A low-complexity adaptive beamforming method based on phase-varied cross-correlation

Abstract

The application relates to a low-complexity adaptive beamforming method based on phase apodization cross-correlation, and belongs to the technical field of ultrasonic imaging. The method comprises the following steps: focusing and Hilbert transforming a sampling echo signal to obtain a complex echo signal; constructing multiple groups of amplitude apodization functions with different side lobe levels and peak response, weighting the echo signal, calculating and comparing the estimated variances of the apodized signals; constructing multiple groups of complementary phase apodization function pairs, phase apodizing the apodized signal with the minimum estimated variance, and calculating the real part similarity coefficient matrix of the phase-apodized signal pair; summing and averaging the multiple groups of thresholded similarity coefficient matrices and performing two-dimensional mean filtering; and multiplying the sum result of the apodized signal with the minimum variance estimation and the filtered similarity coefficient matrix to obtain the output of a beamformer and form an image. The application has the advantages of low calculation complexity, high robustness, etc., and can significantly improve the resolution and contrast of an ultrasonic image.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of ultrasonic imaging, and relates to a low-complexity adaptive beamforming method based on phase-varying cross-correlation. BACKGROUND

[0002] As a low-cost, non-radiation and non-invasive technology, ultrasonic imaging algorithm is an important tool for medical diagnosis. The most simple and widely used beamforming algorithm is Delay and Sum (DAS), which controls the time alignment of the sensor array through a digital delay line to achieve dynamic focusing. However, the DAS beamformer has a wide main lobe width and high side lobe level, which will result in low resolution and a large amount of clutter in the image.

[0003] The Minimum Variance beamformer (MV) adaptive beamforming algorithm was proposed by Capon in 1969 and applied to narrowband radar, and then improved and applied to wideband medical ultrasonic imaging. This algorithm can significantly improve the resolution of the image, but cannot filter and suppress clutter and noise signals, so it has the disadvantages of poor robustness and inability to improve image contrast. The Generalized Sidelobe Canceller (GSC) as an equivalent structure of the minimum variance adaptive beamforming algorithm has limited improvement on imaging quality, can significantly reduce the main lobe width and improve the lateral resolution, but cannot effectively suppress clutter to improve contrast. At the same time, due to the involvement of spatial covariance matrix inversion in the implementation process of the above two adaptive beamforming algorithms, there is the disadvantage of high computational complexity and cannot be applied to real-time imaging systems.

[0004] In summary, there is an urgent need for a beamforming algorithm that can improve image resolution and contrast at the same time, has low computational complexity and high robustness, and can be applied to real-time imaging systems to improve the overall quality of ultrasonic imaging. SUMMARY

[0005] Therefore, the purpose of the present application is to provide a low-complexity adaptive beamforming method based on phase-varying cross-correlation, which can improve image resolution and contrast while reducing computational complexity and improving robustness to be applied to real-time imaging systems to improve the overall quality of ultrasonic imaging.

[0006] To achieve the above purpose, the present application provides the following technical solutions:

[0007] A low-complexity adaptive beamforming method based on phase-varying cross-correlation, comprising the following steps:

[0008] S1: dynamic delay focusing and Hilbert transform are performed on the signals sampled from the ultrasonic array elements to obtain time-aligned ultrasonic echo signals x(m, n) in complex form;

[0009] S2: a plurality of groups of amplitude apodization functions with different side lobe levels and peak response are constructed, the ultrasonic echo signals are weighted by each group of amplitude apodization functions respectively, and variance estimation is performed on the apodized signals;

[0010] S3: a plurality of groups of complementary phase apodization functions are constructed, phase apodization is performed on the amplitude apodized signal with the minimum estimated variance, and the real part similarity coefficient matrix of each group of phase apodized signal pairs is calculated;

[0011] S4: thresholding is performed on each group of similarity coefficient matrices, and two-dimensional mean filtering is performed on the average value of the thresholded plurality of groups of similarity coefficient matrices;

[0012] S5: the amplitude apodized signal with the minimum estimated variance is summed, the sum result is multiplied by the filtered similarity coefficient matrix as the output of the beamformer and imaging.

[0013] Further, step S2 includes the following steps:

[0014] S21, a plurality of groups of amplitude apodization functions {w1(m), …, wP(m)} with different side lobe levels and peak response are constructed: P (m)}:

[0015]

[0016] In the formula, wP(m) represents the apodization value corresponding to the mth array element in the pth group of amplitude apodization functions, I0 represents the first type of modified Bessel function of zero order, βP represents the side lobe coefficient, φP represents the peak response coefficient, e represents the natural constant, j represents the imaginary unit, and M represents the number of array elements. p p p

[0017] S22, the ultrasonic echo signals are weighted by P groups of apodization functions respectively, and the apodized signals are:

[0018] x Ap (m, n) = w p (m) x(m, n)

[0019] Wherein, x Ap (m, n) represents the amplitude apodized signal, and n represents the time coefficient of ultrasonic focusing.

[0020] S23, variance estimation with a sampling length of 2L+1 is performed on the P groups of apodized signals x Ap (m, n): ​​​

[0021]

[0022] Where, σ 2 p (n) represents the variance of the amplitude apodization function estimate for the p-th group.

[0023] Furthermore, step S3 includes the following steps:

[0024] S31. Construct N sets of phase apodization functions {PA} 11 (m),…,PA 1N (m)} and its complementary function {PA} 21 (m),…,PA 2N (m)}:

[0025]

[0026] Among them, PA 1i (m) and PA 2i (m) represents the complementary apodization value corresponding to the m-th element in the i-th group of phase apodization functions, A i and f i Let sq(t) represent the amplitude and frequency of the i-th phase apodization, respectively, and let sq(t) represent the unit square wave signal.

[0027]

[0028] S32. For the amplitude apodized signal x with the smallest estimated variance. Amin Phase apodization is performed on (m,n) to obtain the phase-apodized signal for y. 1i (n) and y 2i (n):

[0029]

[0030] S33, Signal after phase apodization to y 1i (n) and y 2i The real part of (n) is the similarity coefficient ρ at the g-th focal point on the k-th scan line. i (k,g) is represented as:

[0031]

[0032] Where 2A+1 represents the sample length for calculating the similarity coefficient, G represents the number of focal points on a scan line, and real(·) represents the operation of taking the real part.

[0033] Further, step S4 includes the following steps:

[0034] S41. For N sets of similarity coefficient matrices ρ i Thresholding is performed on (k,g):

[0035] ρ′ i (k,g)=max(ρ i (k,g),ε),i=1,2,...,N

[0036] Where, ρ′ i (k,g) represents the thresholded similarity coefficient matrix, and ε represents the pre-set threshold.

[0037] S42: Calculate the thresholded similarity coefficient matrix ρ′ of N groups. i The average value ρ′(k,g) of (k,g):

[0038]

[0039] S43: Perform two-dimensional mean filtering on the average value ρ′(k,g) of the thresholded similarity coefficient matrix:

[0040]

[0041] Where ρ(k,g) represents the similarity coefficient matrix after filtering, 2B+1 and 2C+1 represent the length and width of the two-dimensional mean filtering window, respectively, K represents the total number of scan lines, and G represents the number of focal points on a scan line.

[0042] Further, step S5 includes the following steps:

[0043] S51. Estimate the amplitude apodization signal x with the minimum variance. Amin The summation result y of (m,n) Amin (n) is shown below:

[0044]

[0045] S52: Subtract the summation result y Amin (n) is multiplied by the filtered similarity coefficient matrix ρ(k,g) to obtain the beamformer output y(k,g):

[0046] y(k,g)=ρ(k,g)y Amin (Gk+g)

[0047] The beneficial effects of this invention are as follows: This invention can simultaneously improve the resolution and contrast of images, has good robustness, and the implementation process does not involve the inversion of the spatial covariance matrix, but only involves numerical operations of numbers, which has low computational complexity. When applied to a real-time ultrasound imaging system, it can improve the overall quality of ultrasound imaging.

[0048] Additional advantages, objects, and features of the application will be apparent to those skilled in the art upon examination of the following specification. It is intended that the application not be limited by any of the details of the specification. Instead, such details are intended to be illustrative of the general features of the application. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to make the objectives, technical solutions and advantages of the present application clearer, the preferred embodiments of the present application will be described in detail below with reference to the drawings, in which:

[0050] Figure 1 Flow chart of the method of the present application;

[0051] Figure 2 Comparison chart of imaging effects of four algorithms on point targets;

[0052] Figure 3 Curve chart of lateral resolution of four algorithms on point targets at 55 mm;

[0053] Figure 4 Comparison chart of imaging results of four algorithms on sound absorption spots;

[0054] Figure 5 Comparison chart of imaging results of four algorithms on sound absorption spots with 5 dB / 0 dB / -5 dB Gaussian white noise;

[0055] Figure 6 Comparison chart of CR, CNR and sSNR of four algorithms under 5 dB / 0 dB / -5 dB channel Gaussian white noise;

[0056] Figure 7 Comparison chart of imaging results of four algorithms on experimental sound absorption spot data. DETAILED DESCRIPTION

[0057] The present application can be implemented or applied in other different specific embodiments, and the details in the specification can be modified or changed based on different views and applications without departing from the spirit of the present application. It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present application in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0058] The drawings are only used for exemplary illustration, and the representation is only a schematic diagram, not a physical diagram, and cannot be understood as a limitation on the present application; in order to better illustrate the embodiments of the present application, some components of the drawings will be omitted, enlarged or reduced, and do not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings can be omitted.

[0059] The same or similar reference numerals in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it should be understood that if the terms "upper", "lower", "left", "right", "front", "back" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the positional relationship described in the drawings is only used for exemplary illustration, and cannot be understood as a limitation on the present application, for those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0060] As Figure 1 shown is a low-complexity adaptive beamforming method based on phase apodization cross-correlation, specifically as follows:

[0061] S1: dynamic delay focusing and Hilbert transform are performed on the signals sampled by the ultrasonic array elements to obtain the time-aligned ultrasonic echo signals x(m, n) in complex form;

[0062] S2: a plurality of sets of amplitude apodization functions with different side lobe levels and peak response are constructed, each set of amplitude apodization function is used to weight the ultrasonic echo signals, and variance estimation is performed on the apodized signals:

[0063] S21, a plurality of sets of amplitude apodization functions {w1(m), …, w P (m)} with different side lobe levels and peak response are constructed:

[0064]

[0065] In the formula, w p (m) represents the apodization value corresponding to the mth array element in the pth set of amplitude apodization functions, I0 represents the first modified Bessel function of zero order, β p represents the side lobe coefficient, φ p represents the peak response coefficient, e represents the natural constant, and j represents the imaginary unit, and M represents the number of array elements;

[0066] S22, P sets of apodization functions are used to weight the ultrasonic echo signals, and the apodized signals are:

[0067] x Ap(m, n) = w p (m) x (m, n)

[0068] wherein x Ap (m, n) represents an amplitude apodized signal, and n represents a time coefficient of ultrasonic focusing;

[0069] S23, the P-group apodized signal x Ap (m, n) is sampled to estimate the variance of the length of 2L+1:

[0070]

[0071] wherein σ 2 p (n) represents the variance of the pth group of amplitude apodization function estimates;

[0072] S3, construct a plurality of complementary phase apodization function pairs, phase apodize the amplitude apodized signal with the minimum estimated variance, and calculate the real part similarity coefficient matrix of each phase apodized signal pair:

[0073] S31, construct N groups of phase apodization functions {PA 11 (m), …, PA 1N (m)} and their complementary functions {PA 21 (m), …, PA 2N (m)}:

[0074]

[0075] wherein PA 1i (m) and PA 2i (m) represent the complementary apodization values corresponding to the mth element pair in the ith group of phase apodization functions, A i and f i represent the amplitude and frequency of the ith group of phase apodization, respectively, and sq(t) represents a unit square wave signal:

[0076]

[0077] S32, phase apodize the amplitude apodized signal x Amin (m, n) with the minimum estimated variance to obtain a phase apodized signal pair y 1i (n) and y 2i (n):

[0078]

[0079] S33, the real part similarity coefficient ρ of the phase apodized signal pair y 1i (n) and y 2i (n) at the gth focal point on the kth scan linei (k, g) is represented as:

[0080]

[0081] wherein 2A+1 represents the sample length for calculating the similarity coefficient, G represents the number of focus points on a scanning line, and real(·) represents the real part operation;

[0082] S4, thresholding is performed on each group of similarity coefficient matrices, and two-dimensional mean filtering is performed on the average values of the thresholded groups of similarity coefficient matrices:

[0083] S41, N groups of similarity coefficient matrices ρ i (k, g) are thresholded:

[0084] ρ i '(k, g) = max(ρ i (k, g), ε), i = 1, 2,..., N

[0085] wherein ρ' i (k, g) represents the thresholded similarity coefficient matrix, and ε represents a pre-set threshold value;

[0086] S42: the average value ρ'(k, g) of the N groups of thresholded similarity coefficient matrices ρ' i (k, g) is calculated:

[0087]

[0088] S43: two-dimensional mean filtering is performed on the average value ρ'(k, g) of the thresholded similarity coefficient matrices:

[0089]

[0090] wherein ρ(k, g) represents the filtered similarity coefficient matrix, 2B+1 and 2C+1 respectively represent the length and width of the two-dimensional mean filtering window, and K represents the total number of scanning lines;

[0091] S5, the amplitude apodized signals with the minimum estimated variance are summed up, the sum result is multiplied by the filtered similarity coefficient matrix as the output of the beamformer and imaging is performed;

[0092] wherein the sum result y Amin (m, n) of the amplitude apodized signals x Amin (n) with the minimum estimated variance is as follows:

[0093]

[0094] the sum result y Amin(n) multiplying the filtered similarity coefficient matrix p(k, g) to obtain the output of the beamformer y(k, g):

[0095] y(k, g) = p(k, g)y Amin (Gk+g).

[0096] In this embodiment, the beneficial effects of the present application are demonstrated by experimental verification:

[0097] Field II is an ultrasound simulation platform developed by Technical University of Denmark based on acoustic principles, which has been widely recognized and used in theoretical research. In order to verify the effectiveness of the present application, Field II is used to image the point scattering target and the sound absorbing spot target commonly used in ultrasonic imaging, and the experimental sound absorbing spot data is used for imaging comparison experiment. In the point target simulation experiment, 18 point targets with longitudinal spacing of 5mm and transverse spacing of 5mm are set, which are uniformly distributed in the imaging range of 30mm to 70mm in depth and-10mm to 10mm in transverse distance, and the imaging dynamic range of the image is set to 60dB, so as to observe the strength of the transverse resolution of each algorithm. In the sound absorbing spot simulation experiment, a circular sound absorbing spot with a radius of 4mm is set, the center of which is located at a depth of 40mm, the longitudinal imaging range is between 30mm and 50mm, and the transverse imaging range is between-10mm and 10mm, 200000 scattering points are randomly distributed in the imaging area, the amplitude of the scattering points in the background area is 1000 times that of the internal area of the sound absorbing spot, and the imaging dynamic range is set to 60dB. In order to verify the robustness of the algorithm, for the sound absorbing spot simulation experiment, Gaussian white noise with SNR of 5dB / 0dB / -5dB is added to the received data before beamforming to simulate the actual noise situation, and the imaging dynamic range is set to 60dB. The simulation adopts the method of transmitting fixed focusing and receiving dynamic focusing. The center frequency of the array element used in the experiment is 6MHz, the number of array elements is 128, the spacing is 0.24mm, the sampling frequency is 40MHz, the sound speed is 1540m / s, and the imaging dynamic range is set to 60dB.

[0098] The four experimental targets described above are compared and imaged by using the delay-and-sum algorithm (DAS), the low-complexity apodization algorithm (LCA), the phase-apodization cross-correlation algorithm (PAC), and the method described in the present application (LCA-PAC).

[0099] Figure 2 The point target imaging results of the four algorithms are shown, from which it can be seen that the LCA-PAC algorithm has better imaging quality than the other three algorithms. Figure 2It can be seen that the imaging quality of the DAS algorithm is the worst, the sidelobe artifact is serious, the lateral artifact is higher and the main lobe width is wider compared with other algorithms, and it is difficult to distinguish the target point. The PAC has similar main lobe width with the DAS, but the sidelobe artifact is suppressed to a certain extent. The LCA algorithm narrows the main lobe width obviously, and the lateral resolution is improved obviously, but it performs poorly in the suppression of the sidelobe artifact. The application has similar main lobe width with the LCA, but it further suppresses the sidelobe compared with the LCA. In summary, the main lobe width and the sidelobe level of the application are the best among the imaging quality of the four algorithms.

[0100] Figure 3 For the lateral resolution comparison of the four algorithms at the point target 55mm, it can be directly seen that the sidelobe suppression ability of the application is the strongest, the main lobe width can be effectively narrowed, and the resolution is improved. In order to more intuitively compare the imaging resolution of the four algorithms, table 1 gives the comparison of the half peak width (FWHM) and the intermediate amplitude (MA) data of the four algorithms at different depths. It can be seen from table 1 that the resolution of the DAS is the lowest, the resolution of the PAC is slightly improved compared with the DAS, the resolution of the LCA is obviously improved, and the application achieves better resolution than the other three algorithms at different depths.

[0101] Table 1 comparison of FWHM and MA of four algorithms at different depths of simulated point target

[0102]

[0103]

[0104] Figure 4 For the imaging results of the four algorithms on the simulated sound absorbing spot target. From Figure 4 It can be seen that the imaging effect of the DAS is the worst, there are a large number of sidelobe artifacts in the spot, which is caused by high sidelobe level. The LCA algorithm has higher improvement compared with the DAS, and only a small amount of sidelobe artifact exists, which is caused by the LCA which can select the apodization function with the smallest variance estimation to effectively suppress the sidelobe level. The PAC and the application can obviously suppress the sidelobe artifact in the sound absorbing spot, so that the contour of the sound absorbing spot is clear.

[0105] Table 2 provides the CR, CNR and sSNR of the imaging of the simulated sound absorbing spot by different algorithms. It can be seen that the average power in the sound absorbing spot is too high for the DAS, that is, the artifact suppression ability in the spot is weak, so the imaging effect is not good. The LCA algorithm suppresses the average power in the sound absorbing spot to a certain extent, so it achieves better imaging effect than the DAS. The PAC and the application suppress the average power in the sound absorbing spot by 36dB and 78dB respectively, so higher contrast can be achieved. In summary, the simulation experiment shows that the comprehensive imaging effect of the application is the best compared with the other three methods.

[0106] Table 2 CR, CNR and sSNR of different algorithms for simulated sound absorption spot imaging

[0107]

[0108] To verify the robustness of the present application, Figure 5 The imaging effect comparison chart of four algorithms respectively adding channel Gaussian white noise with signal-to-noise ratio of 5dB / 0dB / -5dB is given. From the chart, it can be seen that due to the addition of Gaussian white noise, the imaging contrast of each algorithm has different degrees of decline, and the present application is least disturbed by noise signals and the sound absorption spot profile is the clearest. Figure 5 The imaging effect comparison chart of four algorithms respectively adding channel Gaussian white noise with signal-to-noise ratio of 5dB / 0dB / -5dB is given. From the chart, it can be seen that due to the addition of Gaussian white noise, the imaging contrast of each algorithm has different degrees of decline, and the present application is least disturbed by noise signals and the sound absorption spot profile is the clearest. Figure 6 The index comparison chart of CR, CNR and sSNR of four algorithms under channel Gaussian white noise with signal-to-noise ratio of 5dB / 0dB / -5dB is given. It can be seen that with the increase of channel noise, the sidelobe suppression ability of DAS and LCA rapidly weakens, and the imaging quality rapidly declines. PAC and the present application both show good robustness to noise, and the CR and CNR remain at a high level.

[0109] Figure 7 The imaging results of four algorithms for experimental sound absorption spots are shown. From the chart, it can be seen that in DAS and LCA, the left sound absorption spot has obvious sidelobe artifacts, and the right sound absorption spot is almost indistinguishable from the background. PAC and the present application can effectively suppress the sidelobe artifacts in the left sound absorption spot and distinguish the right sound absorption spot from the background. In summary, the present application can improve the image resolution and contrast at the same time, has low computational complexity and high robustness, and can be applied in real-time imaging systems to improve the overall quality of ultrasonic imaging.

[0110] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit it. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should be covered in the scope of the claims of the present application.

Claims

1. A low-complexity adaptive beamforming method based on phase apodization cross-correlation, characterized in that: The method includes the following steps: S1: Perform dynamic delay focusing and Hilbert transform on the signal sampled from the ultrasonic array elements to obtain a time-aligned ultrasonic echo signal in complex form. , m For array element sequence number, n The time coefficient for ultrasound focusing; S2: Construct multiple sets of amplitude apodization functions with different sidelobe levels and peak responses, use each set of amplitude apodization functions to apodize and weight the ultrasound echo signal, and estimate the variance of the apodized signal. S3: Construct multiple pairs of complementary phase apodization functions, perform phase apodization on the amplitude apodized signal with the smallest estimated variance, and calculate the real part similarity coefficient matrix of each pair of phase apodized signals. S4: Threshold each similarity coefficient matrix, and perform two-dimensional mean filtering on the average of the thresholded similarity coefficient matrices. S5: Summate the amplitude apodized signal with the smallest estimated variance, multiply the summation result by the filtered similarity coefficient matrix, and use the result as the output of the beamformer for imaging.

2. The beamforming method according to claim 1, characterized in that: Step S2 includes the following steps: S21. Construct multiple sets of amplitude apodization functions with different sidelobe levels and peak responses. : In the formula, Indicates the first The first group of amplitude apodization functions The apodization value corresponding to each array element. P This represents the total number of groups with agnostic changes. This represents the zeroth-order modified Bezos function of the first kind. Indicates the sidelobe coefficient. Represents the peak response coefficient. Represents the natural constant. Represents the imaginary unit. M Indicates the number of array elements; S22, Utilization The group of apodization functions are used to weight the ultrasound echo signal, and the apodized signal is: in, This indicates the signal after amplitude apodization. Indicates the time coefficient of ultrasound focusing; S23, to Group apodization signal The sampling length is Variance estimation: in, Indicates the first The variance of the group amplitude apodization function estimate. n This represents the time coefficient for ultrasound focusing.

3. The beamforming method according to claim 1, characterized in that: Step S3 includes the following steps: S31, Construction Group phase apodization function and its complementary functions : in, and Indicates the first The first in the group of phase apodization functions The complementary apodization values ​​corresponding to each array element N This represents the total number of phase apodization functions. and They represent the first The amplitude and frequency of the phase apodization. Represents a unit square wave signal: S32. For the amplitude apodization signal with the smallest estimated variance. Perform phase apodization to obtain the phase-apodized signal pair and : in, M For the number of array elements, n The time coefficient for ultrasound focusing; S33, Signal pair after phase apodization and The real part in the first The first scan line Similarity coefficient of each focal point Represented as: in, k Indicates the scan line index. Indicates the focal point index. This represents the sample length used to calculate the similarity coefficient. This indicates the number of focal points on a scan line. This indicates the operation of taking the real part.

4. The beamforming method according to claim 1, characterized in that: Step S4 includes the following steps: S41, to Group similarity coefficient matrix Thresholding: in, This represents the similarity coefficient matrix after thresholding. This indicates a pre-set threshold. This indicates that the real part of each signal pair after phase apodization is at the th... The first scan line The similarity coefficient matrix of each focal point i Index for the azo group number; S42: Calculation Group thresholded similarity coefficient matrix average : S43: The average value of the thresholded similarity coefficient matrix Perform two-dimensional mean filtering: in, This represents the similarity coefficient matrix after filtering. and These represent the length and width of the two-dimensional mean filter window, respectively. Indicates the total number of scan lines. This indicates the number of focal points on a scan line.

5. The beamforming method according to claim 1, characterized in that: Step S5 includes the following steps: S51. Estimate the amplitude apodization signal with the minimum variance. The summation result As shown below: in, m For array element sequence number, M For the number of array elements, n The time coefficient for ultrasound focusing; S52: Subtract the summation result Similarity coefficient matrix after filtering Multiply to obtain the output of the beamformer : in, g Indicates the first k The first scan line g One focal point G This indicates the number of focal points on a scan line.

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