CN105954750A  Stripmap synthetic aperture radar nonsparse scene imaging method based on compressed sensing  Google Patents
Stripmap synthetic aperture radar nonsparse scene imaging method based on compressed sensing Download PDFInfo
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 CN105954750A CN105954750A CN201610284244.6A CN201610284244A CN105954750A CN 105954750 A CN105954750 A CN 105954750A CN 201610284244 A CN201610284244 A CN 201610284244A CN 105954750 A CN105954750 A CN 105954750A
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 238000003384 imaging method Methods 0.000 title claims abstract description 57
 239000011159 matrix material Substances 0.000 claims abstract description 69
 238000004422 calculation algorithm Methods 0.000 claims abstract description 45
 238000002592 echocardiography Methods 0.000 claims abstract description 26
 238000005070 sampling Methods 0.000 claims abstract description 24
 238000005457 optimization Methods 0.000 claims abstract description 11
 230000001131 transforming Effects 0.000 claims abstract description 9
 238000006243 chemical reaction Methods 0.000 claims abstract description 4
 238000007906 compression Methods 0.000 claims description 15
 230000015572 biosynthetic process Effects 0.000 claims description 11
 238000005755 formation reaction Methods 0.000 claims description 10
 230000005012 migration Effects 0.000 claims description 7
 230000000875 corresponding Effects 0.000 claims description 3
 ROHFNLRQFUQHCHYFKPBYRVSAN Lleucine Chemical compound 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Classifications

 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING 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
 G01S13/88—Radar or analogous systems specially adapted for specific applications
 G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
 G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
 G01S13/904—SAR modes
 G01S13/9054—Stripmap mode

 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING 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
 G01S13/88—Radar or analogous systems specially adapted for specific applications
 G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
 G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
 G01S13/904—SAR modes
Abstract
The invention relates to a stripmap synthetic aperture radar nonsparse scene imaging method based on compressed sensing and belongs to the technical field of radar imaging. The method comprises the steps that: an analog/digital conversion module on a satellite samples radar receiving analog signals at a Nyquist sampling rate, and an original echo complex number data matrix is obtained; downsampling is carried out on echo complex number data randomly, an imaging matrix of a distance doppler algorithm is constructed, and an observed value of a scene amplitude image is obtained; a sparse reconstruction model of compressed sensing is established, and the observed value of the scene amplitude image is utilized to recover a discrete cosine transform coefficient of a target scene amplitude image; and twodimensional discrete cosine inverse transformation is carried out on the reconstructed coefficient, and an amplitude image of a target scene is obtained. The method is used for a nonsparse scene, and the scene amplitude image with a relatively high resolution is reconstructed by means of a small number of observed values, the compressed sensing model and an L1 norm convex optimization means.
Description
Technical field
The invention belongs to radar imaging technology field, particularly to the spaceborne synthesis of striptype based on range Doppler compressed sensing
Aperture radar is to nonsparse scene formation method.
Background technology
Synthetic aperture radar (SAR, Synthetic Aperture Radar) is a kind of highresolution imaging radar, it is possible to whole day
Time, region roundtheclock, big, carry out target actively observing, not by the shadow of the conditions such as weather, light, weather highresolution
Ring, be widely used in radar imagery field.SAR obtains highresolution in distance upwardly through launching big bandwidth signal
Rate, upwards relies on radar platform motion equivalence to form long synthetic aperture to obtain highresolution in orientation.Owing to SAR is at radar
The superiority that imaging field is possessed, the research of SAR imaging algorithm is always a big focus.
Traditional striptype Spaceborne SAR Imaging algorithm is mainly based upon the theory of pulse compression, completes to be focused into echo data
As operation.Range Doppler algorithm (RDA) is one of the most classical SAR imaging algorithm.This algorithm is at distance and bearing
Utilize matched filtering to complete pulse compression in both direction, the imaging process of two dimension is divided into two onedimensional operations；And according to
Large scale time difference on distance and bearing, completes distance unit migration between two onedimensional operations and corrects (RCMC),
Adjust the distance and bearing data decouples.In order to improve the efficiency of process, the matched filtering convolution operation of two dimensions is all changed
To frequency domain by being multiplied realization.In order to process the data under relatively large slanting view angle machine, range Doppler algorithm introduces secondary range pressure
Contracting (SRC) compensates the coupling of rangeazimuth target phase course, thus contributes to eliminating the phase place under stravismus and large aperture
Coupling distortion.
Resolution is to weigh the important indicator of radar imagery quality, differentiates theory according to radar, and SAR system resolution is by radar
The bandwidth of signal determines.And according to nyquist sampling theorem, the real sample frequency of system must be at least the radar letter of twice
Number bandwidth.Higher resolution needs higher bandwidth and sample rate, also imply that the storage of higher data and transmission demand with
And more complicated system design.For satelliteborne synthetic aperture radar, down data links bandwidth becomes raising radar imagery and divides
The bottleneck of resolution, traditional imaging algorithm such as RDA has been difficult to meet highresolution demand, find new data acquisition and
The method of signal processing becomes the most urgent.
Compressed sensing (CS, Compressed Sensing) theory utilizes the openness of signal, and signal is compressed sampling,
Primary signal is recovered by the algorithm of sparse reconstruct.Utilize the novel SAR imaging algorithm that compressive sensing theory designs, its letter
Number sample rate is no longer limited by nyquist sampling theorem, thus reduces signal sampling rate and transmitted data amount, can dash forward
The bottleneck that broken traditional algorithm is met with.
In recent years, academia has carried out the research that compressive sensing theory introduces radar imagery.Baraniuk et al. proposes first
Compressive sensing theory can be introduced in radar imagery.Potter et al. have studied and uses sparse reconstruction to calculate in Radar Imaging Processing
Method and stochastic sampling strategy.Ender et al. is from the framework of existing radar system, it is proposed that thunder based on compressed sensing
Reach some problems that system is faced to practicality from theory.Introduce two representative compressed sensing SAR below
The main contributions of imaging technique and the deficiency of existence.
1.S.Samadi.,and M.A.MasnadiShirazi.,Sparse representation based
synthetic aperture radar imaging,IET Radar Sonar Navig.,vol.5,no.2,pp.182–193,
Feb.2011.
Article proposes a kind of SAR imaging algorithm based on compressed sensing.This algorithm investigates signal to be restored based on crossing complete word
The sparse representation that allusion quotation is set up.The target scene amplitude of imaging generally possesses sparse in some transform domains such as wavelet field, DCT domain
Property, by corresponding mistake complete dictionary, scene amplitude carried out sparse representation, and set up scene amplitude sparse representation coefficient and field
The combined optimization problem of scape phase information.The process of SAR imaging is converted into and solves this combined optimization problem, thus weight
Build out scene amplitude, and estimate scene phase information.Article refer to solve the coordinate decline side of this combined optimization problem
Method, but convergence is not issued a certificate.
Compressed sensing SAR imaging algorithm in abovementioned article is compared with traditional imaging algorithm, can reduce radar return data
Realize the image forming job to nonsparse target scene while amount, but be disadvantageous in that the derivation algorithm of combined optimization problem
Complexity is big, and convergence is the most accurately proved.
2. the Wu Yirong of CAS Electronics Research Institute, Hong Wen, Zhang Bingchen et al. " sparse microwave imaging study into
Exhibition [J] " in article (radar journal, 2014,3 (4): 383 395.)
Propose the algorithm frame directly carrying out sparse SAR imaging from initial data territory.This algorithm is first based on nyquist sampling
Theorem receives echo to radar and completes sampling, then adjusts the distance and randomly draws to Data in Azimuth Direction, sets up echo data
Sparse representation relation between observation and scene scatters point intensity, recycles sparse restructing algorithm and realizes the connection of distance/direction
Occlusal reconstruction.This algorithm avoids the pretreatment work of the series of complex to radar return data, simplifies radar imaging system
Complexity, reduces the echo data amount needed for radar imagery.Meanwhile, for directly carrying out sparse reconstruction from initial data territory
The problem of huge amount of calculation, this article proposes sparse SAR imaging algorithm based on analogue echoes operator and quickly realizes,
Echo data is carried out two dimension decoupling, makes computational efficiency by O (N^{2}) improve to O (NlogN).
Comparing with traditional range Doppler algorithm etc., the sparse SAR imaging algorithm in this article can be under conditions of downsampled
Rebuild sparse target scene, and reduce the echo data amount needed for imaging, reduce data transmission and storage burden；Simultaneously can be
Nonsparse target scene is rebuild under conditions of fully sampled.Additionally, this algorithm restrained effectively the secondary lobe in conventional imaging method
Effect, improves the resolution capability of target, improves picture quality.This algorithm main disadvantage is that cannot be downsampled
Under the conditions of reconstruct nonsparse target scene, it is impossible to embody compressed sensing technology and regain one's integrity from a small amount of observation data information
Ability.
By the abovementioned summary to existing striptype Spaceborne SAR Imaging method based on compressed sensing it can be seen that existing
Compressed sensing SAR formation method has the strongest advantage for sparse scene imaging, can improve while reducing data volume
Picture quality.But target scene does not the most possess good openness during the work of actual radar, existing for nonsparse scene
Compressed sensing imaging algorithm there is the problems such as data volume is huge, computation complexity is high.The transmission link bandwidth of satelliteborne SAR is tight
Heavily constraining transmitted data amount, existing compressed sensing SAR imaging algorithm is difficult to apply to the nonof actual spaceborne radar system
In sparse scene.
Summary of the invention
It is an object of the invention to be directed to the confinement problems of current spaceborne compressed sensing SAR imaging algorithm application scenarios, propose
The nonsparse scene formation method of a kind of stripmap synthetic aperture radar based on compressed sensing, the method for nonsparse scene,
Utilize a small amount of observation by compressed sensing model and L_{1}The convex optimization means of norm, reconstructs highresolution scene map of magnitudes
Picture.
The nonsparse scene formation method of a kind of based on compressed sensing stripmap synthetic aperture radar that the present invention proposes, its feature
Being, the method comprises the following steps:
1) the analog/digital conversion module on satellite receives analog signal sampling with nyquist sampling rate to radar, it is thus achieved that former
Beginning echo complex data matrix X_{0}, matrix X_{0}Horizontal direction represent orientation to, vertical direction represent distance to；
2) to step 1) in echo complex data the most downsampled, and construct the imaging array Ψ of range Doppler algorithm,
Obtain the observation of scene magnitude image；
3) set up the sparse reconstruction model of compressed sensing, utilize step 2) in scene magnitude image observation recover target
Discrete cosine transform (DCT) coefficient of scene magnitude image
4) to step 3) the middle DCT coefficient rebuildCarry out 2D discrete cosine inverse transformation and obtain the amplitude of target scene
Image  X_{6}。
The feature of the present invention and beneficial effect:
Unlike existing compressed sensing formation method, the method for the present invention is directed to nonsparse scene.By dilute
Dredge inverting to combine with range Doppler algorithm, it is possible to realize nonfrom a small amount of echo observation data of striptype satelliteborne SAR
The imaging of sparse scene.The method can reduce to conventional imaging method observation data volume on the premise of not losing image property
About the 10% of data volume, thus significantly reduce satelliteborne SAR down data links bandwidth demand, breach tradition imaging
The data volume bottleneck that algorithm is met with.Result in RADARSAT1 actual satelliteborne SAR data illustrates the method
Effectiveness.Simultaneously because the reservation of matched filtering operation, the inventive method has preferable noise robustness.
Accompanying drawing explanation
Fig. 1 is the overall procedure block diagram of the inventive method.
Fig. 2 is the target scene image of a piece 50 × 50 that utilizes traditional range Doppler algorithm imaging to obtain.
Fig. 3 is the scene magnitude image that method based on the present invention reconstructs.
Detailed description of the invention
The nonsparse scene formation method of stripmap synthetic aperture radar based on compressed sensing that the present invention proposes combines attached
Figure and embodiment are described as follows:
The main flow of the inventive method is as it is shown in figure 1, comprise the following steps:
Step 1: the analog/digital conversion module on satellite receives analog signal sampling with nyquist sampling rate to radar, obtains
Obtain original echo complex data matrix X_{0}, matrix X_{0}Horizontal direction represent orientation to, vertical direction represent distance to；
Step 2: the most downsampled to the echo complex data in step 1, and construct the imaging array of range Doppler algorithm
Ψ, it is thus achieved that the observation of scene magnitude image；
If radar is positive sidelooking, the target scene of imaging is made up of the discrete space dot matrix of L × L, and wherein L is positive integer, table
Show distance to orientation scattering point number in a dimension.Raw radar data matrix X_{0}It it is the plural square of a N × N
Battle array, wherein N is positive integer, represent echo data distance to orientation to sampling number (actual imaging scene distance to
Orientation to scattering point number the most equal, echo data distance to orientation to sampling number the most equal.This
The hypothesis of invention without loss of generality, has no effect on method performance, more succinct on formula.When being embodied as, L depends on choosing
The image scene size taken, N depends on the sampling number of actual admission data)；Specifically include:
Step 2.1: to original echo complex data matrix X_{0}Along distance to orientation to making two dimensional discrete Fourier transform
(2DDFT) twodimensional frequency data matrix X, is obtained_{1}, as shown in formula (1):
X_{1}=FX_{0}F^{T} (1)
Wherein F is DFT transform matrix, ()^{T}The transposition operation of representing matrix, each element F (k, such as formula of form n) in matrix F
(2) shown in:
Step 2.2: in distance to twodimensional frequency data matrix X_{1}Operate, including pulse compression, range migration and
Secondary range compression operates: specifically include first to X_{1}Vectorization operates, and each leu of original matrix is spliced from top to bottom
Constitute a column vector, be expressed as ()^{vec}(i.e. for the matrix X, X of a N × N^{vec}It is an a length of N^{2}Row
Vector)；Then, distance to operation such as formula (3) shown in:
X in formula_{2}Represent X_{1}Data matrix after Range compress, the N being made up of the diagonal matrix of N number of N × N^{2}×N^{2}Diagonal angle
Battle array P, as shown in formula (4):
Wherein P_{i}It is by p_{i,0},p_{i,1},…,p_{i,N1}The diagonal matrix constituted for diagonal element, p_{i,m}Form such as formula (5) shown in:
Wherein i=0,1 ... N1, m=0,1 ... N1, R_{s}For the distance of band scene center line Yu radar route, K_{r}It is that radar is sent out
The frequency modulation rate of the linear FM signal penetrated, c represents the light velocity, and v is the speed of radar platform motion, and λ is radar center wavelength,
f_{0}It is radar carrier frequency, f_{0}=c/ λ.F_{s}It is radar echo signal sample rate, F_{p}It it is radar pulse tranmitting frequency；In formulaWithThree phase places
Item is corresponding in turn to pulse compression, secondary range compression and the distance unit migration correction (spacevariant of distance unit migration in scene
It is left in the basket, i.e. assumes that the target at different distance has identical distance unit migration curve)；
Step 2.3: data X after pulse compression of adjusting the distance_{2}Make distance to inverse discrete Fourier transform (IDFT), by number
According to transforming to distanceDoppler territory, obtain matrix X_{3}, as shown in formula (6):
X_{3}=F^{1}·X_{2} (6)
Step 2.4: to data X_{3}Carry out Azimuth Compression, pass throughOne phase compensation matrix W of premultiplication realizes, such as formula
(7) shown in:
Wherein X_{4}Representing the data matrix after distance, Azimuth Compression, W is to be made up of the diagonal matrix of N number of N × Ndimensional degree
N^{2}×N^{2}Diagonal matrix, as shown in formula (8):
Wi is by w_{i,0},w_{i,1},…,w_{i,N1}The diagonal matrix constituted for diagonal element, the form of wherein wi, m is:
Wherein i=0,1 ... N1, m=0,1 ... N1 (remaining each parameter physical significance with step 2.2 described in identical)；
Step 2.5: along orientation to X_{4}In each distance unit make IDFT, obtain airspace data matrix X_{5}, such as formula
(10) shown in:
X_{5}=X_{4}·(F^{1})^{T} (10)
Scene complex image matrix X_{6}By being calculated of formula (11):
X_{6}=U X_{5}·U^{T} (11)
Wherein U=[I_{L}O_{L×(NL)}], I_{L}It is the unit matrix of L × L, O_{L×(NL)}It it is the full null matrix of L × (NL)；
(in sum, every single stepping of range Doppler algorithm has all been organized into the computing of matrixvector multiplication.) basis
Kronecker product theorem (Kroneker product theorem), has following identity to set up:
Wherein A, B and X represent three matrixes,Represent the Kronecker product of two matrixes.Simultaneous formula (1)(11), obtain away from
From the matrix multiplication operation form of range and Doppler, as shown in formula (13):
Wherein I_{N}It is the unit matrix of N × N,It is the column vector of original echo complex data composition,It is that target scene is multiple
The column vector that number image array changes into；So shown in the concrete form such as formula (14) of the imaging array Ψ of range Doppler algorithm:
Step 3: set up the sparse reconstruction model of compressed sensing, utilizes the scene magnitude image observation in step 2 to recover
The DCT coefficient of target scene magnitude imageSpecifically include:
(the magnitude image data of imageable target scene are sparse or compressible in DCT domain.) by magnitude image is made two
Dimension discrete cosine transform (2DDCT) can obtain DCT coefficient X of its correspondence_{DCT}, this DCT coefficient is done two dimension from
Dissipate cosine inverse transformation and obtain original amplitude view data, as shown in formula (15):
X_{6}=D^{1}X_{DCT}(D^{1})^{T} (15)
Wherein  X_{6} represent target scene magnitude image, X_{DCT}It it is the coefficient square of scene magnitude image twodimension discrete cosine transform
Battle array, this coefficient matrix contains the big component of minority and more small component, possesses typical compressibility；D represents onedimensional
Dct transform matrix, each element D in matrix D (k, shown in the such as formula of form n) (16):
Wherein
Kronecker product theorem is used to obtain equation as shown in formula (17):
Wherein
Simultaneous formula (13) and (17), obtain equation as shown in formula (19):
Wherein Ψ is the range Doppler algorithm imaging array as shown in formula (14):
(owing to dct transform matrix D is an orthogonal matrix, so Φ is an orthogonal matrix equally,It is sparse
Or compressible)
IfBe Ksparse (In only K bigger component, K ＜ ＜ L^{2}), the method utilizing compressed sensing
Setting up sparse reconstruction model just can be from scene magnitude imageIndividual observation recoversThe magnitude image of scene is obtained again by 2D discrete cosine inverse transformation；Randomly select the unduplicated M of Ψ and Φ
Row constitutes two submatrix Ψ_{M}And Φ_{M}, as shown in formula (20):
WhereinAnd for 1≤m, n≤M, i_{M}≠i_{N}；
Pass throughObtain M observation of scene magnitude image, set up the compressed sensing observation mould as shown in formula (21)
Type:
Recover by solving the L1 norm optimization problem as shown in formula (22)
Wherein ε is error threshold, and value is vectorL_{2}The 5% of norm.Use (Boyd et al. exploitation)
Convex majorized function bag cvx realizes L_{1}Solving of norm optimization problem；
(present invention obtains its amplitude to complex image modulo operation, it is ensured that openness in DCT domain of data, also makes
Feasibility has been possessed by the means solution SparseField scape imaging problem by no means of the sparse reconstruction of compressed sensing.)
Step 4:
To the DCT coefficient rebuild in step 3Carry out 2D discrete cosine inverse transformation and obtain the magnitude image of target scene
X_{6}, as shown in formula (23):
X_{6}=D^{1}X_{DCT}(D^{1})^{T} (23)
Present invention is generally directed to, in the confinement problems of current spaceborne compressed sensing SAR imaging algorithm application scenarios, be proposed for
Nonsparse scene, utilizes a small amount of observation by compressed sensing model and L_{1}The convex optimization means of norm, reconstructs highresolution
The New Type Radar formation method of scene image.Compare with existing striptype Spaceborne SAR Imaging algorithm based on compressed sensing,
The inventive method can be generalized to nonsparse scene, and reduces the echo data amount needed for imaging；Simultaneously because matched filtering behaviour
The reservation made, the inventive method has preferable noise robustness.
The technique effect of the inventive method:
Choose true striptype satelliteborne SAR echo data and carry out emulation experiment to verify formation method proposed by the invention
Effect.
Have chosen the actual satelliteborne SAR data of RADARSAT1, these data are by list of references: Ian G, Frank H. synthesizes
Aperture radar imagingalgorithm and realization [M]. Hong Wen, flood east brightness etc. is translated. Beijing: Electronic Industry Press, with book in 2007:5.
The attached CD given provides.Data acquisition is from the RADARSAT1 fine pattern 2 on June 16th, 2002, and system is relevant joins
Number is as shown in the table:
For the consideration of amount of calculation, the resolution of RADARSAT1 is reduced to about 20m in proportion.In order to be simplified to as mistake
Journey, the doppler ambiguity of image is calibrated in advance.Choose 125 × 125 sizes raw radar data matrix (N=125),
Utilize the target scene (L=50) that traditional range Doppler algorithm imaging obtains a piece 50 × 50, as shown in Figure 2.Figure
Middle transverse axis represent orientation to, the longitudinal axis represent distance to.Three roads having a generally triangular shape distribution of shapes can be told from image
The significant target in road and rightside course roadside.Can be seen that scene moderately and strongly inverse scattering point is more from imaging results, structure is complex,
Being typical nonsparse scene, existing SAR imaging algorithm based on compressed sensing cannot be in the condition reducing imaging data amount
Under complete the accurate imaging to this scene.
Next M=1300 is set and generates 1300Observation, method based on the present invention rebuild appear on the scene
Scape magnitude image, as shown in Figure 3.In figure transverse axis represent orientation to, the longitudinal axis represent distance to.Still can be clear in image
Tell road and target, and and the relative error of Fig. 2 is about 4%.In the premise losing imaging performance hardly
Under, needed for the inventive method, observation is less than the 10% of tradition range Doppler algorithm, greatly reduces satelliteborne SAR data
Transmission demand.Simulation result in true SAR data has confirmed the inventive method and can calculate far below tradition range Doppler
Needed for method in the case of observation, reconstruct the target scene magnitude image suitable with traditional method quality, and can be fine
Ground is applicable to nonsparse target scene.
Claims (3)
1. the nonsparse scene formation method of stripmap synthetic aperture radar based on compressed sensing, it is characterised in that should
Method comprises the following steps:
1) the analog/digital conversion module on satellite receives analog signal sampling with nyquist sampling rate to radar, it is thus achieved that former
Beginning echo complex data matrix X_{0}, matrix X_{0}Horizontal direction represent orientation to, vertical direction represent distance to；
2) to step 1) in echo complex data the most downsampled, and construct the imaging array Ψ of range Doppler algorithm,
Obtain the observation of scene magnitude image；
3) set up the sparse reconstruction model of compressed sensing, utilize step 2) in scene magnitude image observation recover target
Discrete cosine transform (DCT) coefficient of scene magnitude image
4) to step 3) the middle DCT coefficient rebuildCarry out 2D discrete cosine inverse transformation and obtain the amplitude of target scene
Image  X_{6}。
2. as claimed in claim 1 method, it is characterised in that described step 2) specifically include: set radar as positive sidelooking,
The target scene of imaging is made up of the discrete space dot matrix of L × L, and wherein L is positive integer, represent distance to orientation to one
Scattering point number in dimension.Raw radar data matrix X_{0}Being the complex matrix of a N × N, wherein N is positive integer,
Represent echo data distance to orientation to sampling number；
2.1) to original echo complex data matrix X_{0}Along distance to orientation to making two dimensional discrete Fourier transform
(2DDFT) twodimensional frequency data matrix X, is obtained_{1}, as shown in formula (1):
X_{1}=FX_{0}F^{T} (1)
Wherein F is DFT transform matrix, ()^{T}The transposition operation of representing matrix, each element F (k, such as formula of form n) in matrix F
(2) shown in:
2.2) in distance to twodimensional frequency data matrix X_{1}Operate, including pulse compression, range migration and secondary
Range compress operates: specifically include first to X_{1}Vectorization operates, secondary for each leu of the original matrix structure that is stitched together from top to bottom
Become a column vector, be expressed as ()^{vec}(i.e. for the matrix X, X of a N × N^{vec}It is an a length of N^{2}Column vector)；
Then, distance to operation such as formula (3) shown in:
X in formula_{2}Represent X_{1}Data matrix after Range compress, the N being made up of the diagonal matrix of N number of N × N^{2}×N^{2}Diagonal angle
Battle array P, as shown in formula (4):
Wherein P_{i}It is by p_{i,0},p_{i,1},…,p_{i,N1}The diagonal matrix constituted for diagonal element, p_{i,m}Form such as formula (5) shown in:
Wherein i=0,1 ... N1, m=0,1 ... N1, R_{s}For the distance of band scene center line Yu radar route, K_{r}It is that radar is sent out
The frequency modulation rate of the linear FM signal penetrated, c represents the light velocity, and v is the speed of radar platform motion, and λ is radar center wavelength,
f_{0}It is radar carrier frequency, f_{0}=c/ λ.F_{s}It is radar echo signal sample rate, F_{p}It it is radar pulse tranmitting frequency；In formulaWithThree phase places
Item is corresponding in turn to pulse compression, secondary range compression and distance unit migration and corrects；
2.3) adjust the distance data X after pulse compression_{2}Make distance to inverse discrete Fourier transform (IDFT), transform the data into
To distanceDoppler territory, obtain matrix X_{3}, as shown in formula (6):
X_{3}=F^{1}·X_{2} (6)
2.4) to data X_{3}Carry out Azimuth Compression, pass throughOne phase compensation matrix W of premultiplication realizes, such as formula (7)
Shown in:
Wherein X_{4}Representing the data matrix after distance, Azimuth Compression, W is to be made up of the diagonal matrix of N number of N × Ndimensional degree
N^{2}×N^{2}Diagonal matrix, as shown in formula (8):
W_{i}It is by w_{i,0},w_{i,1},…,w_{i,N1}The diagonal matrix constituted for diagonal element, wherein w_{i,m}Form be:
Wherein i=0,1 ... N1, m=0,1 ... identical described in N1 (remaining each parameter physical significance and step 2.2))；
2.5) along orientation to X_{4}In each distance unit make IDFT, obtain airspace data matrix X_{5}, such as formula (10)
Shown in:
X_{5}=X_{4}·(F^{1})^{T} (10)
Scene complex image matrix X_{6}By being calculated of formula (11):
X_{6}=U X_{5}·U^{T} (11)
Wherein U=[I_{L}O_{L×(NL)}], I_{L}It is the unit matrix of L × L, O_{L×(NL)}It it is the full null matrix of L × (NL)；
According to Kronecker product theorem (Kroneker product theorem), following identity is had to set up:
Wherein A, B and X represent three matrixes,Represent the Kronecker product of two matrixes.Simultaneous formula (1)(11), obtain away from
From the matrix multiplication operation form of range and Doppler, as shown in formula (13):
Wherein I_{N}It is the unit matrix of N × N,It is the column vector of original echo complex data composition,It is that target scene is multiple
The column vector that number image array changes into；So shown in the concrete form such as formula (14) of the imaging array Ψ of range Doppler algorithm:
3. method as claimed in claim 2, it is characterised in that described step 3) specifically include:
DCT coefficient X of its correspondence can be obtained by magnitude image being made twodimension discrete cosine transform (2DDCT)_{DCT},
This DCT coefficient is done 2D discrete cosine inverse transformation and obtains original amplitude view data, as shown in formula (15):
Wherein  X_{6} represent target scene magnitude image, X_{DCT}It it is the coefficient square of scene magnitude image twodimension discrete cosine transform
Battle array, this coefficient matrix contains the big component of minority and more small component, possesses typical compressibility；D represents onedimensional
Dct transform matrix, each element D in matrix D (k, shown in the such as formula of form n) (16):
Wherein K=0,1 ..., L1, n=0,1 ..., L1；
Kronecker product theorem is used to obtain equation as shown in formula (17):
Wherein
Simultaneous formula (13) and (17), obtain equation as shown in formula (19):
Wherein Ψ is the range Doppler algorithm imaging array as shown in formula (14):
IfIt is that Kis sparse,In only K bigger component, K ＜ ＜ L^{2}, utilize the method for compressed sensing to build
Vertical sparse reconstruction model just can be from scene magnitude imageM=O (Klog (L^{2}/ K)) individual observation recoversThe magnitude image of scene is obtained again by 2D discrete cosine inverse transformation；Randomly select the unduplicated M of Ψ and Φ
Row constitutes two submatrix Ψ_{M}And Φ_{M}, as shown in formula (20):
WhereinAnd for 1≤m, n≤M, i_{M}≠i_{N}；
Pass throughObtain M observation of scene magnitude image, set up the compressed sensing observation mould as shown in formula (21)
Type:
By solving the L as shown in formula (22)_{1}Norm optimization problem recovers
Wherein ε is error threshold, and value is vectorL_{2}The 5% of norm.Use (Boyd et al. exploitation)
Convex majorized function bag cvx realizes L_{1}Solving of norm optimization problem.
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Inventor after: Li Gang Inventor after: Yang Xiaoyu Inventor after: Zhang Qingjun Inventor after: Tang Zhihua Inventor before: Li Gang Inventor before: Yang Xiaoyu Inventor before: Zhang Qingjun Inventor before: Tang Zhihua 