An ultrasonic cardiovascular imaging method based on RSVD-ST algorithm

Abstract

The application relates to an ultrasonic cardiovascular imaging method based on an RSVD-ST algorithm and belongs to the technical field of cardiovascular disease diagnosis. The ultrasonic cardiovascular imaging method comprises the following steps: S1, an ultrasonic instrument emits ultrasonic waves to a lesion position and receives echo signals, and multi-angle tissue structure signals are acquired; S2, the multi-angle tissue structure signals are subjected to noise reduction processing; and S3, an inverse FFT image is generated, and a high signal-to-noise ratio cardiovascular image is output. The ultrasonic receiving signals are decomposed and reduced in noise through the RSVD-ST algorithm and Fourier transform, so that precise imaging of the cardiovascular system can be realized without contrast agent.

Description

Technical Field

[0001] This invention relates to an ultrasound cardiovascular imaging method based on the RSVD-ST algorithm, belonging to the field of cardiovascular disease diagnosis technology. Background Technology

[0002] Cardiovascular disease is one of the leading causes of death worldwide, and its early diagnosis relies on high-resolution imaging technology. Medical ultrasound imaging diagnostic equipment acquires ultrasound images of tissue and organ structures by transmitting ultrasound waves through the body. Due to its advantages such as safety, wide applicability, high intuitiveness, high repeatability, outstanding ability to differentiate soft tissues, high flexibility, and affordability, ultrasound diagnosis has become the preferred technology for modern medical imaging diagnosis.

[0003] An ultrasound probe is a transducer composed of multiple array elements arranged in an array. Each element emits an ultrasonic beam based on a driving electrical signal and simultaneously converts the received ultrasonic beam into an electrical signal. Therefore, each element can be used to achieve the mutual conversion between electrical pulse signals and ultrasonic beams, thereby enabling the emission of ultrasonic waves to target tissues in the human cardiovascular system, and also to receive echoes of ultrasonic waves reflected back from cardiovascular tissues. The elements on the transducer can be simultaneously excited by electrical signals to emit ultrasonic waves concurrently, or the elements involved in ultrasonic wave emission can be excited by several electrical signals at specific time intervals to continuously emit ultrasonic waves at specific time intervals.

[0004] Singular Value Decomposition (SVD) is a batch processing method for multi-frame image data. The singular values ​​of the image matrix and its feature space reflect the different components and features in the image. SVD is equivalent to decomposing a matrix into a linear combination of several sub-signal spaces, where the singular values ​​are the energy levels corresponding to each sub-signal space. In data without tissue structure extraction, there are three main components: tissue signal, tissue structure signal, and noise signal. Among them, the tissue signal has the strongest energy, corresponding to larger singular values; the tissue structure signal is next, corresponding to medium-sized singular values; and the noise signal is the weakest, corresponding to smaller singular values. Since the dynamic signals of the heart vessels and blood flow are collected, the overall data volume is large and the noise is strong. Therefore, random singular value decomposition can be used for noise reduction, and the radio frequency signal of the tissue structure can be obtained through these singular values ​​and their corresponding feature vectors.

[0005] In cardiovascular imaging, due to the complex and constantly changing spatial and temporal characteristics of cardiac tissue, SVD, as a key element in ultrasound imaging, requires SVD filters to adapt quickly and effectively to these changes in order to efficiently separate blood flow signals from tissue signals. Traditional SVD-based ultrasound contrast imaging methods suffer from computational burden and algorithmic complexity, thus reducing imaging speed and making it difficult to achieve the goal of more refined images. Summary of the Invention

[0006] To address the challenges of computational burden, algorithmic complexity, and difficulty in achieving high image refinement in traditional SVD-based ultrasound contrast imaging methods for cardiovascular imaging, this invention provides an ultrasound cardiovascular imaging method based on Random Singular Value Decomposition-Soft Thresholding (RSVD-ST) algorithms. This method fully utilizes low-rank approximation and spatiotemporal feature fusion to separate weak blood flow signals from noise. Furthermore, to avoid the inability to locate and track isolated tissue structures in the absence of contrast agents, complex data processing of the ultrasound signal is necessary. Based on the RSVD-ST algorithm, a dynamic adaptive projection matrix improvement is first implemented, dynamically adjusting the projection dimension according to the signal spectral energy to balance computational efficiency and decomposition accuracy. A hybrid iterative acceleration strategy is employed, fusing Krylov subspaces and random sampling to improve the convergence speed of the low-rank approximation. Finally, joint noise reduction using Fast Fourier Transform (FFT) and RSVD-ST (FFT-RSVD-ST) is implemented, leveraging FFT frequency domain filtering and matrix operations for acceleration to further reduce noise interference. Even without contrast agents, precise imaging of the cardiovascular system is possible, as detailed below.

[0007] An ultrasound cardiovascular imaging method based on the RSVD-ST algorithm is performed using an ultrasound instrument. This ultrasound instrument includes an eight-channel ultrasound transmitting circuit module, an eight-channel ultrasound receiving circuit module, a display, a 4G and GPS positioning circuit module, a SW programming port, a UART communication port, a storage circuit module, a USB interface, an ultrasound receiving clock drive circuit, and a crystal oscillator circuit. All components are connected to a central processing unit.

[0008] The eight-channel ultrasound transmitter / receiver probes are sequentially paired, and their positions are planned according to the structural characteristics of the human heart, such as the carotid artery and femoral artery.

[0009] According to the pre-set transmission sequence, the central processing unit controls the eight-channel ultrasonic transmitting circuit module to drive the transmission of ultrasonic waves, and controls the eight-channel ultrasonic receiving circuit module to receive the sequential ultrasonic echo signals to obtain multi-angle tissue structure signals.

[0010] The acquired multi-angle tissue structure signals are processed to filter out static tissue radio frequency signals in the spatial radio frequency signals and then fused.

[0011] The fused structural signals are reconstructed to obtain target cardiovascular image data, and the cardiovascular imaging data is then displayed as follows.

[0012] First, in cardiovascular ultrasound imaging, the structure of heart tissue is examined through the transmission and reception of signals during the ultrasound imaging process.

[0013] Ultrasonic emission signal model:

[0014] Central processing unit transmits signals Its mathematical expression is:

[0015]

[0016] in: The amplitude represents the signal and is used to measure the signal's strength or magnitude. It is the fundamental frequency, that is, the signal at... The initial frequency when =0; It is the frequency modulation slope, which determines the rate at which the signal frequency changes with time. When the value is positive, the frequency increases with time; when the value is negative, the frequency decreases with time. The duration of the signal is the total duration of the signal, that is, the time period from the start to the end of the signal.

[0017] Ultrasonic signal receiving model:

[0018] Received signal It is composed of the superposition of signals reflected from multiple scatterers and is affected by noise; its expression is:

[0019]

[0020] in: It is the first The scattering coefficient of a scatterer measures the intensity of the signal reflected by that scatterer; different scatterers may have different scattering coefficients. It is the first The time delay of a scatterer represents the time required for the signal reflected by that scatterer to reach the receiver. The time delay depends on the location of the scatterer and the propagation speed of the ultrasonic wave. R is the total number of scatterers, which determines the amount of reflected signal superimposed in the received signal. Additive White Gaussian Noise (AWGN) represents random noise components in the received signal. This noise is unavoidable and affects the quality of signal reception.

[0021] Process the received signal:

[0022] A spatiotemporal two-dimensional matrix is ​​established based on the original signal.

[0023] The core idea of ​​spatiotemporal joint processing (ST) is to expand the original one-dimensional time series into a two-dimensional spatiotemporal matrix by integrating the spatiotemporal information of the signal, thereby capturing the correlation between the signal in time and space. The specific construction steps are as follows:

[0024] Design the raw signal matrix for echocardiography

[0025] Assuming the ultrasonic receiving array contains M elements, and each element samples at N time points, the original signal matrix can be represented as:

[0026]

[0027] Implement spatiotemporal sliding window expansion

[0028] Choose a time window length L (usually much smaller than N), and use a sliding window method to expand the timing signal of each array element into a spatiotemporal block. For example, the spatiotemporal block of the m-th array element is:

[0029]

[0030] Constructing the spacetime matrix Stacking all M spatiotemporal blocks by row yields the complete spatiotemporal joint matrix:

[0031]

[0032] To simplify the analysis, assumptions are usually made. ,at this time The dimensions are approximately M×N, and the dimensional changes caused by sliding windows are ignored.

[0033] Based on the two-dimensional spacetime matrix Constructing Gaussian random matrices

[0034] Signal frequency domain energy analysis

[0035] For the spacetime matrix Perform an FFT to obtain the frequency domain energy distribution:

[0036]

[0037] in, This represents the energy at frequency f. This is a Fourier transform.

[0038] Cumulative Energy and Projection Dimension Selection

[0039] Set energy threshold Choose the smallest k such that the accumulated energy covers η times the total energy:

[0040]

[0041] Projection matrix generation

[0042] Constructing Gaussian random matrices Its column vector corresponds to the first column in the frequency domain. Weight enhancement is applied at the dominant frequencies:

[0043]

[0044] in, This is the total number of frequencies, which forms the basis for constructing the Gaussian random matrix Ω, where the distribution of the matrix elements is related to the value of the frequency f. >1 is a weighting factor used to improve the projection efficiency of the signal subspace.

[0045] Error bounds and rationality analysis of dynamic projection

[0046] According to Parseval's theorem, the total energy of an ultrasonic signal satisfies:

[0047]

[0048] in, It is the signal energy at frequency f.

[0049] QR decomposition is performed using Krylov subspaces, and further decomposed using SVD. Decompose into subspaces.

[0050] QR decomposition is a norm-preserving transformation and does not change the norm of the matrix. The error of small matrix SVD lies in the fact that when performing SVD decomposition on R, a more accurate approximation is obtained due to the lower dimension of R. This approximation error mainly depends on the singular value distribution and dimensionality parameter of R. The choice of method is crucial. Finally, the errors of the entire processing are combined to obtain the overall error of the RSVD algorithm. In cardiovascular ultrasound imaging, data dimensionality is high and complex. Using the RSVD algorithm can effectively reduce data dimensionality while preserving the main features of the data. This is significant for real-time processing and accurate diagnosis. Through random projection and QR decomposition, the RSVD algorithm can provide accurate and efficient results in cardiovascular ultrasound imaging.

[0051] Traditional RSVD algorithms improve the accuracy of low-rank approximations through exponential iterations, but their convergence speed depends on the spectral gaps of the matrix. For ill-conditioned matrices (such as those with severe noise interference in cardiovascular signals), traditional exponential iterations require multiple iterations to converge. Therefore, the inventors employ a hybrid iteration acceleration strategy, fusing Krylov subspaces and random projections to achieve fast convergence within a finite number of iterations. The specific implementation steps are as follows:

[0052] Construction of Krylov subspaces

[0053] Given an initial random matrix Construct a Krylov subspace of depth d steps:

[0054]

[0055] in, Denotes the spanned space generated by the Krylov subspace. It is the initial random matrix. Represents the original matrix Perform a matrix exponentiation operation to the order j.

[0056] Orthogonalization and basis merging

[0057] Performing QR decomposition on the Krylov subspace yields an orthogonal matrix. :

[0058]

[0059]

[0060] in This represents the QR decomposition of the Krylov subspace, where R is an upper triangular matrix and Q is an orthogonal matrix. The symbol represents orthogonality, and I is the identity matrix. This is mainly to ensure that the column vectors of Q are mutually orthogonal.

[0061] Low-latitude projection and SVD decomposition

[0062] Calculate the low-latitude projection matrix B, and perform exact SVD decomposition on B:

[0063]

[0064] Where B is the low-latitude projection matrix, through Projected onto the subspace of Q to generate, and They are orthogonal matrices, each containing a left singular vector and a right singular vector. It is a diagonal matrix containing singular values.

[0065] Therefore, the approximation of the original matrix is:

[0066]

[0067] Step-by-step noise reduction of subspace

[0068] In cardiovascular ultrasound imaging, the model for receiving signals can be defined as:

[0069]

[0070] in This is the true signal (low rank). It is additive noise, typically Gaussian white noise, full rank. The ultimate goal is to achieve... Separation , minimize .

[0071] For the original signal matrix Perform a two-dimensional FFT:

[0072]

[0073] in and Let be the Fourier transform matrix, satisfying

[0074] Frequency domain bandpass filtering

[0075] Design a frequency domain filter Preserve blood flow signal frequency band :

[0076]

[0077] The filtered signal is:

[0078]

[0079] in This is for element-wise multiplication.

[0080] The time-domain signal reconstructed by the inverse FFT is:

[0081]

[0082] Assume the noise power spectral density is The filtered noise power is:

[0083]

[0084] The signal-to-noise ratio is improved to:

[0085]

[0086] Toeplitz matrix multiplication FFT acceleration

[0087] Spacetime Matrix Constructing a system involving Toeplitz matrix multiplication The traditional computational complexity is .

[0088] FFT accelerates computation by using the convolution theorem to convert time-domain convolution into frequency-domain product:

[0089]

[0090] The actual calculation steps are as follows:

[0091] 1) To and Pad with zeros to length To avoid interference from circular convolution;

[0092] 2) Calculate the FFT: , ;

[0093] 3) Frequency domain product:

[0094] 4) Inverse FFT:

[0095] The complexity is:

[0096] Traditional computational complexity:

[0097] The complexity after FFT acceleration is:

[0098] According to the convolution theorem, for any signal and filter :

[0099]

[0100] Zero-padding ensures the equivalence between linear convolution and circular convolution.

[0101] Frequency domain guided projection matrix generation

[0102] The specific steps are as follows:

[0103] Dominant frequency detection

[0104] Calculate the energy distribution of the signal spectrum:

[0105]

[0106] Select the dominant frequency:

[0107]

[0108] Projection matrix frequency domain weighting

[0109] Generate Gaussian random matrices At that time, increase the weight near the dominant frequency:

[0110]

[0111] in, As a weighting factor, For bandwidth

[0112] Assuming the signal energy is concentrated in the frequency band Its energy percentage is After weighting, the probability of the projected military array capturing the signal subspace is... , for P.

[0113] The overall algorithm flow is as follows:

[0114] Input original signal matrix

[0115] FFT preprocessing

[0116] Frequency domain filtering removes Gaussian noise and low-frequency clutter.

[0117] Toeplitz matrix multiplication accelerates the construction of spacetime matrices.

[0118] Improved RSVD-ST algorithm processing

[0119] RSVD-ST with dynamic projection and round-based iteration

[0120] Temporal joint noise reduction

[0121] Noise power estimation and soft threshold shrinkage

[0122] Inverse FFT image generation outputs high signal-to-noise ratio cardiovascular images.

[0123] Noise power estimation

[0124] The noise is typically white noise, and its power can be estimated using the singular values ​​of the noise subspace:

[0125]

[0126] in, This represents the estimated noise power, where Q represents the dimension of the noise subspace, r represents the dimension of the signal subspace, and P represents the number of channels in the observation data.

[0127] The formula calculates the values ​​from the (r+1)th singular value to the th singular value. The total noise power is estimated by summing the squares of the singular values. Finally, through... Normalization is performed to obtain an estimate of the noise power. .

[0128] If noise If the noise is independent and identically distributed Gaussian, then the estimator The unbiased estimate of the noise variance is:

[0129]

[0130] According to the theory of random matrices, when When the noise is Gaussian white noise, its singular values ​​follow a Marchenko-Pastur distribution. For a large-dimensional matrix, the expectation of the sum of squares of the singular values ​​in the noise subspace satisfies:

[0131]

[0132] therefore, The estimate is unbiased.

[0133] Spatiotemporal soft threshold shrinkage

[0134] Adaptive shrinkage of all singular values ​​suppresses noise.

[0135]

[0136] in, The threshold coefficient is derived from the extremum theory of the Gaussian distribution of noise.

[0137] The optimality of soft threshold shrinkage: Soft threshold shrinkage is optimal in the sense of minimizing variance, expressed as:

[0138]

[0139] Assuming observed singular values ,in For real signals, .

[0140] Minimize and sparsity penalty terms as follows:

[0141]

[0142] Taking the derivative of the function and setting it to zero, we obtain the soft threshold formula:

[0143]

[0144] Ultrasound signal reconstruction, inverse FFT image generation, output of high signal-to-noise ratio cardiovascular images.

[0145] The denoised signal is reconstructed using the singular values ​​after shrinkage:

[0146]

[0147] Frequency domain projection error analysis

[0148] Select dynamic projection dimension Yes, the above formula is correct:

[0149]

[0150] in It is the dynamic projection dimension. It is the signal energy at frequency f. It is the energy threshold.

[0151] Ignore frequency band The energy of , and its residual energy is:

[0152]

[0153] Therefore, the upper bound of the approximation error caused by frequency domain truncation is:

[0154]

[0155] Assuming the signal energy is concentrated in the frequency band Projection dimension Then the approximation error satisfies:

[0156]

[0157] in It is the maximum frequency component. Its computational complexity is , It is the original signal matrix. It is an approximate signal matrix. Norms are used to measure the size or energy of a matrix. It is the upper bound parameter of the error, which represents the proportional relationship between the approximation error and the energy of the original signal.

[0158] Error Augmentation Analysis of Random Projections

[0159] According to the Johnson-Lindenstrauss lemma, the error of a random projection satisfies:

[0160]

[0161] Based on the frequency domain truncation error, the total error bound is:

[0162]

[0163] For static regions: if the signal energy is concentrated in a narrow band ,but The complexity is significantly reduced.

[0164] Dynamic Region: Extension To preserve high-frequency components and avoid loss of detail.

[0165] Complexity Comparison: The complexity of the original fixed-dimensional work is: Dynamic dimensions The complexity is:

[0166] Through energy threshold Controlling residual energy to ensure approximation error ;

[0167] According to theoretical assessment, when When the value is 0.9, the actual error is reduced by 20% compared to the case with a fixed dimension K, thus ensuring image accuracy;

[0168] Regarding changes in blood flow velocity, the algorithm automatically expands upon the high-frequency components corresponding to high-velocity blood flow or capillary flow. ;

[0169] In terms of organizing movement, such as the signal spectrum broadening caused by breathing and heartbeat, dynamic adjustments are made. Track changes;

[0170] As can be seen from the above analysis results, the present invention achieves enhanced adaptability and expands k throughout the optimization process as blood flow velocity changes to preserve high-frequency details, thereby reducing k in static regions to save computational resources.

[0171] Approximation capability analysis of Krylov subspaces

[0172] Krylov subspace The first k singular vector spaces that can be effectively approximated. According to Krylov subspace theory, its approximation error satisfies:

[0173]

[0174] Analysis of the acceleration mechanism of hybrid iteration

[0175] The upper bound of the error for traditional power iteration is:

[0176]

[0177] Hybrid iteration, by incorporating information from multi-step exponential iterations—that is, constructing a Krylov subspace—exponentially increases the convergence speed to the order of magnitude:

[0178]

[0179] Boundary analysis of constant C

[0180] According to matrix perturbation theory, the constant C satisfies:

[0181]

[0182] when hour, The error is mainly caused by leading.

[0183] Improved Advantages Analysis

[0184] The convergence speed is increased exponentially.

[0185] Traditional power iteration: error is expressed as Speed ​​decreases;

[0186] Hybrid iteration: error is... The speed decreases, and the convergence speed doubles.

[0187] Computational complexity optimization

[0188] Traditional power iteration: The complexity of each iteration is O(n log n). Total complexity ;

[0189] Hybrid iteration: Constructing the Krylov subspace has a complexity of O(n log n). However, the number of iterations required is halved.

[0190] Enhanced numerical stability

[0191] Orthogonalization process: QR decomposition avoids numerical instability problems in power iteration.

[0192] Condition number effect: Krylov subspaces are insensitive to the condition number of a matrix, making them suitable for handling ill-conditioned matrices.

[0193] Beneficial effects

[0194] 1. Joint spatiotemporal correlation

[0195] Time dimension: Blood flow signals are stable within a short time window, and signals at adjacent time points are highly correlated; Spatial dimension: Received primitive signals are modulated by the same scattering source, and the spatial distribution is coherent; Joint processing: Through RSVD-ST decomposition, and by utilizing spatiotemporal correlation, noise is suppressed by approximately 3-5 dB more than when processing the time or spatial domains separately.

[0196] 2. Advantages in adaptive thresholding

[0197] Spatial Adaptive: Dynamically adjusts based on different primitive signal strengths To avoid signal loss caused by uniform threshold; time-adaptive: increases when blood flow velocity changes abruptly. Artifacts that inhibit blood flow;

[0198] 3. Robustness

[0199] Unbiased noise estimation: Based on the Marchenko-Pastur distribution, subjective parameter settings are avoided; Optimal shrinkage: The soft threshold minimizes the error in the MSE sense, preserving signal details. The improved spatiotemporal joint denoising design separates the signal and noise subspaces through RSVD-ST decomposition and combines it with adaptive soft threshold shrinkage to theoretically achieve optimal noise suppression. Attached Figure Description

[0200] Figure 1 Comparison of denoising results for different homogeneous values;

[0201] Figure 2 To preserve the signal-to-noise ratio for different singular values, the horizontal axis represents the singular value and the vertical axis represents the signal strength;

[0202] Figure 3 The noise reduction effect when using different noise reduction methods;

[0203] Figure 4 The signal-to-noise ratio is represented by different denoising methods, with the horizontal axis representing singular values ​​and the vertical axis representing signal strength. Detailed Implementation

[0204] To better illustrate the purpose and advantages of this invention, the following description, in conjunction with the accompanying drawings and embodiments, further explains the invention. It should be noted that the embodiments of this invention are merely illustrative to make the invention more easily understood and do not constitute any limitation on the invention.

[0205] Referring to the accompanying drawings, an ultrasound cardiovascular imaging method based on the RSVD-ST algorithm mainly includes: an ultrasound instrument emitting ultrasound waves towards the lesion location and receiving echo signals to acquire multi-angle tissue structure signals; and establishing a spatiotemporal two-dimensional matrix based on the original signals. Based on the two-dimensional spatiotemporal matrix Hou Jian Gaussian Random Matrix QR decomposition is performed using Krylov subspaces, and then SVD decomposition is performed to... Decomposed into subspace; ultrasound signal reconstruction; S6 inverse FFT image generation, outputting high signal-to-noise ratio cardiovascular images, the specific content is as follows.

[0206] A two-dimensional spatiotemporal matrix is ​​constructed from the acquired raw signal. .

[0207] The original echocardiogram signal is organized into a matrix form. Assuming the ultrasound receiving array contains M elements, and each element samples at N time points, the original signal matrix can be represented as follows:

[0208] ;

[0209] To implement spatiotemporal sliding window expansion, a time window length L (usually much smaller than N) is selected, and the timing signal of each array element is expanded into a spatiotemporal block using the sliding window method. For example, the spatiotemporal block of the m-th array element is:

[0210]

[0211] Constructing the spacetime matrix Stacking all M spatiotemporal blocks by row yields the complete spatiotemporal joint matrix:

[0212]

[0213] To simplify the analysis, assumptions are usually made. ,at this time The dimensions are approximately M×N, and the dimensional changes caused by sliding windows are ignored.

[0214] For the spacetime matrix Perform an FFT to obtain the frequency domain energy distribution, and then construct a Gaussian random matrix. The specific steps are as follows.

[0215] For the spacetime matrix Perform an FFT to obtain the frequency domain energy distribution:

[0216]

[0217] in, This represents the energy at frequency f. Fourier transform;

[0218] Accumulated energy and projection dimension selection, setting energy threshold Choose the smallest k such that the accumulated energy covers η times the total energy:

[0219]

[0220] Projection matrix generation, constructing Gaussian random matrices Its column vector corresponds to the first column in the frequency domain. Weight enhancement is applied at the dominant frequencies:

[0221]

[0222] in, This represents the total number of frequencies. This is the basis for constructing the Gaussian random matrix Ω, whose element distribution is related to the value of the frequency f; >1 is a weighting factor used to improve the projection efficiency of the signal subspace.

[0223] Using the constructed Gaussian random matrix to the space-time matrix Perform singular value decomposition.

[0224] The specific process of the above steps involves constructing a Krylov subspace based on the random matrix in step two. Construct a Krylov subspace of depth d steps:

[0225]

[0226] in, Denotes the spanned space generated by the Krylov subspace. It is the initial random matrix. Represents the original matrix Perform a matrix exponentiation operation to the order j;

[0227] Orthogonalization and basis merging are performed, and QR decomposition is applied to the Krylov subspace to obtain orthogonal matrices:

[0228]

[0229]

[0230]

[0231] in This represents the QR decomposition of the Krylov subspace, where R is an upper triangular matrix and Q is an orthogonal matrix. To ensure the orthogonality of the matrices, where I is the identity matrix, the main purpose here is to ensure that the column vectors of Q are mutually orthogonal;

[0232] Calculate the low-latitude projection matrix B, and perform exact SVD decomposition on B:

[0233]

[0234] Where B is the low-latitude projection matrix, through Projected onto the subspace of Q to generate, and They are orthogonal matrices, each containing a left singular vector and a right singular vector. It is a diagonal matrix containing singular values; therefore, the approximation of the original matrix is:

[0235]

[0236] Adaptive spatiotemporal soft thresholding is applied to all decomposed singular values ​​to suppress noise.

[0237] The specific process described above is as follows: In cardiovascular ultrasound imaging, the model for defining the received signal can be:

[0238]

[0239] in This is the true signal (low rank). It is additive noise, typically Gaussian white noise, full rank, and the ultimate goal is to achieve... Separation , minimize

[0240] The noise power is estimated by using the singular values ​​of the noise subspace if the noise is white noise:

[0241]

[0242] in, This represents the estimated noise power, where Q represents the dimension of the noise subspace, r represents the dimension of the signal subspace, and P represents the number of channels in the observed data; if the noise... If the noise is independent and identically distributed Gaussian, then the estimator The unbiased estimate of the noise variance is:

[0243]

[0244] Spatiotemporal soft thresholding adaptively shrinks all singular values ​​to suppress noise.

[0245]

[0246] in, The threshold coefficient is derived from the extremum theory of the Gaussian distribution of noise; the soft threshold is expressed as:

[0247]

[0248] Assuming observed singular values ,in For real signals, The minimum and sparsity penalty term is: Taking the derivative of the function and setting it to zero, we obtain the soft threshold formula:

[0249]

[0250] The denoised signal is reconstructed using the condensed singular values.

[0251] The specific formulas for the above steps are as follows:

[0252]

[0253] To further illustrate the effectiveness of the control algorithm, a simulation experiment of the overall algorithm was designed. RSVD-ST was used to denoise cardiac ultrasound images. The SNR value was used to evaluate the experimental results under different numbers of singular values ​​retained. The results are shown below. It can be seen from the figure that the more singular values ​​retained, the better the image denoising effect; however, as the number of retained singular values ​​increases, the improvement in image denoising effect slows down.

[0254] This section presents the denoising results of different algorithms on echocardiogram images, allowing for observation. Figure 1 The comparison of denoising results with different homogeneous values ​​is not very obvious, and the experimental results need to be further measured by the evaluation index signal-to-noise ratio (SNR).

[0255] from Figure 2 As can be seen, the RSVD-ST algorithm proposed in this invention has the best denoising effect, proving the effectiveness of the algorithm proposed in this patent.

[0256] The noise reduction effects of different noise reduction methods are shown in the figure. Figure 3 It's not very obvious just by looking at the image, but through SNR evaluation, see... Figure 4 Therefore, it can be seen that the invention has better results than other existing methods.

[0257] The present invention has been described in detail above through embodiments. It should be noted that the above embodiments are merely preferred embodiments of the present invention and not all embodiments thereof, nor do they constitute any limitation on the scope of protection of the present invention. Technical solutions or embodiments obtained by those skilled in the art through equivalent substitutions or other modifications to the technical features of the present invention without departing from the spirit and essence of the present invention all fall within the scope of protection of the present invention.

Claims

1. A method for ultrasound cardiovascular imaging based on the RSVD-ST algorithm, characterized in that: The ultrasound cardiovascular imaging method includes: S1, an ultrasound instrument emits ultrasound waves to the lesion location and receives echo signals to acquire multi-angle tissue structure signals; S2, noise reduction processing is performed on the multi-angle tissue structure signals; S3, inverse FFT image generation is performed to output a high signal-to-noise ratio cardiovascular image.

2. The ultrasound cardiovascular imaging method based on the RSVD-ST algorithm according to claim 1, characterized in that: Step S2 includes: S2.1, designing the original echocardiogram signal matrix. Assuming the ultrasound receiving array contains M array elements, and each array element is sampled at N time points, the original signal matrix can be represented as: ； S2.2 implements spatiotemporal sliding window expansion. A time window length L (usually much smaller than N) is selected, and the timing signal of each array element is expanded into a spatiotemporal block using the sliding window method. For example, the spatiotemporal block of the m-th array element is: Constructing the spacetime matrix Stacking all M spatiotemporal blocks by row yields the complete spatiotemporal joint matrix: To simplify the analysis, assumptions are usually made. ,at this time The dimensions are approximately M×N, ignoring the dimensional changes caused by the sliding window. S2.3, Signal frequency domain energy analysis, for the spatiotemporal matrix Perform an FFT to obtain the frequency domain energy distribution: in, This represents the energy at frequency f. Fourier transform; S2.4 Cumulative Energy and Projection Dimension Selection, Setting Energy Threshold Choose the smallest k such that the accumulated energy covers η times the total energy: S2.5 Projection matrix generation, constructing a Gaussian random matrix Its column vector corresponds to the first column in the frequency domain. Weight enhancement is applied at the dominant frequencies: in, This represents the total number of frequencies. This forms the basis for constructing a Gaussian random matrix Ω, where the distribution of the matrix elements depends on the value of the frequency f. >1 is a weighting factor used to improve the projection efficiency of the signal subspace; S2.6, Construction of Krylov subspaces, given an initial random matrix Construct a Krylov subspace of depth d steps: in, Denotes the spanned space generated by the Krylov subspace. It is the initial random matrix. Represents the original matrix Perform a matrix exponentiation operation to the order j; S2.7 Orthogonalization and basis merging: Perform QR decomposition on the Krylov subspace to obtain orthogonal matrices. : , in This represents the QR decomposition of the Krylov subspace, where R is an upper triangular matrix and Q is an orthogonal matrix. This indicates the guarantee of orthogonality. I is the identity matrix, and its main purpose here is to ensure that the column vectors of Q are mutually orthogonal. S2.8 Low-latitude projection and SVD decomposition: Calculate the low-latitude projection matrix B and perform exact SVD decomposition on B: Where B is the low-latitude projection matrix, through Projected onto the subspace of Q to generate, and They are orthogonal matrices, each containing a left singular vector and a right singular vector. It is a diagonal matrix containing singular values; therefore, the approximation of the original matrix is: In cardiovascular ultrasound imaging, the model for the received signal can be defined as follows: in This is the true signal (low rank). It is additive noise, typically Gaussian white noise, full rank, and the ultimate goal is to achieve... Separation , minimize S2.9 Noise power estimation: If the noise is white noise, it is estimated using the singular values ​​of the noise subspace as follows: in, This represents the estimated noise power, where Q represents the dimension of the noise subspace, r represents the dimension of the signal subspace, and P represents the number of channels in the observed data; if the noise... If the noise is independent and identically distributed Gaussian, then the estimator The unbiased estimate of the noise variance is: S2.10 Spatiotemporal soft thresholding shrinks, adaptively shrinking all singular values ​​to suppress noise. in, The threshold coefficient is derived from the extremum theory of the Gaussian distribution of noise; the soft threshold is expressed as: Assuming observed singular values ,in For real signals, The minimum and sparsity penalty term is: Taking the derivative of the function and setting it to zero, we obtain the soft threshold formula: The denoised signal is reconstructed using the contracted singular values, as shown in the following formula:

3. The ultrasound cardiovascular imaging method based on the RSVD-ST algorithm according to claim 2, characterized in that: S3 includes: processing the original signal matrix Perform a two-dimensional FFT: in and Let be the Fourier transform matrix, satisfying Frequency domain bandpass filtering, design a frequency domain filter. Preserve blood flow signal frequency band : The filtered signal is: in To perform element-wise multiplication, the inverse FFT reconstructs the time-domain signal as follows: 。

Images