Terahertz SAR image self-focusing method without vibration model constraint

Abstract

The invention discloses a terahertz SAR (Synthetic Aperture Radar) image self-focusing method without vibration model constraint, relates to a terahertz SAR image self-focusing method, and belongs to the technical field of terahertz SAR. The invention aims to solve the problems that in the terahertz SAR image focusing process, image focusing is insufficient due to limitation of a specific vibration model, and the nonlinear equation solving process in the self-focusing process is complex. The method comprises the following steps: acquiring a terahertz SAR echo signal; the terahertz SAR echo signal comprises a phase error; the image entropy of the terahertz SAR image is obtained; solving a first-order derivative of the image entropy S of the terahertz SAR image about the phase error, and enabling the first-order derivative of the image entropy S about the phase error to be zero to obtain a nonlinear equation to be solved; solving the nonlinear equation based on a Gaussian-Newton method to obtain a phase error estimation value which is not constrained by a specific model; and constructing a compensation function based on the phase error estimation value to obtain a final clear SAR imaging result.

Description

Technical Field

[0001] The invention relates to a terahertz SAR image self-focusing method and belongs to the technical field of terahertz SAR. Background Art

[0002] Terahertz SAR has significant advantages. It can better capture and distinguish the details of the target, obtain better imaging resolution, and thus achieve fine imaging. At the same time, due to the all-weather working ability of terahertz SAR, it is particularly outstanding in the fields of security monitoring, environmental monitoring and disaster assessment. However, the large bandwidth of terahertz SAR will make its wavelength smaller while obtaining high imaging resolution, which makes it extremely susceptible to the influence of small disturbances of the platform. Such small disturbances will seriously interfere with terahertz SAR imaging, blur the imaging results, and cause the imaging results to be severely defocused or even unrecognizable. In addition, the terahertz SAR image focusing algorithms are usually based on simple harmonic vibrations. However, such algorithms based on specific models cannot fully handle complex actual situations, resulting in residual model fitting errors, platform speed changes, noise, etc. that are not fully compensated after the image is self-focused, causing further defocusing of the image. The vibration compensation method that relies on traditional specific models is difficult to completely eliminate the error, and usually requires additional compensation steps. Therefore, it is urgent to develop a terahertz image focusing algorithm without specific vibration model constraints to cope with the complex terahertz SAR image focusing problem. At the same time, the core challenge of the terahertz SAR image autofocus algorithm lies in solving nonlinear equations. Since the phase error caused by vibration exhibits nonlinear characteristics in complex scenes, it is also particularly important to choose an appropriate nonlinear equation solving algorithm. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that in the process of terahertz SAR image focusing, the image focusing is insufficient due to the limitation of a specific vibration model, and the nonlinear equation solving process in the self-focusing process is relatively complicated, and a terahertz SAR image self-focusing method without vibration model constraints is proposed.

[0004] The specific process of the terahertz SAR image self-focusing method without vibration model constraints is as follows:

[0005] Step 1: Acquire the terahertz SAR echo signal; the terahertz SAR echo signal contains a phase error;

[0006] Step 2: Based on the terahertz SAR echo signal obtained in step 1, the image entropy of the terahertz SAR image is obtained;

[0007] Step 3: Calculate the first-order derivative of the image entropy S of the terahertz SAR image obtained in step 2 with respect to the phase error, and make the first-order derivative of the image entropy S with respect to the phase error zero, so as to obtain the nonlinear equation to be solved;

[0008] Step 4: Solve the nonlinear equation in step 3 based on the Gauss-Newton method to obtain the final phase error estimate that is not constrained by a specific model;

[0009] Step 5: Based on the phase error estimation value obtained in step 4, a compensation function is constructed to suppress the defocus of the terahertz SAR image and obtain the final SAR imaging result.

[0010] The beneficial effects of the present invention are:

[0011] The present invention proposes a terahertz SAR image self-focusing method without vibration model constraints. This method breaks away from the limitations of the traditional simple harmonic vibration model, starts from the image entropy, and estimates the phase error that causes image defocus in the echo by solving nonlinear equations, thereby dealing with complex terahertz SAR image focusing problems. This method can flexibly cope with complex vibration conditions, is not bound by a specific vibration model, and is adapted to a wider range of imaging scenarios. In order to effectively solve the problem of solving nonlinear equations, the present invention introduces the Gauss-Newton method. This method has high computational efficiency and good numerical stability, and can quickly converge to the optimal solution during the solution process, thereby accurately estimating the phase error. By directly processing the phase error, the present invention can effectively compensate for complex interferences including platform vibration, platform speed change, noise, etc., so that the phase error in the terahertz SAR echo signal is significantly corrected, and finally a clear terahertz SAR imaging result is obtained.

[0012] Aiming at the problem of terahertz SAR image focusing, the present invention first constructs a terahertz SAR echo signal model containing phase errors under the condition of no vibration model constraints. Based on this model, the terahertz SAR image self-focusing algorithm suitable for the condition of no vibration model constraints is further studied. Different from the traditional algorithm that relies on a specific vibration model, this model has a wider applicability and can cope with a variety of imaging scenarios and process more complex phase errors, including platform vibration, platform speed changes and noise, etc. These errors are the key factors leading to image defocus. Without relying on additional focusing steps, the self-focusing algorithm under the constraint of no vibration model can effectively process phase errors from various sources, thereby generating clearer imaging results. Since the algorithm proposed in the present invention can process phase errors that are not dependent on a specific vibration model, it is not only applicable to common vibration models, but also can cope with more complex phase error interference, reflecting its superior adaptability and robustness.

[0013] The core of the self-focusing algorithm proposed in the present invention is to solve the nonlinear equation therein, so the present invention introduces the Gauss-Newton method to solve the nonlinear equation. The Gauss-Newton method has significant advantages in solving the phase error estimation problem due to its efficient computing performance, good numerical stability and applicability in processing nonlinear equations. Through this method, the present invention can quickly and accurately estimate the phase error, thereby achieving clear focusing of the terahertz SAR image, and effectively improving the imaging quality and the robustness of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart of the present invention;

[0015] Figure 2 This is the SAR imaging result obtained before the image is focused under the condition of a signal-to-noise ratio of 10dB;

[0016] Figure 3 This is the SAR imaging result obtained after image focusing using the algorithm proposed by the present invention under the condition of a signal-to-noise ratio of 10dB;

[0017] Figure 4 This is the SAR imaging result obtained before image focusing under the condition of -10dB signal-to-noise ratio;

[0018] Figure 5 This is the SAR imaging result obtained after image focusing using the algorithm proposed in the present invention under the condition of a signal-to-noise ratio of -10dB. DETAILED DESCRIPTION

[0019] Specific implementation method 1: The specific process of the terahertz SAR image self-focusing method without vibration model constraint in this implementation method is as follows:

[0020] Step 1: Under the condition of no vibration model constraint, a terahertz SAR echo signal is obtained; the terahertz SAR echo signal contains a phase error that causes image defocusing, and the phase error is not constrained by a specific model;

[0021] Step 2: Based on the terahertz SAR echo signal obtained in step 1, the image entropy of the terahertz SAR image is obtained;

[0022] Step 3: Calculate the first-order derivative of the image entropy S of the terahertz SAR image obtained in step 2 with respect to the phase error, and make the first-order derivative of the image entropy S with respect to the phase error zero, so as to obtain the nonlinear equation to be solved;

[0023] Step 4: Solve the nonlinear equation in step 3 based on the Gauss-Newton method to obtain the final phase error estimate that is not constrained by a specific model;

[0024] Step 5: Based on the phase error estimation value obtained in step 4, a compensation function is constructed to suppress the defocus of the terahertz SAR image and obtain the final clear SAR imaging result.

[0025] Specific implementation method 2: This implementation method is different from specific implementation method 1 in that: in step 1, the terahertz SAR echo signal is obtained under the condition of no vibration model constraint; the terahertz SAR echo signal contains a phase error that causes image defocusing, and the phase error is not constrained by a specific model;

[0026] The specific process is:

[0027] Acquire terahertz SAR echo signal;

[0028] Performing distance compression processing on the terahertz SAR echo signal to obtain a terahertz SAR echo signal after distance compression processing;

[0029] Performing range migration correction processing on the terahertz SAR echo signal after the range compression processing to obtain the terahertz SAR echo signal x(n,m) after the range migration correction processing;

[0030] The terahertz SAR echo signal x(n,m) after range migration correction contains phase errors that cause image defocus.

[0031]

[0032] Typically, the phase error in the terahertz SAR echo signal is described by a simple harmonic model, but this means that the phase error outside the simple harmonic model cannot be processed, which will cause the image to still be defocused. It is a summary of the factors that cause defocusing of terahertz SAR images, rather than using a specific model to describe phase error. The terahertz SAR echo signal model x(n,m) is obtained by fitting, so the terahertz SAR echo signal model x(n,m) is not constrained by a specific model and can be applied to more diverse and complex terahertz SAR imaging scenarios;

[0033] The expression of the terahertz SAR echo signal x(n,m) after range migration correction is:

[0034]

[0035] Wherein, x(n,m) is the model of the terahertz SAR echo signal after range compression and range migration correction;

[0036] n is the discrete fast time, n=0,1,...,N-1, N is the number of discrete fast times;

[0037] m is the discrete slow time, m=0,1,...,M-1, M is the number of discrete slow times;

[0038] σ is the complex amplitude of the echo signal; B is the signal bandwidth; r 0 is the ideal shortest slant distance between the terahertz SAR platform and the target; c is the speed of light; is the ideal phase of the THz SAR echo; represents the phase error, Not constrained by a specific model; λ is the signal wavelength; r(m) is the ideal slant distance between the THz SAR platform and the target; j is an imaginary unit, j 2 =-1.

[0039] The other steps and parameters are the same as those in the first embodiment.

[0040] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that: the ideal phase of the terahertz SAR echo The expression is:

[0041]

[0042] The other steps and parameters are the same as those in the first or second embodiment.

[0043] Specific implementation method 4: This implementation method is different from any one of specific implementation methods 1 to 3 in that: in step 2, the image entropy of the terahertz SAR image is obtained based on the terahertz SAR echo signal obtained in step 1; the specific process is:

[0044] Step 21: Perform azimuth compensation on the terahertz SAR echo signal x(n,m) obtained in step 1 to obtain an azimuth-compensated signal, and perform phase error compensation on the azimuth-compensated signal to obtain a phase error-compensated signal.

[0045] Step 22: Signal after phase error compensation Perform Fourier transform processing to obtain the terahertz SAR image I(n,k), as shown in formula (3):

[0046]

[0047] Where k is the Doppler frequency index; H 1 is the azimuth compensation function; H 2 is the phase error compensation function;

[0048] Azimuth compensation function H 1 The expression is:

[0049] H 1 =exp(-jπKa m 2 ) (4)

[0050] Phase error compensation function H 2 The expression is:

[0051]

[0052] Among them, K a Tune frequency for Doppler;

[0053] Step 23: Based on the terahertz SAR image I(n,k), obtain the image Tsallis entropy of the terahertz SAR image.

[0054] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0055] Specific implementation method 5: This implementation method is different from any one of specific implementation methods 1 to 4 in that: in the steps 2 and 3, based on the terahertz SAR image I (n, k), the image Tsallis entropy of the terahertz SAR image is obtained, as shown in formula (6):

[0056]

[0057] Where q is the Tsallis entropy index.

[0058] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0059] Specific implementation method 6: This implementation method is different from any one of specific implementation methods 1 to 5 in that: in step 3, the image entropy S of the terahertz SAR image obtained in step 2 is calculated with respect to the first-order derivative of the phase error, and the first-order derivative of the image entropy S with respect to the phase error is made zero, thereby obtaining a nonlinear equation to be solved;

[0060] The specific process is:

[0061] When the image entropy S obtained in step 2 is the smallest, the focused SAR imaging result is obtained;

[0062]

[0063] in, is the first derivative of the entropy with respect to the phase error.

[0064] Formula (7) represents the process of derivation of image entropy with respect to phase error. By making it zero, the corresponding minimum point can be obtained. This means that at this point, the entropy of the image reaches the minimum value, that is, the system reaches the best focusing state. Therefore, by minimizing the image entropy, the terahertz SAR imaging results with good focusing can be effectively obtained.

[0065] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0066] Specific implementation method 7: This implementation method is different from any one of specific implementation methods 1 to 6 in that: in step 4, the nonlinear equation in step 3 is solved based on the Gauss-Newton method to obtain the final phase error estimate that is not constrained by a specific model; the specific process is as follows:

[0067] Step 41: Set the number of iterations i = 1; set the termination condition threshold Q;

[0068] Set the initial value of phase error

[0069] Step 42: Based on phase error Calculate the phase error obtained at the i-th iteration When the set termination condition threshold Q is met, the final phase error estimation result that is not constrained by a specific model is obtained;

[0070] The specific process is:

[0071] The specific iteration formula of the Gauss-Newton method is:

[0072]

[0073] in, is the phase error obtained in the i-th iteration; is the phase error obtained in the i-1th iteration; F i-1 represents the first-order derivative of the entropy obtained at the i-1th iteration with respect to the phase error; Jac i-1 represents the second-order derivative of the entropy obtained at the i-1th iteration with respect to the phase error; the superscript T represents the matrix transpose; the superscript -1 represents the inverse of the matrix; · represents the multiplication sign;

[0074] The first-order derivative of the entropy obtained in the i-1th iteration with respect to the phase error is F i-1 The expression is:

[0075]

[0076] The second-order derivative of the entropy obtained at the i-1th iteration with respect to the phase error Jac i-1 The expression is:

[0077]

[0078] The phase error obtained from the i-1th iteration Substituting into formula (6), we get the image entropy S obtained at the i-1th iteration: i-1 ;

[0079] The phase error obtained from the i-th iteration Substituting into formula (6), we get the image entropy S obtained at the i-th iteration: i ;

[0080] If the image entropy S of the i-th iteration i and the image entropy S of the i-1th iteration i-1 If the absolute value of the difference is greater than the termination condition threshold Q, then set i=i+1 and continue to execute step 42 until the image entropy S of the i-th iteration is obtained. i and the image entropy S of the i-1th iteration i-1 If the absolute value of the difference is less than or equal to the termination condition threshold Q, the image entropy is considered to be minimum, and the final phase error estimation result is obtained without being constrained by a specific model.

[0081] If the image entropy S of the i-th iteration i and the image entropy S of the i-1th iteration i-1 If the absolute value of the difference is less than or equal to the termination condition threshold Q, the image entropy is considered to be minimum, and the final phase error estimation result is obtained without being constrained by a specific model.

[0082] The expression is:

[0083] S i -S i-1 |≤Q (11)

[0084] Among them, S i is the image entropy obtained at the i-th iteration; S i-1 is the image entropy obtained at the i-1th iteration.

[0085] The other steps and parameters are the same as those in Specific Implementations 1 to 6-1.

[0086] Specific implementation eight: This implementation differs from any one of the specific implementations one to seven in that: in step four-two, the phase error obtained by the i-1th iteration is Substituting into formula (6), we get the image entropy S obtained at the i-1th iteration: i-1 , the specific process is:

[0087] The phase error obtained from the i-1th iteration Substituting into formula (5) The phase error compensation function H obtained by the i-1th iteration is calculated 2 ; The phase error compensation function H obtained in the i-1th iteration 2Substitute into formula (3) to calculate the terahertz SAR image I(n,k) obtained at the i-1th iteration; Substitute the terahertz SAR image I(n,k) obtained at the i-1th iteration into formula (6) to calculate the image entropy S obtained at the i-1th iteration i-1 ; The expression is:

[0088]

[0089] The other steps and parameters are the same as those in Specific Implementation 1 to 7-1.

[0090] Specific implementation method 9: This implementation method is different from any one of the specific implementation methods 1 to 8 in that: in step 42, the phase error obtained in the i-th iteration is Substituting into formula (6), we get the image entropy S obtained at the i-th iteration: i , the specific process is:

[0091] The phase error obtained from the i-th iteration Substituting into formula (5) The phase error compensation function H obtained by the i-th iteration is calculated 2 ; The phase error compensation function H obtained in the i-th iteration 2 Substitute the terahertz SAR image I(n, k) obtained at the i-th iteration into formula (3); Substitute the terahertz SAR image I(n, k) obtained at the i-th iteration into formula (6) to calculate the image entropy S obtained at the i-th iteration i ; The expression is:

[0092]

[0093] The other steps and parameters are the same as those in Specific Implementation 1 to 8-1.

[0094] Specific implementation ten: This implementation differs from any one of specific implementations one to nine in that: in step five, based on the phase error estimation value obtained in step four, a compensation function is constructed to suppress the defocus of the terahertz SAR image, thereby obtaining a final clear SAR imaging result;

[0095] The specific process is:

[0096] Step 51: Based on the estimated value of the final phase error obtained in step 4 Construct the final phase error compensation function H final , as shown in formula (14):

[0097]

[0098] Step 52: The terahertz SAR echo signal is compensated by the phase error compensation function established in formula (14). The specific compensation process is shown in formula (15). Through the final phase error compensation, the defocus of the terahertz SAR image can be suppressed, and the final clear SAR imaging result I can be obtained. focus (n,k);

[0099]

[0100] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 9.

[0101] The following examples are used to verify the beneficial effects of the present invention:

[0102] Embodiment 1:

[0103] First, a terahertz SAR imaging system is constructed with a signal-to-noise ratio of 10dB, a carrier frequency of 220GHz, and a bandwidth of 3GHz. The error model that causes terahertz SAR image defocusing constructed in the simulation is not based on the traditional specific simple harmonic vibration model, so in this case, the effectiveness of the algorithm proposed in this paper can be better demonstrated without the constraints of a specific vibration model. Figure 2 The SAR imaging results without image focusing at a signal-to-noise ratio of 10dB are shown. It can be seen that the image is severely defocused and point targets cannot be distinguished. Figure 3 The SAR imaging results obtained by focusing the image with the algorithm proposed in the present invention under 10 dB are shown in Table 1. The imaging results have good focusing effect and point targets are clearly visible. In addition, Table 1 shows the Tsallis entropy of the image before and after image focusing. Figure 2 and Figure 3 The comparison of and Table 1 can prove that the terahertz SAR image self-focusing algorithm without vibration model constraint proposed in the present invention can well suppress the defocusing of SAR images and obtain a clearly focused imaging result.

[0104] Table 1 SAR image entropy before and after image focusing under the condition of SNR 10dB

[0105]

[0106] Embodiment 2:

[0107] In this embodiment, a terahertz SAR imaging system with a signal-to-noise ratio of -10dB, a carrier frequency of 220GHz, and a bandwidth of 3GHz is constructed. Similarly, the error model that causes SAR image defocusing constructed in the simulation system is not based on the traditional simple harmonic vibration model, so the simulation experiment that is not based on a specific vibration model can prove that the image focusing algorithm proposed in the present invention is free from vibration model constraints. Figure 4 and Figure 5 The SAR imaging results at -10dB are shown respectively. Figure 4 is the imaging result before the image is focused, and Figure 5 It is the imaging result after being processed by the terahertz SAR image self-focusing algorithm without vibration model constraint proposed in the present invention. The Tsallis entropy of the image before and after image focusing is shown in Table 2. It can be seen from the comparison that the image processed by the terahertz SAR image self-focusing algorithm proposed in the present invention is clearer, and the defocus along the azimuth direction is also effectively suppressed. At the same time, it also further proves that the algorithm proposed in the present invention is still effective in the terahertz SAR imaging scenario that is not based on a specific vibration model. It can be seen from the above experimental results that the terahertz SAR image self-focusing algorithm without vibration model constraint proposed in the present invention is effective and feasible in suppressing image defocus.

[0108] Table 2 SAR image entropy before and after image focusing under the condition of SNR -10dB

[0109]

[0110] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A terahertz SAR image self-focusing method without vibration model constraints, characterized by: The specific process of the method is: Step 1: Acquire the terahertz SAR echo signal; the terahertz SAR echo signal contains a phase error; Step 2: Based on the terahertz SAR echo signal obtained in step 1, the image entropy of the terahertz SAR image is obtained; Step 3: Calculate the first-order derivative of the image entropy S of the terahertz SAR image obtained in step 2 with respect to the phase error, and make the first-order derivative of the image entropy S with respect to the phase error zero, so as to obtain the nonlinear equation to be solved; Step 4: Solve the nonlinear equation in step 3 based on the Gauss-Newton method to obtain the final phase error estimate that is not constrained by a specific model; Step 5: Based on the phase error estimation value obtained in step 4, a compensation function is constructed to suppress the defocus of the terahertz SAR image and obtain the final SAR imaging result.

2. The terahertz SAR image self-focusing method without vibration model constraint according to claim 1, characterized in that: In the step 1, a terahertz SAR echo signal is obtained; the terahertz SAR echo signal contains a phase error; the specific process is: Acquire terahertz SAR echo signal; Performing distance compression processing on the terahertz SAR echo signal to obtain a terahertz SAR echo signal after distance compression processing; Performing range migration correction processing on the terahertz SAR echo signal after the range compression processing to obtain the terahertz SAR echo signal x(n,m) after the range migration correction processing; The terahertz SAR echo signal x(n,m) after range migration correction contains phase error The expression of the terahertz SAR echo signal x(n,m) after range migration correction is: Wherein, x(n,m) is the model of the terahertz SAR echo signal after range compression and range migration correction; n is the discrete fast time, n=0,1,...,N-1, N is the number of discrete fast times; m is the discrete slow time, m=0,1,...,M-1, M is the number of discrete slow times; σ is the complex amplitude of the echo signal; B is the signal bandwidth; r0 is the ideal shortest slant distance between the terahertz SAR platform and the target; c is the speed of light; is the ideal phase of the THz SAR echo; represents the phase error; λ is the signal wavelength; r(m) is the ideal slant distance between the THz SAR platform and the target; j is the imaginary unit, j 2 =-1.

3. The terahertz SAR image self-focusing method without vibration model constraint according to claim 2, characterized in that: The ideal phase of the THz SAR echo The expression is:

4. The terahertz SAR image self-focusing method without vibration model constraint according to claim 3 is characterized in that: In the step 2, based on the terahertz SAR echo signal obtained in the step 1, the image entropy of the terahertz SAR image is obtained; the specific process is: Step 21: Perform azimuth compensation on the terahertz SAR echo signal x(n,m) obtained in step 1 to obtain an azimuth-compensated signal, and perform phase error compensation on the azimuth-compensated signal to obtain a phase error-compensated signal. Step 22: Signal after phase error compensation Perform Fourier transform processing to obtain the terahertz SAR image I(n,k), as shown in formula (3): Where, k is the Doppler frequency index; H1 is the azimuth compensation function; H2 is the phase error compensation function; The expression of the azimuth compensation function H1 is: H1=exp(-jπK a m 2 ) (4) The expression of the phase error compensation function H2 is: Among them, K a Tune frequency for Doppler; Step 23: Based on the terahertz SAR image I(n,k), obtain the image Tsallis entropy of the terahertz SAR image.

5. The terahertz SAR image self-focusing method without vibration model constraint according to claim 4, characterized in that: In the steps 2 and 3, based on the terahertz SAR image I(n, k), the image Tsallis entropy of the terahertz SAR image is obtained, as shown in formula (6): Where q is the Tsallis entropy index.

6. The terahertz SAR image self-focusing method without vibration model constraint according to claim 5, characterized in that: In the step 3, the first-order derivative of the image entropy S of the terahertz SAR image obtained in the step 2 with respect to the phase error is calculated, and the first-order derivative of the image entropy S with respect to the phase error is made zero, so as to obtain a nonlinear equation to be solved; The specific process is: in, is the first derivative of the entropy with respect to the phase error.

7. The terahertz SAR image self-focusing method without vibration model constraint according to claim 6, characterized in that: In the step 4, the nonlinear equation in step 3 is solved based on the Gauss-Newton method to obtain a final phase error estimate that is not constrained by a specific model; The specific process is: Step 41: Set the number of iterations i = 1; set the termination condition threshold Q; Set the initial value of phase error Step 42: Based on phase error Calculate the phase error obtained at the i-th iteration When the set termination condition threshold Q is met, the final phase error estimation result is obtained without being constrained by a specific model. The specific process is: in, is the phase error obtained in the i-th iteration; is the phase error obtained in the i-1th iteration; F i-1 represents the first-order derivative of the entropy obtained at the i-1th iteration with respect to the phase error; Jac i-1 represents the second-order derivative of the entropy obtained at the i-1th iteration with respect to the phase error; The superscript T indicates the transpose of the matrix; the superscript -1 indicates the inverse of the matrix; · indicates the multiplication sign; The first-order derivative of the entropy obtained in the i-1th iteration with respect to the phase error is F i-1 The expression is: The second-order derivative of the entropy obtained at the i-1th iteration with respect to the phase error Jac i-1 The expression is: The phase error obtained from the i-1th iteration Substituting into formula (6), we get the image entropy S obtained at the i-1th iteration: i-1 ; The phase error obtained by the i-th iteration Substituting into formula (6), we get the image entropy S obtained at the i-th iteration: i ; If the image entropy S of the i-th iteration i and the image entropy S of the i-1th iteration i-1 If the absolute value of the difference is greater than the termination condition threshold Q, then set i=i+1 and continue to execute step 42 until the image entropy S of the i-th iteration is obtained. i and the image entropy S of the i-1th iteration i-1 If the absolute value of the difference is less than or equal to the termination condition threshold Q, the image entropy is considered to be minimum, and the final phase error estimation result is obtained without being constrained by a specific model. If the image entropy S of the i-th iteration i and the image entropy S of the i-1th iteration i-1 If the absolute value of the difference is less than or equal to the termination condition threshold Q, the image entropy is considered to be minimum, and the final phase error estimation result is obtained without being constrained by a specific model. The expression is: |S i -S i-1 |≤Q (11) where S i is the image entropy obtained at the i-th iteration; S i-1 is the image entropy obtained at the i-1th iteration.

8. The terahertz SAR image self-focusing method without vibration model constraint according to claim 7, characterized in that: In step 42, the phase error obtained by the i-1th iteration is Substituting into formula (6), we get the image entropy S obtained at the i-1th iteration: i-1 , the specific process is: The phase error obtained from the i-1th iteration Substituting into formula (5) The phase error compensation function H2 obtained at the i-1th iteration is calculated; the phase error compensation function H2 obtained at the i-1th iteration is substituted into formula (3) to calculate the terahertz SAR image I(n, k) obtained at the i-1th iteration; the terahertz SAR image I(n, k) obtained at the i-1th iteration is substituted into formula (6) to calculate the image entropy S obtained at the i-1th iteration i-1 ; The expression is:

9. The terahertz SAR image self-focusing method without vibration model constraint according to claim 8, characterized in that: In step 42, the phase error obtained by the i-th iteration is Substituting into formula (6), we get the image entropy S obtained at the i-th iteration: i , the specific process is: The phase error obtained by the i-th iteration Substituting into formula (5) The phase error compensation function H2 obtained at the i-th iteration is calculated; the phase error compensation function H2 obtained at the i-th iteration is substituted into formula (3) to calculate the terahertz SAR image I(n, k) obtained at the i-th iteration; the terahertz SAR image I(n, k) obtained at the i-th iteration is substituted into formula (6) to calculate the image entropy S obtained at the i-th iteration i ; The expression is:

10. The terahertz SAR image self-focusing method without vibration model constraint according to claim 9, characterized in that: In the step 5, based on the phase error estimation value obtained in the step 4, a compensation function is constructed to suppress the defocus of the terahertz SAR image, so as to obtain a final SAR imaging result; The specific process is: Step 51: Based on the estimated value of the final phase error obtained in step 4 Construct the final phase error compensation function H final , as shown in formula (14): Step 52: Compensate the terahertz SAR echo signal using the phase error compensation function established in formula (14) to obtain the final SAR imaging result I focus (n,k);

Images