A frequency domain fast imaging method for forward-looking scanning radar based on Gaussian prior

Abstract

The application discloses a kind of front-looking scanning radar frequency domain fast imaging methods based on Gaussian prior, first obtains echo data and carries out pre-processing, then based on Gaussian prior Bayesian framework, carries out Bayesian inference, again constructs time-domain deconvolution problem, adds smoothing filter operator in equivalent regularization process, and the time-domain deconvolution problem is converted to frequency domain by Fourier transform, and fast frequency domain is solved.The method of the application adds smoothing filter operator when processing time-domain deconvolution problem, can smooth the noise and details of image, while retaining the basic structure of image, improve imaging quality, by Fourier transform into frequency domain, using the property that Fourier transform time-domain convolution is equal to frequency multiplication, successfully convert inverse operation into division operation, greatly reduce the calculation complexity, with higher imaging efficiency under the condition of not losing imaging quality.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar imaging, and particularly relates to a front-looking scanning radar frequency domain fast imaging method based on a Gaussian prior. BACKGROUND

[0002] The high-resolution imaging of the forward-looking area of airborne scanning radar has urgent application requirements in the fields of instrument landing system and sea detection. The antenna aperture of real aperture radar is limited, so the azimuth resolution is low. In order to improve the azimuth resolution, a method of adjustable angle super-resolution is proposed in the literature “Yin Zhang, Changlin Li, Deqing Mao, Yulin Huang, and Jianyu Yang, ‘Bayesian superresolution method of forward-looking imaging with generalized gaussian constraint,’ in IGARSS 2018-2018 IEEE International Geoscience and Remote Sensing Symposium, 2018, pp. 5128 5131” to realize high azimuth resolution in the forward-looking area of scanning radar imaging. How to select the appropriate scale parameter to obtain better super-resolution performance in different scenes is discussed, but the method has low computational efficiency. A super-resolution imaging method based on Weibull distribution is proposed in the literature “Yin Zhang, Jiahao Shen, Xingyu Tuo, Haiguang Yang, Yongchao Zhang, Yulin Huang, and Jianyu Yang, ‘Scanning radar forward-looking superresolution imaging based on the weibull distribution for a sea-surface target,’ IEEE Transactions on Geoscience and Remote Sensing, vol. 60, pp. 1-11, 2022”. This method introduces the generalized Gaussian distribution and the Weibull distribution to represent the prior information of the target and the statistical distribution function of sea clutter, respectively. The corresponding objective function is derived under the maximum a posteriori (MAP) criterion. In order to solve the nonlinear problem of the objective function, the Newton-Raphson iteration method is used to solve the problem. The simulation and experimental data evaluation show that the proposed method has better super-resolution imaging performance compared with other existing sea surface target super-resolution methods, but the computational complexity is high and the operation efficiency is low.The document 'Yasser Radouane Haddadi and Boualem Mansouri, 'Ultrasound medical image deconvolution using l2 regularization method and artificial bee colony optimization algorithm,' in 2022 7th International Conference on Image and Signal Processing and their Applications (ISPA), 2022, pp.1-6' proposes a new method for estimating the regularization parameter of ultrasound medical image deconvolution based on the L2 regularization method and artificial bee colony optimization algorithm, which studies the influence of regularization parameter selection on the deconvolution process and evaluates the regularization parameter estimation, and proves that the method improves the high efficiency of the ultrasound medical image deconvolution operation, but the operation efficiency is low.

[0003] Although the above method can avoid the ill-condition caused by direct inverse convolution reconstruction of the target and improve the azimuth resolution of the forward-looking scanning radar, the imaging calculation complexity is high and the imaging efficiency is low. SUMMARY

[0004] To solve the above technical problems, the present application provides a forward-looking scanning radar frequency domain fast imaging method based on Gaussian prior, which adds a smoothing filter operator when dealing with the deconvolution problem in the time domain, which can smooth the noise and details of the image while preserving the basic structure of the image, improve the imaging quality, and convert the time domain to the frequency domain by Fourier transform, and successfully convert the inverse operation to division operation, greatly reducing the calculation complexity.

[0005] The technical scheme adopted by the present application is: a forward-looking scanning radar frequency domain fast imaging method based on Gaussian prior, the specific steps are as follows:

[0006] Step 1, echo data acquisition and pretreatment;

[0007] Construct the forward-looking scanning radar azimuth echo convolution model, set the flight height of the aircraft platform as H, the motion direction along the Y axis direction of the three-dimensional coordinate system, the speed size as V, the radar beam scans counterclockwise at a speed of ω', the beam elevation angle is α, and the aircraft platform is located at the positive of the coordinate origin A point at zero time.

[0008] Suppose a target P in space is located at the center of the beam at zero time, the distance relative to the aircraft platform is R0, and the horizontal azimuth angle is The spatial azimuth is θ0, and according to the spatial geometry, we have

[0009] At time t, the carrier platform moves from point A to point D, and at this time, the horizontal azimuth of target P relative to the carrier platform is The spatial azimuth is θ, and the distance R(t) between the carrier platform and the target is expressed as follows:

[0010]

[0011] The Taylor series expansion of the distance history expression at t = 0 is as follows:

[0012]

[0013] The distance history expression can be approximated as follows:

[0014] R(t) ≈ R0-Vcosθ0t (3)

[0015] Let the radar transmit signal be a linear frequency modulation signal S(τ), expressed as follows:

[0016]

[0017] where τ represents the distance-time variable, T r represents the pulse width of the linear frequency modulation signal, f0 represents the carrier frequency, K r represents the frequency modulation slope, and rect[·] represents the window function in the distance-time domain, which is specifically as follows:

[0018]

[0019] For any point target P in the imaging scene, the echo signal received by the forward-looking scanning radar after down-conversion is expressed as follows:

[0020]

[0021] where σ0 represents the target scattering coefficient, ψ(t) represents the antenna pattern modulation function, t represents the azimuth-time variable, τ d = 2R(t) / c represents the two-way echo delay, and c represents the speed of light.

[0022] The antenna pattern modulation function is expressed as represents the transposed antenna pattern function, and

[0023] Let the slant range of any point target in the imaging scene be R, and the spatial azimuth be θ, then we have

[0024]

[0025] Substituting equations (7) and (8) into the signal expression, we get:

[0026]

[0027] Where B represents the transmitted signal bandwidth, λ represents the wavelength, the last term is the Doppler phase caused by the platform motion, and σ represents the target scattering coefficient σ0 and the two-way echo delay τ. d The product of the resulting additional phases is expressed as follows:

[0028]

[0029] Let the target unit impact response function be h(R,θ), and its expression is as follows:

[0030]

[0031] The echo signal after pulse compression and motion correction is represented in two-dimensional convolution form, as shown in the following expression:

[0032]

[0033] in, The symbol represents a two-dimensional convolution operation, and δ(·) represents the impulse function. Ignoring the Doppler phase in equation (12), a simplified form of the point target echo is obtained, as shown in the following expression:

[0034]

[0035] in, This represents the target scattering distribution function.

[0036] The target echo y can be represented as the convolution of the antenna measurement matrix h′ and the target scattering coefficient x, as shown in the following expression:

[0037] y=h′*x (14)

[0038] Where * represents the convolution operator. The Richardson-Lucy deconvolution algorithm is used to solve for x in equation (14).

[0039] A frequency domain solution strategy is proposed to estimate x, and equation (14) is rewritten as follows:

[0040] y = hx (15)

[0041] Where h is an N×N matrix representing the antenna pattern matrix, y is an N×1 vector, x is an N×1 vector, and N represents the number of azimuth sampling points. Equation (15) is expressed in frequency domain form as follows:

[0042] Y(ω)=H(ω)X(ω) (16)

[0043] Here, Y(ω), H(ω), and X(ω) are the frequency domain representations of y, h, and x, respectively, and ω represents the coordinates in the frequency domain.

[0044] If the echo is affected by noise, then equation (16) can be expressed as follows:

[0045] Y(ω)=H(ω)X(ω)+N(ω) (17)

[0046] Where N(ω) represents the frequency domain representation of the noise.

[0047] If the antenna pattern matrix h is a full-rank matrix, the target scattering coefficient x is determined by solving the inverse function. Calculating x in the frequency domain, if the antenna pattern matrix is ​​low-rank, the high-frequency component H(ω) is 0 or close to 0. The echo is affected by noise; the expression for X(ω) is as follows:

[0048]

[0049] Step 2: Perform Bayesian inference based on the Gaussian prior Bayesian framework;

[0050] The goal is to determine the most likely solution for x based on y, expressed as follows:

[0051]

[0052] Where p(·) represents the probability distribution, Let x represent the maximum a posteriori estimate.

[0053] Assuming the noise follows a Gaussian distribution with mean 0 and variance ξ, the likelihood function is derived as follows:

[0054]

[0055] For the prior x, use a set of filters g k The representation is as follows:

[0056]

[0057] Where β represents the weight, i represents the number of sampling points, f(·) represents the filter function, and g i,k This represents the k-th filter centered at i.

[0058] Selecting a filter, i.e., the horizontal derivative g x = [1, -1] and the vertical derivative g y =[1,-1] T filter.

[0059] Where T represents transpose.

[0060] g x g y Substituting into equation (21), the expression is as follows:

[0061]

[0062] Substituting equations (20) and (21) into (19), we obtain the maximum a posteriori expression for x as follows:

[0063]

[0064] The negative logarithm expression of equation (23) is as follows:

[0065]

[0066] Where w=βξ 2 The estimated value of x is obtained by minimizing equation (24).

[0067] Step 3: Based on Step 2, construct the temporal deconvolution problem;

[0068] Assuming the prior is a Gaussian prior, differentiating equation (24) yields the following expression:

[0069]

[0070] Setting equation (25) to zero, we obtain the following expression:

[0071]

[0072] Among them, C gk G represents i,k Linear operators. When I represents the identity matrix, and equation (26) is equivalent to L2 regularization. Its solution expression is as follows:

[0073]

[0074] Equation (27) is the azimuth solution for the range cell. The solution process is optimized using ADMM to obtain... The estimated value is expressed as follows:

[0075]

[0076] Where H, X, and Y represent the antenna matrix, target matrix, and echo matrix, respectively. Z and U represent introduced relaxation variables, and ρ represents the Lagrange parameter. Let (k) represent the shrinkage parameter, and (k) represent the k-th iteration. The shrinkage operator... The expression is as follows:

[0077]

[0078] Step 4: Transform the time-domain deconvolution problem into the frequency domain using Fourier transform, and then perform a fast frequency domain solution.

[0079] The vector form in equation (26) is transformed into matrix form to accelerate the solution, as shown in the following expression:

[0080]

[0081] The optimal solution is derived by solving a set of sparse linear equations A'X=B', as shown in the following expression:

[0082]

[0083] Then A'X = B' can be expressed as the following expression:

[0084]

[0085] Solving for A'X = B' in the frequency domain yields the following frequency domain expression:

[0086]

[0087] Among them, G k (ω) represents C gk Fourier transform.

[0088] Solving equation (33) yields the following expression for X(ω):

[0089]

[0090] The scattering coefficient of the target is obtained by inverse transformation, and the expression is as follows:

[0091]

[0092] Here, IFFT(·) represents the inverse Fourier transform operator.

[0093] The beneficial effects of this invention are as follows: The method of this invention first acquires and preprocesses echo data, then performs Bayesian inference based on a Gaussian prior Bayesian framework, and then constructs a time-domain deconvolution problem. A smoothing filter operator is added during the equivalent regularization process, and the time-domain deconvolution problem is transformed to the frequency domain through Fourier transform for fast frequency domain solution. This invention adds a smoothing filter operator when processing the time-domain deconvolution problem, which can smooth image noise and details while preserving the basic image structure and improving imaging quality. By transforming the data to the frequency domain through Fourier transform and utilizing the property that time-domain convolution equals frequency-domain multiplication, the inverse operation is successfully converted into a division operation, greatly reducing computational complexity and achieving higher imaging efficiency without sacrificing imaging quality. Attached Figure Description

[0094] Figure 1 This is a flowchart of a fast frequency domain imaging method for forward-looking scanning radar based on Gaussian prior according to the present invention.

[0095] Figure 2 This is a diagram of the azimuth echo convolution model of the forward-looking scanning radar in an embodiment of the present invention.

[0096] Figure 3 This is a simulation imaging result diagram from an embodiment of the present invention.

[0097] Figure 4 The images are time-mapping diagrams for different algorithms in the embodiments of the present invention. Detailed Implementation

[0098] This invention employs simulation experiments to demonstrate the effectiveness of the proposed method. All steps and conclusions of the method are verified on the Matlab 2019b simulation platform. To enable those skilled in the art to understand the invention, the method is further described below with reference to the accompanying drawings and embodiments.

[0099] like Figure 1 The flowchart of a fast frequency domain imaging method for forward-looking scanning radar based on Gaussian prior is shown below. The specific steps are as follows:

[0100] Step 1: Echo data acquisition and preprocessing;

[0101] Construct a forward-looking radar azimuth echo convolution model, as shown in the figure below. Figure 2 As shown in the figure, the flight altitude of the carrier platform is H, the direction of motion is along the Y-axis of the three-dimensional coordinate system, the speed is V, the radar beam scans counterclockwise at a speed ω', the beam elevation angle is α, and at time zero, the carrier platform is located at point A directly above the origin of the coordinate system. The simulation parameters of the radar system in this example are shown in Table 1.

[0102] Table 1

[0103] Simulation parameters Numerical Carrier frequency 10 GHz Bandwidth 60 MHz Main lobe beam width 3° Pulse repetition frequency 4000 Hz Scan speed 30° / s Scan range ±5°

[0104] At time zero, a target P in space is located at the beam center, at a distance of R0 relative to the carrier platform, and has a horizontal azimuth angle of θ. The spatial azimuth angle is θ0, which can be known from spatial geometric relationships.

[0105] At time t, the carrier platform moves from point A to point D. At this time, the horizontal azimuth angle of target P relative to the carrier platform is . Let the spatial azimuth angle be θ. The distance R(t) between the carrier platform and the target is expressed as follows:

[0106]

[0107] The Taylor series expansion of the distance history expression at t=0 is as follows:

[0108]

[0109] Because radar antenna beams scan quickly and take very little time to scan a target, and because forward-looking radars generally have a long range, the influence of the quadratic term in equation (2) is often ignored in practical applications. Therefore, the range history expression can be approximated as follows:

[0110] R(t)≈R0-Vcosθ0t(3)

[0111] Let the radar transmitted signal be a linear frequency modulated signal S(τ), with the following expression:

[0112]

[0113] Where τ represents the distance-time variable, T r f0 represents the pulse width of the linear frequency modulated signal, and K represents the carrier frequency. r Represents the frequency modulation slope, and rect[·] represents the window function in the range-time domain, as follows:

[0114]

[0115] For any target P in the imaging scene, the echo signal received by the forward-looking scanning radar after down-conversion is expressed as follows:

[0116]

[0117] Where σ0 represents the target scattering coefficient, ψ(t) represents the antenna pattern modulation function, t represents the azimuth time variable, and τ d =2R(t) / c represents the two-way echo delay, and c represents the speed of light.

[0118] The antenna pattern modulation function is expressed as follows: Let represent the pattern function of the transposed antenna, and

[0119] As can be seen from equation (6), the echo is a two-dimensional time variable matrix with respect to variables τ and t. For ease of understanding, it can be compared to the "stop-go-stop" mode of echo reception in SAR imaging. During the scanning process of the forward-looking radar, when the antenna beam scans to a certain angle, it can be assumed that the carrier platform and the antenna beam remain stationary. A linear frequency modulated pulse signal is emitted, which propagates at the speed of light to the illumination area and is then reflected back to be received by the receiver. After down-conversion and channeling, a complex form of baseband echo signal is obtained and stored as a column of the data matrix. Then the platform continues to move forward. When the antenna beam scans to the next angle position, it remains stationary at this position and emits and receives pulse signals again, which are stored in the next column of the data matrix. This process is repeated until a two-dimensional echo data matrix is ​​obtained. According to the generation process of the echo matrix, the column vectors of the matrix reflect the target range information, called the range direction, i.e., the τ direction; the row vectors of the matrix reflect the target azimuth angle information, called the azimuth direction, i.e., the t direction.

[0120] Let R be the slant range of any target point in the imaging scene, and θ be the spatial azimuth angle, then we can obtain:

[0121]

[0122] Substituting equations (7) and (8) into the signal expression, we get:

[0123]

[0124] Where B represents the transmitted signal bandwidth, λ represents the wavelength, the last term is the Doppler phase caused by the platform motion, and σ represents the target scattering coefficient σ0 and the two-way echo delay τ. d The product of the resulting additional phases is expressed as follows:

[0125]

[0126] Let the unit impact response function of the point target be h(R,θ), and its expression is as follows:

[0127]

[0128] The echo signal after pulse compression and motion correction is represented in two-dimensional convolution form, as shown in the following expression:

[0129]

[0130] in, The symbol represents the two-dimensional convolution operation, δ represents the impulse function, and ignoring the Doppler phase in equation (12), we obtain a simplified form of the point target echo, as shown in the following expression:

[0131]

[0132] in, This represents the target scattering distribution function.

[0133] The target echo y can be represented as the convolution of the antenna measurement matrix h′ and the target scattering coefficient x, as shown in the following expression:

[0134] y=h′*x (14)

[0135] Here, * represents the convolution operator. The Richardson-Lucy deconvolution algorithm is used to solve for x in equation (14). However, this algorithm can only solve problems in the real number field and cannot solve problems in the complex number field, resulting in low imaging accuracy when the platform is moving.

[0136] A frequency domain solution strategy is proposed to estimate x, and equation (14) is rewritten as follows:

[0137] y = hx (15)

[0138] Where h is an N×N matrix representing the antenna pattern matrix, y is an N×1 vector, x is an N×1 vector, and N represents the number of azimuth sampling points. Equation (15) is expressed in frequency domain form as follows:

[0139] Y(ω)=H(ω)X(ω) (16)

[0140] Here, Y(ω), H(ω), and X(ω) are the frequency domain representations of y, h, and x, respectively, and ω represents the coordinates in the frequency domain.

[0141] If the echo is affected by noise, then equation (16) can be expressed as follows:

[0142] Y(ω)=H(ω)X(ω)+N(ω) (17)

[0143] Where N(ω) represents the frequency domain representation of the noise.

[0144] If the antenna pattern matrix h is a full-rank matrix, the target scattering coefficient x is determined by solving the inverse function. Calculating x in the frequency domain is equally straightforward. However, the antenna pattern matrix is ​​low-rank, resulting in the high-frequency component H(ω) being 0 or close to 0. The target belongs to the low-frequency component, while noise fills the entire spectrum. In the high-frequency range, the noise is amplified, significantly impacting image quality. The echo is affected by noise, and the expression for X(ω) is as follows:

[0145]

[0146] Step 2: Perform Bayesian inference based on the Gaussian prior Bayesian framework;

[0147] To address the aforementioned issues, utilizing prior information during the deconvolution process is beneficial for recovering the target scattering coefficient x. That is, the target determines the most probable solution for x based on y.

[0148]

[0149] Where p(·) represents the probability distribution, Let x represent the maximum a posteriori estimate.

[0150] Assuming the noise follows a Gaussian distribution with mean 0 and variance ξ, the likelihood function is derived as follows:

[0151]

[0152] For the prior x, use a set of filters g k The representation is as follows:

[0153]

[0154] Where β represents the weight, i represents the number of sampling points, f(·) represents the filter function, and g i,k This represents the k-th filter centered at i.

[0155] The simplest filter choice is based on the horizontal derivative g. x = [1, -1] and the vertical derivative g y =[1,-1] T filter.

[0156] Where T represents transpose.

[0157] g x g y Substituting into equation (21), the expression is as follows:

[0158]

[0159] The priors mentioned above indicate that the image tends to be smooth and the derivative is close to zero.

[0160] Substituting equations (20) and (21) into (19), we obtain the maximum a posteriori expression for x as follows:

[0161]

[0162] To simplify the calculation, the negative logarithm expression of equation (23) is as follows:

[0163]

[0164] Where w=βξ 2 The estimated value of x is obtained by minimizing equation (24).

[0165] Step 3: Based on Step 2, construct the temporal deconvolution problem;

[0166] We assume the prior is a Gaussian prior, and in reality, most images satisfy the Gaussian prior property, that is, the function f(z) is |z|. 2 Differentiating equation (24) yields the following expression:

[0167]

[0168] Setting equation (25) to zero, we get the following equation:

[0169]

[0170] Among them, C gk G represents i,k Linear operators. When I represents the identity matrix, and equation (26) is equivalent to L2 regularization. Its solution expression is as follows:

[0171]

[0172] Equation (27) is the azimuth solution for the range cell, which is inefficient. ADMM is used to optimize the solution process, resulting in... The estimated value is expressed as follows:

[0173]

[0174] Where H, X, and Y represent the antenna matrix, target matrix, and echo matrix, respectively. Z and U represent introduced relaxation variables, and ρ represents the Lagrange parameter. Let (k) represent the shrinkage parameter, and (k) represent the k-th iteration. The shrinkage operator... The expression is as follows:

[0175]

[0176] Step 4: Transform the time-domain deconvolution problem into the frequency domain using Fourier transform, and then perform a fast frequency domain solution.

[0177] The vector form in equation (26) is transformed into matrix form to accelerate the solution, as shown in the following expression:

[0178]

[0179] Equation (28) provides an iterative solution for the entire echo matrix, but it still cannot avoid inverse operations. Therefore, the optimal solution is derived by solving a set of sparse linear equations A'X = B', as shown in the following expression:

[0180]

[0181] Then A'X = B' can be expressed as the following expression:

[0182]

[0183] The simplest and most efficient way to solve A'X = B' is in the frequency domain, and the resulting frequency domain expression is as follows:

[0184]

[0185] Among them, G k (ω) represents Fourier transform.

[0186] Solving equation (33) yields the following expression for X(ω):

[0187]

[0188] The scattering coefficient of the target is obtained by inverse transformation, and the expression is as follows:

[0189]

[0190] Here, IFFT(·) represents the inverse Fourier transform operator.

[0191] To demonstrate the effectiveness of the method of this invention, simulation experiments were conducted on the Matlab2019b platform.

[0192] The most computationally complex parts of the algorithm in this invention are the Fourier transform and inverse Fourier transform, but it has still proven to be very efficient compared to other operations (such as inversion). Table 2 compares the computational complexity of the algorithm proposed in this invention with other L2 regularization-related algorithms. It can be seen that the complexity of the method in this invention is much lower than that of other processing methods.

[0193] Table 2

[0194] Method Complexity L2 method [M(O(N 3 +N 2 ))]]> Batch L2 method max{O(N 3 ),O(MN 2 )} Inventive method O(MNlog(MN))

[0195] Where M represents the number of distance sampling points.

[0196] Figure 3 This is a simulation imaging result image from this example. Figure 3 (a) is the target scenario. Figure 3 (b) is the echo. The imaging results of the method of this invention were compared with those obtained by the L2 correlation method and the Lucy method. Figure 3 (c) and Figure 3 As shown in (d), neither Lucy's method nor existing L2 methods can distinguish between two targets that are very close to each other. However, as Figure 3 (e) and Figure 3As shown in (f), both the batch L2 method and the method of this invention can effectively separate these targets. The results demonstrate that the method of this invention exhibits superior resolution performance compared to existing L2 methods and the Lucy method. Furthermore, the method of this invention demonstrates performance similar to the batch L2 method. Table 3 compares the imaging efficiency of different algorithms; by comparing the processing times shown in Table 3, it can be seen that the processing efficiency of the method of this invention is more than 30 times that of other methods.

[0197] Table 3

[0198] Method Lucy Existing L2 L2 batch Inventive method Time (s) 1.4031 14.3993 1.7733 0.0460

[0199] To demonstrate the effectiveness of the method of the present invention, this embodiment sets both the distance and azimuth dimensions to a fixed value of 300. Then, the imaging time of various methods is compared by increasing the size of another dimension.

[0200] Figure 4 This is a time-mapping diagram of the imaging algorithms used in this example. Figure 4 (a) shows the imaging time for different methods (changing the number of azimuth sampling points). Figure 4 (b) shows the imaging time of different methods (changing the number of range sampling points). When processing large scenes, the method of this invention is significantly more efficient than existing L2 and batch L2 methods. While these methods may require processing times of up to 100 seconds, the method of this invention only requires 0.1 seconds. On the other hand, the Lucy method has good processing efficiency. However, the processing efficiency of the method of this invention is more than 100 times higher than that when processing large scenes.

[0201] In summary, within the Bayesian framework, the Bayesian derivation of the Gaussian prior distribution and the Gaussian likelihood distribution is equivalent to the L2 regularization optimization problem. The method of this invention, based on the Gaussian prior Bayesian framework, adds a smoothing filter operator during the equivalent regularization process, which can smooth image noise and details while preserving the basic image structure, thus improving imaging quality. The deconvolution problem in the time domain is transformed to the frequency domain using Fourier transform. Utilizing the property that time-domain convolution equals frequency-domain multiplication after Fourier transform, the inversion operation is successfully converted into a division operation, greatly reducing computational complexity. In the entire imaging process, the main computational complexity of the method of this invention comes from the Fourier transform and inverse Fourier transform. This computational cost is extremely low compared to the inversion, ensuring the real-time application of the imaging algorithm. Compared to methods such as L2 regularization and Lucy-Richardson (a more widely used deconvolution method), the method of this invention has higher imaging efficiency without sacrificing imaging quality.

[0202] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A fast frequency domain imaging method for forward-looking scanning radar based on Gaussian prior, the specific steps of which are as follows: Step 1: Echo data acquisition and preprocessing; Construct a forward-looking scanning radar azimuth echo convolution model, set the flight altitude of the carrier platform to H, the direction of motion along the Y-axis of the three-dimensional coordinate system, the speed to V, the radar beam to scan counterclockwise at speed ω', the beam pitch angle to α, and at time zero, the carrier platform is located at point A directly above the origin of the coordinate system. Suppose a target P in space is located at the beam center at time zero, with a distance R0 relative to the carrier platform and a horizontal azimuth angle of θ. The spatial azimuth angle is θ0, which can be known from spatial geometric relationships. At time t, the carrier platform moves from point A to point D. At this time, the horizontal azimuth angle of target P relative to the carrier platform is . Let the spatial azimuth angle be θ. The distance R(t) between the carrier platform and the target is expressed as follows: The Taylor series expansion of the distance history expression at t=0 is as follows: The distance to history expression can be approximated by the following expression: R(t)≈R0-Vcosθ0t (3) Let the radar transmitted signal be a linear frequency modulated signal S(τ), with the following expression: in, τ represents the distance-time variable, T r f0 represents the pulse width of the linear frequency modulated signal, and K represents the carrier frequency. r Represents the frequency modulation slope, and rect[·] represents the window function in the range-time domain, as follows: For any target P in the imaging scene, the echo signal received by the forward-looking scanning radar after down-conversion is expressed as follows: Where σ0 represents the target scattering coefficient, ψ(t) represents the antenna pattern modulation function, t represents the azimuth time variable, and τ d =2R(t) / c represents the two-way echo delay, where c represents the speed of light; The antenna pattern modulation function is expressed as follows: Let represent the pattern function of the transposed antenna, and Let R be the slant range of any target point in the imaging scene, and θ be the spatial azimuth angle, then we can obtain: Substituting equations (7) and (8) into the signal expression, we get: Where B represents the transmitted signal bandwidth, λ represents the wavelength, the last term is the Doppler phase caused by the platform motion, and σ represents the target scattering coefficient σ0 and the two-way echo delay τ. d The product of the resulting additional phases is expressed as follows: Let the target unit impact response function be h(R,θ), and its expression is as follows: The echo signal after pulse compression and motion correction is represented in two-dimensional convolution form, as shown in the following expression: in, The symbol represents a two-dimensional convolution operation, and δ(·) represents the impulse function. Ignoring the Doppler phase in equation (12), a simplified form of the point target echo is obtained, as shown in the following expression: in, Represents the target scattering distribution function; The target echo y can be represented as the convolution of the antenna measurement matrix h′ and the target scattering coefficient x, as shown in the following expression: y=h′*x (14) Where * represents the convolution operator; the Richardson-Lucy deconvolution algorithm is used to solve for x in equation (14); A frequency domain solution strategy is proposed to estimate x, and equation (14) is rewritten as follows: y = hx (15) Where h is an N×N matrix representing the antenna pattern matrix, y is an N×1 vector, x is an N×1 vector, and N represents the number of azimuth sampling points; Equation (15) is expressed in frequency domain form as follows: Y(ω)=H(ω)X(ω) (16) Where Y(ω), H(ω) and X(ω) are the frequency domain representations of y, h and x, respectively, and ω represents the coordinates in the frequency domain; If the echo is affected by noise, then equation (16) can be expressed as follows: Y(ω)=H(ω)X(ω)+N(ω) (17) Where N(ω) represents the frequency domain representation of the noise; If the antenna pattern matrix h is a full-rank matrix, the target scattering coefficient x is determined by solving the inverse function; when calculating x in the frequency domain, if the antenna pattern matrix is ​​low-rank, the high-frequency component H(ω) is 0 or close to 0; the echo is affected by noise, and the expression for X(ω) is as follows: Step 2: Perform Bayesian inference based on the Gaussian prior Bayesian framework; The goal is to determine the most likely solution for x based on y, expressed as follows: Where p(·) represents the probability distribution, This represents the maximum a posteriori estimate of x; Assuming the noise follows a Gaussian distribution with mean 0 and variance ξ, the likelihood function is derived as follows: For the prior x, use a set of filters g k The representation is as follows: Where β represents the weight, i represents the number of sampling points, f(·) represents the filter function, and g i,k This represents the k-th filter centered at i; Selecting a filter, i.e., the horizontal derivative g x = [1, -1] and the vertical derivative g y =[1,-1] T filter; Where T represents transpose; g x g y Substituting into equation (21), the expression is as follows: Substituting equations (20) and (21) into (19), we obtain the maximum a posteriori expression for x as follows: The negative logarithm expression of equation (23) is as follows: Where w=βξ 2 The estimated value of x is obtained by minimizing equation (24); Step 3: Based on Step 2, construct the temporal deconvolution problem; Assuming the prior is a Gaussian prior, differentiating equation (24) yields the following expression: Setting equation (25) to zero, we obtain the following expression: Among them, C gk G represents i,k Linear operators; when I represents the identity matrix, and equation (26) is equivalent to L2 regularization. Its solution expression is as follows: Equation (27) is the azimuth solution for the range cell. The solution process is optimized using ADMM to obtain... The estimated value is expressed as follows: X (k) =(H T H+wI) -1 H T Y+ρ((Z)−(U)) U (k) =U (k-1) +X (k) -Z (k) Where H, X, and Y represent the antenna matrix, target matrix, and echo matrix, respectively; Z and U represent introduced relaxation variables; and ρ represents the Lagrange parameter. Let (k) represent the shrinkage parameter, and (k) represent the k-th iteration. The shrinkage operator... The expression is as follows: Step 4: Transform the time-domain deconvolution problem into the frequency domain using Fourier transform, and then perform a fast frequency domain solution. The vector form in equation (26) is transformed into matrix form to accelerate the solution, as shown in the following expression: The optimal solution is derived by solving a set of sparse linear equations A'X=B', as shown in the following expression: B'=H T Y Then A'X = B' can be expressed as the following expression: Solving for A'X = B' in the frequency domain yields the following frequency domain expression: Among them, G k (ω) represents C gk Fourier transform; Solving equation (33) yields the following expression for X(ω): The scattering coefficient of the target is obtained by inverse transformation, and the expression is as follows: Here, IFFT(·) represents the inverse Fourier transform operator.

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