Terahertz sar compensation method based on lm algorithm under complex platform vibration

Abstract

The application belongs to the technical field of radars, and particularly relates to a terahertz SAR compensation method. The application aims to solve the problem that the existing vibration model cannot accurately describe complex platform vibration, and the complex platform vibration is difficult to be compensated, resulting in poor focusing of the obtained terahertz SAR imaging result. The process is as follows: a multi-component platform vibration model with time-varying amplitude is established; a terahertz SAR echo signal s(m, n) of the multi-component platform vibration with time-varying amplitude is obtained; the s(m, n) is processed to obtain a SAR imaging result, and Tsallis entropy of the SAR imaging result is calculated; a compensation function is constructed to compensate the platform vibration, and a compensated SAR image is obtained; Tsallis entropy of the compensated SAR image is calculated, the LM algorithm is used to find the compensation function that makes the Tsallis entropy of the compensated SAR image minimum; and the platform vibration is compensated based on the compensation function that makes the Tsallis entropy of the compensated SAR image minimum, so that a final focused SAR imaging result is obtained.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a terahertz SAR compensation method. Background Technology

[0002] Terahertz SAR, with its short wavelength and large signal bandwidth, can achieve higher imaging resolution and better imaging detail, making it a research hotspot. However, due to the short wavelength of terahertz SAR, even small platform vibration errors can cause severe defocusing along the azimuth direction, necessitating compensation to obtain clear, focused imaging results. Platform vibration error compensation requires establishing a suitable and accurate model to describe it. Typically, platform vibration is described as a superposition of multiple simple harmonic vibrations. However, real-world platform vibrations are more complex, potentially exhibiting amplitude variations over time. Simple harmonic vibrations alone cannot accurately describe complex platform vibrations, which are multi-component platform vibrations with time-varying amplitudes. Furthermore, complex platform vibrations are difficult to compensate for and can lead to severe defocusing in terahertz SAR imaging results. Summary of the Invention

[0003] The purpose of this invention is to solve the problem that existing vibration models cannot accurately describe the vibration of complex platforms and that the vibration of complex platforms is difficult to compensate, resulting in poor focusing of the obtained terahertz SAR imaging results. Therefore, this invention proposes a terahertz SAR compensation method based on the LM algorithm under the vibration of complex platforms.

[0004] The specific process of the terahertz SAR compensation method based on the LM algorithm under complex platform vibration is as follows:

[0005] Step 1: Establish a multi-component platform vibration model with time-varying amplitude;

[0006] Represented as;

[0007]

[0008] Where ΔR(m) represents the platform vibration, a j (m) represents the time-varying amplitude of the platform vibration, where m is the discrete slow time, m = 0, 1, ..., M-1, and M is the number of discrete slow times. j The vibration frequency of the platform. Let J be the phase of the platform vibration, j be the j-th platform vibration component, and J be the total number of platform vibration components.

[0009] Step 2: Based on the multi-component platform vibration model with time-varying amplitude from Step 1, the terahertz SAR echo signal s(m,n) of the multi-component platform vibration with time-varying amplitude is obtained.

[0010] Step 3: Process the terahertz SAR echo signal s(m,n) from Step 2 to obtain the SAR imaging result, and calculate the Tsallis entropy of the SAR imaging result;

[0011] Step 4: Construct a compensation function to compensate for platform vibration and obtain the compensated SAR image;

[0012] Calculate the Tsallis entropy of the compensated SAR image, and use the LM algorithm to find the compensation function that minimizes the Tsallis entropy of the compensated SAR image.

[0013] Step 5: Compensate for platform vibration based on the compensation function that minimizes the Tsallis entropy of the compensated SAR image to obtain the final focused SAR imaging result.

[0014] The beneficial effects of this invention are as follows:

[0015] Based on the analysis of complex platform vibration, this invention establishes a multi-component platform vibration model with time-varying amplitude and studies the corresponding platform vibration compensation algorithm. This model can more accurately describe the complex and variable platform vibration in real-world scenarios. The purpose of platform vibration compensation is to obtain imaging results with good image quality. Tsallis entropy is introduced to evaluate the image focusing effect. As the Tsallis entropy is minimized, the SAR image quality reaches its best. Simultaneously, the problem of minimizing Tsallis entropy is transformed into a problem of solving a system of nonlinear equations. Tsallis entropy is an extended form of Shannon entropy and is a commonly used indicator to describe SAR image quality. When the Tsallis entropy is minimized, a well-focused imaging result can be considered obtained. Furthermore, in the aforementioned problem of solving the nonlinear equations based on Tsallis entropy, how to solve the complex higher-order derivatives of the Tsallis entropy of the SAR image and obtain the actual platform vibration error through fast and accurate iterative solutions is also a key research focus. To address the aforementioned problems, this invention introduces the Levenberg-Marquardt (LM) algorithm to solve the nonlinear equations. The LM algorithm can be viewed as an optimization method combining the ideas of gradient descent and the Gauss-Newton method. By dynamically adjusting the step size to balance the advantages of both methods, the LM algorithm can quickly and accurately construct the platform vibration compensation function. Finally, the constructed compensation function is used to compensate for the platform vibration, resulting in clear and focused SAR imaging results. Attached Figure Description

[0016] Figure 1 This is a flowchart of the present invention;

[0017] Figure 2 SAR image of the platform before vibration compensation in a 10dB scenario;

[0018] Figure 3 The image is a SAR image after platform vibration compensation using the method proposed in this invention in a 10dB scene.

[0019] Figure 4 SAR image of the platform before vibration compensation in a -10dB scenario;

[0020] Figure 5 The image is a SAR image after platform vibration compensation using the method proposed in this invention in a -10dB scenario. Detailed Implementation

[0021] Specific implementation method one: Combining Figure 1 This embodiment describes the specific process of the terahertz SAR compensation method based on the LM algorithm under complex platform vibration.

[0022] The purpose of this invention is to compensate for complex platform vibrations in terahertz SAR systems using the LM algorithm and obtain focused imaging results. Since complex platform vibrations in terahertz SAR systems can severely affect the final imaging quality, this invention first considers the complex characteristics of platform vibrations in real-world scenarios and establishes a time-varying platform vibration model. Secondly, it introduces Tsallis entropy to describe SAR image quality and transforms the Tsallis entropy minimization problem into an equivalent nonlinear equation solution problem. Finally, it solves for the complex higher-order derivatives of the Tsallis entropy and introduces the LM algorithm to iteratively obtain focused SAR imaging results by dynamically adjusting the step size.

[0023] Step 1: Establish a multi-component platform vibration model with time-varying amplitude;

[0024] Represented as;

[0025]

[0026] Where ΔR(m) represents the platform vibration, a j (m) represents the time-varying amplitude of the platform vibration, where m is the discrete slow time, m = 0, 1, ..., M-1, and M is the number of discrete slow times. j The vibration frequency of the platform. Let J be the phase of the platform vibration, j be the j-th platform vibration component, and J be the total number of platform vibration components.

[0027] Multi-component means that there are J vibrational components superimposed; a j (m) represents the change of amplitude with time m;

[0028] Step 2: Based on the multi-component platform vibration model with time-varying amplitude from Step 1, the terahertz SAR echo signal s(m,n) of the multi-component platform vibration with time-varying amplitude is obtained.

[0029] Step 3: Process the terahertz SAR echo signal s(m,n) from Step 2 to obtain the SAR imaging result that is defocused due to the presence of platform vibration, and calculate the Tsallis entropy of the SAR imaging result.

[0030] Step 4: Construct a compensation function to compensate for platform vibration and obtain the compensated SAR image;

[0031] Calculate the Tsallis entropy of the compensated SAR image, and use the LM algorithm to find the compensation function that minimizes the Tsallis entropy of the compensated SAR image.

[0032] Step 5: Compensate the platform vibration based on the compensation function that minimizes the Tsallis entropy of the compensated SAR image to obtain the final focused SAR imaging result (substitute the compensation function that minimizes the Tsallis entropy of the compensated SAR image into formula (7) to obtain the final focused SAR imaging result).

[0033] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that, in step two, based on the time-varying amplitude multi-component platform vibration model of step one, a terahertz SAR echo signal s(m,n) with time-varying amplitude multi-component platform vibration is obtained.

[0034] The specific process is as follows:

[0035] Suppose there is a target point in the scene, and the target point's coordinates are (x, y, 0);

[0036] Based on the multi-component platform vibration model with time-varying amplitude established in step one, the terahertz SAR echo signal is range compressed, and the range migration correction is performed on the range-compressed terahertz SAR echo signal to obtain the terahertz SAR echo signal s(m,n) with time-varying amplitude multi-component platform vibration.

[0037] The expression for the terahertz SAR echo signal s(n,m) with time-varying amplitude multi-component platform vibration is as follows:

[0038]

[0039] Where s(m,n) is the terahertz SAR echo signal with time-varying amplitude and multi-component platform vibration, n is the discrete fast time, n=0,1,…,N-1, N is the number of discrete fast times; ξ is the complex amplitude; B is the signal bandwidth; R0 is the shortest slant range from the radar platform to the target; c is the speed of light; j is the imaginary unit, j 2 =-1; k a λ is the Doppler modulation frequency; v is the platform velocity; λ is the wavelength; ΔR is the platform vibration.

[0040] The other steps and parameters are the same as in Specific Implementation Method 1.

[0041] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that, in step 3, the terahertz SAR echo signal s(m,n) from step 2 is processed to obtain the SAR imaging result that is defocused due to the presence of platform vibration, and the Tsallis entropy of the SAR imaging result is calculated.

[0042] The specific process is as follows:

[0043] Step 31: Compensate the terahertz SAR echo signal s(m,n) from Step 2 along the azimuth direction to obtain the azimuth-compensated signal s0(m,n);

[0044] The expression is:

[0045] s0(m,n)=s(m,n)×exp(-jπk a m 2 (3)

[0046] Step 32: Perform a Fourier transform on the azimuth-compensated signal s0(n,m) along the azimuth direction to obtain the SAR imaging result g0(h,n) that is defocused due to the presence of platform vibration.

[0047] The expression is:

[0048]

[0049] Where h is the Doppler frequency index;

[0050] Step 33: Calculate the Tsallis entropy T0 of the defocused SAR imaging result g0(h,n);

[0051] The expression is:

[0052]

[0053] Where α is a real number; S0 is an intermediate variable.

[0054] Other steps and parameters are the same as in specific implementation method one or two.

[0055] Specific Implementation Method Four: This implementation method differs from one of the specific implementation methods one to three in that, in step four, a compensation function is constructed to compensate for platform vibration, and a compensated SAR image is obtained.

[0056] Calculate the Tsallis entropy of the compensated SAR image, and use the LM algorithm to find the compensation function that minimizes the Tsallis entropy of the compensated SAR image.

[0057] The specific process is as follows:

[0058] Step 41: Construct the compensation function;

[0059] The expression for the compensation function is:

[0060] H=exp(jΔΦ(m)) (6)

[0061] Where ΔΦ(m) is the phase error caused by platform vibration. The phase error is the error introduced by the platform vibration ΔR(m) in the phase of the terahertz SAR echo signal s(m,n), which is the main factor causing SAR image defocusing; H is the compensation function.

[0062] Step 42: Based on the compensation function H, compensate for the platform vibration to obtain the compensated SAR image g(h,n);

[0063] The expression is:

[0064]

[0065] Step 43: Calculate the Tsallis entropy of the compensated SAR image g(h,n);

[0066] The expression is:

[0067]

[0068] Where T is the Tsallis entropy of the compensated SAR image g(h,n); S is an intermediate variable.

[0069] Step 44: Use the LM algorithm to find the compensation function that minimizes the Tsallis entropy of the compensated SAR image g(h,n).

[0070] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0071] Specific Implementation Method 5: This implementation method differs from one of the specific implementation methods one to four in that, in step four, the LM algorithm is used to find the compensation function that minimizes the Tsallis entropy of the compensated SAR image g(h,n).

[0072] The specific process is as follows:

[0073] Step 441: Transform the Tsallis entropy minimization problem into an equivalent problem of solving a system of nonlinear equations;

[0074] The expression is:

[0075]

[0076] Step 442: Solve for the first and second partial derivatives of the Tsallis entropy of the compensated SAR image g(h,n);

[0077] Step 443: Initialize the phase error and the maximum number of loops K;

[0078] Let the number of iterations k = 1;

[0079] Step 444: Based on the first and second partial derivatives of the Tsallis entropy of the compensated SAR image g(h,n), the LM algorithm is used to solve the nonlinear equation system (Equation (9)) to obtain the updated phase error ΔΦ. k (m);

[0080] Steps 445: Utilize the updated phase error ΔΦ k (m) Construct the compensation function H for the k-th iteration. k The platform vibration is compensated for by the signal s0(m,n), resulting in the compensated SAR imaging result g(h,n). Based on the compensated SAR imaging result g(h,n), the Tsallis entropy T of the SAR image after the k-th iteration of compensation is calculated. k ;

[0081] Step 446: Based on the Tsallis entropy T of the compensated SAR image k Adjusting the step size μ of the LM algorithm k ;

[0082] Step 447: If the loop termination condition is met or the maximum number of loops is reached, the algorithm ends, finding the compensation function H that minimizes the Tsallis entropy of the compensated SAR image g(h,n). k Otherwise, let k = k + 1 and repeat steps 444 to 447.

[0083] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0084] Specific Implementation Method Six: This implementation method differs from one of Specific Implementation Methods One to Five in that, in step four-four-two, the first and second order partial derivatives of the Tsallis entropy of the compensated SAR image g(h,n) are calculated.

[0085] The specific process is as follows:

[0086] Step 4421: Solve for the first-order partial derivative F(ΔΦ(m)) of the Tsallis entropy of the compensated SAR image g(h,n); the expression is:

[0087]

[0088] Where F(ΔΦ(m)) represents the first-order partial derivative of the Tsallis entropy of the compensated SAR image g(h,n); Im[] represents the imaginary part operation; conj(·) represents the conjugate operation; IFT(·) represents the inverse Fourier transform operation;

[0089] Step 4422: Solve for the second-order partial derivative J(ΔΦ(m)) of the Tsallis entropy of the compensated SAR image g(h,n); the expression is:

[0090]

[0091] Where T_s1, T_s2, and T_s3 represent intermediate variables;

[0092] The expressions for intermediate variables T_s1, T_s2, and T_s3 are:

[0093]

[0094] Where Re{} denotes the real part extraction operation; g * (h,n) denotes the conjugate of g(h,n); [s0(m,n)] * This represents the conjugate of s0(m,n).

[0095] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0096] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that, in step four, the first and second partial derivatives of the Tsallis entropy of the compensated SAR image g(h,n) are used to solve the nonlinear equations using the LM algorithm to obtain the updated phase error ΔΦ. k (m);

[0097] The specific process is as follows:

[0098] Step 4441: Calculate the search direction s in the k-th iteration. k-1 (m); the expression is:

[0099] s k-1 (m)=-(J T (ΔΦ k-1 (m))J(ΔΦ k-1 (m))+μ k-1 I) -1 J T (ΔΦ k-1 (m))F(ΔΦ k-1 (m))(15)

[0100] Wherein, J(ΔΦ k-1(m)) represents the second-order partial derivative of the Tsallis entropy of the compensated SAR image g(h,n) obtained in the (k-1)th iteration; the superscript T denotes matrix transpose, ΔΦ k-1 (m) represents the phase error caused by platform vibration obtained in the (k-1)th iteration, μ k-1 μ represents the step size corresponding to the (k-1)th iteration. k-1 >0; I is the identity matrix, F(ΔΦ) k-1 (m)) represents the first-order partial derivative of the Tsallis entropy of the compensated SAR image g(h,n) obtained in the (k-1)th iteration;

[0101] Step 4442: Utilize the search direction s k-1 (m) Update the phase error to obtain the updated phase error ΔΦ k (m); the expression is:

[0102] ΔΦ k (m)=ΔΦ k-1 (m)+s k-1 (m) (16)

[0103] Where, ΔΦ k (m) represents the phase error caused by platform vibration obtained in the k-th iteration.

[0104] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0105] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that, in step four, four, and five, the updated phase error ΔΦ is utilized. k (m) Construct the compensation function H for the k-th iteration. k The platform vibration is compensated for by the signal s0(m,n), resulting in the compensated SAR imaging result g(h,n). Based on the compensated SAR imaging result g(h,n), the Tsallis entropy T of the SAR image after the k-th iteration of compensation is calculated. k ;

[0106] The specific process is as follows:

[0107] The updated phase error ΔΦ k Substituting (m) into formula (6), we obtain the compensation function H for the k-th iteration. k ;

[0108] The compensation function H in the k-th iteration k Substituting into formula (7), we obtain the SAR image g(h,n) after the kth iteration compensation;

[0109] Substituting the SAR image g(h,n) after the kth iteration compensation into formula (8), we obtain the Tsallis entropy T of the SAR image g(h,n) after the kth iteration compensation. k .

[0110] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0111] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that, in step four four six, the Tsallis entropy T of the compensated SAR image is used... k Adjusting the step size μ of the LM algorithm k ;

[0112] The specific process is as follows:

[0113] If T k ≥T k-1 Then μ k =μ k-1 ×δ, and ΔΦ k (m)=ΔΦ k-1 (m), T k =T k-1 ;

[0114] If T k <T k-1 Then μ k =μ k-1 / β;

[0115] Where δ and β are constants, δ > 1, β > 1.

[0116] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0117] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the loop termination condition in step four-four-seven is:

[0118] |T k -T k-1 |≤threshold (17)

[0119] Here, threshold represents the threshold value.

[0120] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0121] Example 1:

[0122] In this implementation example, a terahertz SAR simulation system with a carrier frequency of 220 GHz and a bandwidth of 3 GHz is first constructed under a signal-to-noise ratio of 10 dB. Simultaneously, a multi-component platform vibration with time-varying amplitude is established, and a terahertz SAR echo signal is constructed based on this. After range compression and range migration correction processing, a Fourier transform is performed along the azimuth direction to obtain a defocused SAR echo image, as shown below. Figure 2 As shown. It can be seen that, Figure 2 The SAR image in the image is severely defocused along the azimuth direction, caused by complex time-varying amplitude multi-component platform vibration. To suppress azimuth defocus and obtain a focused terahertz SAR image, platform vibration compensation is necessary. Therefore, we use the LM-based terahertz SAR compensation algorithm proposed in this invention to compensate for terahertz platform vibration. Through iteration, the final compensation function can be obtained to compensate for platform vibration and obtain a focused SAR image, as shown below. Figure 3 As shown in the figure, after processing by the terahertz SAR compensation algorithm based on the LM algorithm proposed in this invention, the platform vibration is well compensated, and the image is focused. Furthermore, the Tsallis entropy of the SAR images obtained before and after platform vibration compensation under 10dB conditions is shown in Table 1. It can be seen that the reduction in Tsallis entropy further proves the effectiveness of the algorithm proposed in this invention.

[0123] Table 1. SAR images before and after platform vibration compensation under a signal-to-noise ratio of 10 dB. Tsallis entropy.

[0124]

[0125] Example 2

[0126] In this implementation example, a terahertz SAR simulation system with a carrier frequency of 220 GHz and a bandwidth of 3 GHz is constructed under a signal-to-noise ratio of -10 dB. A multi-component platform vibration with time-varying amplitude is established, and a terahertz SAR echo signal is constructed based on this. The terahertz SAR echo signal containing complex platform vibration is processed, and a Fourier transform is performed along the azimuth direction to obtain a defocused SAR image, such as... Figure 4 As shown. Due to the influence of multi-component platform vibration with time-varying amplitude, a clear, focused terahertz SAR image cannot be obtained. Therefore, we use the LM-based platform vibration compensation algorithm proposed in this invention for compensation. Through iteration, the phase error introduced by platform vibration can be estimated, and a compensation function can be constructed to compensate for the platform vibration. The terahertz SAR image after compensation by the algorithm proposed in this invention is shown below. Figure 5As shown, the image defocus is well suppressed after compensation by the LM-based platform vibration compensation algorithm, and the point targets in the image are clearly visible. Furthermore, Table 2 presents the Tsallis entropy results of the image before and after compensation by the algorithm proposed in this invention under a -10dB condition. It can be seen that the reduction in entropy further proves the effectiveness of the algorithm proposed in this invention.

[0127] Table 2. SAR images before and after platform vibration compensation under a signal-to-noise ratio of -10dB. Tsallis entropy.

[0128]

[0129] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A terahertz SAR compensation method based on the LM algorithm under complex platform vibration, characterized in that: The specific process of the method is as follows: Step 1: Establish a multi-component platform vibration model with time-varying amplitude; Represented as: Where ΔR(m) represents the platform vibration, a j (m) represents the time-varying amplitude of the platform vibration, where m is the discrete slow time, m = 0, 1, ..., M-1, and M is the number of discrete slow times. j The vibration frequency of the platform. Let J be the phase of the platform vibration, j be the j-th platform vibration component, and J be the total number of platform vibration components. Step 2: Based on the multi-component platform vibration model with time-varying amplitude from Step 1, obtain the terahertz SAR echo signal s(m,n) of the multi-component platform vibration with time-varying amplitude; the specific process is as follows: Suppose there is a target point in the scene, and the target point's coordinates are (x, y, 0); Based on the multi-component platform vibration model with time-varying amplitude established in step one, the terahertz SAR echo signal is range compressed, and the range migration correction is performed on the range-compressed terahertz SAR echo signal to obtain the terahertz SAR echo signal s(m,n) with time-varying amplitude multi-component platform vibration. Where s(m,n) is the terahertz SAR echo signal with time-varying amplitude and multi-component platform vibration, n is the discrete fast time, n=0,1,…,N-1, N is the number of discrete fast times; ξ is the complex amplitude; B is the signal bandwidth; R0 is the shortest slant range from the radar platform to the target; c is the speed of light; j is the imaginary unit, j 2 =-1; k a λ is the Doppler modulation frequency; v is the platform velocity; λ is the wavelength; ΔR is the platform vibration. Step 3: Process the terahertz SAR echo signal s(m,n) from Step 2 to obtain the SAR imaging result, and calculate the Tsallis entropy of the SAR imaging result; the specific process is as follows: Step 31: Compensate the terahertz SAR echo signal s(m,n) from Step 2 along the azimuth direction to obtain the azimuth-compensated signal s0(m,n); s0(m,n)=s(m,n)×exp(-jπk a m 2 ) (3) Step 32: Perform a Fourier transform on the azimuth-compensated signal s0(n,m) along the azimuth direction to obtain the SAR imaging result g0(h,n); Where h is the Doppler frequency index; Step 33: Calculate the Tsallis entropy T0 of the SAR imaging result g0(h,n); Where α is a real number; S0 is an intermediate variable. Step 4: Construct a compensation function to compensate for platform vibration and obtain the compensated SAR image; The Tsallis entropy of the compensated SAR image is calculated, and the LM algorithm is used to find the compensation function that minimizes the Tsallis entropy of the compensated SAR image; the specific process is as follows: Step 41: Construct the compensation function; H=exp(jΔΦ(m)) (6) Where ΔΦ(m) is the phase error caused by platform vibration; H is the compensation function; Step 42: Based on the compensation function H, compensate for the platform vibration to obtain the compensated SAR image g(h,n); Step 43: Calculate the Tsallis entropy of the compensated SAR image g(h,n); Where T is the Tsallis entropy of the compensated SAR image g(h,n); S is an intermediate variable. Step 44: Use the LM algorithm to find the compensation function that minimizes the Tsallis entropy of the compensated SAR image g(h,n); the specific process is as follows: Step 441: Transform the Tsallis entropy minimization problem into an equivalent problem of solving a system of nonlinear equations; Step 442: Solve for the first and second partial derivatives of the Tsallis entropy of the compensated SAR image g(h,n); Step 443: Initialize the phase error and the maximum number of loops K; Let the number of iterations k = 1; Step 444: Based on the first and second partial derivatives of the Tsallis entropy of the compensated SAR image g(h,n), the LM algorithm is used to solve the nonlinear equations to obtain the updated phase error ΔΦ. k (m); Steps 445: Utilize the updated phase error ΔΦ k (m) Construct the compensation function H for the k-th iteration. k The platform vibration is compensated for by the signal s0(m,n), resulting in the compensated SAR imaging result g(h,n). Based on the compensated SAR imaging result g(h,n), the Tsallis entropy T of the SAR image after the k-th iteration of compensation is calculated. k ; Step 446: Based on the Tsallis entropy T of the compensated SAR image k Adjusting the step size μ of the LM algorithm k ; Step 447: If the loop termination condition is met or the maximum number of loops is reached, the algorithm ends, finding the compensation function H that minimizes the Tsallis entropy of the compensated SAR image g(h,n). k Otherwise, let k = k + 1, and repeat steps 444 to 447. Step 5: Compensate for platform vibration based on the compensation function that minimizes the Tsallis entropy of the compensated SAR image to obtain the final focused SAR imaging result.

2. The terahertz SAR compensation method based on the LM algorithm under complex platform vibration as described in claim 1, characterized in that: In step 442, the first and second partial derivatives of the Tsallis entropy of the compensated SAR image g(h,n) are calculated; the specific process is as follows: Step 4421: Solve for the first-order partial derivative F(ΔΦ(m)) of the Tsallis entropy of the compensated SAR image g(h,n); the expression is: Where F(ΔΦ(m)) represents the first-order partial derivative of the Tsallis entropy of the compensated SAR image g(h,n); Im[ ] represents the imaginary part operation; conj(·) represents the conjugate operation; IFT(·) represents the inverse Fourier transform operation; Step 4422: Solve for the second-order partial derivative J(ΔΦ(m)) of the Tsallis entropy of the compensated SAR image g(h,n); the expression is: Where T_s1, T_s2, and T_s3 represent intermediate variables; The expressions for intermediate variables T_s1, T_s2, and T_s3 are: Where Re{} denotes the real part extraction operation; g * (h,n) denotes the conjugate of g(h,n); [s0(m,n)] * This represents the conjugate of s0(m,n).

3. The terahertz SAR compensation method based on the LM algorithm under complex platform vibration as described in claim 2, characterized in that: In step four, based on the first and second partial derivatives of the Tsallis entropy of the compensated SAR image g(h,n), the LM algorithm is used to solve the nonlinear equations to obtain the updated phase error ΔΦ. k (m); The specific process is as follows: Step 4441: Calculate the search direction s in the k-th iteration. k-1 (m); the expression is: s k-1 (m)=-(J T (DF k-1 (m))J(ΔΦ k-1 (m))+μ k-1 I) -1 J T (DF k-1 (m))F(ΔΦ k-1 (m)) (15) Wherein, J(ΔΦ k-1 (m)) represents the second-order partial derivative of the Tsallis entropy of the compensated SAR image g(h,n) obtained in the (k-1)th iteration; the superscript T denotes matrix transpose, ΔΦ k-1 (m) represents the phase error caused by platform vibration obtained in the (k-1)th iteration, μ k-1 μ represents the step size corresponding to the (k-1)th iteration. k-1 >0; I is the identity matrix, F(ΔΦ) k-1 (m)) represents the first-order partial derivative of the Tsallis entropy of the compensated SAR image g(h,n) obtained in the (k-1)th iteration; Step 4442: Utilize the search direction s k-1 (m) Update the phase error to obtain the updated phase error ΔΦ k (m); the expression is: ΔΦ k (m)=ΔΦ k-1 (m)+s k-1 (m) (16) Where, ΔΦ k (m) represents the phase error caused by platform vibration obtained in the k-th iteration.

4. The terahertz SAR compensation method based on the LM algorithm under complex platform vibration as described in claim 3, characterized in that: In steps four and four, the updated phase error ΔΦ is utilized. k (m) Construct the compensation function H for the k-th iteration. k The platform vibration is compensated for by the signal s0(m,n), resulting in the compensated SAR imaging result g(h,n). Based on the compensated SAR imaging result g(h,n), the Tsallis entropy T of the SAR image after the k-th iteration of compensation is calculated. k ; The specific process is as follows: The updated phase error ΔΦ k Substituting (m) into formula (6), we obtain the compensation function H for the k-th iteration. k ; The compensation function H in the k-th iteration k Substituting into formula (7), we obtain the SAR image g(h,n) after the kth iteration compensation; Substituting the SAR image g(h,n) after the kth iteration compensation into formula (8), we obtain the Tsallis entropy T of the SAR image g(h,n) after the kth iteration compensation. k .

5. The terahertz SAR compensation method based on the LM algorithm under complex platform vibration as described in claim 4, characterized in that: In step four four six, the Tsallis entropy T of the compensated SAR image is used. k Adjusting the step size μ of the LM algorithm k ; The specific process is as follows: If T k ≥ T k-1 , then μ k = μ k-1 × δ, and ΔΦ k (m) = ΔΦ k-1 (m), T k = T k-1 ; If T k <T k-1 , then μ k = μ k-1 / β; Where δ and β are constants, δ > 1, β > 1.

6. The terahertz SAR compensation method based on the LM algorithm under complex platform vibration as described in claim 5, characterized in that: The loop termination condition in step 447 is: |T k -T k-1 |≤threshold (17) Here, threshold represents the threshold value.

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