A radar super-resolution imaging method for mixed noise environments

Abstract

This invention discloses a radar super-resolution imaging method for mixed noise environments, belonging to the field of radar detection and imaging. By analyzing the noise characteristics of the actual environment, a new radar echo model is constructed, and the adaptive noise resistance capability of the modified loss function is utilized to achieve high-resolution target reconstruction in mixed noise environments. First, the traditional echo model is optimized to obtain an echo mathematical model closer to the actual environment. Then, the mathematical properties of the modified loss function are used to achieve good suppression of mixed noise. Finally, a generalized ridge regression estimation algorithm based on the minimization criterion is used to achieve a closed-loop solution of the objective function, thereby completing accurate reconstruction of the target scene in mixed noise environments. Compared with traditional super-resolution methods, the method of this invention can achieve forward-looking super-resolution radar imaging in mixed noise environments.

Description

Technical Field

[0001] This invention belongs to the field of radar detection and imaging, and is particularly suitable for radar forward-looking super-resolution imaging. Specifically, it relates to a radar super-resolution imaging method in a mixed noise environment. Background Technology

[0002] Radar, with its all-weather, all-day imaging capabilities, is widely used in many military and civilian fields. However, traditional radar imaging methods, such as synthetic aperture radar (SAR), cannot achieve forward-looking area imaging due to limitations in their imaging mechanisms. Real aperture radar (RAR), on the other hand, can quickly acquire omnidirectional target detection information through radar beam scanning, achieving forward-looking imaging, but its azimuth resolution is usually limited by antenna size, making it impossible to acquire high-resolution images of the forward-looking area.

[0003] To improve the angular resolution of real aperture radar (RAR), Yildirim S et al. applied the classic Richardson-Lucy method from image restoration to forward-looking super-resolution radar imaging, significantly improving the azimuth resolution of RAR imaging. However, this method suffers from target reconstruction failure under low signal-to-noise ratio (SNR) conditions. In recent years, due to similar mathematical structures, array signal processing methods have been widely applied to RAR imaging. Zhang et al. introduced the adaptive spectral estimation method from array signal processing into RAR imaging, effectively improving noise resistance while maintaining azimuth super-resolution performance. However, this method still relies on an ideal Gaussian noise environment, limiting its imaging capabilities in real-world environments. Furthermore, to improve RAR imaging capabilities in real-world non-ideal Gaussian noise environments, Zhang et al. proposed a robust angular super-resolution method for scanning radar in heavy-tailed noise environments. This method considers that the noise encountered by RAR in real-world environments typically exhibits large-amplitude spike anomalies. To address the characteristics of such large-amplitude, irregular, and discontinuous impulse noise, a minimum absolute deviation (LAD)-LASSO constraint criterion is introduced to suppress heavy-tailed noise. However, because this method does not take into account the mixed noise environment that RAR usually faces in real-world environments, which consists of uniform Gaussian noise and random impulse noise, its resolution drops significantly in mixed noise environments, leading to target reconstruction failure. Summary of the Invention

[0004] In view of the above-mentioned technical background, the robust angle super-resolution method of scanning radar in heavy tail noise environment does not take into account the mixed noise environment that RAR usually faces in real environment, which is a mixture of uniform Gaussian noise and random impulse noise. As a result, it fails to reconstruct the target in the mixed noise environment. This invention proposes a radar super-resolution imaging method in mixed noise environment.

[0005] The solution of this invention first optimizes the traditional echo model to obtain an echo mathematical model that more closely resembles the actual environment; then, it utilizes the mathematical properties of the modified loss function to achieve good suppression of mixed noise; finally, it achieves a closed-loop solution for the objective function through a generalized ridge regression estimation algorithm based on the minimization criterion, thereby completing accurate reconstruction of the target scene in a mixed noise environment. Compared with traditional angular super-resolution methods, the method of this invention can achieve forward-looking super-resolution imaging of radar in mixed noise environments.

[0006] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0007] A radar super-resolution imaging method for mixed noise environments includes the following steps:

[0008] Step 1: Establishment of azimuth echo convolution model; The radar transmits a linear frequency modulated signal to obtain the original target echo; The obtained original echo is subjected to range-dimensional pulse compression and range travel correction to obtain the echo signal; The echo signal is described along the azimuth direction as the convolution of the antenna pattern function and the target scattering coefficient to obtain the convolution echo model;

[0009] Step 2: Optimization of the convolutional echo model based on mixed noise; a noise term is superimposed on the convolutional echo model, which is random impulse noise following a Laplace distribution;

[0010] Step 3: Construct the objective function and refine it using the log-hyperbolic cosine function;

[0011] Step 4: Based on the minimization criterion, the generalized ridge regression estimation algorithm is used to solve the target scattering coefficient in the mixed noise environment, thereby completing the accurate reconstruction of the target scene in the mixed noise environment.

[0012] Furthermore, step 3 is detailed as follows:

[0013] First, construct the objective function as follows:

[0014] ;

[0015] in, Represents the scattering coefficient of the target The optimal estimate, Describes the 1-norm of a vector. It is a regularization parameter;

[0016] The objective function is modified using the log-hyperbolic cosine function:

[0017] ;

[0018] in, It is a logarithmic hyperbolic cosine function. Represents the convolution matrix, This indicates echo data.

[0019] Furthermore, step 4 is detailed as follows:

[0020] Using the minimization criterion, the target scattering coefficient Global quadratic upper bound function for:

[0021] ;

[0022] Where the superscript k indicates the k-th iteration, Describes the 2-norm of a vector. For the function formula, , ;

[0023] The second term in the objective function is obtained through iterative reweighting. Converting to a diagonally loaded L2 norm for easier solution yields the latest global upper bound function for the objective function:

[0024] ;

[0025] in, Represented as an intermediate variable, , For diagonal add-ins;

[0026] Then, the solution is based on the traditional ridge regression problem:

[0027] ;

[0028] The analytical solution with closed-form is:

[0029] ;

[0030] in, Represents the identity matrix;

[0031] Treating the global upper bound function as a closed-form analytical solution to a generalized ridge regression-iterative reweighting problem, we obtain the final closed-form analytical solution of the global upper bound function as follows:

[0032] .

[0033] Furthermore, step 2 is detailed as follows:

[0034] The convolutional echo model is optimized as follows:

[0035]

[0036] in, This represents zero-mean Gaussian white noise. Let represent random impulse noise that follows a Laplace distribution. The distribution of Laplace noise is shown below:

[0037]

[0038] in, The probability density function representing the noise parameter t, It is a position parameter. It is a scale parameter.

[0039] The beneficial effects of this invention are as follows:

[0040] This invention first optimizes the traditional echo model to obtain an echo mathematical model that more closely resembles the actual environment. Then, it utilizes the mathematical properties of the modified loss function to achieve good suppression of mixed noise. Finally, it employs a generalized ridge regression estimation algorithm based on the minimization criterion to achieve a closed-loop solution for the objective function, thereby completing accurate reconstruction of the target scene in a mixed-noise environment. Compared with traditional super-resolution methods, this invention enables forward-looking super-resolution imaging of radar in mixed-noise environments. Attached Figure Description

[0041] Figure 1 This is the geometric model of an airborne real aperture radar.

[0042] Figure 2 This is a graph of the logarithmic-cosine-hyperbolic function.

[0043] Figure 3 This is a flowchart of the method of the present invention.

[0044] Figure 4 The images show the original and noisy beam echoes during the simulation.

[0045] Figure 5 This is a comparison chart of results from different imaging methods.

[0046] Figure 6 This is a schematic diagram illustrating the results of the method of the present invention. Detailed Implementation

[0047] This invention is primarily verified using simulation experiments; all steps and conclusions are presented in [the relevant documentation / documentation]. The above verification is correct. The method of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0048] Example 1

[0049] This embodiment provides a radar super-resolution imaging method for mixed noise environments, including the following steps:

[0050] Step 1: Establishing the azimuth echo convolution model; the radar transmits a linear frequency modulated signal to obtain the original target echo; the obtained original echo undergoes range-dimensional pulse compression and range travel correction to obtain the echo signal; the echo signal along the azimuth direction is described as the convolution of the antenna pattern function and the target scattering coefficient, resulting in the convolution echo model, expressed by the following formula:

[0051]

[0052] in Represents echo data Represents the target scattering coefficient. This represents zero-mean Gaussian white noise; This represents the convolution matrix.

[0053] Step 2: Optimization of the convolutional echo model based on mixed noise; a noise term is superimposed on the convolutional echo model, which is random impulse noise following a Laplace distribution;

[0054] The convolutional echo model is optimized as follows:

[0055]

[0056] in, This represents zero-mean Gaussian white noise. Let represent random impulse noise that follows a Laplace distribution. The distribution of Laplace noise is shown below:

[0057]

[0058] in, The probability density function representing the noise parameter t, It is a position parameter. It is a scale parameter.

[0059] Step 3: Construct the objective function and refine it using the log-hyperbolic cosine function;

[0060] First, construct the objective function as follows:

[0061] ;

[0062] in, Represents the scattering coefficient of the target The optimal estimate, Describes the 1-norm of a vector. It is a regularization parameter;

[0063] The objective function is modified using the log-hyperbolic cosine function:

[0064] ;

[0065] in, It is a logarithmic hyperbolic cosine function.

[0066] Step 4: Based on the minimization criterion, the generalized ridge regression estimation algorithm is used to solve the target scattering coefficient in the mixed noise environment, thereby completing the accurate reconstruction of the target scene in the mixed noise environment;

[0067] Using the minimization criterion, the target scattering coefficient Global quadratic upper bound function for:

[0068] ;

[0069] Where the superscript k indicates the k-th iteration, Describes the 2-norm of a vector. , ;

[0070] The second term in the objective function is obtained through iterative reweighting. Converting to a diagonally loaded L2 norm for easier solution yields the latest global upper bound function for the objective function:

[0071] ;

[0072] in, Represented as an intermediate variable, , For diagonal add-ins;

[0073] Then, the solution is based on the traditional ridge regression problem:

[0074] ;

[0075] The analytical solution with closed-form is:

[0076] ;

[0077] in, Represents the identity matrix;

[0078] Treating the global upper bound function as a closed-form analytical solution to a generalized ridge regression-iterative reweighting problem, we obtain the final closed-form analytical solution of the global upper bound function as follows:

[0079] .

[0080] Example 2

[0081] This embodiment is a further explanation based on Embodiment 1, and adds derivation steps for constructing and solving the objective function. The specific implementation process is as follows: Figure 3As shown, it includes the following steps:

[0082] Step 1: Establish the azimuth echo convolution model;

[0083] Adopting such Figure 1 The airborne radar forward-looking imaging geometric model shown is used, and the radar simulation system parameters are selected as shown in Table 1.

[0084] Table 1: Simulation System Parameters

[0085] parameter numerical values carrier frequency 10GHz bandwidth 45MHz Time width 2us Antenna scanning speed 30° / s Main lobe beamwidth 3° Pulse repetition frequency 1000Hz

[0086] Gaussian noise signal-to-noise ratio set to .like Figure 1 As shown, the airborne radar platform operates at a constant speed. Along The radar antenna flies at a constant speed along the axial direction, with an angular velocity of... Scanning the oblique forward-looking area. The platform's flight altitude is... Platform and target The initial slope distance is .exist At any given moment, the distance between the platform and the goal is historical. Represented as:

[0087]

[0088] in, and These represent the azimuth and elevation angles, respectively.

[0089] The radar acquires the raw echo of the target by transmitting a linear frequency modulated signal with a large time-bandwidth product. The acquired raw echo undergoes range-dimensional pulse compression and range-travel correction, and the echo signal is represented as:

[0090]

[0091] in, This indicates the received echo signal. It is time in the azimuth dimension determined by the antenna scanning speed. It is time in the distance dimension related to the speed of light. and These represent the number of sampling points for distance and direction, respectively. Represents the nth element in the target scattering matrix The magnitude of each target, where i and j are target indices. Represents the antenna pattern function. It is a rectangular window function. It is the carrier frequency. It represents the time delay, and J represents the imaginary part.

[0092] Based on the scanning imaging process, the echo signal along the azimuth direction can be described as the convolution of the antenna pattern function and the target scattering coefficient, in the... The echo data of each distance cell can be written in convolutional form as follows:

[0093]

[0094] in Represents echo data, This represents the echo signal at the Nth azimuth sampling point. Represents the target scattering coefficient. This represents the target scattering coefficient at the Nth azimuth sampling point. This represents zero-mean Gaussian white noise; The convolution matrix can be represented as:

[0095]

[0096] in, For the antenna pattern samples, the number of samples From the pulse repetition frequency ( ), beamwidth ( ) and antenna scanning speed Decision, that is .

[0097] Step 2: Optimization of the convolutional echo model based on mixed noise;

[0098] Step 1 effectively established a discrete convolution model using the relationship between the antenna pattern and the target scattering coefficient. However, due to the assumptions... Representing zero-mean Gaussian white noise, in real-world mixed noise environments, traditional algorithms struggle to accurately represent the target scattering coefficients. Errors will inevitably occur during the solution process.

[0099] Therefore, considering that mixed noise in real-world environments is typically composed of a uniform Gaussian noise floor and randomly occurring impulse noise, the convolutional echo model can be optimized as follows:

[0100]

[0101] in, This represents zero-mean Gaussian white noise. Let represent random impulse noise that follows a Laplace distribution. The distribution of the Laplace noise is shown below:

[0102]

[0103] in, The probability density function representing the noise parameter t, It is a position parameter. It is a scale parameter.

[0104] Step 3: Construct the objective function;

[0105] For the traditional echo model, using a sparse L1 regularization framework, the target reconstruction problem in step 1 of the traditional convolutional echo model can be regarded as an optimal estimation problem:

[0106]

[0107] However, this is an ill-posed problem, and a direct solution will inevitably lead to noise amplification. Therefore, in order to suppress noise amplification and improve angular resolution, a regularization framework is introduced... Norm as a constraint term:

[0108]

[0109] in, Represents the scattering coefficient of the target The optimal estimate, and Then these represent the 1-norm and 2-norm of the vector, respectively. It is a regularization parameter that controls the weights added to the constraint terms.

[0110] The second term in the above equation can be equivalently expressed by the minimization criterion as:

[0111]

[0112] in, Represents a diagonally loaded matrix. The first goal The result of the next iteration.

[0113] Therefore, the objective function can be expressed as:

[0114]

[0115] And it can be easily solved through iteration:

[0116]

[0117] Based on the above derivation, the iterative formula for the sparse L1 regularization algorithm under traditional Gaussian noise environment is obtained. However, when facing real-world mixed noise environments, the traditional constraint function becomes inapplicable, making it difficult to achieve target reconstruction.

[0118] Step 4: Objective function transformation;

[0119] To overcome the above problems and suppress mixed noise, the loss function first needs to be transformed. (Step 3) norm form Because it is highly sensitive to strong impulse noise, it becomes unrobust and is no longer applicable. To address this, previous research has proposed using the 1-norm instead of the F-norm to suppress anomalous noise; the model is as follows:

[0120]

[0121] This model effectively suppresses anomalous noise when When the value is large, it performs well in multi-pulse noise environments. However, when... When the value is small, the model loses the advantage of the F-norm preservation term in reconstructing near-Gaussian noise. Secondly, Since neither of the two terms in the model is differentiable, the solver design has to use more approximations to obtain the analytical solution in closed form, which inevitably introduces some errors.

[0122] Therefore, in order to effectively suppress random impulse noise while retaining the ability to cope with conventional Gaussian noise, this invention selects the log-hyperbolic cosine function. As an alternative to the modified loss function It becomes a new store of value. Among them, the hyperbolic cosine function The definition is as follows:

[0123]

[0124] in, This represents an exponential function.

[0125] The graph of the logarithmic hyperbolic cosine function versus two common norms is shown below. Figure 2 As shown. When hour, ;when hour, It can be seen that when When the noise level is high, i.e. when abnormal noise is encountered, near The loss function has a good effect on suppressing continuous impulse noise; when When the noise level is low, i.e. when encountering Gaussian noise, near The loss function also maintains a good effect in dealing with Gaussian noise. Meanwhile, compared to... Norm, Differentiable in all feasible regions, which implicitly reduces the error caused by approximation during the solution process.

[0126] Therefore, based on the above analysis, the objective function can be replaced with:

[0127]

[0128] Step 5: Solve using the generalized ridge regression estimation algorithm based on the minimization criterion;

[0129] For the latest objective function in the above equation, its second term The minimization criterion can be transformed into a diagonal loading method that is easier to solve. Norm, however, the first term log-cosine function Although it is differentiable, its independent variable is in the exponential term, which makes it impossible to directly obtain the analytical solution in closed form using some traditional algorithms.

[0130] Therefore, using the minimization criterion, let Then its global quadratic upper bound function for:

[0131]

[0132] This can be further summarized as the target scattering coefficient. Matrix form:

[0133]

[0134] in, For the function formula, , .

[0135] Meanwhile, the second term in the objective function It can be transformed into a diagonal loading method that is easier to solve by using the idea of ​​iterative reweighting. Norm, i.e. ,in This is a diagonal loading term. Substituting the above upper bound function and omitting the constant term, we find the global upper bound function of the latest objective function:

[0136]

[0137] in, Represented as an intermediate variable, , For diagonal add-ins.

[0138] To solve for the global upper bound function, we might first consider the traditional ridge regression problem, i.e.

[0139]

[0140] The analytical solution with closed-form is:

[0141]

[0142] in, Represents the identity matrix. The difference between the global upper bound function and the analytical solution in its closed-form form lies in the fact that the fixed terms in its preservation and regularization terms become iterative terms that need to be updated each time. , Therefore, we can regard the global upper bound function as a closed-form analytical solution of a generalized ridge regression-iterative reweighting problem.

[0143] Therefore, the analytical solution of the closed-form global upper bound function can be further obtained as follows:

[0144]

[0145] In summary, this invention utilizes a generalized ridge regression estimation algorithm based on the minimization criterion to solve for the target scattering coefficient in a mixed noise environment.

[0146] To verify the effectiveness of the method of the present invention, simulated echoes were used as follows: Figure 4 As shown, the scanning area is set to... The original scene is as follows: Figure 4 As shown in (a) in the figure, in Two point targets, each with an amplitude of 1, were set at each location.

[0147] Real beam echo contaminated with Gaussian noise, such as Figure 4 As shown in (b) above, it can be seen that the real beam echoes are merged together, making it impossible to distinguish the two point targets. Figure 4 Based on (b) in the previous example, if Laplace noise is further added, the echo after mixed noise pollution will be as follows: Figure 4 As shown in (c) in the figure, it is compared to Figure 4 (b) contains much more random impulse noise.

[0148] After target reconstruction method, such as Figure 5 As shown in (a), the Bayesian prior method (MAP_LL) based on the target following a Laplace distribution and the noise following a Laplace distribution significantly improves the resolution, but the azimuth position of the target is significantly shifted. Figure 5 (b) and Figure 5 The Lucy method shown in (c) and the sparse L1 regularization processing results have certain noise resistance and resolution effects. However, both of the above methods have the problems of target energy loss and serious false targets. Figure 5 Figure (d) in the figure shows the results of the sparse iterative estimation covariance (q-SPICE) method. Although it has a certain resolution effect, the target is split, indicating that the target cannot be reconstructed at all. Figure 5(e) and Figure 5 Figure (f) presents the results of the Iterative Adaptive (IAA) method and the Iterative Reweighted Least Squares (IRLS) method based on the Least Absolute Deviation (LAD) criterion, respectively, demonstrating good anti-mixed noise reconstruction performance. However, the resolution of both methods is not ideal. Figure 6 The result is the processing result of the method proposed in this invention. It can be seen that both the ability to resist mixed noise and the resolution are extremely excellent. This shows that the method maintains the excellent performance of high resolution and noise resistance that other traditional super-resolution methods do not have in mixed noise environment, and can achieve target reconstruction.

[0149] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A radar super-resolution imaging method in a mixed noise environment, characterized in that, The method comprises the following steps: Step 1: azimuth echo convolution model establishment; specifically, a radar transmits a linear frequency modulation signal to obtain a target original echo; the obtained original echo is subjected to distance dimension pulse compression and distance walk correction to obtain an echo signal; the echo signal is described as a convolution of an antenna directional diagram function and a target scattering coefficient along an azimuth direction to obtain a convolution echo model; Step 2: convolution echo model optimization based on mixed noise; specifically, a noise term is superimposed in the convolution echo model, and the noise is random impulse noise obeying a Laplace distribution; the convolution echo model is optimized as follows: ； wherein, denotes a convolution matrix, denotes echo data, denotes a target scattering coefficient, denotes zero-mean Gaussian white noise, denotes random impulse noise subject to a Laplace distribution; Step 3: constructing a target function and using a logarithmic hyperbolic cosine function to modify the target function; Step 4: generalized ridge regression estimation algorithm based on a maximum minimization criterion is used to solve the target scattering coefficient in a mixed noise environment and complete target scene reconstruction in the mixed noise environment; The step 3 is specifically as follows: Firstly, a target function is constructed as follows: ； wherein, denotes the optimal estimate of the target scatter coefficient denotes the optimal estimate of the target scatter coefficient denotes the vector 1-norm, is a regularization parameter; The term is modified using a hyperbolic cosine function of the target function using a logarithmic function.

2. The method of claim 1, wherein, The step 4 is specifically as follows: Using the max-min criterion, the global upper bound function of the target scattering coefficient is given by: ​ ； wherein the superscript k denotes the kth iteration, denotes the vector 2-norm, is a function formula reference, in particular, , ; The second term in the objective function is obtained through iterative reweighting. Converting to a diagonally loaded L2 norm for easier solution yields the latest global upper bound function for the objective function: ； wherein is an intermediate variable, , is a diagonal loading term; Then, a traditional ridge regression problem is solved as follows: ； There is a closed-form analytical solution, which is as follows: ； wherein denotes the identity matrix; The global upper bound function is regarded as a generalized ridge regression-iterative reweighting problem of the closed-form analytical solution, so that the final closed-form analytical solution of the global upper bound function is as follows: 。 3. The method of claim 2, wherein, The random impulse noise obeying the Laplace distribution is as follows: ； wherein, denotes the probability density function of the noise parameter t, is a location parameter, is a scale parameter.

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