopted in the process of iteratively updating the sound velocity distribution and the quality factor Q distribution. The two-stage simultaneous inversion strategy employs a frequency domain multi-scale inversion method in both stages, stably guiding the inversion process by gradually advancing from low frequency to high frequency, and jointly inverting the sound velocity distribution and quality factor Q distribution at each frequency point. In the first stage, a joint inversion strategy is used to simultaneously update the initial sound velocity distribution and the initial quality factor Q distribution to obtain preliminary two-parameter imaging results. In the second stage, the quality factor Q distribution obtained from the first-order inversion is discarded, and only the updated sound velocity distribution is retained as the basis for updating. Based on the updated sound velocity distribution and the initial quality factor Q distribution, the joint inversion is carried out again until the iteration ends, and the final sound velocity distribution and quality factor Q distribution are obtained.

6. The regularization-based multi-parameter full-waveform inversion ultrasound imaging method according to claim 5, characterized in that, The model to be imaged is biological tissue.

7. The regularization-based multi-parameter full-waveform inversion ultrasound imaging method according to claim 6, characterized in that, The method for obtaining the forward modeling simulation sound field is as follows: solving the computational domain sound field using the nine-point finite difference and LU decomposition algorithm. Using sparse sampling operators The sound field extracted at the multi-element ring ultrasonic transducer array This yields a forward-modeled simulated sound field.

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