CN113640793A - MRF-based real aperture scanning radar super-resolution imaging method - Google Patents
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Abstract
The invention discloses a MRF-based real aperture scanning radar super-resolution imaging method, which comprises the following steps: introducing structural prior information represented by a hidden Markov random field into an objective function through a regularization frame; and solving the optimization problem of the objective function by using a fast iterative threshold contraction method, and finally obtaining the super-resolution imaging result of the target. According to the method, the two-dimensional spatial correlation of the pixels can be better described by introducing the Markov random field prior model, so that the shape of a scene can be better recovered.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a real aperture scanning radar super-resolution imaging method based on MRF.
Background
Forward looking radar imaging has a wide range of application scenarios such as aircraft navigation, landing and airport surveillance. However, the sharply decreased doppler bandwidth and left/right doppler ambiguity in the forward looking direction make the conventional single station synthetic aperture radar and doppler beam sharpening techniques difficult to apply in forward looking imaging.
The convolution inversion technology carries out super-resolution processing on RASR from the signal processing angle, and can break through the limitation of radar real aperture on the position resolution. The method has the advantages of simple imaging mode, high compatibility, no increase of physical aperture, capability of distinguishing a plurality of targets in the same beam and the like, and gradually becomes a great research hotspot of radar forward-looking imaging.
However, many deconvolution methods are sensitive to noise due to the ill-conditioned nature of the deconvolution problem. The regularization method can effectively relieve the ill-posed property of the convolution inversion problem, constructs different regularization punishment items according to the known prior information to apply constraint on a target solution, and can solve the problem that the convolution inversion solution is sensitive to noise and discontinuously depends on observation data. For example, the document "Iterative non-systematic angular super resolution" (Richards M. radius Conference, 1988, Proceedings of the 1988 IEEE national. IEEE, 1988:100-1The norm constraint regularization algorithm carries out super-resolution imaging on the target, because l1The sparse representation capability of the norm on the solution can effectively distinguish sparse targets in a scene, but the background contour information is damaged when the number of optimization iterations is too many; the document "Bayesian deconstruction for Angular Super-Resolution in Forward-Looking Scanning Raar" (ZHa Y, Huang Y, Sun Z, et al. Sensors,2015,15(3):6924-6946) utilizes a Super-Resolution algorithm of total variation plus sparse constraint, which can better retain the contour of a scene while distinguishing sparse objects. However, due to the limitation of the sequential processing mode according to the distance units, the methods only use the prior information in the one-dimensional distance units. In the imaging task, each pixel is considered as a result determined by surrounding pixels, so the scene usually has a two-dimensional structure characteristic, and therefore, the two-dimensional structure prior information of the scene is still to be mined and utilized.
Disclosure of Invention
The invention aims to provide an RASR super-resolution imaging method based on MRF (Markov random field) aiming at the defects in the background technology.
The technical solution for realizing the purpose of the invention is as follows: a MRF-based real aperture scanning radar super-resolution imaging method comprises the following steps:
introducing structural prior information represented by a hidden Markov random field into an objective function through a regularization frame;
and solving the optimization problem of the objective function by using a fast iterative threshold contraction method, and finally obtaining the super-resolution imaging result of the target.
A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the above-mentioned super-resolution imaging method when executing the computer program.
A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the above-mentioned super-resolution imaging method.
Compared with the prior art, the invention has the following remarkable advantages: the invention introduces the structural prior information expressed by the hidden Markov random field into the target function through the regularization frame, then solves the optimization problem of the target function by using the FIST method, and finally obtains the super-resolution imaging result of the target. The method has the advantages that the two-dimensional spatial correlation of the pixels can be better described by introducing the Markov random field prior model, so that the shape of the scene can be better recovered.
Drawings
FIG. 1 is a block flow diagram of a method provided by the present invention.
Fig. 2 is a diagram of the spatial relationship of motion scanning of a real aperture scanning radar used in the embodiment of the present invention.
FIG. 3 is a schematic diagram of a simulated imaging scene used in accordance with an embodiment of the present invention.
Fig. 4 is an echo signal superimposed with white gaussian noise according to an embodiment of the present invention.
Fig. 5 shows the signal-to-noise ratio of the signal after correction for range-wise compression and migration, which is 18 dB.
Fig. 6 is an enlarged view of the target area of fig. 5.
FIG. 7 is a graphical representation of the imaging results after processing by the method of the present invention and by a comparison algorithm.
Detailed Description
The solution of the invention is to apply a Markov random field prior model to the real aperture scanning radar super-resolution imaging. Introducing structural prior information expressed by a hidden Markov random field into a target function through a regularization frame, then solving the optimization problem of the target function by using a fast iterative threshold shrinkage (FIST) method, and finally obtaining a super-resolution imaging result of the target.
For the convenience of describing the contents of the present invention, the following terms are first explained:
the term 1: real aperture scanning radar
The Real Aperture Scanning Radar (RASR) is a radar system relative to a Synthetic Aperture Radar (SAR), and is different from the SAR in that a synthetic aperture mode is adopted in the azimuth direction to improve the resolution, a beam system is adopted in the azimuth direction to obtain a two-dimensional echo, no signal processing is carried out in the azimuth direction, and only real beams are utilized to distinguish a target.
The term 2: markov random field
Markov (MRF) means that under certain conditions dictated by "current", the result produced by the "last" will not affect the "future" result. In the one-dimensional case, the state of a random chain is only related to the state of its neighboring pixel points, that is, only affected by the state of the neighboring pixel points. For a two-dimensional image, the image may be defined in a two-dimensional space while being considered as a random field and a two-dimensional markov random field with markov properties.
The invention provides a RASR super-resolution imaging method, as shown in figure 1, comprising:
the method comprises the following steps: imaging system parameter initialization
The platform moving speed is v, the antenna wave beam scanning speed is omega, and the radar lower visual angle is
The coordinates of the target point are denoted as P (r)0,θ0) T is azimuth time, target point distance history rP(x, y) is
Due to the fast scanning speed and small imaging sector, the slope distance obtained by the approximation of Taylor expansion and first order term is
The expression of the point target echo is recorded as sP(τ,t),
Where τ is the distance-wise time variable, σ0For point target scattering intensity, h (t) for the dual-pass beam pattern of the antenna, t0Rect [. for the time when the beam center hits point P]Representing the distance time window, c is the speed of light, TrRepresenting the distance-time pulse width, f0Is the carrier frequency, KrIs the time chirp rate of the transmitted signal.
Step two: radial pulse compression
For a scattering function of
For a surface target, the echo is the integral of the echoes of all point targets, wherein
Is the initial slope distance of the target,
is the azimuth coordinate of the target. Because t is (theta-theta)a) ω and τ 2r/c, where θaFor the initial scan angle, the surface target echo can be obtained according to equations (2) and (3):
aiming at the acquired two-dimensional echo data s (r, theta), a matched filter is constructed by using radar emission signal parameters, the range direction is subjected to pulse compression, and the data s after range compression is obtainedout(r,θ)。
Step three: linear migration correction
After compressing in the range direction, for the target plane
Up located on arc line
The center of the echo position of all point targets is overlapped on a straight line
The above. For the subsequent super-resolution processing, the echo needs to be corrected by linear migration, and the order is
The variable r is scaled. Eliminating range migration corrected echo as
Step four: constructing an azimuthal convolution signal model
Only the bearing signal amplitude is studied, the bearing signal can be written as,
s(θ)＝σ(θ)*h(θ) (6)
where is the convolution operation. Considering the influence of noise, the azimuth signal expression is,
s(θ)＝σ(θ)*h(θ)+n(θ) (7)
and (3) constructing an azimuth convolution signal vector model aiming at the model:
s＝Hσ+n (8)
wherein s ═ s1,…,sN]TAnd σ ═ σ [ σ ]1,...,σN]TRespectively representing the echo data and the target scattering coefficient in a range gate, n ═ n1,...,nN]TN is the number of vectors, and H is the convolution matrix constructed by the antenna directional diagram H (theta).
Step five: constructing an imaging objective function
For the problem of noise sensitivity in deconvolution operation, a regularization method is adopted to solve the problem, and a standard regularization equation for solving the problem is as follows:
wherein the content of the first and second substances,
for data fidelity terms, | Γ (σ) | purpleqFor the regularization term, Γ (σ) is the specific operation of the regularization term, q is the norm of the regularization term, and λ is used to balance the fidelity of the measured data with the effect of the constraints of the regularization term, which can be determined by the L-curve method.
In this patent, Huber-Markov is chosen as the regularization term
Where ρ isT(. cndot.) is a function of Huber,
is a coefficient vector of the cluster c, tau is a temperature parameter, Z is a normalized constant, superscript (·)tDenoted as a transpose operation. The roughness of the image is obtained from the second derivative:
the Huber function is defined as:
the threshold T penalizes the gray scale variation of the image. The square penalty term smoothes out small-scale noise, e.g., σ ≦ T, for regions with smooth gray-scale changes, while the linear penalty term is used to smooth out boundary regions with strong gray-scale changes in the image, e.g., σ > T.
Substituting equations (10), (11) and (12) into equation (9), the objective function of RASR super-resolution imaging can become:
step six: determining the gradient of an objective function
Because the obtained objective function is a convex function, the optimization problem of the formula (13) is solved by adopting a fast iterative shrinkage/threshold (FIST) algorithm to obtain the gradient of the objective function
Wherein, (.)mThe mth element of the vector in parentheses, diag (. cndot.) is the diagonal matrix, ε is a solutionSmall constants introduced due to the non-microminiaturization caused by the non-smoothness of the objective function. The one-time iterative threshold shrinkage operation process is as follows:
wherein the content of the first and second substances,
is a shrink operator, defined as:
step seven: fast iterative solution of objective function
The specific solving process is as follows:
step k (k > 1):
σk＝ψ(yk) (17)
wherein σkIs the result of the k-th cycle, ykIs a prediction vector, t, for accelerating the iterative processkIs a parameter that controls the rate of convergence.
Compared with the existing angular super-resolution method, the method can better recover the scene outline and the details by utilizing the two-dimensional space prior information. By selecting a proper neighborhood system, the MRF can model the structural features of the image; then, utilizing a regularization frame to absorb MRF prior information to obtain a target function; and finally, solving the objective function through a fast iterative threshold shrinkage algorithm, and realizing the super-resolution imaging of the RASR.
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
In one embodiment, the method is mainly verified by a simulation experiment method, and all the steps and conclusions are verified to be correct on Matlab 2018. The present invention will be described in further detail with reference to specific embodiments.
The method comprises the following steps: fig. 2 is a schematic view of the scanning radar imaging according to the embodiment, in which the radar transmits a chirp signal while scanning, and parameters required for simulation are shown in table 1.
TABLE 1 simulation parameter table for real aperture scanning radar imaging
| Parameter(s) | Numerical value |
| Platform velocity | 100m/s |
| Pulse repetition frequency | 2000Hz |
| Main lobe beamwidth | 2.5° |
| Scanning speed of antenna | 60°/s |
| Antenna scanning range | ±10° |
| Minimum pitch | 3km |
Target scene as shown in fig. 3, the simulation scene is two X-shaped planar targets composed of 84 point targets, the scattering coefficients of which are both 1, the azimuth distribution is-3.7 ° to-0.7 ° and 3.7 ° to 0.7 °, and the distance distribution is 2980m to 3020 m. At a sampling rate frThe range Echo is sampled at 100MHz to obtain an Echo matrix, denoted Echo (τ, t), with a size Mr×NaAs shown in fig. 4.
Step two: distance direction pulse compression is carried out on the echo waves, and a distance direction pulse compression reference function refer (tau) ═ exp (i pi k) is constructed according to system parametersrτ2) Wherein k isr-1. mu.s.ltoreq.τ.ltoreq.1. mu.s at 20 MHz/. mu.s. Fourier transform is carried out on the echo in the step one along the distance direction, and the echo is subjected to Fourier transform with a conjugate refer of the distance direction reference function*(f) Multiplying, then inversely transforming the multiplied result to the time domain to complete the range-wise pulse compression of the simulated echo, and recording the data after range compression as sout(τ, t), the size of which remains unchanged.
Step three: performing migration correction on the data obtained in the step two, and constructing a distance frequency vector f ═ fr/2,fr/Mr,…,fr/2-fr/Mr]T，MrIs the distance vector number and time vector t ═ 0, Tscan/Na,2×Tscan/Na,…,Tscan]Tscan is the scan time; and then constructing a migration correction function correct (f, t) ═ exp (-i2f × dr (t)/c) according to the system parameters, wherein dr (t) ═ vt. Fourier transform is carried out on the echo along the distance direction, and the transform is recorded as sout(f, t) and multiplying with a migration correction function correct (f, t), then reversely converting the multiplied result into a time domain to finish the range-direction pulse compression of the simulation echo, and recording the data after the migration correction as sc(τ, t) as shown in fig. 5 and 6. The third step is to theoretically describe the migration correction in the time domain, and the third step is to perform the correction in the distance frequency domain because the third step is performed in the time domainCan be achieved by phase multiplication in the frequency domain.
Step four: discretizing the scanning antenna pattern according to the antenna pattern width theta, the pulse repetition frequency prf and the scanning speed omega
Obtaining the point number m of the discretized antenna directional diagram, then h (theta) is h0 h1...hm-1]From which a convolution matrix H is constructed
Step five: to scompressAnd (tau, t) taking the amplitude of the jth data (j is 1) which is the original echo s to be processed, constructing an MRF imaging target function according to an expression (13), wherein s is a vector obtained by taking a specific distance unit from the data after the migration correction in the third step, and H is a convolution matrix constructed in the fourth step.
Step six: the gradient of the objective function is obtained according to the expression (14), and epsilon is 10-8The regularization parameter λ is determined using an L-curve method. Obtaining a basic iterative formula of FIST solution by a fixed point solution strategy:
wherein sigmakAnd σk+1For the results of two adjacent iterations, γ is taken as 1 and δ is taken as 0.001.
Step seven: iteratively solving an objective function, and assigning the target echo s to be processed as an iteration initial value sigma0. Obtaining an iteration result sigma by using the formula (20)1(ii) a Then using the obtained sigma0And σ1Performing one-step prediction according to the formulas (18) and (19), and substituting the prediction into the formula (17) to obtain the next iteration result sigma2，tkThe initial assignment is 1. When the results of two iterations satisfy the following formula
||σ2-σ1||2＜κ (21)
The result converges, i.e. a target solution is found, where κ is set to 0.025 based on empirical values. If not, then sigma is added2、σ1、tk+1Respectively assign to sigma1、σ0And tkAnd continuing to perform the iteration step seven until the iteration termination condition is met to obtain the target solution.
The MRF-based real aperture scanning radar super-resolution imaging processing is completed, and the imaging result is shown in fig. 7. As can be seen from the figure, the method provided by the invention can well realize the super-resolution imaging of the real aperture radar, and the recovery of the X shape is far better than the result of the comparison algorithm.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (10)
1. A MRF-based real aperture scanning radar super-resolution imaging method is characterized by comprising the following steps:
introducing structural prior information represented by a hidden Markov random field into an objective function through a regularization frame;
and solving the optimization problem of the objective function by using a fast iterative threshold contraction method, and finally obtaining the super-resolution imaging result of the target.
2. The MRF-based real aperture scanning radar super-resolution imaging method according to claim 1, wherein the structural prior information represented by the hidden markov random field is introduced into the objective function through the regularization framework, and firstly, parameters of the imaging system are initialized, specifically:
let the platform moving speed be v, the antenna beam scanning speed omega, and the radar down-view angle be
The coordinates of the target point are denoted as P (r)0，θ0) T is azimuth time, target point distance history rP(x, y) is
The slope distance obtained by approximation of Taylor's expansion and first order term is
The expression of the point target echo is recorded as sP(τ，t)：
Where τ is the distance-wise time variable, σ0For point target scattering intensity, h (t) for the dual-pass beam pattern of the antenna, t0Rect [. for the time when the beam center hits point P]Representing the distance time window, c is the speed of light, TrRepresenting the distance-time pulse width, f0Is the carrier frequency, KrIs the time chirp rate of the transmitted signal.
3. The MRF-based real aperture scanning radar super-resolution imaging method according to claim 2, wherein after the initialization of the imaging system parameters, the range-wise pulse compression is performed on the echo, specifically as follows:
for a scattering function of
For a surface target, the echo is the integral of the echoes of all point targets, wherein
Is the initial slope distance of the target,
is the azimuth coordinate of the target; because t is (theta-theta)a) ω and τ 2r/c, where θaFor the initial scan angle, the surface target echo can be obtained according to equations (2) and (3):
aiming at the acquired two-dimensional echo data s (r, theta), a matched filter is constructed by using radar emission signal parameters, the range direction is subjected to pulse compression, and the data s after range compression is obtainedout(r,θ)；
4. The MRF-based real aperture scanning radar super-resolution imaging method according to claim 3, wherein linear migration correction is performed after range-wise pulse compression, specifically:
after compressing in the range direction, for the target plane
Up located on arc line
The center of the echo position of all point targets is overlapped on a straight line
The above step (1); the variable r can be subjected to linear scale transformation to eliminate distance walking generated by platform motion
5. The MRF-based real aperture scanning radar super-resolution imaging method according to claim 4, wherein after linear migration correction, an orientation convolution signal model is constructed, specifically:
writing an orientation signal as
s(θ)＝σ(θ)*h(θ) (6)
Wherein is a convolution operation; considering the influence of noise, the azimuth signal expression is:
s(θ)＝σ(θ)*h(θ)+n(θ) (7)
and (3) constructing an azimuth convolution signal vector model aiming at the model:
s＝Hσ+n (8)
wherein s ═ s1,…,sN]TAnd σ ═ σ [ σ ]1,...,σN]TRespectively representing the echo data and the target scattering coefficient in a range gate, n ═ n1,...，nN]TN is the number of vectors, and H is the convolution matrix constructed by the antenna directional diagram H (theta).
6. The MRF-based real aperture scanning radar super-resolution imaging method according to claim 5, wherein after constructing the azimuth convolution signal model, constructing an imaging objective function, specifically:
for the problem of noise sensitivity in deconvolution operation, a regularization method is adopted to solve the problem, and a standard regularization equation for solving the problem is as follows:
wherein the content of the first and second substances,
for data fidelity terms, | Γ (σ) | purpleqThe method is characterized in that the method is a regular term, gamma (sigma) is a specific operation of the regular term, q is a norm of the regular term, and lambda is used for balancing the fidelity of measured data and the influence of the constraint of the regular term and can be determined by an L-curve method;
selecting Huber-Markov as regularization term
Where ρ isT(. cndot.) is a function of Huber,
is a coefficient vector of the cluster c, tau is a temperature parameter, Z is a normalized constant, superscript (·)tDenoted as a transpose operation; the roughness of the image is obtained from the second derivative:
the Huber function is defined as:
the threshold value T can punish the gray level change of the image;
substituting equations (10), (11), (12) into equation (9), the objective function of RASR super-resolution imaging can become:
7. the MRF-based real aperture scanning radar super-resolution imaging method according to claim 6, wherein a complete image objective function is constructed to obtain an objective function gradient, specifically as follows:
because the obtained objective function is a convex function, the optimization problem of the formula (13) is solved by adopting a fast iterative shrinkage/threshold algorithm, and the gradient of the objective function is obtained
Wherein, (.)mThe mth element of the vector in brackets, diag (·) is a diagonal matrix, ε is a constant introduced to account for the irreducibility due to the non-smoothness of the objective function; the one-time iterative threshold shrinkage operation process is as follows:
wherein the content of the first and second substances,
is a shrink operator, defined as:
8. the MRF-based real aperture scanning radar super-resolution imaging method according to claim 7, wherein after the gradient of the objective function is solved, the objective function is solved by fast iteration, and the specific solving process is as follows:
step k:
σk＝ψ(yk) (17)
wherein k is>1，σkIs the result of the k-th cycle, ykIs a prediction vector, t, for accelerating the iterative processkIs a parameter that controls the rate of convergence.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the computer program implements the steps of the super-resolution imaging method according to any one of claims 1 to 8.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the super-resolution imaging method according to any one of claims 1 to 8.
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| 焦淑红等: "迭代收缩阈值雷达前视成像方法", 《航空学报》, vol. 35, no. 12, pages 3384 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117420553A (en) * | 2023-12-13 | 2024-01-19 | 南京理工大学 | Super-resolution imaging method for sea surface target scanning radar |
| CN117420553B (en) * | 2023-12-13 | 2024-03-12 | 南京理工大学 | Super-resolution imaging method for sea surface target scanning radar |
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| CN113640793B (en) | 2023-12-26 |
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