Vibration model free self-focusing method for terahertz sar image

Abstract

The present application relates to a vibration model constraint-free terahertz SAR image self-focusing method, and belongs to the technical field of terahertz SAR. The present application aims to solve the problem that the image focusing is insufficient due to the limitation of a specific vibration model in the terahertz SAR image focusing process, and the nonlinear equation solving process in the self-focusing process is relatively complex. The process is as follows: obtaining a terahertz SAR echo signal; the terahertz SAR echo signal contains phase errors; obtaining the image entropy of a terahertz SAR image; taking the first-order derivative of the image entropy S of the terahertz SAR image with respect to the phase error and making the first-order derivative of the image entropy S with respect to the phase error zero to obtain a nonlinear equation to be solved; solving the nonlinear equation based on the Gauss-Newton method to obtain a phase error estimation value that is not constrained by a specific model; based on the phase error estimation value, constructing a compensation function to obtain a final clear SAR imaging result.

Description

TECHNICAL FIELD

[0001] The present application relates to a terahertz SAR image self-focusing method, belonging to the technical field of terahertz SAR. BACKGROUND

[0002] Terahertz SAR has more obvious advantages, it can better capture and distinguish the details of the target, and obtain better imaging resolution, so as to realize fine imaging. At the same time, due to the all-weather working ability of terahertz SAR, it performs 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 when obtaining high imaging resolution, so it is easily affected by the slight disturbance of the platform. Such slight disturbance will seriously interfere with the terahertz SAR imaging, blur the imaging results, cause the imaging results to be seriously defocused, and even cannot be recognized. In addition, the terahertz SAR image focusing algorithm under normal circumstances is based on simple harmonic vibration. However, this kind of algorithm based on a specific model cannot fully process complex actual situations, resulting in residual model fitting errors, platform speed changes, noise and other errors that are not fully compensated after image self-focusing, causing further defocusing of the image. The vibration compensation method relying on the traditional specific model is difficult to completely eliminate the error, and usually needs 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 self-focusing algorithm is the solution of the nonlinear equation. Since the phase error caused by vibration shows nonlinear characteristics in complex scenes, it is also important to choose an appropriate nonlinear equation solving algorithm. SUMMARY

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

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

[0005] Step one: obtaining a terahertz SAR echo signal; the terahertz SAR echo signal contains a phase error;

[0006] Step two: obtaining the image entropy of the terahertz SAR image based on the terahertz SAR echo signal obtained in step one;

[0007] Step three: taking the first derivative of the image entropy S of the terahertz SAR image obtained in step two with respect to the phase error, and making the first derivative of the image entropy S with respect to the phase error zero, to obtain a nonlinear equation to be solved;

[0008] Step four: solving the nonlinear equation in step three based on the Gauss-Newton method to obtain the final phase error estimation value without specific model constraints;

[0009] Step five: based on the phase error estimation value obtained in step four, constructing a compensation function to suppress the defocusing of the terahertz SAR image, and obtaining the final SAR imaging result.

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

[0011] The present application proposes a vibration model constraint-free terahertz SAR image autofocusing method. This method breaks out of the constraints of the traditional simple harmonic vibration model, starts from image entropy, estimates the phase error causing image defocusing in the echo through solving nonlinear equations, and thus processes the complex terahertz SAR image focusing problem. This method can flexibly cope with complex vibration situations and is not bound by specific vibration models, making it suitable for a wider range of imaging scenarios. In order to effectively solve the problem of solving nonlinear equations, the present application introduces the Gauss-Newton method. This method has high computational efficiency and good numerical stability, and can quickly converge to the optimal solution in the solving process, thus accurately estimating the phase error. By directly processing the phase error, the present application can effectively compensate for complex interference including platform vibration, platform speed variation, noise, etc., so that the phase error in the terahertz SAR echo signal is significantly corrected, and finally clear terahertz SAR imaging results are obtained.

[0012] For the terahertz SAR image focusing problem, the present application first constructs a terahertz SAR echo signal model containing phase error under the condition of no vibration model constraint. Based on this model, the terahertz SAR image autofocusing algorithm suitable for the condition of no vibration model constraint is further studied. Unlike traditional algorithms that rely on specific vibration models, this model has wider applicability and can handle more complex phase errors, including platform vibration, platform speed variation and noise, etc., which are key factors leading to image defocusing. Without relying on additional focusing steps, the autofocusing algorithm under the condition of no vibration model constraint can effectively process phase errors from multiple sources, thereby generating clearer imaging results. Since the algorithm proposed by the present application can process phase errors that do not depend on specific vibration models, it is not only suitable for common vibration models, but also can cope with more complex phase error interference, demonstrating its superior adaptability and robustness.

[0013] The core of the self-focusing algorithm is to solve the nonlinear equation, and the Gauss-Newton method is introduced to solve the nonlinear equation. The Gauss-Newton method has high calculation performance, good numerical stability and applicability in solving nonlinear equations, so that the algorithm has obvious advantages in solving phase error estimation problems. Through the method, the phase error can be quickly and accurately estimated, so that the terahertz SAR image is clearly focused, and the imaging quality and the robustness of the algorithm are effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 is a flowchart of the present application;

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

[0016] Figure 3 is the SAR imaging result obtained after image focusing under the condition of signal-to-noise ratio 10dB through the algorithm of the present application;

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

[0018] Figure 5 is the SAR imaging result obtained after image focusing under the condition of signal-to-noise ratio-10dB through the algorithm of the present application. DETAILED DESCRIPTION

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

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

[0021] Step two: based on the terahertz SAR echo signal obtained in step one, the image entropy of the terahertz SAR image is obtained;

[0022] Step three: the first derivative of the image entropy S of the terahertz SAR image obtained in step two with respect to the phase error is obtained, and the first derivative of the image entropy S with respect to the phase error is zero, to obtain a nonlinear equation to be solved;

[0023] Step four: the nonlinear equation in step three is solved based on the Gauss-Newton method, to obtain the final phase error estimation value not constrained by a specific model;

[0024] Step five: based on the phase error estimation value obtained in step four, construct a compensation function to suppress the defocus of the terahertz SAR image, and obtain the final clear SAR imaging result.

[0025] Specific implementation method two: the difference between this implementation method and the specific implementation method one is that: in step one, the terahertz SAR echo signal is obtained without vibration model constraint; the phase error causing image defocus is contained in the terahertz SAR echo signal, and the phase error is not constrained by a specific model;

[0026] The specific process is as follows:

[0027] Obtain the terahertz SAR echo signal;

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

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

[0030] The terahertz SAR echo signal x(n,m) after distance migration correction processing contains the phase error causing image defocus

[0031]

[0032] Generally, 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. In the present application, the phase error is a generalization of the factors causing the defocus of the terahertz SAR image, rather than being obtained by fitting a certain specific model to the phase error Therefore, the terahertz SAR echo signal model x(n,m) is not constrained by a specific model, and can be applied to more complex terahertz SAR imaging scenarios;

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

[0034]

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

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

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

[0038] σ is a complex amplitude of the echo signal; B is a signal bandwidth; r0 is an ideal minimum slant range between the terahertz SAR platform and the target; c is a light speed; is an ideal phase of the terahertz SAR echo; represents a phase error, not subject to a specific model; λ is a signal wavelength; r(m) is an ideal slant range between the terahertz SAR platform and the target; j is an imaginary unit, j 2 =-1.

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

[0040] The third embodiment is different from the first or second embodiment in that the expression of the ideal phase of the terahertz SAR echo is:

[0041]

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

[0043] The fourth embodiment is different from any one of the first to third embodiments in that the image entropy of the terahertz SAR image is obtained based on the terahertz SAR echo signal obtained in step one in step two; the specific process is as follows:

[0044] Step two one: azimuth compensation is performed on the terahertz SAR echo signal x(n, m) obtained in step one to obtain an azimuth-compensated signal, and phase error compensation is performed on the azimuth-compensated signal to obtain a phase error-compensated signal

[0045] Step two two: Fourier transform processing is performed on the phase error-compensated signal to obtain a terahertz SAR image I(n, k), as shown in formula (3):

[0046]

[0047] wherein, k is a Doppler frequency index; H1 is an azimuth compensation function; H2 is a phase error compensation function;

[0048] The expression of the azimuth compensation function H1 is:

[0049] H1=exp(-jπK a m 2 ) (4)

[0050] The expression of the phase error compensation function H2 is:

[0051]

[0052] wherein K a is the Doppler frequency;

[0053] Step two and three: based on the terahertz SAR image I(n, k), the image Tsallis entropy of the terahertz SAR image is obtained.

[0054] The other steps and parameters are the same as one of the first to third embodiments.

[0055] The fifth embodiment is different from one of the first to fourth embodiments in that: in the step two and three, 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] wherein q is the Tsallis entropy index.

[0058] The other steps and parameters are the same as one of the first to fourth embodiments.

[0059] The sixth embodiment is different from one of the first to fifth embodiments in that: in the step three, the first order derivative of the image entropy S of the terahertz SAR image obtained in the step two 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 zero, so as to obtain a nonlinear equation to be solved;

[0060] The specific process is:

[0061] When the image entropy S obtained in the step two is the minimum, the focused SAR imaging result is obtained.

[0062]

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

[0064] Formula (7) represents the process of the derivation of the image entropy with respect to the phase error, and the corresponding minimum point can be obtained by making it zero. 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 result with good focusing can be effectively obtained.

[0065] The other steps and parameters are the same as one of the first to fifth embodiments.

[0066] Specific implementation seven: different from one of the specific implementations one to six, the step four is based on the Gauss-Newton method to solve the nonlinear equation in step three, and an ultimate phase error estimation value not constrained by a specific model is obtained; the specific process is as follows:

[0067] Step four one: let the iteration number i = 1; set a termination condition threshold Q;

[0068] Set the initial phase error value

[0069] Step four two: based on the phase error Calculate the phase error obtained in the i-th iteration When the set termination condition threshold Q is met, the ultimate phase error estimation result not constrained by a specific model is obtained;

[0070] The specific process is as follows:

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

[0072]

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

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

[0075]

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

[0077]

[0078] Substitute the phase error obtained in the i-1-th iteration into formula (6), and the image entropy S i-1 obtained in the i-1-th iteration is obtained.

[0079] Substitute the phase error obtained in the i-th iteration into formula (6), and the image entropy S i;

[0080] If the image entropy S in the i-th iteration is i and the image entropy S in the (i-1)th iteration i-1 If the absolute value of the difference is greater than the termination condition threshold Q, then let i = i + 1 and continue to execute step four two until the image entropy S of the i-th iteration is obtained. i and the image entropy S in the (i-1)th iteration i-1 If the absolute value of the difference is less than or equal to the termination threshold Q, the image entropy is considered to have reached its minimum, and the final phase error estimation result, which is not constrained by a specific model, is obtained.

[0081] If the image entropy S in the i-th iteration is i and the image entropy S in the (i-1)th iteration i-1 If the absolute value of the difference is less than or equal to the termination threshold Q, the image entropy is considered to have reached its minimum, and the final phase error estimation result, which is not constrained by a specific model, is obtained.

[0082] The expression is:

[0083] S i -S i-1 |≤Q (11)

[0084] Among them, S i S is the image entropy obtained in the i-th iteration; i-1 Let be the image entropy obtained in the (i-1)th iteration.

[0085] The other steps and parameters are the same as those in specific implementation methods one through six.

[0086] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that: in step four-two, the phase error obtained from the (i-1)th iteration is... Substituting into formula (6), we obtain the image entropy S obtained in the (i-1)th iteration. i-1 The specific process is as follows:

[0087] The phase error obtained in the (i-1)th iteration Substituting into formula (5) The phase error compensation function H2 obtained in the (i-1)th iteration is calculated; the phase error compensation function H2 obtained in the (i-1)th iteration is substituted into formula (3) to calculate the terahertz SAR image I(n,k) obtained in the (i-1)th iteration; the terahertz SAR image I(n,k) obtained in the (i-1)th iteration is substituted into formula (6) to calculate the image entropy S obtained in the (i-1)th iteration. i-1 The expression is:

[0088]

[0089] Other steps and parameters are the same as those in embodiment one to eight.

[0090] Embodiment nine: different from one of embodiments one to eight is that: the phase error is substituted into formula (6) to obtain the image entropy S i of the i-th iteration.

[0091] The phase error of the i-th iteration is substituted into formula (5) to calculate the phase error compensation function H2 of the i-th iteration. The phase error compensation function H2 of the i-th iteration is substituted into formula (3) to calculate the terahertz SAR image I(n, k) of the i-th iteration. i The terahertz SAR image I(n, k) of the i-th iteration is substituted into formula (6) to calculate the image entropy S

[0092]

[0093] Other steps and parameters are the same as those in embodiment one to eight.

[0094] Embodiment ten: different from one of embodiments one to nine is 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, and a final clear SAR imaging result is obtained.

[0095] The specific process is as follows:

[0096] Step five one: based on the final phase error estimation value obtained in step four , a final phase error compensation function H final is constructed, as shown in formula (14).

[0097]

[0098] Step five two: through the phase error compensation function established in formula (14), the terahertz SAR echo signal is compensated, and 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 a final clear SAR imaging result I focus (n, k) can be obtained.

[0099]

[0100] Other steps and parameters are the same as Embodiment 1 to 9-1.

[0101] The beneficial effects of the present application are verified by the following examples:

[0102] Example 1:

[0103] Firstly, a terahertz SAR imaging system is constructed under the condition of signal-to-noise ratio 10dB, carrier frequency 220GHz and bandwidth 3GHz. The error model causing the defocusing of the terahertz SAR image in the simulation is not based on the traditional specific simple harmonic vibration model, so the effectiveness of the algorithm proposed in this paper under the condition of no specific vibration model constraint can be better proved in this case. Figure 2 The SAR imaging result without image focusing under the condition of signal-to-noise ratio 10dB is shown, and it can be seen that the image is seriously defocused and the point target cannot be distinguished. Figure 3 The SAR imaging result obtained after image focusing by the algorithm proposed in this application under the condition of 10dB is shown in FIG. 6, and the focusing effect of the imaging result is good and the point target is clear. In addition, Table 1 shows the Tsallis entropy of the image before and after image focusing. Therefore, by comparing Figure 2 and Figure 3 and Table 1, it can be proved that the terahertz SAR image self-focusing algorithm proposed in this application without vibration model constraint can well suppress the defocusing of the SAR image and obtain a clear and focused imaging result.

[0104] Table 1 SAR image entropy before and after image focusing under the condition of signal-to-noise ratio 10dB

[0105]

[0106] Example 2:

[0107] In this embodiment, a terahertz SAR imaging system is constructed under the condition of signal-to-noise ratio-10dB, carrier frequency 220GHz and bandwidth 3GHz. Similarly, the error model causing the defocusing of the SAR image in this simulation system is not based on the traditional simple harmonic vibration model, so the image focusing algorithm proposed in this application is proved to be without vibration model constraint through the simulation experiment without specific vibration model. Figure 4 and Figure 5 respectively show the SAR imaging results under the condition of-10dB. Among them, Figure 4 is the imaging result before image focusing, and Figure 5is the imaging result of the vibration model unconstrained terahertz SAR image self-focusing algorithm after processing. The image Tsallis entropy before and after image focusing is shown in Table 2. It can be compared that the image after processing by the terahertz SAR image self-focusing algorithm proposed in the application is clearer, the defocusing along the azimuth direction is effectively suppressed, and it is further proved that the algorithm proposed in the application is still effective in the terahertz SAR imaging scene without being based on a specific vibration model. It can be seen from the above experimental results that the vibration model unconstrained terahertz SAR image self-focusing algorithm proposed in the application is effective and feasible in the image defocusing suppression.

[0108] Table 2 SAR image entropy before and after image focusing under the condition of signal-to-noise ratio-10dB

[0109]

[0110] The application also has other various embodiments, and those skilled in the art can make various corresponding changes and modifications according to the application without departing from the spirit and essence of the application, but these corresponding changes and modifications should all belong to the protection scope of the claims attached to the application.

Claims

1. A vibration model free terahertz SAR image self-focusing method, characterized in that: The method specifically comprises the following steps: Step 1: obtaining a terahertz SAR echo signal; the terahertz SAR echo signal contains phase errors; Step 2: obtaining image entropy of a terahertz SAR image based on the terahertz SAR echo signal obtained in step 1; the specific process comprises the following steps: Step two: obtaining the THz SAR echo signal of the target from the THz SAR echo signal obtained in step one azimuth direction compensation is performed to obtain an azimuth direction compensated signal, and phase error compensation is performed on the azimuth direction compensated signal to obtain a phase error compensated signal is a discrete slow time, is a number of discrete slow times; is a discrete fast time, is a number of discrete fast times;​​​ Step two: phase error compensation Fourier transform processing is performed to obtain a terahertz SAR image As shown in formula ​ wherein, is the Doppler frequency exponent; is a unitless imaginary number, ; is an azimuth compensation function; is a phase error compensation function; Azimuthal compensation function The expression for the azimuthal compensation function is Phase error compensation function The expression is: wherein, is the Doppler frequency; denotes the phase error; is the ideal phase of the terahertz SAR echo; Step two three: based on terahertz SAR image , get the image Tsallis entropy of terahertz SAR image, as shown in formula : wherein, is the Tsallis entropy exponent; Step three: calculate the image entropy of the terahertz SAR image obtained in step two The first derivative of the phase error is calculated, and the image entropy is made The first derivative of the phase error is zero, and a nonlinear equation to be solved is obtained; Step 4: solving the nonlinear equation in step 3 based on a Gauss-Newton method to obtain a final phase error estimation value which is not constrained by a specific model; Step 5: constructing a compensation function based on the phase error estimation value obtained in step 4 to suppress defocus of the terahertz SAR image, and obtaining a final SAR imaging result.

2. The vibration-free model-constrained terahertz SAR image self-focusing method according to claim 1, characterized in that: In step 1, the terahertz SAR echo signal is obtained; the terahertz SAR echo signal contains phase errors; the specific process comprises the following steps: The terahertz SAR echo signal is obtained; The terahertz SAR echo signal is subjected to distance compression processing to obtain a terahertz SAR echo signal after distance compression processing; The distance-compressed terahertz SAR echo signal is subjected to range migration correction processing to obtain a range migration corrected terahertz SAR echo signal ; Distance migration corrected terahertz sar echo signal Including phase error ; Distance migration correction processed terahertz SAR echo signal The expression is: wherein, is a model of the terahertz SAR echo signal after range compression and range migration correction; is the complex amplitude of the echo signal; is the signal bandwidth; is the ideal shortest slant range between the terahertz SAR platform and the target; is the speed of light; is the signal wavelength; is the ideal slant range between the THz SAR platform and the target.

3. The vibrationless model constrained terahertz SAR image self-focusing method according to claim 2, characterized in that: Ideal phase of the terahertz sar echo The expression is: 。 4. The vibrationless model constrained terahertz SAR image self-focusing method according to claim 3, characterized in that: the image entropy of the terahertz SAR image obtained in step two in step three a first derivative with respect to the phase error is obtained, and the image entropy the first derivative with respect to the phase error is zero, obtaining a nonlinear equation to be solved; The specific process comprises the following steps: wherein is the first derivative of the entropy with respect to the phase error.

5. The vibrationless model constrained terahertz SAR image self-focusing method according to claim 4, characterized in that: In step 4, the nonlinear equation in step 3 is solved based on a Gauss-Newton method to obtain a final phase error estimation value which is not constrained by a specific model; The specific process comprises the following steps: Step four one: let the number of iterations ; Setting termination condition threshold ; Setting phase error initial value ; Step four two: based on phase error the phase error for the first iteration ; When the set termination condition threshold is met , the final phase error estimation result not constrained by a specific model is obtained ; the specific process is as follows: wherein is the phase error obtained at the th iteration; is the phase error obtained at the th iteration; denotes the first derivative of the entropy obtained in the kth iteration with respect to the phase error; denotes the second order derivative of the entropy obtained in the first iteration with respect to the phase error; upper index denotes the matrix transpose; upper index denotes the inverse of a matrix; denotes the multiplication sign; wherein the first the first derivative of the entropy with respect to the phase error is given by The first iteration of the entropy with respect to the phase error The second iteration of the entropy with respect to the phase error The expression for the second iteration of the entropy with respect to the phase error is: The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula ; If the absolute value of the difference between the image entropy of the first iteration and the image entropy of the second iteration is greater than a termination condition threshold , then let continue to perform step four two until the absolute value of the difference between the image entropy of the first iteration and the image entropy of the second iteration is less than or equal to the termination condition threshold , then consider that the image entropy reaches the minimum, and obtain the final phase error estimation result not constrained by a specific model . ​​​​​​​​ If the absolute value of the difference between the image entropy of the first iteration and the image entropy of the second iteration is less than or equal to a termination condition threshold , then the image entropy is considered to have reached a minimum, and a final, model-specific constraint-free phase error estimation result is obtained . ;​​​ The expression is as follows: wherein is the image entropy obtained at the th iteration; is the image entropy obtained at the th iteration.

6. The vibrationless model constrained terahertz SAR image self-focusing method according to claim 5, characterized in that: The step four two in the formula Phase error of the second iteration Substitute the formula In the formula, the first Image entropy of the second iteration The specific process is: The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the second iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the second iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the second iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the second iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the second iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the second iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the second iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the second iteration is substituted into the formula The expression is: 。 7. The vibrationless model constrained terahertz SAR image self-focusing method according to claim 6, characterized in that: The step four two will get the first Phase error of the second iteration Substitute the formula The first iteration, get the Image entropy of the second iteration The specific process is: The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula The phase error obtained in the first iteration is substituted into the formula 。 8. The vibrationless model constrained terahertz SAR image self-focusing method according to claim 7, characterized in that: In step 5, the compensation function is constructed based on the phase error estimation value obtained in step 4 to suppress defocus of the terahertz SAR image, and a final SAR imaging result is obtained; The specific process comprises the following steps: Step five: constructing a final phase error compensation function based on the estimate of the final phase error obtained in step four , constructing a final phase error compensation function as shown in equation ​ Step five two: the phase error compensation function established by formula The final SAR imaging result is obtained by compensating the terahertz SAR echo signal through the phase error compensation function established in step five one ; 。

Images