CN105954750A - Strip-map synthetic aperture radar non-sparse scene imaging method based on compressed sensing - Google Patents

Abstract

The invention relates to a strip-map synthetic aperture radar non-sparse 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 two-dimensional 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 non-sparse 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

The non-sparse scene formation method of stripmap synthetic aperture radar based on compressed sensing

Technical field

The invention belongs to radar imaging technology field, particularly to the spaceborne synthesis of strip-type based on range Doppler compressed sensing Aperture radar is to non-sparse scene formation method.

Background technology

Synthetic aperture radar (SAR, Synthetic Aperture Radar) is a kind of high-resolution imaging radar, it is possible to whole day Time, region round-the-clock, big, carry out target actively observing, not by the shadow of the conditions such as weather, light, weather high-resolution Ring, be widely used in radar imagery field.SAR obtains high-resolution in distance upwardly through launching big bandwidth signal Rate, upwards relies on radar platform motion equivalence to form long synthetic aperture to obtain high-resolution 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 strip-type Space-borne 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 one-dimensional operations；And according to Large scale time difference on distance and bearing, completes distance unit migration between two one-dimensional 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 range-azimuth 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 satellite-borne 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 high-resolution 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.Masnadi-Shirazi.,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 above-mentioned article is compared with traditional imaging algorithm, can reduce radar return data Realize the image forming job to non-sparse 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 (N²) improve to O (NlogN).

Comparing with traditional range Doppler algorithm etc., the sparse SAR imaging algorithm in this article can be under conditions of down-sampled Rebuild sparse target scene, and reduce the echo data amount needed for imaging, reduce data transmission and storage burden；Simultaneously can be Non-sparse 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 down-sampled Under the conditions of reconstruct non-sparse 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 above-mentioned summary to existing strip-type Space-borne 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 non-sparse scene Compressed sensing imaging algorithm there is the problems such as data volume is huge, computation complexity is high.The transmission link bandwidth of satellite-borne SAR is tight Heavily constraining transmitted data amount, existing compressed sensing SAR imaging algorithm is difficult to apply to the non-of 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 non-sparse scene formation method of a kind of stripmap synthetic aperture radar based on compressed sensing, the method for non-sparse scene, Utilize a small amount of observation by compressed sensing model and L₁The convex optimization means of norm, reconstructs high-resolution scene map of magnitudes Picture.

The non-sparse 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 X₀, matrix X₀Horizontal direction represent orientation to, vertical direction represent distance to；

2) to step 1) in echo complex data the most down-sampled, 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 2-D discrete cosine inverse transformation and obtain the amplitude of target scene Image | X₆|。

The feature of the present invention and beneficial effect:

Unlike existing compressed sensing formation method, the method for the present invention is directed to non-sparse scene.By dilute Dredge inverting to combine with range Doppler algorithm, it is possible to realize non-from a small amount of echo observation data of strip-type satellite-borne 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 satellite-borne SAR down data links bandwidth demand, breach tradition imaging The data volume bottleneck that algorithm is met with.Result in RADARSAT-1 actual satellite-borne 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 non-sparse 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 X₀, matrix X₀Horizontal direction represent orientation to, vertical direction represent distance to；

Step 2: the most down-sampled 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 side-looking, 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 X₀It 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 X₀Along distance to orientation to making two dimensional discrete Fourier transform (2D-DFT) two-dimensional frequency data matrix X, is obtained₁, as shown in formula (1):

X₁=FX₀F^T (1)

Wherein F is DFT transform matrix, ()^TThe transposition operation of representing matrix, each element F (k, such as formula of form n) in matrix F (2) shown in:

$F(k,n)=\frac{1}{\sqrt{N}}\exp (-j2\mathrm{\π}\frac{kn}{N}),k=0,1,...,N-1,n=0,1,...,N-1---\left(2\right)$

Step 2.2: in distance to two-dimensional frequency data matrix X₁Operate, including pulse compression, range migration and Secondary range compression operates: specifically include first to X₁Vectorization 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^vecIt is an a length of N²Row Vector)；Then, distance to operation such as formula (3) shown in:

$X_2^{vec}={\mathrm{PX}}_1^{vec}---\left(3\right)$

X in formula₂Represent X₁Data matrix after Range compress, the N being made up of the diagonal matrix of N number of N × N²×N²Diagonal angle Battle array P, as shown in formula (4):

Wherein P_iIt is by p_i,0,p_i,1,…,p_i,N-1The diagonal matrix constituted for diagonal element, p_i,mForm such as formula (5) shown in:

$p_{i,m}=\exp \{j\frac{\mathrm{\π}}{K_r}{\left(\frac{{\mathrm{mF}}_s}{N}\right)}^2-j\mathrm{\π}\frac{{\mathrm{cR}}_s}{2v^2{f}_0^3}{\left(\frac{{\mathrm{iF}}_p}{N}\right)}^2{(1-\frac{{\mathrm{\λ}}^2}{4v^2}{\left(\frac{{\mathrm{iF}}_p}{N}\right)}^2)}^{-3/2}{\left(\frac{{\mathrm{mF}}_s}{N}\right)}^2+j\frac{4{\mathrm{\πR}}_s}{c}\[{(1-\frac{{\mathrm{\λ}}^2}{4v^2}{\left(\frac{{\mathrm{iF}}_p}{N}\right)}^2)}^{-1/2}-1\]\left(\frac{{\mathrm{mF}}_s}{N}\right)\}---\left(5\right)$

Wherein i=0,1 ... N-1, m=0,1 ... N-1, R_sFor the distance of band scene center line Yu radar route, K_rIt 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, f₀It is radar carrier frequency, f₀=c/ λ.F_sIt is radar echo signal sample rate, F_pIt 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 (space-variant 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 distance₂Make distance to inverse discrete Fourier transform (IDFT), by number According to transforming to distance-Doppler territory, obtain matrix X₃, as shown in formula (6):

X₃=F^-1·X₂ (6)

Step 2.4: to data X₃Carry out Azimuth Compression, pass throughOne phase compensation matrix W of premultiplication realizes, such as formula (7) shown in:

$X_4^{vec}=W\·X_3^{vec}---\left(7\right)$

Wherein X₄Representing the data matrix after distance, Azimuth Compression, W is to be made up of the diagonal matrix of N number of N × N-dimensional degree N²×N²Diagonal matrix, as shown in formula (8):

Wi is by w_i,0,w_i,1,…,w_i,N-1The diagonal matrix constituted for diagonal element, the form of wherein wi, m is:

$w_{i,m}=\exp \{j\frac{4\mathrm{\π}}{\mathrm{\λ}}\·\[R_s+(m-N/2)\·\frac{c}{2F_s}\]\·\sqrt{1-\frac{{\mathrm{\λ}}^2}{4v^2}\left(\frac{{\mathrm{iF}}_p}{N}\right)}\}---\left(9\right)$

Wherein i=0,1 ... N-1, m=0,1 ... N-1 (remaining each parameter physical significance with step 2.2 described in identical)；

Step 2.5: along orientation to X₄In each distance unit make IDFT, obtain airspace data matrix X₅, such as formula (10) shown in:

X₅=X₄·(F^-1)^T (10)

Scene complex image matrix X₆By being calculated of formula (11):

X₆=U X₅·U^T (11)

Wherein U=[I_L|O_L×(N-L)], I_LIt is the unit matrix of L × L, O_L×(N-L)It it is the full null matrix of L × (N-L)；

(in sum, every single stepping of range Doppler algorithm has all been organized into the computing of matrix-vector multiplication.) basis Kronecker product theorem (Kroneker product theorem), has following identity to set up:

$(B^T\⊗A)\·X^{vec}={\left(AXB\right)}^{vec}---\left(12\right)$

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):

$X_6^{vec}=(U\⊗U)\·(F^{-1}\⊗I_N)\·W\·(I_N\⊗F^{-1})\·P\·(F\⊗F)\·X_0^{vec}---\left(13\right)$

Wherein I_NIt 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:

$\mathrm{\Ψ}=(U\⊗U)\·(F^{-1}\⊗I_N)\·W\·(I_N\⊗F^{-1})\·P\·(F\⊗F)---\left(14\right)$

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 (2D-DCT) 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):

|X₆|=D^-1X_DCT(D^-1)^T (15)

Wherein | X₆| represent target scene magnitude image, X_DCTIt it is the coefficient square of scene magnitude image two-dimension discrete cosine transform Battle array, this coefficient matrix contains the big component of minority and more small component, possesses typical compressibility；D represents one-dimensional Dct transform matrix, each element D in matrix D (k, shown in the such as formula of form n) (16):

$D(k,n)=\mathrm{\α}\left(k\right)cos\left(\mathrm{\π}\frac{(2n+1)k}{2L}\right)---\left(16\right)$

Wherein

Kronecker product theorem is used to obtain equation as shown in formula (17):

${\left|X_6\right|}^{vec}=\mathrm{\Φ}\·X_{DCT}^{vec}---\left(17\right)$

Wherein

$\mathrm{\Φ}=D^{-1}\⊗D^{-1}---\left(18\right)$

Simultaneous formula (13) and (17), obtain equation as shown in formula (19):

$\left|\mathrm{\Ψ}\·X_0^{vec}\right|=\mathrm{\Φ}\·X_{DCT}^{vec}---\left(19\right)$

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 K-sparse (In only K bigger component, K ＜ ＜ L²), 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 2-D discrete cosine inverse transformation；Randomly select the unduplicated M of Ψ and Φ Row constitutes two submatrix Ψ_MAnd Φ_M, as shown in formula (20):

${\mathrm{\Ψ}}_M\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cccc}\mathrm{\Ψ}(i_1,1)& \mathrm{\Ψ}(i_1,2)& ...& \mathrm{\Ψ}(i_1,N^2)\\ \mathrm{\Ψ}(i_2,1)& \mathrm{\Ψ}(i_2,2)& ...& \mathrm{\Ψ}(i_2,N^2)\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ \mathrm{\Ψ}(i_M,1)& \mathrm{\Ψ}(i_M,2)& ...& \mathrm{\Ψ}(i_M,N^2)\end{array}\right],{\mathrm{\Φ}}_M\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cccc}\mathrm{\Φ}(i_1,1)& \mathrm{\Φ}(i_1,2)& ...& \mathrm{\Φ}(i_1,N^2)\\ \mathrm{\Φ}(i_2,1)& \mathrm{\Φ}(i_2,2)& ...& \mathrm{\Φ}(i_2,N^2)\\ .& .& & .\\ .& .& ...& .\\ .& .& & .\\ \mathrm{\Φ}(i_M,1)& \mathrm{\Φ}(i_M,2)& ...& \mathrm{\Φ}(i_M,N^2)\end{array}\right]---\left(20\right)$

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:

$\left|{\mathrm{\Ψ}}_M\·X_0^{vec}\right|={\mathrm{\Φ}}_M\·X_{DCT}^{vec}---\left(21\right)$

Recover by solving the L1 norm optimization problem as shown in formula (22)

$\begin{array}{ccc}min\left|\right|X_{DCT}^{vec}|{|}_1& s.t.& \left|\right|\left|{\mathrm{\Ψ}}_M\·X_0^{vec}\right|-{\mathrm{\Φ}}_M\·X_{DCT}^{vec}|{|}_2\≤\mathrm{\ϵ}\end{array}---\left(22\right)$

Wherein ε is error threshold, and value is vectorL₂The 5% of norm.Use (Boyd et al. exploitation) Convex majorized function bag cvx realizes L₁Solving 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 Sparse-Field scape imaging problem by no means of the sparse reconstruction of compressed sensing.)

Step 4:

To the DCT coefficient rebuild in step 3Carry out 2-D discrete cosine inverse transformation and obtain the magnitude image of target scene |X₆|, as shown in formula (23):

|X₆|=D^-1X_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 Non-sparse scene, utilizes a small amount of observation by compressed sensing model and L₁The convex optimization means of norm, reconstructs high-resolution The New Type Radar formation method of scene image.Compare with existing strip-type Space-borne SAR Imaging algorithm based on compressed sensing, The inventive method can be generalized to non-sparse 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 strip-type satellite-borne SAR echo data and carry out emulation experiment to verify formation method proposed by the invention Effect.

Have chosen the actual satellite-borne SAR data of RADARSAT-1, these data are by list of references: Ian G, Frank H. synthesizes Aperture radar imaging-algorithm 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 RADARSAT-1 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 RADARSAT-1 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 right-side course roadside.Can be seen that scene moderately and strongly inverse scattering point is more from imaging results, structure is complex, Being typical non-sparse 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 satellite-borne 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 non-sparse target scene.

Claims (3)

1. the non-sparse 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 X₀, matrix X₀Horizontal direction represent orientation to, vertical direction represent distance to；

2) to step 1) in echo complex data the most down-sampled, 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 2-D discrete cosine inverse transformation and obtain the amplitude of target scene Image | X₆|。

2. as claimed in claim 1 method, it is characterised in that described step 2) specifically include: set radar as positive side-looking, 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 X₀Being 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 X₀Along distance to orientation to making two dimensional discrete Fourier transform (2D-DFT) two-dimensional frequency data matrix X, is obtained₁, as shown in formula (1):

X₁=FX₀F^T (1)

Wherein F is DFT transform matrix, ()^TThe transposition operation of representing matrix, each element F (k, such as formula of form n) in matrix F (2) shown in:

$F(k,n)=\frac{1}{\sqrt{N}}\exp (-j2\mathrm{\π}\frac{kn}{N}),k=0,1,...,N-1,n=0,1,...,N-1---\left(2\right)$

2.2) in distance to two-dimensional frequency data matrix X₁Operate, including pulse compression, range migration and secondary Range compress operates: specifically include first to X₁Vectorization 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^vecIt is an a length of N²Column vector)； Then, distance to operation such as formula (3) shown in:

$X_2^{vec}={\mathrm{PX}}_1^{vec}---\left(3\right)$

X in formula₂Represent X₁Data matrix after Range compress, the N being made up of the diagonal matrix of N number of N × N²×N²Diagonal angle Battle array P, as shown in formula (4):

Wherein P_iIt is by p_i,0,p_i,1,…,p_i,N-1The diagonal matrix constituted for diagonal element, p_i,mForm such as formula (5) shown in:

$p_{i,m}=\exp \{j\frac{\mathrm{\π}}{K_r}{\left(\frac{{\mathrm{mF}}_s}{N}\right)}^2-j\mathrm{\π}\frac{{\mathrm{cR}}_s}{2v^2{f}_0^3}{\left(\frac{{\mathrm{iF}}_p}{N}\right)}^2{(1-\frac{{\mathrm{\λ}}^2}{4v^2}{\left(\frac{{\mathrm{iF}}_p}{N}\right)}^2)}^{-3/2}{\left(\frac{{\mathrm{mF}}_s}{N}\right)}^2+j\frac{4{\mathrm{\πR}}_s}{c}\[{(1-\frac{{\mathrm{\λ}}^2}{4v^2}{\left(\frac{{\mathrm{iF}}_p}{N}\right)}^2)}^{-1/2}-1\]\left(\frac{{\mathrm{mF}}_s}{N}\right)\}---\left(5\right)$

Wherein i=0,1 ... N-1, m=0,1 ... N-1, R_sFor the distance of band scene center line Yu radar route, K_rIt 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, f₀It is radar carrier frequency, f₀=c/ λ.F_sIt is radar echo signal sample rate, F_pIt 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 compression₂Make distance to inverse discrete Fourier transform (IDFT), transform the data into To distance-Doppler territory, obtain matrix X₃, as shown in formula (6):

X₃=F^-1·X₂ (6)

2.4) to data X₃Carry out Azimuth Compression, pass throughOne phase compensation matrix W of premultiplication realizes, such as formula (7) Shown in:

$X_4^{vec}=W\·X_3^{vec}---\left(7\right)$

Wherein X₄Representing the data matrix after distance, Azimuth Compression, W is to be made up of the diagonal matrix of N number of N × N-dimensional degree N²×N²Diagonal matrix, as shown in formula (8):

W_iIt is by w_i,0,w_i,1,…,w_i,N-1The diagonal matrix constituted for diagonal element, wherein w_i,mForm be:

$w_{i,m}=\exp \{j\frac{4\mathrm{\π}}{\mathrm{\λ}}\·\[R_s+(m-N/2)\·\frac{c}{2F_s}\]\·\sqrt{1-\frac{{\mathrm{\λ}}^2}{4v^2}\left(\frac{{\mathrm{iF}}_p}{N}\right)}\}---\left(9\right)$

Wherein i=0,1 ... N-1, m=0,1 ... identical described in N-1 (remaining each parameter physical significance and step 2.2))；

2.5) along orientation to X₄In each distance unit make IDFT, obtain airspace data matrix X₅, such as formula (10) Shown in:

X₅=X₄·(F^-1)^T (10)

Scene complex image matrix X₆By being calculated of formula (11):

X₆=U X₅·U^T (11)

Wherein U=[I_L|O_L×(N-L)], I_LIt is the unit matrix of L × L, O_L×(N-L)It it is the full null matrix of L × (N-L)；

According to Kronecker product theorem (Kroneker product theorem), following identity is had to set up:

$(B^T\⊗A)\·X^{vec}={\left(AXB\right)}^{vec}---\left(12\right)$

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):

$X_6^{vec}=(U\⊗U)\·(F^{-1}\⊗I_N)\·W\·(I_N\⊗F^{-1})\·P\·(F\⊗F)\·X_0^{vec}---\left(13\right)$

Wherein I_NIt 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:

$\mathrm{\Ψ}=(U\⊗U)\·(F^{-1}\⊗I_N)\·W\·(I_N\⊗F^{-1})\·P\·(F\⊗F)---\left(14\right).$

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 two-dimension discrete cosine transform (2D-DCT)_DCT, This DCT coefficient is done 2-D discrete cosine inverse transformation and obtains original amplitude view data, as shown in formula (15):

$\left|X_6\right|=D^{-1}{X}_{DCT}{\left(D^{-1}\right)}^T---\left(15\right)$

Wherein | X₆| represent target scene magnitude image, X_DCTIt it is the coefficient square of scene magnitude image two-dimension discrete cosine transform Battle array, this coefficient matrix contains the big component of minority and more small component, possesses typical compressibility；D represents one-dimensional Dct transform matrix, each element D in matrix D (k, shown in the such as formula of form n) (16):

$D(k,n)=\mathrm{\α}\left(k\right)cos\left(\mathrm{\π}\frac{(2n+1)k}{2L}\right)---\left(16\right)$

Wherein K=0,1 ..., L-1, n=0,1 ..., L-1；

Kronecker product theorem is used to obtain equation as shown in formula (17):

$|X_6{|}^{vec}=\mathrm{\Φ}\·X_{DCT}^{vec}---\left(17\right)$

Wherein

$\mathrm{\Φ}=D^{-1}\⊗D^{-1}---\left(18\right)$

Simultaneous formula (13) and (17), obtain equation as shown in formula (19):

$|\mathrm{\Ψ}\·X_0^{vec}|=\mathrm{\Φ}\·X_{DCT}^{vec}---\left(19\right)$

Wherein Ψ is the range Doppler algorithm imaging array as shown in formula (14):

IfIt is that K-is sparse,In only K bigger component, K ＜ ＜ L², utilize the method for compressed sensing to build Vertical sparse reconstruction model just can be from scene magnitude imageM=O (Klog (L²/ K)) individual observation recoversThe magnitude image of scene is obtained again by 2-D discrete cosine inverse transformation；Randomly select the unduplicated M of Ψ and Φ Row constitutes two submatrix Ψ_MAnd Φ_M, as shown in formula (20):

${\mathrm{\Ψ}}_M\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cccc}\mathrm{\Ψ}(i_1,1)& \mathrm{\Ψ}(i_1,2)& ...& \mathrm{\Ψ}(i_1,N^2)\\ \mathrm{\Ψ}(i_2,1)& \mathrm{\Ψ}(i_2,2)& ...& \mathrm{\Ψ}(i_2,N^2)\\ \·& \·& & \·\\ \·& \·& ...& \·\\ \·& \·& & \·\\ \mathrm{\Ψ}(i_M,1)& \mathrm{\Ψ}(i_M,2)& ...& \mathrm{\Ψ}(i_M,N^2)\end{array}\right],{\mathrm{\Φ}}_M\stackrel{\mathrm{\Δ}}{=}\left[\begin{array}{cccc}\mathrm{\Φ}(i_1,1)& \mathrm{\Φ}(i_1,2)& ...& \mathrm{\Φ}(i_1,N^2)\\ \mathrm{\Φ}(i_2,1)& \mathrm{\Φ}(i_2,2)& ...& \mathrm{\Φ}(i_2,N^2)\\ \·& \·& & \·\\ \·& \·& ...& \·\\ \·& \·& & \·\\ \mathrm{\Φ}(i_M,1)& \mathrm{\Φ}(i_M,2)& ...& \mathrm{\Φ}(i_M,N^2)\end{array}\right]---\left(20\right)$

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:

$|{\mathrm{\Ψ}}_M\·X_0^{vec}|={\mathrm{\Φ}}_M\·X_{DCT}^{vec}---\left(21\right)$

By solving the L as shown in formula (22)₁Norm optimization problem recovers

$min\left|\right|X_{DCT}^{vec}|{|}_{1}s.t.|\left|\right|{\mathrm{\Ψ}}_M\·X_0^{vec}|-{\mathrm{\Φ}}_M\·X_{DCT}^{vec}|{|}_2\≤\mathrm{\ϵ}---\left(22\right)$

Wherein ε is error threshold, and value is vectorL₂The 5% of norm.Use (Boyd et al. exploitation) Convex majorized function bag cvx realizes L₁Solving of norm optimization problem.