A method for high-resolution ultrasound imaging based on memory-enhanced prior dynamic model

Abstract

The present invention discloses an ultrasonic high-resolution imaging method based on a memory-enhanced a priori dynamic model. The method proposes a memory-enhanced a priori dynamic model, constructs a loss function containing a sparsity constraint, establishes a deconvolution optimization solver and a proximal mapping network to integrate and iteratively solve the loss function according to a semi-quadratic splitting optimization algorithm, uses a PSF to initialize the deconvolution optimization solver and sets it as a learnable parameter, and dynamically updates it during training, thereby enhancing the physical interpretability of the model; establishes an LSTM unit and places it after the proximal mapping network, thereby clearing redundant information during the iteration process, ensuring that necessary features are provided for the next iteration, and obtaining a memory-enhanced a priori dynamic model; and optimizes the model parameters to effectively obtain accurate PSF and image fidelity weight factors, thereby achieving the goal of automatic parameter adjustment and realizing high-resolution reconstruction of ultrasonic images.

Description

Technical Field

[0001] The invention relates to a high-resolution reconstruction method for ultrasonic images, and in particular to an ultrasonic high-resolution imaging method based on a memory-enhanced priori dynamic model. Background Art

[0002] Ultrasound imaging is a non-invasive, low-cost, real-time imaging method that is widely used in clinical imaging. The higher the number of channels of an ultrasound device, the higher the resolution of the acquired ultrasound image, and the higher the cost of the ultrasound device. Acquiring potential high-channel ultrasound images from low-channel ultrasound images can greatly reduce the cost of ultrasound equipment.

[0003] The degradation process of ultrasound images can be modeled as the convolution between the tissue reflection function and the point spread function (PSF) of the ultrasound image. At present, the main methods for high-resolution reconstruction of ultrasound images are traditional deconvolution methods and deep learning methods. The principles of the above methods are different. While they are widely used in the field of high-resolution reconstruction of ultrasound images, they also have some shortcomings. Since the PSF between low-channel ultrasound images and high-channel ultrasound images is difficult to solve, traditional deconvolution algorithms are difficult to eliminate the physical deviation between the reconstructed high-resolution ultrasound images and high-channel ultrasound images, which makes it very difficult to obtain high-channel ultrasound images from low-channel ultrasound images. The core of deep learning is to use neural networks to learn to fit the nonlinear mapping between input and label. Although it can greatly improve the resolution of ultrasound images, it lacks physical interpretability. Summary of the invention

[0004] The purpose of the present invention is to provide an ultrasonic high-resolution imaging method based on a memory-enhanced prior dynamic model, which solves the problem that the traditional high-resolution reconstruction method cannot obtain accurate PSF and is prone to generate redundant information during the iteration process, which affects the model performance, thereby improving the reconstruction quality of ultrasonic images. The present invention can dynamically obtain accurate PSF by automatically adjusting parameters, remove redundant information that is prone to be generated during the iteration process, ensure that only necessary features are retained in each iteration, realize model memory enhancement, and improve imaging quality. It has high social significance and economic value in the field of high-resolution reconstruction of ultrasonic images.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for high-resolution ultrasonic imaging based on a memory-enhanced prior dynamic model comprises the following steps:

[0007] Step 1: Model the low-resolution ultrasound image g(x, y) as the convolution of the high-resolution ultrasound image f(x, y) and the point spread function h(x, y) to obtain an ultrasound imaging degradation model, extract the PSF from the low-resolution ultrasound image, and obtain a preliminary estimate of the PSF, denoted as h;

[0008] Step 2: Combine the ultrasound imaging degradation model in step 1 to establish a loss function L1 with sparsity constraints. According to the semi-quadratic splitting optimization algorithm, a deconvolution optimization solver O is constructed. h,μ (·|z (t-1) ) is integrated with the proximal mapping network P(·) to iteratively solve the loss function; the image fidelity weight factor μ is set, h and μ are used to initialize the deconvolution optimization solver, and then h and μ are set as learnable parameters and dynamically updated during training; an LSTM unit is established and placed after the proximal mapping network P(·) to modulate the information flow during the iteration process, remove unnecessary redundant information, and ensure that the necessary features are provided for the next iteration; finally, the memory enhanced prior dynamic model MESPD is obtained θ,h,μ (·|z (0) ,r (0) ,T);

[0009] Step 3: Take the low-resolution ultrasound image g(x,y) as input and the corresponding high-resolution ultrasound image f(x,y) as the target label, and reconstruct the image by minimizing The two-norm difference between the high-resolution ultrasound image f(x,y) is used to update the parameters h, μ of the deconvolution dynamic optimization solver and the memory-enhanced prior dynamic model MESPD based on the gradient backpropagation. θ,h,μ (·|z (0) ,r (0) ,T) in the neural network weights and bias parameters θ, for the memory enhanced prior dynamic model MESPD θ,h,μ (·|z (0) ,r (0) ,T) for end-to-end training; the trained MESPD θ,h,μ (·|z (0) ,r (0) ,T) is applied to low-resolution ultrasound images to achieve high-resolution reconstruction.

[0010] Compared with the prior art, the present invention has the following advantages:

[0011] 1. The present invention proposes a memory-enhanced a priori dynamic model. By constructing a loss function containing a sparsity constraint, a deconvolution optimization solver and a proximal mapping network are integrated to iteratively solve the loss function according to a semi-quadratic splitting optimization algorithm. PSF is used to initialize the deconvolution optimization solver and set as a learnable parameter, which is dynamically updated during training to enhance the physical interpretability of the model. An LSTM unit is established and placed after the proximal mapping network to clear redundant information during the iteration process to ensure that the necessary features are provided for the next iteration, thereby obtaining a memory-enhanced a priori dynamic model. By optimizing the model parameters, accurate PSF and image fidelity weight factors are effectively obtained to achieve the goal of automatic parameter adjustment and realize high-resolution reconstruction of ultrasound images.

[0012] 2. The existing high-resolution reconstruction methods for ultrasound images often assume that the PSF is unchanged, and cannot capture the precise PSF between high-resolution ultrasound images and low-resolution ultrasound images. At the same time, the existing high-resolution reconstruction methods for ultrasound images based on deep learning are not physically interpretable. The memory-enhanced prior dynamic model proposed in the present invention can obtain accurate PSF, improve the resolution of ultrasound images, and while enhancing physical interpretability, it reduces the need for manual parameter adjustment, meeting the requirements for high efficiency and accuracy of image reconstruction in actual work production. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The figure is a flow chart of the ultrasonic high-resolution imaging method of the present invention.

[0014] Figure 2 Low and high resolution b-mode ultrasound images.

[0015] Figure 3 Diagram of the structure of the dynamic model for memory-enhanced priors.

[0016] Figure 4 Reconstruction effect diagram of memory-enhanced prior dynamic model. DETAILED DESCRIPTION

[0017] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0018] The invention provides an ultrasonic high-resolution imaging method based on a memory-enhanced a priori dynamic model. First, a low-resolution ultrasonic image is modeled as a convolution of a high-resolution ultrasonic image and a PSF. The PSF and the high-resolution ultrasonic image are additively related in a complex cepstrum domain and are located in different frequency bands. The PSF is extracted from the low-resolution ultrasonic image to obtain a preliminary estimate of the PSF. Then, a loss function including a sparsity constraint is established. According to a semi-quadratic splitting optimization algorithm, the loss function is iteratively solved by constructing a deconvolution optimization solver and a proximal mapping network integration. The PSF is used to initialize the deconvolution optimization solver and is set as a learnable parameter. The parameter is dynamically updated during training. An LSTM unit is established and placed after the proximal mapping network to clear redundant information during the iteration process, thereby ensuring that necessary features are provided for the next iteration, and the memory-enhanced a priori dynamic model is obtained. Finally, the parameters in the memory-enhanced a priori dynamic model, namely, the PSF, the image fidelity weight factor and the neural network parameters, are optimized to achieve high-resolution reconstruction of ultrasonic images.

[0019] like Figure 1 As shown, the specific steps are as follows:

[0020] Step 1: Model the low-resolution ultrasound image g(x,y) as the convolution of the high-resolution ultrasound image f(x,y) and the point spread function h(x,y) to obtain the ultrasound imaging degradation model, extract the PSF from the low-resolution ultrasound image, and obtain a preliminary estimate of the PSF, denoted as h. The specific steps are as follows:

[0021] Step 1. Establish an ultrasound imaging degradation model:

[0022]

[0023] Wherein, f(x,y) represents a high-resolution ultrasound image, g(x,y) represents a low-resolution ultrasound image, h(x,y) represents the PSF between the high-resolution ultrasound image and the low-resolution ultrasound image, and n(x,y) represents the measurement noise. represents the two-dimensional convolution operator;

[0024] Step 12: read a low-resolution ultrasound image radio frequency data (Radio-Frequency, RF) g(x, y) and its corresponding high-resolution ultrasound image RF data f(x, y);

[0025] Step 13: Ignore the influence of noise, extract the complex cepstrum feature of g(x,y) and obtain feature d;

[0026] Step 14: Using the characteristics that h(x,y) and f(x,y) are additive in the complex cepstrum domain and are located in different frequency bands, the ultrasound image segmentation sequence is divided into two parts:

[0027] d=d h +d f (2)

[0028] Among them, d h represents the complex cepstrum characteristics of h(x,y), d f represents the complex cepstrum characteristics of f(x,y), and then d h Perform an inverse complex cepstrum transform to obtain a preliminary estimate h of the PSF:

[0029]

[0030] in, represents the Fourier transform, represents the inverse Fourier transform.

[0031] Step 2: Combine the ultrasound imaging degradation model in step 1 to establish a loss function L1 with sparsity constraints. According to the semi-quadratic splitting optimization algorithm, a deconvolution optimization solver O is constructed. h,μ (·|z (t-1) ) is integrated with the proximal mapping network P(·) to iteratively solve the loss function; the image fidelity weight factor μ is set, h and μ are used to initialize the deconvolution optimization solver, and then h and μ are set as learnable parameters and dynamically updated during training; an LSTM unit is established and placed after the proximal mapping network P(·) to modulate the information flow during the iteration process, remove unnecessary redundant information, and ensure that the necessary features are provided for the next iteration; finally, the memory enhanced prior dynamic model MESPD is obtained θ,h,μ (·|z (0) ,r (0) ,T). The specific steps are as follows:

[0032] Step 21: Combine the ultrasound imaging degradation model in step 1 and establish a loss function L1 with sparsity constraints:

[0033]

[0034] Among them, ||·||2 represents the second norm, ||·||1 represents the first norm, and λ represents the sparsity weight factor;

[0035] Step 22: Introduce auxiliary variable z and reconstruct the loss function L2:

[0036]

[0037] Where μ represents the fidelity weight factor;

[0038] Step 2 and 3: Solve the loss function L2 through the semi-quadratic splitting optimization algorithm, alternately solve f and z, and the t-th iteration process is as follows:

[0039]

[0040]

[0041] Step 24: For the f subproblem, take the derivative of equation (6) with respect to f and set the derivative to 0, and you can get the deconvolution optimization solver:

[0042]

[0043] Step 25: For the z subproblem, a learnable proximal mapping network P(·) is used to fit the proximal gradient solution, thereby establishing a deconvolution optimization solver and a deep neural network integration;

[0044] Step 26: Set the image fidelity weight factor μ. Use h obtained in step 1 and the image fidelity weight factor μ set in step 22 to initialize the deconvolution optimization solver, and set h and μ as learnable parameters. Dynamically update them during training to obtain the deconvolution dynamic optimization solver, denoted as O. h,μ (·|z (t-1) ):

[0045]

[0046] in, represents the conjugate of Fourier transform;

[0047] Input low-resolution ultrasound image g and get the result f of the tth iteration (t) :

[0048] f (t) =O h,μ (g,z (t-1) ) (10)

[0049] Step 27: Deconvolution dynamically optimizes the solver result f (t) As the input of the proximal mapping network P(·), P(·) will learn a mapping that can transform f after the deconvolution dynamic optimization solver (t) Converted into a high-resolution ultrasound image

[0050]

[0051] Step 28: Deconvolution Dynamic Optimization Solver O h,μ (·|z (t-1) ) and the proximal mapping network P(·) are updated alternately in the iterative process to obtain a sparse prior dynamic model;

[0052] Step 29: Construct a long short-term memory network (LSTM) after the proximal mapping network P(·), and then Passed as input to the LSTM unit and combined with the LSTM state r at the previous moment (t-1) , to calculate the current state r (t) , which enables the model to not only capture the information of the current data, but also take into account the previous historical information, so that the overall model can remove unnecessary redundant information during the iteration process and ensure that the necessary features are provided for the next iteration:

[0053]

[0054] Step 20: Introduce a convolutional layer Conv(·) after the LSTM module. The state r of the LSTM output (t) After the convolution transformation, the result of the zth iteration is obtained:

[0055] z (t) =Conv(r (t) ) (13)

[0056] Step 21: Repeat steps 26 to 20, continuously update the memory in this process, and finally obtain the memory enhancement prior dynamic model, denoted as MESPD θ,h,μ (·|z (0) ,r (0) ,T), where θ represents MESPD θ,h,μ (·|z (0) ,r (0) ,T) are the weights and bias parameters of the neural network, z (0) represents the initial state of z, r (0) represents the initial state of LSTM, and T represents the number of iterations.

[0057] Step 3: Take the low-resolution ultrasound image g(x,y) as input and the corresponding high-resolution ultrasound image f(x,y) as the target label, and reconstruct the image by minimizing The two-norm difference between the high-resolution ultrasound image f(x,y) is used to update the parameters h, μ of the deconvolution dynamic optimization solver and the memory-enhanced prior dynamic model MESPD based on the gradient backpropagation. θ,h,μ (·|z (0) ,r (0) ,T) in the neural network weights and bias parameters θ, for the memory enhanced prior dynamic model MESPD θ,h,μ (·|z (0) ,r (0) ,T) for end-to-end training; the trained MESPD θ,h,μ(·|z (0) ,r (0) ,T) is applied to low-resolution ultrasound images to achieve high-resolution reconstruction. The specific steps are as follows:

[0058] Step 31: During the training of the neural network, the low-resolution ultrasound image g(x,y) is used as input, and the high-resolution ultrasound image f(x,y) is used as a label to train the memory-enhanced prior dynamic model MESPD. θ,h,μ (·|z (0) ,r (0) ,T) is trained end-to-end by minimizing the reconstructed image The difference between the high-resolution ultrasound image f(x,y) and the image f(x,y) is used to optimize the parameters θ,h,μ in the memory-enhanced prior dynamic model:

[0059]

[0060] Step 32: Update the neural network layer parameters θ and the deconvolution dynamic optimization solver parameters h and μ according to the gradient back propagation method. The gradient update formula of the deconvolution dynamic optimization solver parameters h and μ is as follows:

[0061]

[0062]

[0063] in, represents partial differential, f (t) represents the intermediate image obtained by the deconvolution dynamic optimization solver, z (t-1) represents the intermediate image obtained by the neural network, g represents the low-resolution ultrasound image, and during the training process, θ, h, and μ are continuously optimized;

[0064] Step 3. Input the low-resolution ultrasound image g(x,y) into the trained memory-enhanced prior dynamic model MESPD θ,h,μ (·|z (0) ,r (0) ,T), and reconstruct it effectively with high resolution to obtain

[0065] Example:

[0066] The data set used in this embodiment contains 2000 pairs of low- and high-resolution ultrasound images, all of which are acquired using a transducer with 128 activated array elements, and the number of channels distributed therein is 32 and 64, respectively. The low- and high-resolution ultrasound images in the data set are all RF data after beamforming.

[0067] Execute step 1: Establish an ultrasound imaging degradation model, read a low-resolution ultrasound image RF data g(x, y) and its corresponding high-resolution ultrasound image RF data f(x, y), the b-mode diagram is as follows Figure 2 As shown. A preliminary estimate of PSFh is obtained from g(x,y).

[0068] Execute step 2: Set the sparsity weight factor μ to 1 and establish the deconvolution optimization solver O h,μ (·|z (t-1) ), h and μ are used to initialize the layer and set as learnable parameters, which are dynamically updated during training. The low-resolution ultrasound image g is input and the image is obtained by O h,μ (·|z (t-1) ) (t) =O h,μ (g,z (t-1) ), where f (t) represents the result f of the tth iteration (t) Then, f (t) As the input of the proximal mapping network P(·), a high-resolution ultrasound image is obtained. A sparse prior dynamic model is obtained.

[0069] Then, an LSTM unit is established and placed after the proximal mapping network P(·). As input, combined with the previous moment LSTM state r (t-1) , calculate the current state A convolutional layer Conv(·) is introduced after the LSTM module, and the state r of the LSTM output (t) After Conv(·), we get the result of the t-th iteration z (t) =Conv(r (t) ), update f alternately (t) 、z (t) , where t = [0, 1, ..., T]. Finally, the memory enhanced prior dynamic model MESPD is obtained θ,h,μ (·|z (0) ,r (0) ,T), and T is set to 3. The memory-enhanced prior dynamic model structure is as follows Figure 3 shown.

[0070] Execute step 3: Take the low-resolution ultrasound image g(x,y) as input and the high-resolution ultrasound image f(x,y) as label, and apply the memory-enhanced prior dynamic model MESPD θ,h,μ (·|z (0) ,r (0) ,3) Perform end-to-end training. During the training process, the image is reconstructed by minimizing The two-norm difference between the image f(x,y) and the high-resolution ultrasound image f(x,y) is used to optimize the parameters θ,h,μ in the memory-enhanced prior dynamic model.

[0071] According to the gradient back-propagation method, the neural network layer parameters θ and the deconvolution dynamic optimization solver parameters h, μ are updated. During the training process, θ, h, μ are continuously optimized to obtain the memory-enhanced prior dynamic model MESPD after parameter optimization. θ,h,μ (·|z (0) ,r (0) ,3). Finally, the low-resolution ultrasound image g(x,y) is input into the model for effective high-resolution reconstruction. The reconstruction effect is shown in the figure Figure 4 shown.

Claims

1. A method for high-resolution ultrasonic imaging based on a memory-enhanced prior dynamic model, characterized in that The method comprises the following steps: Step 1: Model the low-resolution ultrasound image g(x, y) as the convolution of the high-resolution ultrasound image f(x, y) and the point spread function h(x, y) to obtain an ultrasound imaging degradation model, extract the PSF from the low-resolution ultrasound image, and obtain a preliminary estimate of the PSF, denoted as h; Step 2: Combine the ultrasound imaging degradation model in step 1 to establish a loss function L1 with sparsity constraints. According to the semi-quadratic splitting optimization algorithm, a deconvolution optimization solver O is constructed. h,μ (·|z (t-1) ) is integrated with the proximal mapping network P(·) to iteratively solve the loss function; the image fidelity weight factor μ is set, h and μ are used to initialize the deconvolution optimization solver, and then h and μ are set as learnable parameters and dynamically updated during training; an LSTM unit is established and placed after the proximal mapping network P(·) to modulate the information flow during the iteration process, remove unnecessary redundant information, and ensure that the necessary features are provided for the next iteration; finally, the memory enhanced prior dynamic model MESPD is obtained θ,h,μ (·|z (0) ,r (0) ,T), the specific steps are as follows: Step 21: Combine the ultrasound imaging degradation model in step 1 and establish a loss function L1 with sparsity constraints: Among them, ||·||2 represents the second norm, ||·||1 represents the first norm, and λ represents the sparsity weight factor; Step 22: Introduce auxiliary variable z and reconstruct the loss function L2: Where μ represents the fidelity weight factor; Step 2 and 3: Solve the loss function L2 through the semi-quadratic splitting optimization algorithm, alternately solve f and z, and the t-th iteration process is as follows: Step 24: For the f subproblem, derive equation (6) with respect to f and set the derivative to 0 to obtain the deconvolution optimization solver: Step 25: For the z subproblem, a learnable proximal mapping network P(·) is used to fit the proximal gradient solution, thereby establishing a deconvolution optimization solver and a deep neural network integration; Step 26: Set the image fidelity weight factor μ. Use h obtained in step 1 and the image fidelity weight factor μ set in step 22 to initialize the deconvolution optimization solver, and set h and μ as learnable parameters. Dynamically update them during training to obtain the deconvolution dynamic optimization solver, denoted as O. h,μ (·|z (t-1) ): in, represents the conjugate of Fourier transform; Input low-resolution ultrasound image g and get the result f of the tth iteration (t) : f (t) =O h,μ (g,z (t-1) ) (10) Step 27: Deconvolution dynamically optimizes the solver result f (t) As the input of the proximal mapping network P(·), P(·) will learn a mapping that can transform f after the deconvolution dynamic optimization solver (t) Converted into a high-resolution ultrasound image Step 28: Deconvolution Dynamic Optimization Solver O h,μ (·|z (t-1) ) and the proximal mapping network P(·) are updated alternately in the iterative process to obtain a sparse prior dynamic model; Step 29: Construct LSTM and place it after the proximal mapping network P(·), and then Passed as input to the LSTM unit and combined with the LSTM state r at the previous moment (t-1) , to calculate the current state r (t) : Step 20: Introduce a convolutional layer Conv(·) after the LSTM module. The state r of the LSTM output (t) After the convolution transformation, the result of the zth iteration is obtained: z (t) =Conv(r (t) ) (13) Step 21: Repeat steps 26 to 20, continuously update the memory in this process, and finally obtain the memory enhancement prior dynamic model, denoted as MESPD θ,h,μ (·|z (0) ,r (0) ,T), where θ represents MESPD θ,h,μ (·|z (0) ,r (0) ,T) are the weights and bias parameters of the neural network, z (0) represents the initial state of z, r (0) represents the initial state of LSTM, and T represents the number of iterations; Step 3: Take the low-resolution ultrasound image g(x,y) as input and the corresponding high-resolution ultrasound image f(x,y) as the target label, and reconstruct the image by minimizing The two-norm difference between the high-resolution ultrasound image f(x,y) is used to update the parameters h, μ of the deconvolution dynamic optimization solver and the memory-enhanced prior dynamic model MESPD based on the gradient backpropagation. θ,h,μ (·|z (0) ,r (0) ,T) in the neural network weights and bias parameters θ, for the memory enhanced prior dynamic model MESPD θ,h,μ (·|z (0) ,r (0) ,T) for end-to-end training; the trained MESPD θ,h,μ (·|z (0) ,r (0) ,T) is applied to low-resolution ultrasound images to achieve high-resolution reconstruction.

2. The ultrasonic high-resolution imaging method based on the memory-enhanced prior dynamic model according to claim 1 is characterized in that The specific steps of step one are as follows: Step 1. Establish an ultrasound imaging degradation model: Wherein, f(x,y) represents a high-resolution ultrasound image, g(x,y) represents a low-resolution ultrasound image, h(x,y) represents the PSF between the high-resolution ultrasound image and the low-resolution ultrasound image, and n(x,y) represents the measurement noise. represents the two-dimensional convolution operator; Step 12: read a low-resolution ultrasound image RF data g(x, y) and its corresponding high-resolution ultrasound image RF data f(x, y); Step 13: Ignore the influence of noise, extract the complex cepstrum feature of g(x,y) and obtain feature d; Step 14: Using the characteristics that h(x,y) and f(x,y) are additive in the complex cepstrum domain and are located in different frequency bands, the ultrasound image segmentation sequence is divided into two parts: d=d h +d f (2) Among them, d h represents the complex cepstrum characteristics of h(x,y), d f represents the complex cepstrum characteristics of f(x,y), and then d h Perform an inverse complex cepstrum transform to obtain a preliminary estimate h of the PSF: Where F(·) represents Fourier transform, represents the inverse Fourier transform.

3. The ultrasonic high-resolution imaging method based on the memory-enhanced prior dynamic model according to claim 1 is characterized in that The specific steps of step three are as follows: Step 31: During the training of the neural network, the low-resolution ultrasound image g(x,y) is used as input, and the high-resolution ultrasound image f(x,y) is used as a label to train the memory-enhanced prior dynamic model MESPD. θ,h,μ (·|z (0) ,r (0) ,T) is trained end-to-end by minimizing the reconstructed image The difference between the high-resolution ultrasound image f(x,y) and the image f(x,y) is used to optimize the parameters θ,h,μ in the memory-enhanced prior dynamic model: Step 32: Update the neural network layer parameters θ and the deconvolution dynamic optimization solver parameters h and μ according to the gradient back propagation method. The gradient update formula of the deconvolution dynamic optimization solver parameters h and μ is as follows: in, represents partial differential, f (t) represents the intermediate image obtained by the deconvolution dynamic optimization solver, z (t-1) represents the intermediate image obtained by the neural network, g represents the low-resolution ultrasound image, and during the training process, θ, h, and μ are continuously optimized; Step 3. Input the low-resolution ultrasound image g(x,y) into the trained memory-enhanced prior dynamic model MESPD θ,h,μ (·|z (0) ,r (0) ,T), and reconstruct it effectively with high resolution to obtain

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