Large-rotation-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto prior
By establishing a unified representation model of generalized double Pareto priors and an iterative optimization method, the problem of reconstruction accuracy of ISAR images under complex conditions was solved, achieving high resolution and robust imaging results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-12
- Publication Date
- 2026-04-03
AI Technical Summary
Under complex observation conditions such as echo loss, low signal-to-noise ratio, and large rotation angle, existing technologies suffer from insufficient ISAR image reconstruction accuracy, degraded imaging performance, and difficulty in achieving high-resolution imaging.
A large-angle ISAR joint motion compensation and imaging method based on generalized double Pareto priors is adopted. By establishing a unified representation model, a probabilistic model is constructed by introducing generalized double Pareto priors, and iterative optimization is performed using variational inference algorithm and maximum contrast criterion. Translational and rotational parameters are jointly estimated to achieve high-resolution imaging.
It effectively solves the image defocusing problem caused by MTRC and range-space-varying phase errors, improves the reconstruction accuracy and imaging quality of ISAR images, is suitable for complex environments with echo defects and low signal-to-noise ratio, and achieves fast and accurate image reconstruction.
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Figure CN121784739A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radar remote sensing technology, specifically relating to a large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors. Background Technology
[0002] Inverse Synthetic Aperture Radar (ISAR) imaging technology can achieve high-resolution imaging of non-cooperative targets such as aircraft and satellites under all-weather, long-range conditions, and has significant application value in fields such as space situational awareness and target recognition. However, in real-world complex observation environments, such as those with echo defects, low signal-to-noise ratios, and large target angularities, traditional range-Doppler-based imaging methods often struggle to obtain well-focused images, leading to a severe degradation in imaging performance.
[0003] While some studies have attempted to use sparse reconstruction methods for ISAR imaging, the following shortcomings remain: 1. Most methods assume that the target translational component has been accurately compensated and do not consider the range-to-cell movement (MTRC) and range-space-varying phase errors caused by target rotation under large rotation angles, resulting in defocusing of the imaging results under large rotation angles; 2. Existing sparse reconstruction methods typically employ a step-by-step processing approach, treating translational compensation, rotational compensation, and image reconstruction as independent steps processed sequentially, which easily leads to error accumulation and affects the final imaging accuracy; 3. Existing sparse prior models have limited representational capabilities, making it difficult to achieve high-precision reconstruction of ISAR images under complex conditions such as echo loss and low signal-to-noise ratio.
[0004] Therefore, improving the reconstruction accuracy of ISAR images under complex observation conditions such as echo loss, low signal-to-noise ratio, and large rotation angle is a technical problem that urgently needs to be solved. Summary of the Invention
[0005] To address the challenge of improving the reconstruction accuracy of ISAR images under complex observation conditions such as echo loss, low signal-to-noise ratio, and large rotation angles, this invention provides a joint motion compensation and imaging method for large-rotation ISAR based on generalized dual Pareto priors. The technical problem solved by this invention is achieved through the following technical solution: This invention provides a method for joint motion compensation and imaging of large-angle ISAR based on generalized dual Pareto priors, including: S1: Based on the target's original echo matrix, a unified representation model is established. The unified representation model is used to jointly represent the translational parameters, rotational parameters, and the ISAR image to be reconstructed. S2: Based on the unified representation model, a generalized double Pareto prior is introduced to construct a probabilistic model; S3: Within the framework of the probabilistic model, iterative optimization is performed by alternately executing the following two sub-steps until the convergence condition is met: S3.1: Fix the current rotation and translation parameters, use the variational inference algorithm to solve the probability model, and obtain the updated ISAR image; S3.2: Fix the updated ISAR image, solve the first optimization objective function based on the maximum contrast criterion and the second optimization objective function based on the maximum likelihood estimation method to obtain the updated rotation parameters and translation parameters. The first optimization objective function is used to update the rotation parameters, and the second optimization objective function is used to update the translation parameters. S4: Output the target ISAR image obtained from the last iteration update, as the high-resolution imaging result after motion compensation.
[0006] In one embodiment of the present invention, the expression of the unified representation model is:
[0007] in, Represents the original echo matrix No. Column elements, Representing the translation matrix No. Column elements, Indicates the first The dictionary of directions of the column. This represents the ISAR image to be reconstructed. This refers to the phase correction dictionary, which is used to compensate for range-varying phase errors caused by target rotation. Distance dictionary No. Column elements, Noise matrix No. n Column elements, This indicates element-wise multiplication.
[0008] In one embodiment of the present invention, a probabilistic model is constructed based on a unified representation model and a generalized double Pareto prior is introduced, including: S2.1: Based on the echo matrix after translational compensation, establish the observation likelihood function. The expression for the observation likelihood function is:
[0009] in, This represents the echo matrix after translational compensation. express conjugate, and These represent the total number of sampling points in the azimuth and range directions, respectively. Represents the echo matrix after translational compensation No. Line 1 Column elements, For noise accuracy, Distance dictionary No. Column elements, Indicates the first The first column in the directional dictionary The elements of a row.
[0010] S2.2: Noise accuracy Let the gamma distribution be the prior distribution:
[0011] in, For noise accuracy The probability density function value, and All of these are hyperparameters. Indicates the gamma distribution; S2.3: Assume that all elements in the ISAR image to be reconstructed are independent of each other, where the first element is... Line 1 element It follows a complex Gaussian prior distribution with a mean of 0 and a variance equal to the pre-defined variance.
[0012] in, and The number of rows and columns of the ISAR image to be reconstructed. The variance is preset.
[0013] S2.4: Preset variance Let the exponential distribution be used as its prior distribution:
[0014] in, for The conditional probability density function, It is an exponential distribution function. For the rate parameter of the exponential distribution; S2.5: The rate parameter of the exponential distribution is set to a gamma distribution as its prior distribution:
[0015] in, For rate parameter The probability density function, All are hyperparameters; S2.6: Based on the observation likelihood function and all prior distributions, the probability model is obtained.
[0016] In one embodiment of the present invention, a variational inference algorithm is used to solve a probabilistic model to obtain an updated ISAR image, including: Transform the probability model into a one-dimensional probability model represented in the form of a one-dimensional vector; The variational posterior distributions of all unknown variables in the one-dimensional probabilistic model are constructed. The variational posterior distribution parameters of each unknown variable are iteratively updated by maximizing the lower bound of evidence of the one-dimensional probabilistic model until the convergence condition is met. The updated ISAR image is determined by the expected value of the variational posterior distribution of the ISAR image variables to be reconstructed.
[0017] In one embodiment of the present invention, when iteratively updating the variational posterior distribution of the ISAR image variables to be reconstructed, the Lipschitz lemma is introduced to scale the evidence lower bound, so that when updating the posterior covariance matrix and posterior expectation of the ISAR image variables to be reconstructed, the operation that originally required high-dimensional matrix inversion is transformed into the inversion of the diagonal matrix.
[0018] In one embodiment of the present invention, the first optimization objective function is expressed as:
[0019] in, For the updated rotation parameters, To the current rotation parameters The image expectation below, It is an L2 norm.
[0020] In one embodiment of the present invention, the second optimization objective function is expressed as follows:
[0021] in, The translational compensation matrix to be updated. To maximize the second optimization objective function , and These represent the total number of sampling points in the azimuth and range directions, respectively. For the guiding matrix m Line 1 n Column elements, To Take the conjugate operation. Original echo matrix No. m Line 1 n Column elements, Translational compensation matrix The Middle m Line 1 n The elements of the column.
[0022] In one embodiment of the present invention, the convergence condition is that the mean square root error between the ISAR images obtained from two adjacent iterations is less than the error threshold, or the number of iterations reaches the maximum number of iterations.
[0023] Another aspect of the present invention provides a storage medium storing a computer program for executing the steps of the large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors described in any of the above embodiments.
[0024] Another aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto prior as described in any of the above embodiments.
[0025] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention provides a large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors. It establishes a unified representation model for jointly characterizing translational parameters, rotational parameters, and high-resolution imaging. Then, it introduces generalized dual Pareto priors to construct a probabilistic model and solves the model using a sparse Bayesian learning method. Compared to existing technologies that ignore MTRC and range-space-varying phase errors caused by target rotation, this invention transforms motion compensation and ISAR imaging into a parameter estimation problem, effectively solving the image defocusing problem caused by MTRC and range-space-varying phase errors. Furthermore, it is applicable to complex environments with echo defects and low signal-to-noise ratios.
[0026] (2) This invention introduces a generalized double Pareto prior to construct a probabilistic model, achieving accurate sparse representation of ISAR images. Based on this, the probabilistic model is solved using a variational inference algorithm, and by scaling the variational lower bound, the computational complexity of inverting high-dimensional matrices is effectively reduced, thus achieving fast and accurate reconstruction of ISAR images. Compared with existing technologies that establish probabilistic models based on gamma-Gaussian priors, this invention can obtain stronger sparse representation capabilities, resulting in higher image reconstruction accuracy.
[0027] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0028] Figure 1This is a flowchart of a large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors provided in an embodiment of the present invention; Figure 2 This is a schematic diagram showing the comparison results of envelope alignment between the present invention and an existing fast imaging method based on minimum entropy envelope alignment and sparse Bayesian learning, under a signal-to-noise ratio of 5dB and an azimuth loss of 50%. Figure 3 This is a schematic diagram showing the imaging results of the present invention embodiment and the existing fast imaging method based on minimum entropy envelope alignment and sparse Bayesian learning under a signal-to-noise ratio of 5dB and an azimuth defect of 50%. Detailed Implementation
[0029] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following describes in detail, with reference to the accompanying drawings and specific embodiments, a large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto prior proposed in accordance with the present invention.
[0030] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.
[0031] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element.
[0032] This invention addresses the problem of improving the reconstruction accuracy of ISAR images under complex observation conditions such as echo loss, low signal-to-noise ratio, and large rotation angles. It proposes a joint motion compensation and imaging method for large-rotation ISAR based on generalized dual Pareto priors. Please refer to [link to relevant documentation]. Figure 1 The method includes the following steps: S1: Based on the target's original echo matrix, a unified representation model is established. This unified representation model is used to jointly represent the translational parameters, rotational parameters, and the ISAR image to be reconstructed.
[0033] It should be noted that in ISAR imaging, the complex motion of a target is typically decomposed into two basic motion components: translation and rotation. Translation refers to the overall translational motion of the target relative to the radar; that is, all scattering points on the target have the same motion vector. This motion causes a change in the target's position along the radar's line-of-sight. Translational parameters are used to describe the overall positional change of the target and compensate for range errors. Rotation refers to the rotational motion of the target around its own axis. This motion causes different scattering points on the target to have different velocities, which is the fundamental reason for generating Doppler frequencies and achieving azimuth resolution. Rotation parameters are used to describe the target's own rotation and compensate for azimuth errors and geometric distortions.
[0034] In an embodiment of the present invention, the expression for the unified representation model is:
[0035] in, Represents the original echo matrix No. Column elements, Representing the translation matrix No. Column elements, Indicates the first The dictionary of directions of the column. This represents the ISAR image to be reconstructed. This refers to the phase correction dictionary, which is used to compensate for range-varying phase errors caused by target rotation. Distance dictionary No. Column elements, Noise matrix No. n Column elements, This indicates element-wise multiplication.
[0036] Specifically, the representation of a location dictionary element is as follows:
[0037] in, and These are the indices for the azimuth and range directions, respectively. and These represent the total number of sampling points in the azimuth and range directions, respectively. This represents the total number of units in the azimuth direction. For azimuth unit index, It is the center frequency. , Frequency step size, It refers to bandwidth.
[0038] The expression for phase correction dictionary elements is:
[0039] in, This represents the rotational angular velocity, i.e., the rotational parameter. Indicates the pulse repetition period. At the speed of light, The distance is the total number of units. For distance cell index, It is an exponential function.
[0040] S2: Based on the unified representation model, a probabilistic model is constructed by introducing a generalized double Pareto prior.
[0041] In embodiments of the present invention, a probabilistic model is constructed based on a unified representation model and a generalized double Pareto prior is introduced, comprising: S2.1: Based on the echo matrix after translational compensation, establish the observation likelihood function. The expression of the observation likelihood function is as follows:
[0042] in, This represents the echo matrix after translational compensation. express conjugate, Represents the echo matrix after translational compensation No. Line 1 Column elements, For noise accuracy, Distance dictionary No. Column elements, Indicates the first The first column in the directional dictionary The elements of a row.
[0043] S2.2: Noise accuracy Let the gamma distribution be used as its prior distribution:
[0044] in, For noise accuracy The probability density function value, and All of these are hyperparameters. This represents the Gamma distribution.
[0045] S2.3: Assume that all elements in the ISAR image to be reconstructed are independent of each other, where the first element is... Line 1 element It follows a complex Gaussian prior distribution with a mean of 0 and a variance equal to the pre-defined variance.
[0046] in, and The number of rows and columns of the ISAR image to be reconstructed. The variance is preset.
[0047] S2.4: Preset variance Let the exponential distribution be used as its prior distribution:
[0048] in, for The conditional probability density function, It is an exponential distribution function. This is the rate parameter of the exponential distribution.
[0049] S2.5: The rate parameter of the exponential distribution is set to a gamma distribution as its prior distribution:
[0050] in, For rate parameter The probability density function, All of these are hyperparameters.
[0051] S2.6: Based on the observation likelihood function and all prior distributions, the probability model is obtained.
[0052] It is understandable that, under the above hierarchical prior form, variables The marginal probability density function is a generalized double Pareto (GDP) distribution.
[0053] S3: Within the framework of the probabilistic model, iterative optimization is performed by alternately executing the following two sub-steps (S3.1 and S3.2) until the convergence condition is met.
[0054] The convergence condition is that the mean square root error between two adjacent iterations of the ISAR image is less than the error threshold, or the number of iterations reaches the maximum number of iterations.
[0055] S3.1: Fix the current rotation and translation parameters, use the variational inference algorithm to solve the probability model, and obtain the updated ISAR image.
[0056] It should be noted that during the initial iteration, the rotation parameter is initialized to 0.01 rad / s, and the translation parameter is initialized to a vector with all elements being 0.01.
[0057] In embodiments of the present invention, a variational inference algorithm is used to solve the probabilistic model to obtain an updated ISAR image. This includes: converting the probabilistic model into a one-dimensional probabilistic model represented as a one-dimensional vector; constructing the variational posterior distributions of all unknown variables in the one-dimensional probabilistic model; and iteratively updating the variational posterior distribution parameters of each unknown variable by maximizing the lower bound of evidence in the one-dimensional probabilistic model until the convergence condition is met. The updated ISAR image is determined by the expected value of the variational posterior distribution of the ISAR image variables to be reconstructed.
[0058] Furthermore, when iteratively updating the variational posterior distribution of the ISAR image variables to be reconstructed, the Lipschitz lemma is introduced to scale the evidence lower bound, so that when updating the posterior covariance matrix and posterior expectation of the ISAR image variables to be reconstructed, the operation that originally required high-dimensional matrix inversion is transformed into the inversion of the diagonal matrix.
[0059] Specifically, rewriting the two-dimensional probability model into a one-dimensional vector form yields the following one-dimensional probability model:
[0060]
[0061]
[0062]
[0063]
[0064] in, To observe the echo signal, This means stacking the matrices column-wise into a single column vector. It is the identity matrix. For noise accuracy, , , , All of these are hyperparameters. For vectorized ISAR images, It is the variance vector. For A diagonal matrix with diagonal elements. The first in the ISAR image The variance of each pixel, For the first The variance parameter of each pixel. For the global observation matrix, .
[0065] in, Global observation matrix No. n Column elements, for 3D identity matrix for 3D identity matrix For Kronecker product.
[0066] Using a variational inference algorithm and ignoring the correlation between elements in the posterior distribution, the posterior distribution is solved to obtain:
[0067]
[0068]
[0069] in, for The expectation of the posterior distribution. , for The covariance matrix of the posterior distribution. All of these are posterior parameters of the Gamma distribution.
[0070] Solve The element From the posterior distribution, we obtain:
[0071]
[0072] in, Denotes the expectation of the posterior distribution. This represents the generalized inverse Gaussian distribution. Vectorized ISAR images The Each element.
[0073] Solve The element From the posterior distribution, we obtain:
[0074] Furthermore, by scaling the probabilistic model using Lipschitz's lemma, we obtain:
[0075] in, Image vector The posterior mean vector, Image vector The posterior variance vector, As an auxiliary variable, Image vector The Middle The posterior variance of each element.
[0076] make , ,get:
[0077]
[0078] At this point, the matrix that needs to be inverted... It has become a diagonal array.
[0079] in:
[0080]
[0081]
[0082]
[0083]
[0084] in, Represents the first-order Bessel function. This represents the 0th-order Bessel function.
[0085] Utilizing the properties of the Kronecker product, the update formula for the above parameters can be rewritten in two-dimensional matrix form:
[0086] in, They are respectively The matrix form of L is a Lipschitz lemma. The dimension representing an element that is all 1s is The matrix, , The largest eigenvalue of the matrix. .
[0087] in,
[0088]
[0089]
[0090]
[0091]
[0092]
[0093] in, This indicates element-wise multiplication. This indicates element-wise division.
[0094] S3.2: Fix the updated ISAR image, solve the first optimization objective function based on the maximum contrast criterion and the second optimization objective function based on the maximum likelihood estimation method to obtain the updated rotation parameters and translation parameters. The first optimization objective function is used to update the rotation parameters, and the second optimization objective function is used to update the translation parameters.
[0095] In an embodiment of the present invention, the first optimization objective function is expressed as:
[0096] in, The updated rotation parameters, i.e., the updated rotational angular velocity. To the current rotation parameters The image expectation below, It is an L2 norm.
[0097] Furthermore, the updated rotation parameters are obtained by solving the first optimization objective function using the Gauss-Newton method. For example, let... The objective function is solved using the Gauss-Newton method to obtain the updated rotation parameters:
[0098] in, It is the step size of the Gauss-Newton method. The rotation parameters obtained from the previous iteration .
[0099] The second optimization objective function is expressed as follows:
[0100] in, The translational compensation matrix to be updated. To maximize the second optimization objective function .
[0101] Furthermore, after simplifying the above equation and removing irrelevant terms from the second optimization objective function, we obtain:
[0102] in, For guiding matrix No. m Line 1 n Column elements, To Take the conjugate operation. Original echo matrix No. m Line 1 n Column elements, Translational compensation matrix The Middle m Line 1 n The elements of the column.
[0103] Furthermore, a traversal search is used to solve for the second optimization objective function, yielding the updated translational parameters. The traversal search can be understood as iterating through the search interval to find the translational parameters that maximize the second optimization objective function.
[0104] S4: Output the target ISAR image obtained from the last iteration update, as the high-resolution imaging result after motion compensation.
[0105] In summary, this invention provides a large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors. It establishes a unified representation model for jointly characterizing translational parameters, rotational parameters, and high-resolution imaging. Then, it introduces generalized dual Pareto priors to construct a probabilistic model, which is solved using a sparse Bayesian learning method. Compared to existing technologies that ignore MTRC and range-space-varying phase errors caused by target rotation, this invention transforms motion compensation and ISAR imaging into a parameter estimation problem, effectively solving the image defocusing problem caused by MTRC and range-space-varying phase errors. Furthermore, it is applicable to complex environments with missing echoes and low signal-to-noise ratios.
[0106] Furthermore, this invention introduces a generalized double Pareto prior to construct a probabilistic model, achieving accurate sparse representation of ISAR images. Based on this, a variational inference algorithm is used to solve the probabilistic model, and by scaling the variational lower bound, the computational complexity of inverting high-dimensional matrices is effectively reduced, enabling fast and accurate reconstruction of ISAR images. Compared to existing technologies that establish probabilistic models based on gamma-Gaussian priors, this invention achieves stronger sparse representation capabilities, resulting in higher image reconstruction accuracy.
[0107] In addition, this invention uses the maximum contrast criterion and maximum likelihood estimation to jointly update the target's rotation and translation parameters, and performs iterative optimization with the fast imaging algorithm, effectively avoiding the error accumulation problem and realizing the joint optimization of motion compensation and ISAR reconstruction.
[0108] To verify the technical effects of the method provided in the embodiments of the present invention, a simulation experiment is conducted for comparison. For details, please refer to [link / reference needed]. Figure 2 and Figure 3 .
[0109] in, Figure 2 This diagram illustrates the comparison of envelope alignment results between the present invention and existing fast imaging methods based on minimum entropy envelope alignment and sparse Bayesian learning, under conditions of a signal-to-noise ratio of 5 dB and 50% azimuth loss. Figure 3 This is a schematic diagram showing the imaging results of the present invention and an existing fast imaging method based on minimum entropy envelope alignment and sparse Bayesian learning under a signal-to-noise ratio of 5dB and an azimuth loss of 50%. Figure 2 It can be seen that under complex conditions of low signal-to-noise ratio and high defect rate, the envelope alignment results of existing methods exhibit significant jumps and misalignments, making it difficult to form a stable and continuous range envelope curve. This directly leads to incomplete motion compensation during subsequent imaging. In contrast, the envelope alignment results of the method of this invention are continuous and stable, with high alignment accuracy between pulses. This indicates that the method of this invention can effectively suppress interference caused by noise and defects, and accurately estimate and compensate for distance migration caused by translation. Figure 3 It can be seen that the existing methods result in severe defocusing, blurred target outlines, high background noise levels, and dispersed scattering point energy, making it difficult to identify the target structure. In contrast, the method of this invention produces imaging results with good focus, clear target outlines, clean backgrounds, and concentrated scattering point energy, accurately presenting the distribution of the target's key scattering centers. This verifies the significant advantages of the method of this invention in improving imaging quality and enhancing sparse characterization capabilities.
[0110] Furthermore, the comparison results of the translational parameter estimation error, rotational parameter estimation error, and image entropy between the present invention and the existing minimum entropy envelope alignment plus sparse Bayesian learning-based fast imaging method under a signal-to-noise ratio of 5dB and an azimuth loss of 50% are shown in Table 1 below: Table 1
[0111] Based on the performance index comparison in Table 1 above, it can be seen that the present invention is superior to existing methods in terms of translational parameter estimation error, rotational parameter estimation error, and image entropy. This further quantitatively proves the effectiveness of the present invention in achieving high-resolution and highly robust ISAR imaging in complex observation environments.
[0112] In the several embodiments provided by this invention, it should be understood that the apparatus and methods disclosed in this invention can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For example, the division of modules is merely a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed.
[0113] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated module can be implemented in hardware or in the form of hardware plus software functional modules.
[0114] Another embodiment of the present invention provides a storage medium storing a computer program for executing the steps of the large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors described in the above embodiments.
[0115] Another aspect of the present invention provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor invokes the computer program in the memory, it implements the steps of the large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors as described in the above embodiments. Specifically, the integrated modules implemented as software functional modules can be stored in a computer-readable storage medium. The software functional modules stored in the storage medium include several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0116] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.
Claims
1. A method for joint motion compensation and imaging of large-angle ISAR based on generalized dual Pareto priors, characterized in that, include: S1: Based on the target's original echo matrix, a unified representation model is established. This unified representation model is used to jointly represent translational parameters, rotational parameters, and the ISAR image to be reconstructed. S2: Based on the unified representation model, a generalized double Pareto prior is introduced to construct a probability model; S3: Within the framework of the probabilistic model, iterative optimization is performed by alternately executing the following two sub-steps until the convergence condition is met: S3.1: Fix the current rotation and translation parameters, and use the variational inference algorithm to solve the probability model to obtain the updated ISAR image; S3.2: Fix the updated ISAR image, solve the first optimization objective function based on the maximum contrast criterion and the second optimization objective function based on the maximum likelihood estimation method respectively, to obtain the updated rotation parameters and translation parameters. The first optimization objective function is used to update the rotation parameters, and the second optimization objective function is used to update the translation parameters. S4: Output the target ISAR image obtained from the last iteration update, as the high-resolution imaging result after motion compensation.
2. The method for large-angle ISAR joint motion compensation and imaging based on generalized dual Pareto priors according to claim 1, characterized in that, The expression for the unified representation model is: in, Represents the original echo matrix No. Column elements, Representing the translation matrix No. Column elements, Indicates the first The dictionary of directions of the column. This refers to the ISAR image to be reconstructed. This refers to a phase correction dictionary, which is used to compensate for range-space-varying phase errors caused by target rotation. Distance dictionary No. Column elements, Noise matrix No. n Column elements, This indicates element-wise multiplication.
3. The large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors according to claim 2, characterized in that, The method for constructing a probabilistic model based on the unified representation model, by introducing a generalized double Pareto prior, includes: S2.1: Based on the echo matrix after translational compensation, establish the observation likelihood function, the expression of which is: in, This represents the echo matrix after translational compensation. express conjugate, and These represent the total number of sampling points in the azimuth and range directions, respectively. Represents the echo matrix after translational compensation No. Line 1 Column elements, For noise accuracy, Distance dictionary No. Column elements, Indicates the first The first column in the directional dictionary The elements of a row. S2.2: Regarding the noise accuracy Let the gamma distribution be the prior distribution: in, For noise accuracy The probability density function value, and All of these are hyperparameters. Indicates the gamma distribution; S2.3: Assume that all elements in the ISAR image to be reconstructed are independent of each other, where the first element is... Line 1 element It follows a complex Gaussian prior distribution with a mean of 0 and a variance equal to the pre-defined variance. in, and The number of rows and columns of the ISAR image to be reconstructed. The preset variance is given. S2.4: For the preset variance Let the exponential distribution be used as its prior distribution: in, for The conditional probability density function, It is an exponential distribution function. For the rate parameter of the exponential distribution; S2.5: The rate parameter of the exponential distribution is set to a gamma distribution as its prior distribution: in, For rate parameter The probability density function, All are hyperparameters; S2.6: Based on the observed likelihood function and all prior distributions, the probability model is obtained.
4. The large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors according to claim 1, characterized in that, The step of solving the probability model using a variational inference algorithm to obtain the updated ISAR image includes: The probability model is converted into a one-dimensional probability model represented in the form of a one-dimensional vector. The variational posterior distributions of all unknown variables in the one-dimensional probability model are constructed. The variational posterior distribution parameters of each unknown variable are iteratively updated by maximizing the lower bound of evidence of the one-dimensional probability model until the convergence condition is met. The updated ISAR image is determined by the expected value of the variational posterior distribution of the ISAR image variables to be reconstructed.
5. The large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors according to claim 4, characterized in that, When iteratively updating the variational posterior distribution of the ISAR image variables to be reconstructed, the Lipschitz lemma is introduced to scale the evidence lower bound, so that when updating the posterior covariance matrix and posterior expectation of the ISAR image variables to be reconstructed, the operation that originally required high-dimensional matrix inversion is transformed into the inversion of the diagonal matrix.
6. The method for large-angle ISAR joint motion compensation and imaging based on generalized dual Pareto priors according to claim 1, characterized in that, The first optimization objective function is expressed as: in, For the updated rotation parameters, To the current rotation parameters The image expectation below, It is an L2 norm.
7. The large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors according to claim 1, characterized in that, The second optimization objective function is expressed as follows: in, The translational compensation matrix to be updated. To maximize the second optimization objective function , and These represent the total number of sampling points in the azimuth and range directions, respectively. For the guiding matrix m Line 1 n Column elements, To Take the conjugate operation. The original echo matrix No. m Line 1 n Column elements, Translational compensation matrix The Middle m Line 1 n The elements of the column.
8. The method for large-angle ISAR joint motion compensation and imaging based on generalized dual Pareto priors according to claim 1, characterized in that, The convergence condition is that the mean square root error between two adjacent iterations of the ISAR image is less than the error threshold, or the number of iterations reaches the maximum number of iterations.
9. A storage medium storing a computer program, characterized in that, The computer program is used to execute the steps of the large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors as described in any one of claims 1 to 8.
10. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and when the processor calls the computer program in the memory, it implements the steps of the large-angle ISAR joint motion compensation and imaging method based on generalized dual Pareto priors as described in any one of claims 1 to 8.