Near-field Fast Beamforming Method Based on Sub-region Model and Non-uniform Fourier Transform

Abstract

The present invention discloses a near-field fast beamforming method based on a sub-region model and non-uniform Fourier transform, comprising the following steps: rotating the coordinate system of the observation range clockwise by 45°, and uniformly dividing it into a plurality of sub-regions; simplifying the near-field time-delay parameters of each sub-region, and weighting the simplified parameters by using the least squares method; performing the non-uniform Fourier transform (NUFFT) method on the array response signals generated by the two-dimensional transducer array, and calculating the beams in each sub-region in parallel; remapping the coordinates of the beams to obtain a high-precision beam pattern. The present invention effectively expands the near-field detection range of the phased array three-dimensional imaging sonar system while maintaining a low computational burden, and improves the imaging quality and detection performance of the three-dimensional imaging sonar system.

Description

Technical Field

[0001] The present invention relates to the technical field of phased array three-dimensional imaging sonar systems, and particularly relates to a near-field fast beamforming method based on a sub-region model and non-uniform Fourier transform. Background Art

[0002] A phased array three-dimensional imaging sonar system uses a narrowband acoustic pulse to transmit through the entire underwater scene, and uses a two-dimensional uniform rectangular transducer array to receive the backscattered echo signals in the scene to generate array response signals. These array response signals can be processed by beamforming technology and real-time image processing technology to obtain a high-resolution underwater three-dimensional image.

[0003] In order to improve the resolution of the image and maintain a large detection angle of view at the same time, the two-dimensional uniform rectangular transducer array usually has a large aperture and contains thousands of array elements. In addition, the beam image obtained through signal processing usually contains tens of thousands of beam directions, which results in a huge computational burden.

[0004] The traditional delay-and-sum beamforming method adjusts the time delay of the array element sampling signals according to the beam direction and accumulates them, and can accurately obtain the beam results in any direction, but its huge computational burden cannot guarantee real-time imaging. The frequency-domain direct beamforming method can reduce the computational burden by an order of magnitude, but this is still unbearable. Therefore, some frequency-domain fast beamforming methods have been proposed, such as the Chirp-z transform (CZT) and the non-uniform Fourier transform (NUFFT). These fast beamforming methods utilize the high-efficiency computational performance of the fast Fourier transform in different ways, and their computational burden is reduced by one to two orders of magnitude compared with the frequency-domain direct beamforming method.

[0005] However, these fast beamforming methods have relatively strict requirements for the signal model, which is easily satisfied in the far field. For the near-field region, the Fresnel approximation model is usually adopted to avoid some high-order parameters that do not meet the requirements, which results in a narrow effective field of view in the near-field region. The Fresnel approximation model can only guarantee the beamforming accuracy within 18°, and there are obvious distortions in the beam results outside 18°.

[0006] Patent document CN109283536A discloses a multi-beam sounding sonar water body imaging beamforming algorithm. During each detection sampling time, the propagation loss of sound waves is compensated according to the time gain curve, and the background noise level of the current detection water area is obtained after time averaging; near-field focusing beamforming is performed on the signal, and according to the current background noise level, the number of signal sources at the current snapshot number is estimated; covariance matrix estimation is performed on the signal vector with a snapshot number of 1, and through matrix reconstruction of the data covariance matrix after forward and backward smoothing, a new pseudo-covariance matrix is obtained; singular value decomposition is performed on the pseudo-covariance matrix, and a spatial spectrum function is constructed by using the output result of conventional beamforming and the array manifold to obtain the multi-beam sounding sonar water body imaging result. The computational burden of this beamforming method is still large. Summary of the Invention

[0007] In view of the above, the object of the present invention is to provide a near-field fast beamforming method based on a sub-region model and non-uniform Fourier transform. This near-field fast beamforming method divides the complete near-field detection field of view into multiple sub-regions, constructs a signal model for each sub-region respectively, adopts least squares weighting and coordinate axis rotation operations to ensure model accuracy, and finally uses the non-uniform Fourier transform (NUFFT) method to perform fast beamforming on each sub-region in parallel. After remapping the coordinates of the beam results, a high-precision beam pattern within 90° is obtained, and its computational burden remains at the same or lower level.

[0008] A near-field fast beamforming method based on a sub-region model and non-uniform Fourier transform provided by an embodiment includes the following steps:

[0009] (1) Rotate the coordinate system of the observation range of the two-dimensional transducer array by a preset rotation angle, and evenly divide the rotated observation range into multiple sub-regions, where the rotation angle is positive in the clockwise direction and is an odd multiple of 45°;

[0010] (2) Simplify the near-field delay parameters of the transducer array elements in each sub-region, construct weighted near-field delay parameters according to the simplified near-field delay parameters by using the least squares method, and solve the weighted near-field delay parameters to determine the optimal weighting coefficient;

[0011] (3) Construct an operator for adjoint non-uniform Fourier transform according to the array response signal generated by the two-dimensional transducer array and the beam signal with the weighting coefficient, and perform non-uniform Fourier transform calculation in parallel according to the operator for adjoint non-uniform Fourier transform to obtain the beam in each sub-region;

[0012] (4) Remap the coordinates of the beam in each sub-region to obtain a high-precision beam pattern.

[0013] Preferably, the two-dimensional transducer array is a two-dimensional rectangular array including N×N transducer array elements. This two-dimensional rectangular array is located in the XOY plane of the three-dimensional space. The sides of the two-dimensional rectangular array are respectively parallel to the X and Y coordinate axes. The coordinates of the (n1, n2)th transducer array element are represented as (x n1 , y n2 );

[0014] The focusing distance r0 of the beam is the near-field region. The observation range is represented by two direction parameters θ a and θ e . They are respectively parallel to the X and Y axes, and the value range is (-90°, 90°).

[0015] Preferably, there are P×Q beams to be generated within the observation range. For the (p, q)th beam, its beam direction is (θ ap , θ eq ). The beam signal b(r0, p, q) is expressed as:

[0016]

[0017] where, f l represents the signal frequency, r0 represents the focusing distance of the beam in the near-field region, S l (n1, n2) represents the frequency-domain sampling data of the (n1, n2)th transducer array element, N represents the number of transducers in each direction, τ(r0, p, q, n1, n2) represents the time delay of the (n1, n2)th transducer array element for the beam direction (θ ap , θ eq ), and is expressed as:

[0018]

[0019] where, c represents the speed of sound, (x n1 , y n2 ) represents the coordinates of the (n1, n2)th transducer array element.

[0020] Preferably, in step (1), the rotated observation range is evenly divided into 3×3 or 4×4 sub-regions. The specific operation is as follows:

[0021] (1-1) After rotating the coordinate system of the observation range by a preset rotation angle φ, the new direction parameters θ′ a and θ′ e are as follows:

[0022]

[0023] where, the restricted direction parameters θ′ a and θ′ eThe value range of is (-90°, 90°);

[0024] (1 - 2) Divide the direction parameters θ′ a and θ′ e into three or four equal segments in the sine domain within the value range, and use u and v to represent the indices of each sub-region, that is:

[0025]

[0026] Or,

[0027]

[0028] For the (u, v) sub-region, its position is determined by sinθ′ a and sinθ′ e corresponding value ranges.

[0029] Preferably, in step (2), simplify the near-field delay parameters of the transducer array elements in each sub-region. The simplified near-field delay parameter τ sp (r0, p, q, n1, n2) is expressed as:

[0030]

[0031] where r0 represents the focusing distance of the beam in the near-field region, c represents the speed of sound, sinθ′ ap and sinθ′ eq are the sine domain parameters corresponding to the (p, q) beam direction in the new coordinate system, and

[0032]

[0033]

[0034] where, sinθ′ au and sinθ′ ev are the centers of the (u, v) sub-region. That is, for a 3×3 sub-region, there is

[0035]

[0036] Or for a 4×4 sub-region, there is

[0037]

[0038] Preferably, in step (2), use the least squares method to construct a weighted near-field delay parameter τ LS (r0, p, q, n1, n2), which is expressed as:

[0039]

[0040] where g(n1, n2, u, v) = [3ρ 2 (n1, n2, u, v) - v(n1, n2)] / 2r0;

[0041] According to the least squares method, the weighted near - field time - delay parameter τ LS (r0, p, q, n1, n2) is solved to obtain the optimal values of the weighted coefficients k1 - k6 to minimize the time - delay error within the sub - region.

[0042] Preferably, step (3) includes:

[0043] (3 - 1) Put P×Q beams into the corresponding sub - regions. Each sub - region contains P u ×Q v beams, and indexed by (p u , q v ), then the direction parameters of the corresponding beams are expressed as:

[0044]

[0045]

[0046]

[0047] (3 - 2) For the (p u , q v ) beam, construct the operator b(r0, p u , q v ) of the adjoint non - uniform Fourier transform based on the response signal generated by the two - dimensional transducer array and the beam signal with weighted coefficients, expressed as:

[0048]

[0049] where S(n1, n2) represents the response signal, ξ(n1, n2, u, v) represents the weighted coefficient independent of (p u , q v ), ω a (n1, n2, u, v) and ω e (n1, n2, u, v) represent non - uniform node coordinates, and

[0050]

[0051]

[0052]

[0053] where f lrepresents the signal frequency, r0 represents the focusing distance of the beam in the near-field region, and c represents the speed of sound;

[0054] (3-2) Pre-calculate ξ(n1,n2,u,v), ω a (n1,n2,u,v) and ω e (n1,n2,u,v), as well as the compensation coefficients and interpolation coefficients required by the non-uniform Fourier transform method;

[0055] (3-3) According to the calculation results of step (3-2), perform non-uniform Fourier transform calculation on the operator accompanying the non-uniform Fourier transform in parallel to obtain the beams in each sub-region, that is, determine the direction parameters of the beams and

[0056] Preferably, in step (4), for the p u ,q v )-th beam in the sub-region, perform remapping, and the obtained remapped coordinates are expressed as:

[0057]

[0058] Based on the remapped coordinates, obtain the beam pattern in the original coordinate system.

[0059] Compared with the prior art, the present invention has the following beneficial technical effects:

[0060] The near-field fast beamforming method provided by the present invention divides the observation range of the two-dimensional transducer array into multiple sub-regions, and uses the weighted coordinate rotation and least squares method to ensure the accuracy of the direction delay parameters of all beams in the sub-region; uses non-uniform Fourier transform to achieve fast beamforming in each sub-region to maintain a low computational burden; the fast beamforming of all sub-regions can be executed in parallel, which is beneficial to simplifying the computational structure. Therefore, the present invention is applicable to the near-field region detection of a phased array three-dimensional imaging sonar system, improving the imaging quality and detection performance of the three-dimensional imaging sonar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0062] Figure 1 It is a schematic flowchart of the near-field fast beamforming method based on the sub-region model and non-uniform Fourier transform provided for the embodiment;

[0063] Figure 2 Schematic diagram of the near-field signal model of the transducer array of the phased array three-dimensional imaging sonar system provided for the embodiment;

[0064] Figure 3 Schematic diagram of the coordinate system rotation and sub-region division of the observation range provided for the embodiment;

[0065] Figure 4 Beam pattern obtained by using the near-field fast beamforming method of the present invention provided for the embodiment;

[0066] Figure 5 Beam pattern based on the traditional Fresnel approximation model provided for the embodiment;

[0067] Figure 6 Comparison of the computational burden between the traditional Fresnel approximation model and the present invention under different array parameters provided for the embodiment. Detailed implementation manners

[0068] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific implementation manners described herein are only used to explain the present invention and do not limit the protection scope of the present invention.

[0069] To achieve fast imaging of a two-dimensional transducer array in the near-field region, an embodiment provides a near-field fast beamforming method based on a sub-region model and non-uniform Fourier transform. As Figure 1 shown, the near-field fast beamforming method based on a sub-region model and non-uniform Fourier transform provided by the embodiment includes the following steps:

[0070] Step 1, rotate the coordinate system of the observation range of the two-dimensional transducer array by a preset rotation angle, and evenly divide the rotated observation range into a plurality of sub-regions.

[0071] In the embodiment, it is assumed that the transducer array in a specific phased array three-dimensional imaging sonar system is a 50×50 two-dimensional uniform rectangular array, the element spacing is λ / 2, and λ is the wavelength of the sound wave. As Figure 2 shown, the center of the array is located at the origin of coordinates, the near-field focusing distance r0 is 1 m, and the detection range is the positive half-axis of the z-axis (φ < 90°). Four scattering targets with azimuths of (0°, 0°), (18°, 0°), (-25°, -25°), and (-34.5°, -55°) are set at the focusing distance.

[0072] Each element is indexed by two direction parameters n1 and n2, and its coordinates are represented by (x n1 , y n2 ). The beam direction is determined by two direction parameters θ a and θe It is indicated that they are parallel to the X and Y axes respectively. Assume that 200 beams need to be calculated in each beam direction to ensure high resolution of the image.

[0073] Step 1-1: Rotate the coordinate system of the observation range by a preset rotation angle and establish new direction parameters.

[0074] In the embodiment, when the coordinate system of the observation range is rotated clockwise by 45°, new direction parameters θ′ a and θ′ e are as follows:

[0075]

[0076] Among them, the value ranges of the restricted direction parameters θ′ a and θ′ e are (-90°, 90°).

[0077] The coordinate system of the original observation range is scaled by the sine of θ a and θ e . Since its value range is (-90°, 90°), the sine of θ a and θ e is monotonic and there is no overlap.

[0078] It can be seen that there are differences in the observation ranges before and after rotation. Since the φ < 90° region of the observation range is circular and is the overlapping region in the two coordinate systems, the rotation of the coordinate system will not cause the loss of the field of view. Setting 200 beams in the θ a and θ e directions has the same beam density as setting 200 beams in the θ′ a and θ′ e directions.

[0079] All fast beamforming methods are based on a rectangular observation range to facilitate the separation of coordinate parameters. Although a small amount of results are meaningless, this is necessary.

[0080] Step 1-2: Divide the direction parameters θ′ a and θ′ e into four equal segments in the sine domain within the value range, that is, evenly divide the rotated observation area into 3×3 or 4×4 sub-regions. Taking the 4×4 sub-region as an example, the rotated coordinate system and sub-regions are as Figure 3 shown.

[0081] In the embodiment, use u and v to represent the index of each sub-region, that is:

[0082]

[0083] And each segment contains 50 beam directions, and there are 50×50 beam directions in a sub-region.

[0084] Step 2: Simplify the near-field delay parameters of each sub-region and weight the simplified parameters using the least squares method.

[0085] In the embodiment, simplify the near-field delay parameters of the transducer array elements in each sub-region, construct the weighted near-field delay parameters according to the simplified near-field delay parameters using the least squares method, and solve the weighted near-field delay parameters to determine the optimal weighting coefficient.

[0086] Step 2-1: Simplify the near-field delay parameters of the transducer array elements in each sub-region.

[0087] For the traditional Fresnel approximation, its near-field delay parameter τ FA (r0, p, q, n1, n2) is expressed as:

[0088]

[0089] It is concise enough, but only valid within the range φ < 18°. This method proposes a more accurate delay parameter. In the new coordinate system, the simplified near-field delay parameter τ sp (r0, p, q, n1, n2) is expressed as:

[0090]

[0091] where r0 represents the focusing distance of the beam in the near-field region, c represents the speed of sound, sinθ′ ap and sinθ′ eq are the sine-domain parameters corresponding to the (p, q)th beam direction in the new coordinate system, and

[0092]

[0093]

[0094] where sinθ′ au and sinθ′ ev is the center of the (u, v)th sub-region, that is:

[0095]

[0096] Step 2-2: Weight and solve the simplified parameters using the least squares method.

[0097] The simplified near-field delay parameter τ sp(r0, p, q, n1, n2) has the highest precision at the center of the sub-region and a larger error at the corners of the sub-region. To balance the errors in all directions within the sub-region, a weighted approximate delay parameter τ is constructed. LS (r0, p, q, n1, n2), which is expressed as:

[0098]

[0099] where g(n1, n2, u, v) = [3ρ 2 (n1, n2, u, v) - v(n1, n2)] / 2r0, and the optimal values of k1 - k6 can be obtained for the weighted near-field delay parameter τ LS (r0, p, q, n1, n2) to minimize the total mean square error of the delay within the sub-region.

[0100] In this embodiment, the optimal values of k1 - k6 in some sub-regions are shown in Table 1.

[0101] Table 1

[0102]

[0103] Step 3: Execute the NUFFT method on the array response signal generated by the two-dimensional transducer array and calculate the beams within each sub-region in parallel.

[0104] In the embodiment, an operator for adjoint non-uniform Fourier transform is constructed based on the response signal generated by the two-dimensional transducer array and the beam signal with weighted coefficients, and the non-uniform Fourier transform is calculated in parallel according to the operator for adjoint non-uniform Fourier transform to obtain the beams within each sub-region.

[0105] Specifically, Step 3 includes:

[0106] Step 3-1: Construct the form of the adjoint NUFFT operator for the beam signal within each sub-region.

[0107] In the embodiment, P × Q beams are placed into the corresponding sub-regions, and each sub-region contains P u × Q v beams. The beam direction is represented based on the beam index (p u , q v ) within each sub-region, where 0 ≤ p u ≤ 49 and 0 ≤ q v ≤ 49. The beam direction is expressed as and where and

[0108]

[0109] For the (p u ,q v )-th beam, an operator b(r0,p u ,q v ) for the adjoint non-uniform Fourier transform is constructed based on the response signal generated by the two-dimensional transducer array and the beam signal with weighting coefficients, and is expressed as:

[0110]

[0111] where S(n1,n2) represents the response signal, ξ(n1,n2,u,v) is the weighting coefficient independent of (p u ,q v ), ω a (n1,n2,u,v) and ω e (n1,n2,u,v) are non-uniform node coordinates, and

[0112]

[0113]

[0114]

[0115] Step 3-2: Pre-compute ξ(n1,n2,u,v), ω a (n1,n2,u,v) and ω e (n1,n2,u,v), as well as the compensation coefficients and interpolation coefficients required by the NUFFT method.

[0116] In the embodiment, each transducer element signal requires 4×4 interpolation coefficients, and each beam result requires the calculation of one compensation coefficient, which can be pre-computed and stored in advance through some toolboxes and does not require real-time calculation.

[0117] Step 3-3: According to the calculation results of Step 3-2, perform NUFFT calculations on the operator for the adjoint NUFFT in parallel to obtain the beams in each sub-region, that is, determine the direction parameters of the beams.

[0118] In the embodiment, each sub-region can be calculated in parallel to maintain a low computational burden.

[0119] Step 4: Remap the coordinates of the beams to obtain a high-precision beam pattern.

[0120] In the embodiment, for the (p u ,q v )-th beam in the sub-region, for a clockwise rotation of 45°, the remapped coordinates are:

[0121]

[0122] The beam pattern in the original coordinate system is obtained based on the remapped coordinates, as Figure 4 shown.

[0123] For comparison, Figure 5 the beam pattern results based on the Fresnel approximation model are given.

[0124] Table 2 gives the intensities of the beam directions corresponding to four scatterers obtained by using the Fresnel approximation and the method of the present embodiment.

[0125] Table 2

[0126]

[0127] It can be seen from Table 2 that the method proposed by the present invention maintains a high beam intensity for the beam results within the range of φ < 90°, while the Fresnel approximation model only has a high beam intensity within the range of φ ≤ 18°.

[0128] For different array parameters, the computational burdens of the 4×4 sub-region and the 3×3 sub-region are different. Assuming that an N×N two-dimensional uniform sensor array needs to calculate 4N×4N beams, the required number of online real operations is as Figure 6 shown. It can be seen that the 4×4 sub-region has almost the same computational burden as the Fresnel approximation model, while the 3×3 sub-region has a lower computational amount in some cases, reducing the computational burden by one to two orders of magnitude compared with the direct beamforming in the frequency domain. Therefore, the proposed near-field fast beamforming method based on the sub-region model and the non-uniform Fourier transform has a field of view close to 90° while maintaining a low computational burden, improving the imaging quality and detection performance of the three-dimensional camera sonar system in the near-field region.

[0129] The above-described specific embodiments have detailed the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, supplements, equivalent replacements, etc. made within the scope of the principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A near-field fast beamforming method based on a sub-region model and non-uniform Fourier transform, characterized in that, Including the following steps: (1) Rotate the coordinate system of the observation range of the two-dimensional transducer array by a preset rotation angle, and evenly divide the rotated observation range into multiple sub-regions, where the rotation angle is positive in the clockwise direction and is an odd multiple of 45°; (2) Simplify the near-field time-delay parameters of the transducer array elements in each sub-region, construct weighted near-field time-delay parameters according to the simplified near-field time-delay parameters using the least squares method, and solve the weighted near-field time-delay parameters to determine the optimal weighting coefficient; (3) Construct an operator for adjoint non-uniform Fourier transform based on the response signal generated by the two-dimensional transducer array and the beam signal with the weighting coefficient, and perform non-uniform Fourier transform calculation in parallel according to the operator for adjoint non-uniform Fourier transform to obtain the beam in each sub-region, including: (3-1) Place P×Q beams into the corresponding sub-regions (u, v), where each sub-region contains P u ×Q v beams, and index them with (p u , q v ). Then the direction parameters and of the corresponding beams are expressed as: (3-2) For the (p u , q v )th beam, an operator b(r0, p u , q v ) that constructs an adjoint non-uniform Fourier transform is built based on the response signal generated by the two-dimensional transducer array and the beam signal with weighting coefficients, and is expressed as: Among them, S(n1,n2) represents the response signal, and ξ(n1,n2,u,v) represents the weighting coefficient independent of (p u ,q v ), ω a (n1,n2,u,v) and ω e (n1,n2,u,v) represent non-uniform node coordinates, and N represents the number of transducers in each direction; (3-3) Pre-calculate ξ(n1,n2,u,v), ω a (n1,n2,u,v) and ω e (n1,n2,u,v), as well as the compensation coefficients and interpolation coefficients required by the non-uniform Fourier transform method; (3-4) Based on the calculation result of step (3-3), perform non-uniform Fourier transform calculation on the operator associated with the non-uniform Fourier transform in parallel to obtain the beams within each sub-region, that is, determine the direction parameters of the beams and (4) Remap the coordinates of the beam in each sub-region to obtain a high-precision beam pattern.

2. The near-field fast beamforming method based on the sub-region model and non-uniform Fourier transform according to claim 1, characterized in that The two-dimensional transducer array is a two-dimensional rectangular array including N×N transducer array elements. The two-dimensional rectangular array is located in the XOY plane of the three-dimensional space. The sides of the two-dimensional rectangular array are parallel to the X and Y coordinate axes respectively. The coordinates of the (n1, n2)th transducer array element are expressed as (x n1 , y n2 ); The focusing distance r0 of the beam is the near-field region, and the observation range is determined by two directional parameters θ a and θ e which are parallel to the X and Y axes respectively, and the value ranges are (-90°, 90°).

3. The near-field fast beamforming method based on the sub-region model and non-uniform Fourier transform according to claim 2, wherein There are P×Q beams to be generated within the observation range. For the (p,q)th beam, its beam direction is (θ ap , θ eq ), and the beam signal b(r0,p,q) is expressed as: where, f l represents the signal frequency, r0 represents the focusing distance of the beam in the near-field region, S l (n1,n2) represents the frequency-domain sampling data of the (n1,n2)-th transducer element, N represents the number of transducers in each direction, τ(r0,p,q,n1,n2) represents the time delay of the (n1,n2)-th transducer element for the beam direction (θ ap , θ eq ) and is expressed as: where c represents the speed of sound, (x n1 , y n2 ) represents the coordinates of the (n1, n2)-th transducer element.

4. The near-field fast beamforming method based on the sub-region model and non-uniform Fourier transform according to claim 3, characterized in that In step (1), the rotated observation range is evenly divided into 3×3 or 4×4 sub-regions, and the specific operation is as follows: (1-1) After rotating the coordinate system of the observation range by a preset rotation angle φ, the new direction parameters θ' a and θ' e are as follows: Among them, the restricted direction parameter θ′ a and θ′ e have a value range of (-90°, 90°); (1-2) Divide the direction parameters θ′ a and θ′ e into three or four equal segments in the sine domain within the value range, and use u and v to represent the indices of each sub-region, that is: Or, For the (u, v) sub-region, its position is determined by sinθ′ a and sinθ′ e and the corresponding value range.

5. The near-field fast beamforming method based on the sub-region model and non-uniform Fourier transform according to claim 4, characterized in that, In step (2), simplify the near-field time-delay parameters of the transducer array elements in each sub-region. The simplified near-field time-delay parameter τ sp (r0, p, q, n1, n2) is expressed as: where r0 represents the focusing distance of the beam in the near-field region, c represents the speed of sound, sinθ′ ap and sinθ′ eq are the sine-domain parameters corresponding to the (p,q)-th beam direction in the new coordinate system, and where, sinθ′ au and sinθ′ ev are the centers of the (u, v) sub-region.

6. The near-field fast beamforming method based on the sub-region model and non-uniform Fourier transform according to claim 5, wherein In step (2), the weighted near-field time-delay parameter τ LS (r0, p, q, n1, n2) is constructed according to the simplified near-field time-delay parameter by using the least squares method, and is expressed as: where g(n1, n2, u, v) = [3ρ 2 (n1, n2, u, v) - v(n1, n2)] / 2r0; Solve for the optimal values of the weighted coefficients k1 - k6 according to the least squares method for the weighted near-field time-delay parameter τ LS (r0, p, q, n1, n2) to minimize the time-delay error within the sub-region.

7. The near-field fast beamforming method based on the sub-region model and non-uniform Fourier transform according to claim 6, characterized in that In step (3-2): where f l represents the signal frequency, r0 represents the focusing distance of the beam in the near-field region, and c represents the speed of sound.

8. The near-field fast beamforming method based on the sub-region model and non-uniform Fourier transform according to claim 7, characterized in that, In step (4), for the (p u , q v )-th beam in the sub-region, remapping is performed, and the obtained remapped coordinates are expressed as: Based on the remapped coordinates, obtain the beam pattern in the original coordinate system.

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