A target-driven adaptive super-resolution imaging method based on combinatorial norm

Abstract

This invention discloses a target-driven, combined norm adaptive super-resolution imaging method. First, a generalized combined regularized objective function is constructed by introducing a generalized sparse norm and a generalized total variation norm, integrating the advantages of multiple norms to enhance adaptability to different scenarios. Then, based on a generalized Gaussian distribution model, the sparse norm and total variation norm are modeled as functions of the target scattering coefficients. A hyperbolic fit to the inverse function of the generalized Gaussian ratio is used to achieve dynamic adaptive updating of the norm order with iterative reconstruction results. Finally, an iterative reweighting method is employed to transform the non-convex objective function into a weighted norm form, and a closed-form solution expression is derived. This method significantly reduces the workload of manual parameter tuning, effectively improves the algorithm's adaptability to different target scenarios and imaging quality, and solves the problem of poor scene adaptability caused by a fixed norm order in forward-looking radar super-resolution imaging.

Description

Technical Field

[0001] This invention belongs to the field of radar imaging technology, specifically relating to a target-driven combined norm adaptive super-resolution imaging method. Background Technology

[0002] Forward-looking radar imaging technology has wide applications in missions such as autonomous aircraft landing, precision airdrop of supplies, and ground attack. As a key indicator of imaging performance, azimuth resolution is closely related to radar aperture size: a larger aperture results in higher resolution, but also increases the required space resources, which are often difficult to meet on space-constrained airborne platforms. Existing synthetic aperture radar (SAR) struggles to achieve effective forward-looking imaging because the range line coincides with the equal Doppler line in the forward-looking region; while Doppler beam sharpening (DBS) technology is also significantly limited in its resolution improvement capabilities due to the symmetry of the forward-looking region and the reduction of the Doppler gradient.

[0003] In recent years, several new methods have been proposed for super-resolution imaging of scanning radar. The paper "Stoica, Petre, et al. 'New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data.' IEEE Transactions on Signal Processing 59.1 (2010): 35-47" introduces an iterative covariance estimation method. Experimental results show that this method has higher angular resolution than the iterative adaptive method (IAA). However, the iterative covariance estimation method cannot reconstruct the target contour when the target has obvious edge features. The paper "Zhang, Q., et al. 'Airborne Radar Super-Resolution Imaging Based on Fast Total Variation Method. Remote Sens. 2021, 13, 549.' 2021" successfully recovered the target's edge contour by using the total variation norm as a penalty term. However, its improvement in angular resolution is limited. The paper "Luo, Jiawei, et al. "A SPICE-TV Super-resolution Method for Scanning Radar." 2023 IEEE Radar Conference (RadarConf23). IEEE, 2023" proposes an iterative covariance estimation-total variation method that can maintain high resolution when recovering the target contour. However, the sparse norm and total variation norm of this method are both 1, which means that the fixed norm order cannot be adaptively adjusted according to the changes in the target scattering characteristics when facing different scenarios. This limits its generalization ability to complex environments, which is not conducive to hardware implementation and practical engineering applications in dynamic environments. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a target-driven adaptive super-resolution imaging method based on combinatorial norm, which solves the problem that the parameter values ​​of the sparse norm and total variation term in existing combinatorial regularization methods rely on manual adjustment, making it difficult to guarantee the global optimality of parameter combinations.

[0005] The technical solution adopted in this invention is: a target-driven combinatorial norm adaptive super-resolution imaging method, the specific steps of which are as follows:

[0006] Step 1: Constructing the airborne platform's geometric configuration and historical distance;

[0007] radar platform at speed It moves forward and emits electromagnetic wave signals, while the antenna moves at an angular velocity. The platform scans within the forward-looking imaging area and simultaneously acquires echo information as it moves.

[0008] Then, a geometric motion model of the forward-looking scanning radar is constructed, and the aircraft's flight altitude is set as follows: It moves along the Y-axis at a velocity of v, and the radar beam scans counterclockwise with an angular velocity of v. The elevation angle of the beam is The plane is The object is located at point A at a given time. Suppose there is a target P in space... At that moment, the beam center is located at a distance of ____ from point A. The horizontal azimuth is The spatial azimuth is From geometric relations we get .

[0009] Step 2: Constructing the scanning radar echo convolution model;

[0010] Assume the radar transmits a linear frequency modulated signal. The expression is as follows:

[0011] (1);

[0012] in, Represents a distance-to-time variable. This represents the pulse width of a linear frequency modulated signal. Indicates the carrier frequency. Indicates the frequency modulation slope. The window function representing the distance to the time domain is expressed as follows:

[0013] (2);

[0014] For target P, the echo signal after down-conversion is: The expression is as follows:

[0015] (3);

[0016] in, Represents the target scattering coefficient. This represents the antenna pattern modulation function. This represents the azimuth-time variable. Indicates echo delay, express The instantaneous distance of the target relative to the radar at any given moment. It represents the speed of light.

[0017] Then, pulse compression is performed on the echo signal, as shown in the following expression:

[0018] (4);

[0019] in, This represents the echo signal after pulse compression. Let B represent the range pulse compression response function, and let B represent the transmit signal bandwidth.

[0020] For a single point target, range migration occurs if the range migration exceeds one range cell within one beam dwell time. The expression for the range migration determination condition is as follows:

[0021] (5);

[0022] in, Indicates the antenna's beamwidth. Represents the range-resolved unit. Indicates the distance sampling rate. This indicates whether the distance migration exceeds one distance unit. This indicates the magnitude of the target's radial velocity relative to the radar.

[0023] Then, range migration correction is performed in the frequency domain, and in the time domain, it is corrected by multiplying by the corresponding phase compensation factor in the frequency domain; then, based on the approximate range history expression... The target distance migration is expressed as follows in the time dimension:

[0024] (6);

[0025] in, Indicates the change in distance. This indicates the change in echo delay.

[0026] Frequency domain phase compensation factor The expression is as follows:

[0027] (7);

[0028] After range migration correction, the echo signal is discretized and represented in matrix operation form, as shown in the following expression:

[0029] (8);

[0030] in, Indicates echo, Represents the set of complex numbers. This indicates the number of samples for the azimuth echo. This represents the scattering coefficient of the target. Indicates additive noise. The antenna radiation pattern function is used in modeling, ignoring echoes during beam entry and exit from the scene. A truncated antenna radiation pattern matrix is ​​used, and its precise expression is as follows:

[0031] (9);

[0032] Where, vector The sampling sequence representing the antenna radiation pattern. This indicates the antenna pattern in the azimuth direction. The sampling angle is determined by the pulse repetition frequency, beamwidth, and antenna scanning speed.

[0033] Step 3: Constructing the generalized combinatorial norm objective function;

[0034] First, a generalized sparse norm is selected. As a sparse penalty term, for Its norm expression is as follows:

[0035] (10);

[0036] in, Let represent the norm value of the generalized sparse norm, and , express Lidi Each component.

[0037] Based on the radar echo model established in step two, and introducing the generalized sparse norm and the generalized total variation norm, the objective function is then... The expression is as follows:

[0038] (11);

[0039] in, The regularization parameter represents the generalized sparse norm. The regularization parameter represents the norm of the generalized total variation. Denotes the norm value of the generalized total variation norm. This represents the gradient operator.

[0040] Step 4: Constructing the relationship between the target reflection coefficient and the norm function;

[0041] First, the SPICE algorithm is introduced, and the regularization parameter is replaced by a weighted matrix of regularization parameters. Then, assuming the variance of the noise is consistent, the SPICE and LASSO problems are equivalent, and equation (11) can be rewritten as follows:

[0042] (12);

[0043] Among them, the weighting matrix Satisfy the following expression:

[0044] (13);

[0045] in, Indicates the first The system response vector corresponding to each distance unit.

[0046] Another method for estimating parameters based on the target scattering coefficient is proposed. The norm is modeled as a function of the target scattering coefficient, and equation (12) is rewritten as follows:

[0047] (14);

[0048] in, and Represents the target scattering coefficient The norm parameter of the function mapping. Then equation (14) can be further written as the following expression:

[0049] (15);

[0050] Again To estimate the probability density function of the target scattering coefficients, we use the generalized Gaussian distribution as the prior probability model.

[0051] (16);

[0052] in, Indicates the scale parameter. This represents the standard gamma function. Represents the scattering coefficient The specific value inside, This represents the mean of the data. Scale parameter. The specific expression is as follows:

[0053] (17);

[0054] in, Represents variance. First-order absolute central moment of the generalized Gaussian distribution. With the second-order absolute central moment The expressions are as follows:

[0055] (18);

[0056] Step 5: Adaptive estimation of sparse norm based on iterative reconstruction;

[0057] The scaling parameter is eliminated by comparing the first and second absolute central moments of the generalized Gaussian distribution. And the generalized Gaussian ratio function is obtained. The expression is as follows:

[0058] (19);

[0059] According to equation (19), the norm The value of is related to the first and second absolute central moments of the generalized Gaussian distribution. This is achieved by analyzing the function... By inversely solving the relation, we obtain the norm. The estimation expression is as follows:

[0060] (20);

[0061] Then, the inverse function of the generalized Gaussian ratio function is fitted using a hyperbolic function, and the norm is indirectly obtained by calculating the output value of this hyperbolic function. If the estimate is obtained, then equation (20) can be rewritten as the following expression:

[0062] (twenty one);

[0063] Then, the target scattering coefficients obtained from each iteration of reconstruction are used to calculate the corresponding moment estimate, as shown in the following expression:

[0064] (twenty two);

[0065] in, express Lidi The component is the target scattering coefficient obtained in the current iteration. Then equation (21) can be rewritten as follows:

[0066] (twenty three);

[0067] Step 6: Adaptive estimation of total variation norm based on iterative reconstruction;

[0068] Similarly, for The estimate and the Similar to the estimation, the gradient information of the target scene is obtained through the first-order difference operator. The moment estimation expression is obtained as follows:

[0069] (twenty four);

[0070] in, The first term in the gradient field vector represents the first term. Each component. express The first moment, It represents the second moment.

[0071] Then, the inverse Gaussian ratio function is obtained. The estimated value is expressed as follows:

[0072] (25);

[0073] Similarly, by fitting the inverse function of the generalized Gaussian ratio function with a hyperbolic function, and by calculating the output value of this hyperbolic function, the norm can be indirectly obtained. If the estimate is obtained, then equation (25) can be rewritten as the following expression:

[0074] (26);

[0075] Step 7: Iterative reweighting solution;

[0076] The iterative reweighting method is used to solve equation (15). First, according to the definition of norm, we set... The expression is then obtained as follows:

[0077] (27);

[0078] Then, for the same distance unit, set... , ,and satisfy , satisfy Based on equation (27), the expression is as follows:

[0079] (28);

[0080] in, It is a vector The One portion, It is a vector The Each component. Based on the principle of norm equivalence, a diagonal weighted matrix is ​​introduced. and ,Will and Norm to weighted The norm is expressed in the following form:

[0081] (29);

[0082] in, and Both are diagonal matrices, and their diagonal elements are respectively and .

[0083] Then, from equation (29), we obtain the following expression:

[0084] (30);

[0085] in, This indicates the introduction of a small positive number.

[0086] Based on the derivation, equation (15) can be rewritten as follows:

[0087] (31);

[0088] The solution expression for equation (31) is obtained by differentiation as follows:

[0089] (32);

[0090] in, This indicates the conjugate transpose operation.

[0091] Finally, the iterative reweighting algorithm is used to solve the problem, and the pseudocode expression of the solution algorithm is as follows:

[0092] (33);

[0093] in, This represents the initial solution. and These represent the functions used to control sparsity regularization. With gradient sparsity regularization The initial shape parameters, The first absolute moment of the echo, The second moment of the echo, and These represent the first and second moments of the gradient field calculated after taking the gradient with respect to the echo, respectively, and are used to initialize the shape parameters of the gradient regularization. , This indicates the maximum number of iterations for the algorithm.

[0094] Through iterative iteration, the objective function is optimized and solved, ultimately achieving super-resolution reconstruction of the extended objective.

[0095] The beneficial effects of this invention are as follows: First, the method of this invention introduces a generalized sparse norm and a generalized total variation norm to construct a generalized combined regularization objective function, integrating the advantages of multiple norms to enhance adaptability to different scenarios. Then, based on a generalized Gaussian distribution model, the sparse norm and the total variation norm are modeled as functions of the target scattering coefficients. A hyperbolic fit is used to the inverse function of the generalized Gaussian ratio to achieve dynamic adaptive updating of the norm order with the iterative reconstruction results. Finally, an iterative reweighting method is used to transform the non-convex objective function into a weighted norm form, and a closed-form solution expression is derived. This invention significantly reduces the workload of manual parameter tuning, effectively improves the algorithm's adaptability to different target scenarios and imaging quality, and solves the problem of poor scene adaptability caused by a fixed norm order in forward-looking super-resolution radar imaging. Compared with existing extended target super-resolution methods, this invention combines the generalized sparse norm and the generalized total variation norm into a combined regularization term, effectively maintaining the target edge contour while improving resolution, thus achieving superior reconstruction quality. Furthermore, the method of the present invention achieves adaptive selection of the norm by estimating the norm of the target scattering coefficient, thus avoiding the problem that the resolution improvement is limited by the artificial determination of the norm in existing regularization methods. Attached Figure Description

[0096] Figure 1 This is a flowchart of a target-driven combined norm adaptive super-resolution imaging method according to the present invention.

[0097] Figure 2 This is a geometric model diagram of forward-looking super-resolution imaging in an embodiment of the present invention.

[0098] Figure 3 This is a comparison diagram of the point target imaging results of various methods in the embodiments of the present invention.

[0099] Figure 4 This is a comparison diagram of the imaging results of regular surface targets using various methods in the embodiments of the present invention.

[0100] Figure 5 This is a comparison diagram of the imaging results of irregular surface targets by various methods in the embodiments of the present invention. Detailed Implementation

[0101] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments. This embodiment uses simulation experiments to demonstrate the effectiveness of the method of the present invention. All steps and conclusions of the method of the present invention have been verified to be correct on the Matlab2019b simulation platform.

[0102] like Figure 1 The flowchart of a target-driven combined norm adaptive super-resolution imaging method of the present invention is shown below, and the specific steps are as follows:

[0103] Step 1: Constructing the airborne platform's geometric configuration and historical distance;

[0104] The radar platform moves forward at velocity v and emits electromagnetic wave signals, while the antenna moves at an angular velocity v. Scanning is performed within the forward-looking imaging region, and echo information is acquired synchronously as the platform moves. Because the relative distance between the platform and the target changes continuously over time, the target signal, originally located in the same distance cell, is dispersed into multiple distance cells in the echo. Therefore, it is necessary to study the variation of the distance history between the moving platform and the target with velocity and time to analyze the data distribution characteristics of its echo in the range and azimuth dimensions.

[0105] The geometric motion model of the forward-looking scanning radar in this embodiment is as follows: Figure 2 As shown, the aircraft is flying at an altitude of It moves along the Y-axis at a velocity of v, and the radar beam scans counterclockwise with an angular velocity of v. The elevation angle of the beam is The plane is The object is located at point A at a given time. Suppose there is a target P in space... At that moment, the beam center is located at a distance of ____ from point A. The horizontal azimuth is The spatial azimuth is From geometric relations we get .

[0106] Step 2: Constructing the scanning radar echo convolution model;

[0107] Assume the radar transmits a linear frequency modulated signal. The expression is as follows:

[0108] (1);

[0109] in, Represents a distance-to-time variable. This represents the pulse width of a linear frequency modulated signal. Indicates the carrier frequency. Indicates the frequency modulation slope. The window function representing the distance to the time domain is expressed as follows:

[0110] (2);

[0111] For target P, the echo signal after down-conversion is: The expression is as follows:

[0112] (3);

[0113] in, Represents the target scattering coefficient. This represents the antenna pattern modulation function. This represents the azimuth-time variable. Indicates echo delay, express The instantaneous distance of the target relative to the radar at any given moment. It represents the speed of light.

[0114] Then, pulse compression is performed on the echo signal, as shown in the following expression:

[0115] (4);

[0116] in, This represents the echo signal after pulse compression. Let B represent the range pulse compression response function, and let B represent the transmit signal bandwidth.

[0117] For a single point target, range migration occurs if the range migration exceeds one range cell within one beam dwell time (the key criterion for determining whether range migration has occurred is whether the range migration exceeds one range cell within one beam dwell time). The expression for the range migration determination condition is as follows:

[0118] (5);

[0119] in, Indicates the antenna's beamwidth. Represents the range-resolved unit. Indicates the distance sampling rate. This indicates whether the distance migration exceeds one distance unit. This indicates the magnitude of the target's radial velocity relative to the radar.

[0120] Since range migration often manifests as a time offset of non-integer range units in the data domain, range migration correction (RWC) is typically performed in the frequency domain. The signal shift in the time domain is reflected as a linear phase change in the frequency domain, which can be corrected by multiplying by a corresponding phase compensation factor in the frequency domain. Therefore, based on the approximate range history expression... The target distance migration is expressed as follows in the time dimension:

[0121] (6);

[0122] in, Indicates the change in distance. This indicates the change in echo delay.

[0123] Frequency domain phase compensation factor The expression is as follows:

[0124] (7);

[0125] After range migration correction, the echo signal is discretized and represented in matrix operation form, as shown in the following expression:

[0126] (8);

[0127] in, Indicates echo, Represents the set of complex numbers. This indicates the number of samples for the azimuth echo. This represents the scattering coefficient of the target. Indicates additive noise. The antenna pattern function is represented by the antenna pattern matrix. In this embodiment, the echo during the beam's entry into and exit from the scene is ignored during modeling, and a truncated form of the antenna pattern matrix is ​​used. Its accurate expression is as follows:

[0128] (9);

[0129] Where, vector The sampling sequence representing the antenna radiation pattern. This indicates the antenna pattern in the azimuth direction. The sampling angle is determined by the pulse repetition frequency, beamwidth, and antenna scanning speed.

[0130] Step 3: Constructing the generalized combinatorial norm objective function;

[0131] First, a generalized sparse norm is selected. As a sparse penalty term, for Its norm expression is as follows:

[0132] (10);

[0133] in, Let represent the norm value of the generalized sparse norm, and , express Lidi Each component.

[0134] Based on the radar echo model established in step two, and introducing the generalized sparse norm and the generalized total variation norm, the objective function is then... The expression is as follows:

[0135] (11);

[0136] in, The regularization parameter represents the generalized sparse norm. The regularization parameter represents the norm of the generalized total variation. Denotes the norm value of the generalized total variation norm. This represents the gradient operator.

[0137] In summary, the objective function constructed by equation (11) employs a combined regularization strategy, which can simultaneously integrate the advantages of two norms, thereby achieving performance superior to a single regularization method. Furthermore, by adjusting the order of the regularization norm... and This method can flexibly adapt to the characteristics of different target scenes, significantly enhancing its adaptability to complex imaging environments.

[0138] Step 4: Constructing the relationship between the target reflection coefficient and the norm function;

[0139] As can be seen from equation (11), solving the objective function requires manually tuning four parameters, namely the sparse regularization parameter. Total variation regularization parameter sparse norm and total variation norm To reduce the number of parameters selected, the SPICE algorithm is first introduced, and the regularization parameters are replaced by a weighted matrix of regularization parameters from this algorithm. This avoids manually adjusting the parameter; if the variance of the noise is set to be consistent, then the SPICE and LASSO problems are equivalent, and equation (11) can be rewritten as the following expression:

[0140] (12);

[0141] Among them, the weighting matrix Satisfy the following expression:

[0142] (13);

[0143] in, Indicates the first The system response vector corresponding to each distance unit.

[0144] Another method for estimating parameters based on the target scattering coefficient is proposed. The norm is modeled as a function of the target scattering coefficient, and equation (12) is rewritten as follows:

[0145] (14);

[0146] in, and Represents the target scattering coefficient The norm parameter of the function mapping. Then equation (14) can be further written as the following expression:

[0147] (15);

[0148] Again Estimation shows that in forward-looking super-resolution radar imaging, the target of interest typically exhibits a certain degree of sparsity in the observed scene. Considering the non-Gaussian nature of the statistical distribution of the scattering coefficients of such targets, a generalized Gaussian distribution is chosen as its prior probability model. The probability density function expression for the target scattering coefficients is then as follows:

[0149] (16);

[0150] in, Indicates the scale parameter. This represents the standard gamma function. Represents the scattering coefficient The specific value inside, This represents the mean of the data. Scale parameter. The specific expression is as follows:

[0151] (17);

[0152] in, Represents variance. First-order absolute central moment of the generalized Gaussian distribution. With the second-order absolute central moment The expressions are as follows:

[0153] (18);

[0154] Step 5: Adaptive estimation of sparse norm based on iterative reconstruction;

[0155] The scaling parameter is eliminated by comparing the first and second absolute central moments of the generalized Gaussian distribution. And the generalized Gaussian ratio function is obtained. The expression is as follows:

[0156] (19);

[0157] According to equation (19), the norm The value of is related to the first and second absolute central moments of the generalized Gaussian distribution. This is achieved by analyzing the function... By inversely solving the relation, we obtain the norm. The estimation expression is as follows:

[0158] (20);

[0159] However, since the inverse function of the gamma function is complex and difficult to calculate directly, the conventional approach is to use a lookup table of generalized Gaussian ratio functions. This method is not only inefficient but also cumbersome, making it difficult to directly obtain the norm from the above formula. The value of is determined by the hyperbolic function. Therefore, this embodiment uses a hyperbolic function to fit the inverse function of the generalized Gaussian ratio function, and indirectly obtains the norm by calculating the output value of this hyperbolic function. If the estimate is obtained, then equation (20) can be rewritten as the following expression:

[0160] (twenty one);

[0161] This method not only boasts high computational accuracy but also significantly outperforms the table lookup approach. In this case, only the first and second moment estimates of the data are needed to directly calculate the norm. In forward-looking super-resolution radar imaging, the corresponding moment estimate is calculated using the target scattering coefficients obtained from each iteration of reconstruction. The specific expression is as follows:

[0162] (twenty two);

[0163] in, express Lidi The component is the target scattering coefficient obtained in the current iteration. Then equation (21) can be rewritten as follows:

[0164] (twenty three);

[0165] Step 6: Adaptive estimation of total variation norm based on iterative reconstruction;

[0166] Similarly, for The estimate and the Similar to the estimation, the gradient information of the target scene is obtained through the first-order difference operator. The moment estimation expression is obtained as follows:

[0167] (twenty four);

[0168] in, The first term in the gradient field vector represents the first term. Each component. express The first moment, It represents the second moment.

[0169] Then, the inverse Gaussian ratio function is obtained. The estimated value is expressed as follows:

[0170] (25);

[0171] Similarly, by fitting the inverse function of the generalized Gaussian ratio function with a hyperbolic function, and by calculating the output value of this hyperbolic function, the norm can be indirectly obtained. If the estimate is obtained, then equation (25) can be rewritten as the following expression:

[0172] (26);

[0173] Thus far, norm and With target scattering coefficient The functional relationship between them has been established as shown in equations (23) and (26). The two will be obtained with each iteration. Adaptive adjustment enables dynamic adaptive updating of the model's regularization norm.

[0174] Step 7: Iterative reweighting solution;

[0175] The objective function defined in equation (15) contains non-convex and non-differentiable norm terms. To effectively solve this optimization problem, this embodiment employs an iterative reweighting method. This method is based on the principle of norm equivalence and introduces a series of weights... Norm to approximate the original objective function and Norms are used to make non-convex terms solvable. First, according to the definition of a norm, we set... The expression is then obtained as follows:

[0176] (27);

[0177] Then, for the same distance unit, set... , ,and satisfy , satisfy Based on equation (27), the expression is as follows:

[0178] (28);

[0179] in, It is a vector The One portion, It is a vector The Each component. Based on the principle of norm equivalence, a diagonal weighted matrix is ​​introduced. and ,Will and Norm to weighted The norm is expressed in the following form:

[0180] (29);

[0181] in, and Both are diagonal matrices, and their diagonal elements are respectively and .

[0182] Then, from equation (29), we obtain the following expression:

[0183] (30);

[0184] in, This indicates the introduction of a small positive number to avoid zero values ​​during the iteration process, which would result in no solution.

[0185] Based on the derivation, equation (15) can be rewritten as follows:

[0186] (31);

[0187] In equation (15), all non-convex and non-differentiable norm terms in the objective function are rewritten as differentiable terms. The norm is then used to obtain the solution expression of equation (31) by differentiation, as follows:

[0188] (32);

[0189] in, This indicates the conjugate transpose operation.

[0190] Finally, the iterative reweighting algorithm is used to solve the problem, and the pseudocode expression of the solution algorithm is as follows:

[0191] (33);

[0192] in, This represents the initial solution, which is represented by a matrix containing data fidelity terms. as well as The linear least squares closed-form solution can be directly calculated. and These represent the functions used to control sparse regularization. Gradient sparsity regularization The initial shape parameters are respectively determined by... The first-order statistic and the second-order statistic determine this, among which It is the first absolute moment of the echo. It is the second moment of the echo, and similarly, and These are the first and second moments of the gradient field calculated after taking the gradient of the echo, used to initialize the shape parameters of the gradient regularization. ,and It represents the maximum number of iterations of the algorithm.

[0193] Through iterative iteration, the objective function is optimized and solved, ultimately achieving super-resolution reconstruction of the extended objective.

[0194] This embodiment further verifies and compares with existing methods to demonstrate the effectiveness of the method of the present invention.

[0195] like Figure 3 As shown, Figure 3 The simulation results for point targets using various methods are shown below. The original scene for the scanning radar point target simulation is as follows: Figure 3 As shown in (a), the radar system parameters are specifically set as follows: beamwidth 3°, scanning range -10°~10°, scanning speed 60° / s, and PRF 1000 Hz. Figure 3 (a) shows two targets with identical amplitude and edge characteristics, located at -1° and 1° respectively. After adding 20dB of noise, the echoes are as follows: Figure 3 As shown in (b), because the beamwidth is greater than the distance between the two targets, aliasing occurs in the echoes, making it impossible to distinguish the two targets. In the case of 20 iterations, Figure 3 (c)-(h) show the simulated imaging results of point targets in 10 experiments using different super-resolution methods. Figure 3 (c) is The imaging results of the method show that it can successfully separate two targets, but it cannot recover the outline of the targets. Figure 3 (d) is The imaging results of this method show that it cannot separate the two targets and cannot recover the target contours, exhibiting severe sidelobes. Figure 3 (e) shows the imaging results of the TV method. It can be seen that although the method can recover the edge characteristics of the target well, the target is basically inseparable in the 10 test results, and there are also serious side lobes. Figure 3 (f) is The imaging results of the -TV method, in 10 experiments, were very unstable compared to the previous three methods, although the method could successfully distinguish the target and recover the target outline. Figure 3 (g) is The imaging results of the -TV method show that although it can recover some of the target's outline, it cannot successfully separate two targets and has some side lobes. Figure 3 (h) shows the imaging results of the method of the present invention. It can be seen that the method of the present invention can not only successfully distinguish two targets and restore the contours of the targets at the same time, but also the imaging results are relatively stable.

[0196] like Figure 4 As shown, Figure 4 The simulation results for regular surface targets using various methods are shown below. The original scene for simulating regular surface targets using scanning radar is as follows: Figure 4 As shown in (a), the radar system parameters are set as follows: beamwidth 3°, scanning range -10° to 10°, scanning speed 60° / s, PRF 1000 Hz, carrier frequency 10 GHz, bandwidth 200 MHz. Two adjacent extended targets and two adjacent sparse targets are set in the simulation scenario, as shown... Figure 4 As shown in (a). After adding 20 dB of noise, the echo is as follows: Figure 4 As shown in (b), because the beamwidth is greater than the distance between the two targets, aliasing occurs in the echoes, making it impossible to distinguish between the two extended targets and the two sparse targets. Similar to the point target simulation, after 20 iterations... Figure 4 (c)-(h) show the simulation imaging results of regular surface targets using different super-resolution methods. Figure 4 (c) is The imaging results of the method show that although it can recover the two sparse targets above with high resolution, it cannot recover the outline of the extended target below. Figure 4 (d) is The imaging results of this method show that it not only has low resolution and cannot recover the contour of the target, but also has severe side lobes. Figure 4 (e) shows the imaging results of the TV method. It can be seen that although the method can recover the edge characteristics of the extended target well, the resolution of the sparse target is very low and there are also side lobes. Figure 4 (f) is Compared to the previous three methods, the TV method can recover the target outline while successfully distinguishing the target, but the recovery of the expanded target outline is not accurate. Figure 4 (g) is The imaging results of the -TV method show that although it can recover some of the target's outline, the resolution is very low and there are some side lobes. Figure 4 (h) shows the imaging results of the method of the present invention. It can be seen that the method of the present invention can not only successfully distinguish two sparse targets and recover the outline of the extended target, but its extended target outline recovery results are also better than other methods.

[0197] Figure 5 The simulation results for irregular surface targets by various methods are shown below. The original scene of the scanning radar simulation of irregular surface targets is as follows: Figure 5As shown in (a), the radar system parameters are set as follows: beamwidth 3°, scanning range -10° to 10°, scanning speed 60° / s, PRF 1000 Hz, carrier frequency 10 GHz, bandwidth 200 MHz. The irregular extended target constructed in this embodiment is as follows. Figure 5 As shown in (a), a ship is located to the right of one of the islands. The corresponding real-beam echo results are as follows. Figure 5 As shown in (b), due to the influence of antenna pattern modulation, the scale information of islands and ships cannot be directly identified from the echo. Similar to the previous simulation, after 20 iterations... Figure 5 (c)-(h) show the simulated imaging results of irregular surface targets using different super-resolution methods. For ease of comparison, a white dashed line matching the island edge contour has been added to the imaging results of each method. It can be seen that... method( Figure 5 (d) TV method ( Figure 5 (e) and -TV method ( Figure 5 (g) Due to the poor resolution, the restoration effect of the island's edge outline is quite different from that of the white dashed line. method( Figure 5 (c) Although the resolution is significantly improved, the outline on the right side is severely damaged, and the outline of the island cannot be recovered. -TV method ( Figure 5 (f) compared to The previous method restored the island's outline more completely, but the outline on the right side was still damaged. The method of this invention, while maintaining higher resolution, restores the island's outline more completely than the previous method.

[0198] In summary, the simulation data in this embodiment verifies the superiority of the method of the present invention. Compared with existing extended target super-resolution methods, the method of the present invention combines the generalized sparse norm and the generalized total variation norm into a combined regularization term, which effectively preserves the target edge contour while improving resolution, thereby achieving better reconstruction quality. Furthermore, the method of the present invention achieves adaptive norm selection by estimating the norm of the target scattering coefficients, avoiding the problem of limited resolution improvement caused by manually determining the norm in existing regularization methods.

[0199] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A target-driven, combinatorial norm-adaptive super-resolution imaging method, comprising the following steps: Step 1: Constructing the airborne platform's geometric configuration and historical distance; radar platform at speed It moves forward and emits electromagnetic wave signals, while the antenna moves at an angular velocity. Scanning is performed within the forward-looking imaging area, and echo information is collected synchronously during the platform's movement; Then, a geometric motion model of the forward-looking scanning radar is constructed, and the aircraft's flight altitude is set as follows: It moves along the Y-axis at a velocity of v, and the radar beam scans counterclockwise with an angular velocity of v. The elevation angle of the beam is The plane is At time A, the target P is located at point A; assuming there is a target P in space... At that moment, the beam center is located at a distance of ____ from point A. The horizontal azimuth is The spatial azimuth is From geometric relations we get ; Step 2: Constructing the scanning radar echo convolution model; Assume the radar transmits a linear frequency modulated signal. The expression is as follows: （1）； in, Represents a distance-to-time variable. This represents the pulse width of a linear frequency modulated signal. Indicates the carrier frequency. Indicates the frequency modulation slope. The window function representing the distance to the time domain is expressed as follows: （2）； For target P, the echo signal after down-conversion is: The expression is as follows: （3）； in, Represents the target scattering coefficient. This represents the antenna pattern modulation function. This represents the azimuth-time variable. Indicates echo delay, express The instantaneous distance of the target relative to the radar at any given moment. Represents the speed of light; Then, pulse compression is performed on the echo signal, as shown in the following expression: （4）； in, This represents the echo signal after pulse compression. B represents the range pulse compression response function, and B represents the transmit signal bandwidth. For a single point target, range migration occurs if the range migration exceeds one range cell within one beam dwell time. The expression for the range migration determination condition is as follows: （5）； in, Indicates the antenna's beamwidth. Represents the range-resolved unit. Indicates the distance sampling rate. This indicates whether the distance migration exceeds one distance unit. Indicates the magnitude of the target's radial velocity relative to the radar; Then, range migration correction is performed in the frequency domain, and in the time domain, it is corrected by multiplying by the corresponding phase compensation factor in the frequency domain; then, based on the approximate range history expression... The target distance migration is expressed as follows in the time dimension: （6）； in, Indicates the change in distance. This indicates the change in echo delay; Frequency domain phase compensation factor The expression is as follows: （7）； After range migration correction, the echo signal is discretized and represented in matrix operation form, as shown in the following expression: （8）； in, Indicates echo, Represents the set of complex numbers. This indicates the number of samples for the azimuth echo. This represents the scattering coefficient of the target. Indicates additive noise. The antenna radiation pattern function is used in modeling, ignoring echoes during beam entry and exit from the scene. A truncated antenna radiation pattern matrix is ​​used, and its precise expression is as follows: （9）； Where, vector The sampling sequence representing the antenna radiation pattern. This indicates the antenna pattern in the azimuth direction. Each sampling angle, and the number of sampling points is determined by the pulse repetition frequency, beamwidth, and antenna scanning speed; Step 3: Constructing the generalized combinatorial norm objective function; First, a generalized sparse norm is selected. As a sparse penalty term, for Its norm expression is as follows: （10）； in, Let represent the norm value of the generalized sparse norm, and , express Lidi One component; Based on the radar echo model established in step two, and introducing the generalized sparse norm and the generalized total variation norm, the objective function is then... The expression is as follows: （11）； in, The regularization parameter represents the generalized sparse norm. The regularization parameter represents the norm of the generalized total variation. Denotes the norm value of the generalized total variation norm. Represents the gradient operator; Step 4: Constructing the relationship between the target reflection coefficient and the norm function; First, the SPICE algorithm is introduced, and the regularization parameter is replaced by a weighted matrix of regularization parameters. Then, assuming the variance of the noise is consistent, the SPICE and LASSO problems are equivalent, and equation (11) can be rewritten as follows: （12）； Among them, the weighting matrix Satisfy the following expression: （13）； in, Indicates the first The system response vector corresponding to each distance unit; Another method for estimating parameters based on the target scattering coefficient is proposed. The norm is modeled as a function of the target scattering coefficient, and equation (12) is rewritten as follows: （14）； in, and Represents the target scattering coefficient The norm parameter of the function mapping; then equation (14) can be further written as the following expression: （15）； Again To estimate the probability density function of the target scattering coefficients, we use the generalized Gaussian distribution as the prior probability model. （16）； in, Indicates the scale parameter. This represents the standard gamma function. Represents the scattering coefficient The specific value inside, The mean of the data; scale parameter The specific expression is as follows: （17）； in, Variance; first absolute central moment of the generalized Gaussian distribution With the second-order absolute central moment The expressions are as follows: （18）； Step 5: Adaptive estimation of sparse norm based on iterative reconstruction; The scaling parameter is eliminated by comparing the first and second absolute central moments of the generalized Gaussian distribution. And the generalized Gaussian ratio function is obtained. The expression is as follows: （19）； According to equation (19), the norm The value of is related to the first and second absolute central moments of the generalized Gaussian distribution; by analyzing the function... By inversely solving the relation, we obtain the norm. The estimation expression is as follows: （20）； Then, the inverse function of the generalized Gaussian ratio function is fitted using a hyperbolic function, and the norm is indirectly obtained by calculating the output value of this hyperbolic function. If the estimate is obtained, then equation (20) can be rewritten as the following expression: （21）； Then, the target scattering coefficients obtained from each iteration of reconstruction are used to calculate the corresponding moment estimate, as shown in the following expression: （22）； in, express Lidi The component is the target scattering coefficient obtained in the current iteration; then equation (21) can be rewritten as the following expression: （23）； Step 6: Adaptive estimation of total variation norm based on iterative reconstruction; Similarly, for The estimate and the Similar to the estimation, the gradient information of the target scene is obtained through the first-order difference operator. The moment estimation expression is obtained as follows: （24）； in, The first term in the gradient field vector represents the first term. One component; express The first moment, Indicates the second moment; Then, the inverse Gaussian ratio function is obtained. The estimated value is expressed as follows: （25）； Similarly, by fitting the inverse function of the generalized Gaussian ratio function with a hyperbolic function, and by calculating the output value of this hyperbolic function, the norm can be indirectly obtained. If the estimate is obtained, then equation (25) can be rewritten as the following expression: （26）； Step 7: Iterative reweighting solution; The iterative reweighting method is used to solve equation (15). First, according to the definition of norm, we set... The expression is then obtained as follows: （27）； Then, for the same distance unit, set... , ,and satisfy , satisfy Based on equation (27), the expression is as follows: （28）； in, It is a vector The One portion, It is a vector The Each component; based on the principle of norm equivalence, a diagonal weighted matrix is ​​introduced. and ,Will and Norm to weighted The norm is expressed in the following form: （29）； in, and Both are diagonal matrices, and their diagonal elements are respectively and ; Then, from equation (29), we obtain the following expression: （30）； in, Indicates the introduction of small positive numbers; Based on the derivation, equation (15) can be rewritten as follows: （31）； The solution expression for equation (31) is obtained by differentiation as follows: （32）； in, This represents the conjugate transpose operation; Finally, the iterative reweighting algorithm is used to solve the problem, and the pseudocode expression of the solution algorithm is as follows: （33）； in, This represents the initial solution. and These represent the functions used to control sparsity regularization. With gradient sparsity regularization The initial shape parameters, The first absolute moment of the echo, The second moment of the echo, and These represent the first and second moments of the gradient field calculated after taking the gradient with respect to the echo, respectively, and are used to initialize the shape parameters of the gradient regularization. , Indicates the maximum number of iterations of the algorithm; Through iterative iteration, the objective function is optimized and solved, ultimately achieving super-resolution reconstruction of the extended objective.

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