A High-Frame-Rate Ultrasonic Plane Wave Tensor Completion Method Based on T-SVD and Angle Regularization

Abstract

This invention discloses a high frame rate ultrasound plane wave tensor completion method based on T-SVD and angle regularization, belonging to the field of ultrasound imaging technology. The method includes: acquiring data; encoding selected and unselected angles into TCP codes; transmitting the encoded image along a specified angle; constructing a mask matrix Ω to form an incomplete tensor X containing partially known data; zero-padding the acquired RF data to expand it to the full size; reconstructing the data corresponding to the missing angles from the incomplete tensor; iteratively solving the problem using the alternating direction multiplier method; determining whether the convergence error convergence criterion has been met; and, after iteration, completing the tensor X to obtain the full angles. Composite imaging is then performed based on the obtained complete RF data. This invention solves the problems of slow convergence speed, high computational complexity, and unsmooth completion results in existing tensor completion algorithms. Under conditions of extremely limited angle sampling, this invention achieves a balance between high frame rate and high quality in ultrasound imaging through efficient low-rank tensor completion.

Description

Technical Field

[0001] This invention relates to the field of ultrasound imaging technology, specifically to a high frame rate ultrasound plane wave tensor completion method based on T-SVD and angle regularization. Background Technology

[0002] Ultrasound imaging, as one of the most widely used technologies in medical imaging diagnosis, plays a vital role in the detection and evaluation of diseases in the cardiovascular, hepatobiliary, musculoskeletal, and superficial organs due to its advantages such as high real-time performance, non-invasiveness, low cost, and no radiation. Especially in clinical scenarios such as dynamic tissue function monitoring and blood flow assessment, high-frame-rate ultrasound imaging technology can capture rapid tissue movement and instantaneous changes in real time, providing crucial evidence for early disease diagnosis.

[0003] Traditional line-by-line focusing imaging, while achieving high spatial resolution and contrast, suffers from a low frame rate (typically only tens of frames per second) due to imaging only one sound line at a time, making it unsuitable for real-time imaging of rapidly moving tissues such as myocardium and arterial blood flow. To address this issue, ultrafast ultrasound plane wave imaging technology emerged. This technique achieves full imaging coverage by transmitting a wide-swath plane wave in a single pass, with frame rates reaching up to 20,000 Hz. However, the lack of a focal point significantly increases sidelobes and noise in single-angle plane wave imaging signals, resulting in a marked decrease in image resolution and contrast, failing to meet clinical imaging quality requirements. To balance frame rate and image quality, coherent plane wave composite has become the mainstream approach. This method, by transmitting plane waves from multiple angles and coherently superimposing the echo signals from these angles, can restore the focusing effect to some extent, thereby improving imaging contrast. However, its imaging frame rate is strictly inversely proportional to the number of transmission angles; more transmission angles result in higher image quality, but a lower frame rate. This inherent limitation of "high quality - low frame rate" means that achieving real-time dynamic observation still faces serious performance bottlenecks in scenarios such as cardiac ultrasound, elastography, and blood flow monitoring.

[0004] In recent years, academia and industry have proposed various optimization schemes to overcome this contradiction, such as non-uniform angle design, adaptive beamforming, sparse sampling, and compressed sensing reconstruction. However, these methods suffer from problems such as high computational complexity, mismatched prior assumptions, or sensitivity to noise, making it difficult to balance real-time performance and imaging quality. In particular, when the number of angle samples is significantly reduced, the imaging results are prone to problems such as decreased resolution, enhanced artifacts, and blurred tissue boundaries.

[0005] Against this backdrop, high frame rate ultrasound plane wave imaging methods based on tensor completion have gradually attracted attention. This method models ultrasound radio frequency data as a three-dimensional tensor (axial sampling depth × channel × number of angles), and utilizes its correlation across different dimensions to recover missing angle data through low-rank tensor completion, thereby achieving near-full-angle composite imaging quality under limited angle sampling conditions. However, traditional tensor completion algorithms suffer from slow convergence speed, high computational complexity, and non-smooth completion results, limiting their real-time applications.

[0006] Therefore, there is an urgent need for an improved ultrasound plane wave imaging technology that can achieve both high frame rate and high image quality under conditions of limited angle sampling, breaking through existing bottlenecks at the algorithm level and providing clinical applications with a more efficient, accurate, and real-time ultrasound imaging solution. Summary of the Invention

[0007] The purpose of this invention is to provide a high frame rate ultrasound plane wave tensor completion method based on T-SVD and angle regularization. By using efficient low-rank tensor completion, it achieves a balance between high frame rate and high quality in ultrasound imaging, thereby breaking through the technical bottleneck that frame rate and image quality cannot be achieved simultaneously in coherent plane wave composite imaging and solving the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization includes:

[0010] S1: Collect data, randomly select some angles from all angles, including positive, negative and zero angles, to form an incomplete tensor with partial observation data;

[0011] S2: The selected and unselected angles are combined to form TCP encoding, where 1 represents transmission and acquisition along that angle, and 0 represents missing;

[0012] S3: Based on the obtained TCP, transmit along the specified angle to form an image. If TCP is 1, then that angle participates in the imaging.

[0013] S4: Construct a mask matrix Ω to distinguish between known data and missing data addresses, and ensure that the completion operation in the subsequent tensor completion process only affects unknown data addresses, keeping known data unchanged;

[0014] S5: Based on the mask matrix Ω, form an incomplete tensor X with partially known data, and pad the acquired RF data with zeros to expand it to the full size;

[0015] S6: Tensor completion based on t-SVD and smoothing regularization, reconstructing data corresponding to missing angles from incomplete tensors;

[0016] S7: Based on the objective function, the alternating direction multiplier method is used for iterative solution;

[0017] S8: Determine whether the convergence error convergence criterion has been met; pre-set the criterion. Calculate the relative error;

[0018] S9: After the iteration is complete, the full tensor X of all angles is obtained: Its dimensions are [ ], containing RF data from all angles;

[0019] S10: Perform composite imaging based on the obtained complete RF data:

[0020]

[0021] in, This represents the RF data at the m-th angle. For geometric delay compensation, These are the weighting coefficients.

[0022] Preferably, in step S1, the acquired RF data is represented as a three-dimensional tensor X: ;

[0023] Where Nz is the number of axial sampling points, Nc is the number of channels, and M is the total number of angles, including known and unknown angles;

[0024] Let the complete set of plane wave emission angles be:

[0025]

[0026] As shown above, only a portion of the angles are selected:

[0027]

[0028] Each angle is indicated by TCP encoding as to whether sampling is performed:

[0029] .

[0030] Preferably, in step S2, the TCP encoding vector is formed as follows:

[0031]

[0032] This vector will be used directly as the mask template for the subsequent tensor completion process.

[0033] Preferably, in step S3, the probe emits a plane wave along this direction, receives the echo signal, and generates radio frequency data. The tensor obtained at this time is:

[0034]

[0035] in, = |

[0036] Preferably, in S4, the mask matrix Ω is:

[0037]

[0038] in, =1 indicates that there are known observations at this location. =0 indicates that the data at this location is missing and needs to be completed.

[0039] Preferably, in step S5, the acquired RF data is zero-padded and expanded to the full size:

[0040] =

[0041] in, This represents the Hadamard product (element-by-element multiplication). Provides accurate, comprehensive data.

[0042] Preferably, in step S6, tensor completion based on t-SVD+smoothing regularization reconstructs the data corresponding to the missing angle from the incomplete tensor, and performs the following operations:

[0043] S61: Steps of t-SVD;

[0044] Given a third-order tensor Its t-SVD decomposition is defined as:

[0045]

[0046] in, Let represent tensor t-multiplication, a type of multiplication that performs circular convolution in the third dimension. U and V are orthogonal tensors, and S is an f-diagonal tensor. Based on this, the tensor nuclear norm is defined as a low-rank constraint.

[0047]

[0048] in, Let k be the first slice of the tensor in the third-dimensional Fourier domain. Represents singular values;

[0049] S62: Steps for smoothing regularization;

[0050] Based on the strong correlation between RF data and the angular dimension, a first-order difference operator is introduced. Add a smoothing regularization term during the completion process:

[0051]

[0052] in, This represents the difference in angular direction; the first-order difference in the angular dimension is defined as the difference between adjacent angles.

[0053]

[0054] Its norm square is:

[0055]

[0056] S63: Based on the steps of t-SVD and smooth regularization, combining low-rank constraints and smooth regularization, the optimization problem, i.e., the objective function, is obtained:

[0057]

[0058] in, To smooth out the regularization weights, For observation tensors.

[0059] Preferably, in step S7, based on the objective function, the alternating direction multiplier method is used for iterative solution, and the following operations are performed:

[0060] Introducing an auxiliary variable Z, the objective function is rewritten as:

[0061]

[0062] Its augmented Lagrangian function is:

[0063]

[0064] Where U is a Lagrange multiplier and ρ>0 is a penalty parameter;

[0065] The iterative steps are as follows: In each iteration, X, Z, and U are updated sequentially;

[0066] Among them, update X:

[0067]

[0068] This subproblem is equivalent to tensor singular value thresholding:

[0069] First, perform a Fast Fourier Transform (FFT) along the third dimension on the tensor: fft ( ,[ ],3)。

[0070] Then cut each skin

[0071] Then, soft thresholding is performed on the singular values:

[0072] Finally, the inverse FFT is obtained. ;

[0073] Among them, update Z:

[0074]

[0075] This subproblem can be approximated and updated using a closed-form solution with difference operators:

[0076]

[0077] At the same time, maintain consistency at known locations (data at known locations remains unchanged):

[0078]

[0079] Among them, update U:

[0080] .

[0081] Preferably, in step S8, the relative error is calculated:

[0082]

[0083] when The algorithm converges and the iteration is complete when the maximum number of iterations is reached; otherwise, the ADMM iteration continues.

[0084] Preferably, in S10, during the calculation First, determine based on the speed of sound c and depth z. , for The time it takes for the receiver to receive the echo signal during plane wave transmission is known, as the speed at which ultrasound signals propagate through human tissue is also known. Therefore, the echo signal time can be calculated using the depth of the moving target. Assuming The direction is parallel to the transducer. The direction indicates the imaging depth;

[0085] During plane wave transmission, the transmitted signal passes through a scatterer. Then it backscatters back to another array element. Transmission time It can be calculated using the following formula:

[0086]

[0087] Inclination angle is During the plane wave transmission process, the transmitted signal passes through the scatterer Then it backscatters back to another array element. Transmission time It can be calculated using the following formula:

[0088]

[0089] relative delay = - ,have to:

[0090]

[0091] Finally, the imaging results from each angle are combined using the following method to obtain a high-quality image that approximates the full-angle CPWC.

[0092] Among them, radio frequency signals collected from multiple angles , Coherent recombination is performed to generate a coherently recombinated radio frequency signal. It can be calculated using the following formula:

[0093]

[0094] In estimating unknown values, a rank function, which incorporates both local and global information, is used. The unknown values ​​in the tensor are estimated by minimizing the rank.

[0095]

[0096] Introducing the concept of convex relaxation, we use the minimum nuclear norm problem to achieve low-rank approximation. The minimum nuclear norm problem is denoted as:

[0097]

[0098] in, Since these are singular values, the objective function becomes:

[0099]

[0100] Introducing an auxiliary variable Z, the optimization problem is rewritten as:

[0101]

[0102] For constrained optimization problems, we introduce the Lagrange function for optimization as follows:

[0103]

[0104] in, Let be the Lagrange multipliers, and < > denote the inner product of vectors. The second term is a constraint penalty form. An augmented term is added to transform it into an augmented Lagrange function. An additional quadratic penalty term is added to make the constraint more lenient and stable.

[0105]

[0106] in, For penalty parameters;

[0107] Define a scaling variable as follows:

[0108]

[0109] Substituting the augmented Lagrangian function into the above equation to eliminate get:

[0110]

[0111] because:

[0112]

[0113] so:

[0114]

[0115] make Since B=U, we get:

[0116]

[0117] have to:

[0118]

[0119] After adding the first-order smoothing regularization term, the objective function above becomes:

[0120]

[0121] because This item is not very useful, so omitting it yields:

[0122] .

[0123] Compared with the prior art, the beneficial effects of the present invention are:

[0124] The low-rank tensor modeling method proposed in this invention, based on t-SVD decomposition and first-order difference smoothing regularization in the angle dimension, can fully utilize the correlation of ultrasound radio frequency data in the three-dimensional structure of depth, channel, and angle to recover complete echo information from a small number of angle samples. This reduces the amount of data acquisition while effectively increasing the frame rate, enhancing the continuity and coherence of the angle direction, and significantly suppressing artifacts and sidelobes. Under the condition of a very small number of angle samples, it achieves a balance between high frame rate and high quality in ultrasound imaging through efficient low-rank tensor completion, thereby breaking through the technical bottleneck of the incompatibility between frame rate and image quality in coherent plane wave composite imaging. Attached Figure Description

[0125] Figure 1 This is a flowchart of the high frame rate ultrasonic plane wave tensor completion of the present invention;

[0126] Figure 2 This is a schematic diagram illustrating the time required for the propagation of a non-deflected plane wave (zero degrees) according to the present invention;

[0127] Figure 3 The present invention relates to the deflection of a plane wave (deflection angle). A diagram illustrating the transmission time required for the data.

[0128] Figure 4 This is a schematic diagram of coherent recombination according to the present invention;

[0129] Figure 5 This is a schematic diagram of the mask tensor generation of the present invention;

[0130] Figure 6 This is a schematic diagram of the B-mode ultrasound images of point targets emitted from all angles (45 points) according to the present invention;

[0131] Figure 7 This is a schematic diagram of the point target ultrasound images emitted from 11 angles according to the present invention;

[0132] Figure 8 This is a schematic diagram of a point target ultrasound image after tensor completion according to the present invention. Detailed Implementation

[0133] 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.

[0134] To address the limitations of existing tensor completion algorithms, such as slow convergence, high computational complexity, and non-smooth completion results, which restrict their real-time applications, please refer to [link to relevant documentation]. Figures 1-8This embodiment provides the following technical solution:

[0135] A high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization includes:

[0136] S1: Simulation modeling generates a point target radio frequency data with a total data size of [984, 128, 45]. 984 represents the imaging depth data distribution, 128 represents the number of activated array elements, and 45 represents the number of angles (the number of plane waves transmitted in frames). The data is stored in 45 Matlab .mat files according to the third dimension, with angles ranging from -11 to +11 and a transmission interval of 0.5.

[0137] First, a subset of angles needs to be randomly selected from 45 angles, including positive, negative, and zero angles, ensuring the number of positive and negative angles is consistent. This will form an incomplete tensor with partial observation data. Eleven angles were randomly selected in the experiment as follows:

[0138] {-11°, -8.5°, -5.5°, -3°, -1.5°, 0°, 2.5°, 3°, 5°, 7.5°, 10°}

[0139] Therefore, the acquired RF data can be represented as a three-dimensional tensor (including unknown data):

[0140] Schematic diagram after imaging as follows Figure 7 As shown

[0141] The image obtained by combining the data from the plane wave emission at these 45 selected angles is shown below. Figure 6 As shown.

[0142] S2: The selected and unselected angles in S1 are combined to form a TCP code. "1" represents that the angle is selected and will be transmitted and collected, while "0" represents that it is not selected and is missing. The resulting TCP code vector is as follows:

[0143] TCP=100001000001000010010010000110001000010000100

[0144] There are 45 angles in total. The parts with a value of 0 are unselected and will be filled in later. This vector will be directly used as the mask template for the subsequent tensor completion process.

[0145] S3: The TCP obtained in S2 is transmitted along a specified angle to form an image. If TCP is 1, then this angle participates in imaging. The probe transmits a plane wave along this direction, receives the echo signal, and generates radio frequency (RF) data. The tensor obtained at this time is:

[0146] Schematic diagram after imaging as follows Figure 7As shown

[0147] We call this the observation tensor. Data is only available at 11 selected addresses. The composite image obtained from the plane wave emission data at these 11 selected angles is shown below. Figure 7 As shown.

[0148] S4: Construct a mask matrix Ω. The mask Ω is used to distinguish between known data addresses and missing data addresses, ensuring that the completion operation in the subsequent tensor completion process only affects unknown data addresses and keeps known data unchanged. The mask matrix Ω is:

[0149] Schematic diagram as follows Figure 5 As shown

[0150] in, =1 indicates that there are known observations at this location. =0 indicates that the data at this location is missing and needs to be completed.

[0151] S5: Based on the mask matrix Ω, form an incomplete tensor X containing partially known data, as shown in the tensor in S1. That is, the collected RF data is zero-padded and expanded to the full size to obtain the incomplete tensor X:

[0152]

[0153] This tensor is constrained by a mask matrix Ω, ensuring that the data remains unchanged at known addresses, and subsequent completion operations are only performed at addresses corresponding to unknown data.

[0154] S6: Tensor completion based on t-SVD and smoothing regularization, reconstructing data corresponding to missing angles from incomplete tensors;

[0155] The optimized model obtained by combining T-SVD and the first-order angle smoothing regularization term is as follows:

[0156]

[0157] In the experiment, , .

[0158] S7: Based on the objective function of S6, the Alternating Direction Multiplier Method (ADMM) is used for iterative solution, and the maximum number of iterations is set to max_iter=100;

[0159] The iterative steps are as follows:

[0160] Variable splitting: Decompose a tensor variable into a low-rank part and a smooth part;

[0161] Low-rank update: Singular value soft thresholding is performed on each matrix slice in the Fourier domain;

[0162] Smooth Update: Closed-form solution update based on difference regularization term;

[0163] Multiplier update: Gradually converges to the constraints.

[0164] In each iteration, X, Z, and U are updated alternately in sequence;

[0165] Step 1: Update X (low-rank constraint)

[0166]

[0167] This subproblem is equivalent to tensor singular value thresholding (t-SVT):

[0168] First, perform a Fast Fourier Transform (FFT) along the third dimension on the tensor: fft ( ,[ ],3)。

[0169] Then cut the skin at each frequency in the frequency domain.

[0170] Then, soft thresholding is performed on the singular values, with the threshold set to 1: Remove small singular values ​​and keep large singular values ​​to make the tensor low-rank approximation;

[0171] Finally, the inverse FFT is obtained. ;

[0172] Step 2: Update Z (smoothing constraint + hold observations)

[0173]

[0174] This subproblem can be approximately updated using a closed-form solution with respect to the difference operator. From the previous step, we find the optimal solution with respect to Z and take the partial derivative:

[0175]

[0176] The closed-form solution of the difference operator is approximated:

[0177]

[0178] in,

[0179] And the known location data remains unchanged:

[0180]

[0181] in, It is equivalent to an angle-dimensional "Laplace smoother". When the frame difference between adjacent angles is large, the optimizer will "push" Z to reduce this sudden change and make the angle dimension smoother. When the frame difference between adjacent angles is small, the penalty term has almost no effect.

[0182] Step 3: Update U (multiplier update)

[0183]

[0184] S8: Determine whether the convergence criterion for convergence error has been met, in the experiment. Set to 1e-5, calculate the relative error between Z and X after iteration:

[0185]

[0186] If the relative error is less than 1e-5 or the maximum number of iterations (100) is reached, the iteration is complete.

[0187] S9: After iteration S8 is completed, i.e., the full tensor X of all angles is obtained, is:

[0188]

[0189] Output tensor X, whose dimensions are [ ], containing RF data from all angles.

[0190] S10: Perform composite imaging based on the complete RF data obtained in S9:

[0191]

[0192] in, This represents the RF data at the m-th angle. For geometric delay compensation, These are weighting coefficients;

[0193] This is the most practical and crucial step in plane wave recombination (CPWC): how to align the echo times from different transmission angles so that echoes from the same spatial point have consistent timing during superposition, thereby achieving coherent superposition gain. The first transmission angle is... = -11, its emission angle with the transducer is Calculate the time delay between them from a 0-degree angle. :

[0194]

[0195] Finally, the delays of all angles are calculated, superimposed one by one, and then composited to obtain a high-quality image that is close to full-angle CPWC.

[0196] Radio frequency signals acquired from multiple angles (Negative angle) Coherent recombination is performed at a positive angle to generate a coherently recombinated radio frequency signal. The following formula can be used for calculation, as shown in the diagram:

[0197] Schematic diagram attached Figure 4 As shown

[0198] The final composite ultrasound image is as follows: Figure 8 As shown.

[0199] It should be noted that, , Each is based on the launch angle , A radio frequency signal is generated by transmitting a plane wave, reflecting it through tissue, and then beamforming it. yes , The radio frequency signal after coherent recombination.

[0200] It should be noted that the principle of multi-angle plane wave coherent composite imaging (CPWC) is as follows:

[0201] The core of multi-angle plane wave coherent composite imaging is to emit multiple wide-amplitude plane waves at different angles through an ultrasonic transducer array. A single emission can cover the entire imaging area, breaking through the limitations of traditional line-by-line focusing imaging. After receiving the radio frequency data of the echoes from each angle, the system accurately calculates the time difference of echo propagation at different angles at the same spatial location based on the fixed propagation speed of ultrasound (approximately 1540 m / s) and the deflection angle of the plane waves. This achieves spatiotemporal alignment of multi-angle signals. The coherent superposition effect then enhances the effective signal of the target while canceling random noise and sidelobe interference, balancing the imaging frame rate and image quality.

[0202] The method for multi-angle plane wave coherent composite imaging (CPWC) is as follows:

[0203] First, a preset set of plane wave emission angles is determined. Plane waves at each angle are emitted sequentially, and radio frequency data corresponding to each angle is acquired simultaneously, forming a three-dimensional data matrix of "depth × number of channels × number of angles". Then, for each spatial pixel within the imaging area, the echo propagation time is calculated based on the plane wave deflection angle, and a delay compensation algorithm is used to achieve spatiotemporal alignment of data from different angles. Finally, the aligned multi-angle data is weighted and coherently superimposed, and then processed through envelope detection, logarithmic compression, and other subsequent steps to generate the final ultrasound image.

[0204] The advantages of multi-angle plane wave coherent composite imaging (CPWC) are:

[0205] Compared to traditional line-by-line focusing imaging, the frame rate is significantly improved, which can meet the real-time observation needs of dynamic tissues such as myocardial motion and arterial blood flow; high spatial resolution and contrast are restored through coherent superposition, and there are no blind spots in the imaging field of view, making it suitable for imaging in various scenarios such as superficial organs and deep tissues; the core algorithm only involves delay compensation and linear superposition, with low complexity, and real-time imaging can be achieved through hardware acceleration.

[0206] The disadvantages of multi-angle plane wave coherent composite imaging (CPWC) are:

[0207] First, there is an inherent contradiction between frame rate and image quality—the more angles, the better the image quality. Therefore, when the number of transmission angles increases, the frame rate will decrease exponentially, making it difficult to meet the requirements of high frame rate and high-quality imaging. Second, when the angle density is insufficient, image artifacts and blurred tissue boundaries are prone to occur. Finally, the far-field signal attenuation under this method is significant, resulting in a decrease in signal-to-noise ratio and loss of detail. Moreover, this technology has high requirements for the hardware performance of ultrasound equipment, such as transducer bandwidth and transmission circuit switching speed, which further increases the cost and complexity of the equipment.

[0208] It should be noted that the principle of High-Precision Low-Rank Tensor Completion (HaLRTC) is as follows:

[0209] In high-frame-rate ultrasound plane wave imaging, the imaging system emits plane waves at different angles to achieve rapid scanning over a wide area. However, since the number of angles is inversely proportional to the frame rate, reducing the number of emission angles, while significantly increasing the frame rate, leads to a decrease in image quality. Traditional high-precision low-rank tensor completion methods were proposed to address this contradiction. This method represents multi-angle echo signals as a three-dimensional tensor model and utilizes low-rank characteristics to constrain and recover missing angle data. Its core idea is to approximate the low-rank structure of the tensor by minimizing the nuclear norm. By mining the redundancy and intrinsic correlations of the data across different dimensions, complete ultrasound information can be recovered from limited angle sampling, achieving a balance between high frame rate and high resolution.

[0210] The method for high-precision low-rank tensor completion (HaLRTC) is as follows:

[0211] Ultrasonic radio frequency signals need to be constructed into a three-dimensional tensor. In actual imaging, to improve the frame rate, only partial angle data is acquired, and the data from the remaining angles are considered missing. Traditional high-precision low-rank tensor completion methods recover these missing data by minimizing the rank of the tensor in each dimension. The Alternating Direction Multiplier (ADMM) framework is used in the optimization process, so that each optimization step can be efficiently decomposed into independently solvable subproblems. Finally, after the tensor completion process converges, imaging algorithms such as delayed summation or coherent plane wave composite are used to reconstruct the completed multi-angle echo data, thereby obtaining an ultrasound image with a high frame rate and excellent image resolution.

[0212] The advantages of High-Precision Low-Rank Tensor Completion (HaLRTC) are:

[0213] By utilizing the multidimensional correlation of ultrasound signals, near-full-angle composite imaging can be reconstructed under sparse angle sampling conditions. At the same time, angle completion can be achieved without complex priors, relying only on the inherent low-rank characteristics of the data, and has strong versatility and robustness.

[0214] The drawbacks of High-Precision Low-Rank Tensor Completion (HaLRTC) are:

[0215] First, this method relies solely on low-rank constraints of the tensor, neglecting the physical continuity of ultrasound waves in the angular dimension. Therefore, the completion results often exhibit unevenness in the angular dimension. In composite imaging, this inconsistency can lead to edge blurring and decreased contrast, affecting the final image quality. Second, this method requires modular expansion of the tensor and multiple singular value decompositions in each iteration, resulting in high computational cost and long processing time. Finally, when the proportion of missing angles is high, the completion accuracy drops sharply, and the imaging results are prone to artifacts and reduced signal-to-noise ratio.

[0216] The main drawback of existing high-frame-rate ultrasound plane wave imaging techniques is that traditional tensor completion methods fail to effectively balance the low-rank structure and local continuity of ultrasound radio frequency data. This results in artifacts and sidelobe interference in the completion results, as well as slow convergence speed, making it difficult to meet real-time imaging requirements. Furthermore, existing methods lack sufficient smoothness and consistency modeling in the angular dimension and lack explicit constraints on the physical coupling relationship of ultrasound signals. Under high missing rate conditions, image quality deteriorates significantly, limiting their application in clinical high-frame-rate scenarios.

[0217] To address the main shortcomings of existing technologies, this invention proposes a high frame rate ultrasound plane wave image reconstruction method that integrates t-SVD and angle smoothing regularization. This method, for the first time, combines t-SVD tensor decomposition with first-order difference smoothing regularization in the angle dimension. While preserving the global low-rank structure of the data, it enhances the continuity of adjacent angle data, effectively suppressing artifacts and sidelobes during the completion process. Furthermore, by constructing an angle-dimensional regularization mechanism, it improves the physical rationality and structural consistency of the completion results. In addition, the ADMM solution strategy is optimized by introducing Fourier domain singular value thresholding and closed-loop smoothing updates, significantly improving the algorithm's convergence speed and computational efficiency, providing a feasible algorithmic foundation for real-time high frame rate ultrasound imaging.

[0218] In summary, compared with traditional tensor completion image reconstruction techniques, this invention proposes for the first time a low-rank tensor modeling method based on t-SVD decomposition and first-order difference smoothing regularization in the angle dimension. This method can fully utilize the correlation of ultrasound radio frequency data in the three-dimensional structure of depth, channel, and angle, recover complete echo information from a small number of angle samples, reduce the amount of data acquisition while effectively improving the frame rate, enhance the continuity and coherence of the angle direction, and significantly suppress artifacts and sidelobes. Under the condition of a very small number of angle samples, it achieves both high frame rate and high quality in ultrasound imaging through efficient low-rank tensor completion, thereby breaking through the technical bottleneck of the incompatibility between frame rate and image quality in coherent plane wave composite imaging.

[0219] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0220] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization, characterized in that, include: S1: Collect data, randomly select some angles from all angles, including positive, negative and zero angles, to form an incomplete tensor with partial observation data; S2: The selected and unselected angles are combined to form TCP encoding, where 1 represents transmission and acquisition along that angle, and 0 represents missing; S3: Based on the obtained TCP, transmit along the specified angle to form an image. If TCP is 1, then that angle participates in the imaging. S4: Construct a mask matrix Ω to distinguish between known data and missing data addresses, and ensure that the completion operation in the subsequent tensor completion process only affects unknown data addresses, keeping known data unchanged; S5: Based on the mask matrix Ω, form an incomplete tensor X with partially known data, and pad the acquired RF data with zeros to expand it to the full size; S6: Tensor completion based on t-SVD and smoothing regularization, reconstructing data corresponding to missing angles from incomplete tensors; S7: Based on the objective function, the alternating direction multiplier method is used for iterative solution; S8: Determine whether the convergence error convergence criterion has been met; pre-set the criterion. Calculate the relative error; S9: After the iteration is complete, the full tensor X of all angles is obtained: Its dimensions are [ ], containing RF data from all angles; S10: Perform composite imaging based on the obtained complete RF data: ； in, This represents the RF data at the m-th angle. For geometric delay compensation, These are the weighting coefficients.

2. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 1, characterized in that, In S1, the acquired RF data is represented as a three-dimensional tensor X: ; Where Nz is the number of axial sampling points, Nc is the number of channels, and M is the total number of angles, including known and unknown angles; Let the complete set of plane wave emission angles be: ； As shown above, only a portion of the angles are selected: ； Each angle is indicated by TCP encoding as to whether sampling is performed: 。 3. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 2, characterized in that, In S2, the resulting TCP encoding vector is as follows: ； This vector will be used directly as the mask template for the subsequent tensor completion process.

4. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 3, characterized in that, In step S3, the probe emits a plane wave along this direction, receives the echo signal, and generates radio frequency data. The tensor obtained at this time is: ； in, = | 5. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 4, characterized in that, In S4, the mask matrix Ω is: ； in, =1 indicates that there are known observations at this location. =0 indicates that the data at this location is missing and needs to be completed.

6. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 5, characterized in that, In step S5, the acquired RF data is zero-padded and expanded to the full size: = ； in, This represents the Hadamard product (element-by-element multiplication). Provides accurate, comprehensive data.

7. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 6, characterized in that, In step S6, tensor completion based on t-SVD and smoothing regularization reconstructs the data corresponding to the missing angle from the incomplete tensor, and performs the following operations: S61: Steps of t-SVD; Given a third-order tensor Its t-SVD decomposition is defined as: ； in, Let represent tensor t-multiplication, a type of multiplication that performs circular convolution in the third dimension. U and V are orthogonal tensors, and S is an f-diagonal tensor. Based on this, the tensor nuclear norm is defined as a low-rank constraint. ； in, Let k be the first slice of the tensor in the third-dimensional Fourier domain. Represents singular values; S62: Steps for smoothing regularization; Based on the strong correlation between RF data and the angular dimension, a first-order difference operator is introduced. Add a smoothing regularization term during the completion process: ； in, This represents the difference in angular direction; the first-order difference in the angular dimension is defined as the difference between adjacent angles. ； Its norm square is: ； S63: Based on the steps of t-SVD and smooth regularization, combining low-rank constraints and smooth regularization, the optimization problem, i.e., the objective function, is obtained: ； in, To smooth out the regularization weights, For observation tensors.

8. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 7, characterized in that, In step S7, based on the objective function, the alternating direction multiplier method is used for iterative solution, and the following operations are performed: Introducing an auxiliary variable Z, the objective function is rewritten as: ； Its augmented Lagrangian function is: ； Where U is a Lagrange multiplier and ρ>0 is a penalty parameter; The iterative steps are as follows: In each iteration, X, Z, and U are updated sequentially; Among them, update X: ； This subproblem is equivalent to tensor singular value thresholding: First, perform a Fast Fourier Transform (FFT) along the third dimension on the tensor: fft ( ,[ ],3)。 Then cut each skin ; Then, soft thresholding is performed on the singular values: ; Finally, the inverse FFT is obtained. ; Among them, update Z: ； This subproblem can be approximated and updated using a closed-form solution with difference operators: ； At the same time, maintain consistency at known locations (data at known locations remains unchanged): ； Among them, update U: 。 9. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 8, characterized in that, In step S8, the relative error is calculated: ； when The algorithm converges and the iteration is complete when the maximum number of iterations is reached; otherwise, the ADMM iteration continues.

10. The high frame rate ultrasonic plane wave tensor completion method based on T-SVD and angle regularization according to claim 9, characterized in that, In S10, during the calculation First, determine based on the speed of sound c and depth z. , for The time it takes for the receiver to receive the echo signal during plane wave transmission is known, as the speed at which ultrasound signals propagate through human tissue is also known. Therefore, the echo signal time can be calculated using the depth of the moving target. Assuming The direction is parallel to the transducer. The direction indicates the imaging depth; During plane wave transmission, the transmitted signal passes through a scatterer. Then it backscatters back to another array element. Transmission time It can be calculated using the following formula: ； Inclination angle is During the plane wave transmission process, the transmitted signal passes through the scatterer Then it backscatters back to another array element. Transmission time It can be calculated using the following formula: ； relative delay = - ,have to: ； Finally, the imaging results from each angle are combined using the following method to obtain a high-quality image that approximates the full-angle CPWC. Among them, radio frequency signals collected from multiple angles , Coherent recombination is performed to generate a coherently recombinated radio frequency signal. It can be calculated using the following formula: ； In estimating unknown values, a rank function, which incorporates both local and global information, is used. The unknown values ​​in the tensor are estimated by minimizing the rank. ； Introducing the concept of convex relaxation, we use the minimum nuclear norm problem to achieve low-rank approximation. The minimum nuclear norm problem is denoted as: ； in, Since these are singular values, the objective function becomes: ； Introducing an auxiliary variable Z, the optimization problem is rewritten as: ； For constrained optimization problems, we introduce the Lagrange function for optimization as follows: ； in, Let be the Lagrange multipliers, and < > denote the inner product of vectors. The second term is a constraint penalty form. An augmented term is added to transform it into an augmented Lagrange function. An additional quadratic penalty term is added to make the constraint more lenient and stable. ； in, For penalty parameters; Define a scaling variable as follows: ； Substituting the augmented Lagrangian function into the above equation to eliminate get: ； because: ； so: ； make Since B=U, we get: ； have to: ； After adding the first-order smoothing regularization term, the objective function above becomes: ； because This item is not very useful, so omitting it yields: 。

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