CN113640793B - MRF-based real aperture scanning radar super-resolution imaging method - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
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- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
Abstract
The invention discloses a real aperture scanning radar super-resolution imaging method based on MRF, which comprises the following steps: introducing structure prior information represented by a hidden Markov random field into an objective function through a regularization framework; and solving the problem of optimizing the objective function by using a rapid iteration threshold contraction method, and finally obtaining a super-resolution imaging result of the target. According to the method, the Markov random field prior model is introduced, so that the two-dimensional spatial correlation of the pixels can be better described, and 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 applications such as aircraft navigation, landing, airport surveillance, and the like. However, the drastically reduced doppler bandwidth and left/right doppler ambiguity characteristics of the forward looking direction make 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 the RASR from the angle of signal processing, and can break through the limitation of the 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 wave beam and the like, and gradually becomes a big research hot spot of radar forward-looking imaging.
However, many deconvolution methods are noise-tolerant due to the morbid nature of deconvolution problemsIs relatively sensitive. The regularization method can effectively relieve the pathogenicity of the convolution inversion problem, can construct different regularization penalty terms according to known prior information to apply constraint to the target solution, and can solve the problems that the convolution inversion solution is sensitive to noise and discontinuously depends on observation data. For example, document "Iterative noncoherent angular superresolution" (Richards M. Radar Conference,1988., proceedings of the 1988 IEEE National.IEEE,1988:100-105.) uses l 1 Super-resolution imaging is carried out on a target by using a norm constraint regularization algorithm, and l is the reason that 1 The sparse representation capability of the norm pair solution can effectively resolve sparse targets in a scene, but damage to background contour information is caused when the number of optimization iterations is excessive; document "Bayesian Deconvolution for Angular Super-Resolution in Forward-Looking Scanning Radar" (Zha Y, huang Y, sun Z, et al sense, 2015,15 (3): 6924-6946) utilizes a super-resolution algorithm of total variation plus sparse constraint, which can better preserve the contours of a scene while distinguishing sparse objects. However, due to the limitation of the sequential processing mode according to the distance units, the method only uses prior information in the one-dimensional distance units. In the imaging task, each pixel is considered to be a result of the common decision of surrounding pixels, so that the scene generally has two-dimensional structural characteristics, and therefore, the prior information of the two-dimensional structure of the scene is yet to be mined and utilized.
Disclosure of Invention
Aiming at the defects existing in the background technology, the invention provides an RASR super-resolution imaging method based on MRF.
The technical solution for realizing the purpose of the invention is as follows: an MRF-based real aperture scanning radar super-resolution imaging method comprises the following steps:
introducing structure prior information represented by a hidden Markov random field into an objective function through a regularization framework;
and solving the problem of optimizing the objective function by using a rapid iteration threshold contraction method, and finally obtaining a 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 super-resolution imaging method when the computer program is executed.
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the above-described super-resolution imaging method.
Compared with the prior art, the invention has the remarkable advantages that: according to the method, structural prior information expressed by a hidden Markov random field is introduced into an objective function through a regularization framework, then the optimization problem of the objective function is solved by using a FIST method, and finally a super-resolution imaging result of the target is obtained. 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, and the shape of the scene can be better recovered.
Drawings
Fig. 1 is a flow chart of the method provided by the invention.
Fig. 2 is a diagram of a spatial relationship of motion scanning of a real aperture scanning radar employed in an embodiment of the present invention.
FIG. 3 is a schematic diagram of a simulated imaging scene employed in an embodiment of the invention.
Fig. 4 is an echo signal superimposed with white gaussian noise in an embodiment of the present invention.
Fig. 5 shows the result after distance compression and migration correction, with a signal-to-noise ratio of 18dB.
Fig. 6 is an enlarged view of the target area of fig. 5.
FIG. 7 is a schematic representation of imaging results after processing and comparison algorithms using the method of the present invention.
Detailed Description
The solution of the invention is to apply the Markov random field prior model to real aperture scanning radar super-resolution imaging. The structure prior information expressed by the hidden Markov random field is introduced into the objective function through the regularization framework, then the problem of optimizing the objective function is solved by utilizing a fast iterative threshold contraction (FIST) method, and finally the super-resolution imaging result of the target is obtained.
For convenience in describing the present invention, the following terms are first explained:
terminology 1: real aperture scanning radar
A Real Aperture Scanning Radar (RASR) is a radar system relative to a Synthetic Aperture Radar (SAR), and unlike SAR, which adopts a synthetic aperture method to improve resolution in the azimuth direction, it acquires two-dimensional echoes in the azimuth direction by adopting a beam system, and does not perform any signal processing in the azimuth direction, and only uses real beams to resolve targets.
Term 2: markov random field
Markov (MRF) refers to the fact that under certain conditions determined by "current," the result of "last" will not affect the result of "future. In the one-dimensional case, the state of a random chain is only related to the state of its neighboring pixels, i.e. is only affected by the state of neighboring pixels. For two-dimensional images, the image can be defined in two dimensions while the image is considered to be a random field and a two-dimensional Markov random field with Markov properties.
The invention provides a RASR super-resolution imaging method, which is shown in figure 1 and comprises the following steps:
step one: imaging system parameter initialization
The motion speed of the platform is v, the scanning speed omega of the antenna beam, and the radar lower view angle isThe target point is marked as P (r) 0 ,θ 0 ) T is azimuth time, and the target point distance history r P (x, y) is
Because of the fast scanning speed and small imaging sector, the slant distance obtained by Taylor expansion and one-time term approximation is
The point target echo expression is denoted s P (τ,t),
Where τ is the distance-to-time variable, σ 0 For the scattering intensity of the point target, h (t) is the two-way beam pattern of the antenna, t 0 For the time of beam center irradiation to point P, rect [. Cndot.]Represents a distance time window, c is the speed of light, T r Representing distance-time pulse width, f 0 For carrier frequency, K r Is the time chirp rate of the transmitted signal.
Step two: distance pulse compression
For a scattering function ofThe echo of (2) is the integral of the echo of the whole point target, wherein +.>For the initial skew of the target, +.>Is the azimuthal coordinate of the target. Since t= (θ - θ) a ) ω and τ=2r/c, where θ a For the initial scan angle, according to equations (2) and (3), a surface target echo can be obtained:
for the acquired two-dimensional echo data s (r, theta), constructing a matched filter by utilizing radar emission signal parameters, and performing pulse compression on the distance direction to obtain distance compressed data s out (r,θ)。
Step three: linear migration correction
After distance compression, for the target planeUpper located arc +.>All the above point targets whose echo position centers are to be staggered and overlapped on a straight line +.>And (3) upper part. For the subsequent super resolution processing, the echo needs to be subjected to linear migration correction, so that +.>And (5) performing scale transformation on the variable r. Echo after eliminating range migration correction is
Step four: constructing an azimuthal convolution signal model
Only with respect to the azimuth signal amplitude, the azimuth signal can be written as,
s(θ)＝σ(θ)*h(θ) (6)
where is the convolution operation. Considering the effect of noise, the azimuth signal expression is that,
s(θ)＝σ(θ)*h(θ)+n(θ) (7)
for the above model, constructing an azimuth convolution signal vector model:
s＝Hσ+n (8)
wherein s= [ s ] 1 ,…,s N ] T Sum sigma= [ sigma ] 1 ,...,σ N ] T Respectively representing echo data and target scattering coefficient in a range gate, n= [ n ] 1 ,...,n N ] T N is the number of vectors, and H is the convolution matrix constructed by the antenna pattern H (theta).
Step five: constructing an imaging objective function
For the noise sensitivity problem in deconvolution operation, a regularization method is adopted to solve the problem, and a standard regularization equation for solving the problem is adopted:
wherein,in the case of a data-fidelity item, i Γ (σ) i q For the regularization term, Γ (σ) is a specific operation of the regularization term, q is a norm of the regularization term, and λ is used to balance the fidelity of the measured data and the influence of the constraint of the regularization term, which may be determined by an L-curve method.
In this patent, huber-Markov is chosen as the regularization term
Wherein ρ is T (. Cndot.) is a Huber function,for the coefficient vector of the group c, τ is the temperature parameter, Z is the normalized constant, superscript (·) t Represented as a transpose operation. The roughness of the image is obtained from the second derivative:
the definition of the Huber function is:
the threshold T penalizes the grey scale variation of the image. The square penalty term will smooth small scale noise for regions with smooth gray level changes, such as |σ|+.T, while the linear penalty term is used to smooth boundary regions with strong gray level changes in the image, such as |σ| > T.
Substituting equations (10) (11) (12) into equation (9), the objective function of RASR super-resolution imaging can become:
step six: solving for the gradient of the objective function
Since the obtained objective function is a convex function, a fast iterative contraction/threshold (FIST) algorithm is adopted to solve the optimization problem of the formula (13) and calculate the gradient of the objective function
Wherein ( m For the mth element of the vector in brackets, diag (·) is a diagonal matrix, ε is a small constant introduced to account for the non-microminiaturization due to the non-smoothness of the objective function. The one iteration threshold shrink operation process is:
wherein,for the contraction operator, it is defined as:
step seven: fast iterative solution of objective functions
The specific solving process is as follows:
step k (k > 1):
σ k ＝ψ(y k ) (17)
wherein sigma k Is the result of the kth cycle, y k Is a predictive vector, t, for accelerating the iterative process k Is a parameter controlling the convergence speed.
Compared with the existing angle super-resolution method, the method can better recover the scene contour and detail by utilizing the two-dimensional space prior information. By selecting a suitable neighborhood system, the MRF can model the structural features of the image; then absorbing MRF priori information by using a regularization frame to obtain an objective function; and finally, solving an objective function through a rapid iteration threshold contraction algorithm to realize 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 will be further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the present application.
In one embodiment, the invention is verified by adopting a simulation experiment method, and all steps and conclusions are verified to be correct on Matlab 2018. The present invention is described in further detail with respect to the following detailed description.
Step one: fig. 2 is a schematic diagram of scanning radar imaging in the present embodiment, in which a radar emits a chirp signal while scanning, and parameters required for simulation are shown in table 1.
Table 1 real aperture scanning radar imaging simulation parameter table
| Parameters (parameters) | Numerical value |
| Platform speed | 100m/s |
| Pulse repetition frequency | 2000Hz |
| Main lobe beam width | 2.5° |
| Antenna scanning speed | 60°/s |
| Antenna scanning range | ±10° |
| Minimum pitch | 3km |
The object scene is shown in fig. 3, the simulation scene is a plane object of two X shapes consisting of 84 point objects, the scattering coefficients of which are 1, the azimuth distribution is-3.7 ° to-0.7 ° and 3.7 ° to 0.7 °, and the distance distribution is 2980m to 3020m. At a sampling rate f r The distance Echo is sampled at 100MHz to obtain an Echo matrix, denoted Echo (τ, t), of size M r ×N a As shown in fig. 4.
Step two: performing distance pulse compression on echo, and constructing according to system parametersThe resulting distance pulse compression reference function refer (τ) =exp (i pi k) r τ 2 ) Wherein k is r =20 MHz/μs, -1 μs.ltoreq.τ.ltoreq.1μs. Fourier transforming the echo in the first step along the distance direction and performing Fourier transformation on the echo and the conjugate reference of the Fourier transformation of the echo and the distance direction reference function * (f) Multiplying, inversely transforming the multiplied result to the time domain to complete the distance pulse compression of the simulated echo, and recording the distance compressed data as s out (τ, t) whose size remains unchanged.
Step three: performing migration correction on the data obtained in the second step, and constructing a distance frequency vector f= [ f ] r /2,f r /M r ,…,f r /2-f r /M r ] T ，M r For the distance vector number and the time vector t= [0, tscan/N a ,2×Tscan/N a ,…,Tscan]Tscan is the scan time; then constructing a migration correction function correct (f, t) =exp (-i 2f×dr (t)/c), where dr (t) =vt, according to the system parameters. Fourier transform is carried out on the echo along the distance direction, and the record is s out (f, t) and multiplying the simulated echo with a migration correction function correct (f, t), and inversely transforming the multiplied result to a time domain to finish the distance pulse compression of the simulated echo, wherein the data after migration correction is s c (τ, t) as shown in fig. 5 and 6. The third step is to theoretically describe the migration correction in the time domain, and is implemented in the distance frequency domain, because the displacement in the time domain can be implemented 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, and then performing the pulse repetition frequency prfThe number m of discretized antenna pattern points can be obtained, then h (theta) = [ h ] 0 h 1 ...h m-1 ]Thereby constructing a convolution matrix H
Step five: for s compress Taking amplitude values of (tau, t) jth row data (j initial value is 1), namely, taking the amplitude values as original echo s to be processed, and constructing an MRF imaging objective function according to an expression (13), wherein s is a vector obtained by taking data after migration correction in the third step from a specific distance unit, and H is a convolution matrix constructed in the fourth step.
Step six: according to expression (14), the gradient of the objective function is obtained, and epsilon is 10 -8 The regularization parameter lambda is determined by an L-curve method. The basic iteration formula of the FIST solution is obtained by a fixed point solution strategy:
wherein sigma k Sum sigma k+1 For the results of two adjacent iterations, γ takes 1 and δ takes 0.001.
Step seven: iteratively solving an objective function, and assigning the target echo s to be processed as an iteration initial value sigma 0 . Obtaining an iteration result sigma by using a formula (20) 1 The method comprises the steps of carrying out a first treatment on the surface of the Then use the sigma obtained 0 Sum sigma 1 Performing one-step prediction according to the formulas (18) (19), and then taking the predicted value into the formula (17) to obtain a next iteration result sigma 2 ，t k The initial assignment is 1. When the results of the two iterations meet the following conditions
||σ 2 -σ 1 || 2 ＜κ (21)
The result converges to a target solution, where κ is empirically set to 0.025. If not, sigma is calculated 2 、σ 1 、t k+1 Assigned to sigma respectively 1 、σ 0 And t k And continuing the iteration step seven until the iteration termination condition is met to obtain a target solution.
The MRF-based real aperture scanning radar super-resolution imaging process is completed, and the imaging result is shown in fig. 7. From the figure, the method provided by the invention can well realize super-resolution imaging of the real aperture radar, and the recovery of the X shape is far better than the result of a contrast algorithm.
The foregoing has outlined and described the basic principles, 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, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (5)
1. The MRF-based real aperture scanning radar super-resolution imaging method is characterized by comprising the following steps of:
introducing structure prior information represented by a hidden Markov random field into an objective function through a regularization framework;
solving the problem of optimizing the objective function by using a rapid iteration threshold contraction method, and finally obtaining a super-resolution imaging result of the target;
the structure prior information expressed by a hidden Markov random field is introduced into an objective function through a regularization framework, and firstly, parameters of an imaging system are initialized, specifically:
let the platform motion velocity be v, the antenna beam scanning velocity omega, the radar lower view angle beThe target point is marked as P (r) 0 ,θ 0 ) T is azimuth time, and the target point distance history r P (t) is
The slant distance is obtained by Taylor expansion and one-time term approximation
The point target echo expression is denoted s P (τ,t)：
Where τ is the distance-to-time variable, σ 0 For the scattering intensity of the point target, h (t) is the two-way beam pattern of the antenna, t 0 For the time of beam center irradiation to point P, rect [. Cndot.]Represents a distance time window, c is the speed of light, T r Representing distance-time pulse width, f 0 For carrier frequency, K r Is the time chirp rate of the transmitted signal;
after imaging system parameters are initialized, the echo is subjected to distance pulse compression, and the method specifically comprises the following steps:
for a scattering function ofThe echo of (2) is the integral of the echo of the whole point target, wherein +.>For the initial skew of the target, +.>Azimuthal coordinates of the target; since t= (θ - θ) a ) ω and τ=2r/c, where θ a For the initial scan angle, a surface target echo is obtained according to equations (2) and (3):
for the acquired two-dimensional echo data s (r, theta), constructing a matched filter by utilizing radar emission signal parameters, and performing pulse compression on the distance direction to obtain distance compressed data s out (r，θ)；
After the distance pulse compression, linear migration correction is carried out, specifically:
after distance compression, for the target planeUpper located arc +.>All the above point targets whose echo position centers are to be staggered and overlapped on a straight line +.>Applying; linear scale transformation of variable r to eliminate range walk generated by platform motion
After the linear migration is corrected, constructing an azimuth convolution signal model, which specifically comprises the following steps:
writing azimuth signals 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)
for the above model, constructing an azimuth convolution signal vector model:
s＝Hσ+n (8)
wherein s= [ s ] 1 ，...，s N ] T Sum sigma= [ sigma ] 1 ,…,σ N ] T Respectively representing echo data and target scattering coefficient in a range gate, n= [ n ] 1 ,...,n N ] T The vector is a noise vector, N is the number of vectors, and H is a convolution matrix constructed by an antenna pattern H (theta);
after constructing the azimuth convolution signal model, constructing an imaging objective function, specifically:
for the noise sensitivity problem in deconvolution operation, a regularization method is adopted to solve the problem, and a standard regularization equation for solving the problem is adopted:
wherein,in the case of a data-fidelity item, i Γ (σ) i q For the regularization term, Γ (σ) is a specific operation of the regularization term, q is a norm of the regularization term, λ is used for balancing the fidelity of the measured data and the influence of the constraint of the regularization term, and is determined by an L-curve method;
Huber-Markov is chosen as the regularization term
Wherein ρ is T (. Cndot.) is a Huber function,for coefficient vector of clique c, +.>Is the temperature parameter, Z is the normalized constant, and the superscript (& gt) t Represented as a transpose operation; the roughness of the image is obtained from the second derivative:
the definition of the Huber function is:
the threshold T penalizes the grey level variation of the image;
substituting the formulas (10) (11) (12) into the formula (9), the objective function of RASR super-resolution imaging becomes:
2. the MRF-based real aperture scanning radar super-resolution imaging method of claim 1, wherein constructing a complete image objective function, and solving 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 rapid iterative contraction/threshold algorithm, and the gradient of the objective function is obtained
Wherein ( m For the mth element of the vector in brackets, diag (·) is a diagonal matrix, ε is a constant introduced to solve for the non-microminiaturization due to the non-smoothness of the objective function; the one iteration threshold shrink operation process is:
wherein,R n →R n for the contraction operator, it is defined as:
3. the MRF-based real aperture scanning radar super-resolution imaging method according to claim 2, wherein after objective function gradient is solved, the objective function is solved in a rapid iterative manner, and the specific solving process is as follows:
step k:
σ k ＝ψ(y k ) (17)
wherein k is>1，σ k Is the result of the kth cycle, y k Is a predictive vector, t, for accelerating the iterative process k Is a parameter controlling the convergence speed.
4. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the super-resolution imaging method as claimed in any one of claims 1 to 3 when the computer program is executed by the processor.
5. A computer-readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the super-resolution imaging method as claimed in any one of claims 1 to 3.
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