CN104076360B - The sparse target imaging method of two-dimensional SAR based on compressed sensing - Google Patents

Abstract

The invention discloses a kind of sparse target imaging method of two-dimensional SAR based on compressed sensing, mainly solve tradition SAR formation method observing matrix and expend storage and reconstruct time-consuming problem.Implementation step is: 1. pair original echoed signals carries out pretreatment and two-dimensional random is down-sampled, obtains down-sampled echo-signal Y_s；2. structure distance is to dictionary A_rWith orientation to dictionary A_a, obtain distance to observing matrix Θ_rWith orientation to observing matrix Θ_a；3. utilize Θ_rAnd Θ_aCalculate observation echo-signal Y of target image X_x；4. utilize Y_sAnd Y_xCalculate echo territory residual error Ω_x；5. utilize echo territory residual error Ω_xRebuild image area residual delta X；6. utilize Δ X and target image X to obtain initial target scenario B_x；7. utilize B_xUpdate threshold value；8. utilize iteration hard threshold algorithm and threshold value to rebuild target image X；The present invention has low sidelobe, high-resolution and background clutter and the low advantage of noise, can be used for the SAR imaging of sparse target scene.

Description

The sparse target imaging method of two-dimensional SAR based on compressed sensing

Technical field

The invention belongs to radar imagery field, particularly to the SAR formation method of a kind of sparse scene, can be applicable to The detecting of sparse target.

Background technology

Synthetic aperture radar SAR is one high-resolution radar all-time anf all-weather, is widely used in military affairs, The numerous areas such as agricultural, navigates, geographical supervision.It receives the echo of target reflection and by imaging algorithm to echo Carry out Coherent processing to obtain the distribution of the scattering coefficient of target.Traditional imaging algorithm is by the orientation to echo To with distance to carry out matched filtering process obtain observation scene image.Traditional imaging algorithm is with Nyquist Being sampled as basis, need substantial amounts of data, this is for the storage of data, transmits and processes and causes the biggest difficulty. And image secondary lobe that traditional imaging algorithm obtains is higher, resolution is relatively low, limits the follow-up detection to target And identification.Two kind traditional imaging algorithms are given below.

Range Doppler RD formation method.First this method carries out distance to matched filtering to raw radar data, Again the data after matched filtering are transformed to range-Dopler domain, by interpolation algorithm correction distance migration, the most right Orientation is to carrying out matched filtering.Wherein matched filtering is typically carried out at frequency domain.RD algorithm have simple, efficiently and The advantage such as accurately, is the most still widely used.But, in some conditions, this algorithm comes with some shortcomings. First, when the precision using longer interpolation kernel function to improve range migration correction, operand is very big, the most time-consumingly； Secondly, secondary range compression depends critically upon orientation frequency, limits it to large slanting view angle machine and the place of long aperture SAR Reason precision.

Yardstick becomes mark CS formation method.This method needs to carry out three phase factors and is multiplied: for the first time phase place because of Son is multiplied and carries out at range-Dopler domain, it is therefore an objective to carries out Chirp and becomes mark process, makes the distance of all distance unit Migration curve shape is consistent, identical with the range migration curve at reference distance；Phase factor is multiplied two for the second time Dimension frequency domain carry out, it is therefore an objective to complete simultaneously distance to process and range migration correction, wherein distance to process include away from Tripping contracting and secondary range compression；Phase factor is multiplied and carries out in distance-Doppler territory for the third time, it is therefore an objective to compensate Chirp becomes the phase error introduced when mark processes, and completes Azimuth Compression simultaneously.CS algorithm well solves RD In algorithm, interpolation arithmetic amount is big and the Dependence Problem of the other side's bit frequency in secondary range compression, but some of which is near May be false under conditions of large slanting view angle machine and broad beam like processing.

Compressive sensing theory breaches the restriction of nyquist sampling theorem, with the frequency less than highest signal frequency twice Rate gathers signal, can significantly alleviate signals collecting, store and transmit other burden.Traditional compressed sensing imaging Echo-signal is mainly converted to a column vector by method, then carries out random observation and reconstruct.This method is at weight Needing known degree of rarefication during structure, this not only significantly increases the amount of storage of observing matrix, and the most time-consuming.Also have Method be in orientation to the most down-sampled to echo-signal, then use compressed sensing restructing algorithm rebuild observation Scene, in distance to need nonetheless remain for carrying out the process of the traditional algorithms such as matched filtering.Although this method can reduce Gather data volume, but do not account for distance to information.

Summary of the invention

Present invention aims to the deficiency of above-mentioned prior art, it is proposed that a kind of new based on compressed sensing The sparse SAR formation method of two dimension, to suppress the secondary lobe of target and background clutter and noise, improves the resolution of target Rate, saves memory space and the time of imaging processing of data.

The technical thought realizing the object of the invention is: according to echo-signal 2-d spectrum, construct orientation to and distance To dictionary A_aAnd A_r, and use stochastical sampling matrix to the orientation of echo-signal to down-sampled to carrying out with distance； The acquiring method using new adaptive regularization parameter obtains the value of regularization parameter, hard according to compressed sensing iteration Thresholding algorithm reconstructs sparse scene, and its technical step includes the following:

1) by original echoed signals S_eCarry out two-dimensional Fourier transform, obtain echo-signal S of two-dimensional frequency_f, to S_f Carry out range migration correction and secondary range compression obtains echo-signal S of pretreatment_r；

2) randomly select partial row and the part row of unit matrix, obtain distance to stochastical sampling matrix Φ_rWith orientation to Stochastical sampling matrix Φ_a, echo-signal S to pretreatment_rCarry out distance to orientation to the most down-sampled, dropped Echo-signal Y of sampling_s=Φ_aS_rΦ_r；

3) according to echo-signal S after range migration correction_r2-d spectrum, structure distance to dictionary A_rAnd orientation To dictionary A_a, obtain distance to observing matrix: Θ_r=A_rΦ_rWith orientation to observing matrix: Θ_a=Φ_aA_a；

4) according to down-sampled echo-signal Y_sAnd distance to observing matrix Θ_rWith orientation to observing matrix Θ_aAnd the optimization aim expression formula of imaging, reconstruct target image by iteration hard threshold algorithm:

4.1) set X as target image, for the first time during iteration, X is set to one with original echoed signals matrix S_r The null matrix that size is identical, and specification error threshold epsilon is the positive number between 0 to 1.By step 3) distance To observing matrix Θ_rWith orientation to observing matrix Θ_a, obtain observing echo-signal Y_x=Θ_aXΘ_r；

4.2) according to step 2) in down-sampled echo-signal Y that obtains_sWith step 4.1) in obtain observation echo letter Number Y_x, obtain residual error Ω in echo territory_x=Y_s-Y_x；

4.3) according to echo territory residual error Ω_x, obtain image area residual errorWhereinFor orientation to sight Survey matrix Θ_aPseudoinverse,For distance to observing matrix Θ_rPseudoinverse；

4.4) decline step according to the gradient in iteration hard threshold algorithm and obtain initial target scenario B_xNth iteration After resultWherein, μ is gradient parameter, and μ value is a constant, X_nFor target image X nth iteration result, Δ X_nFor the result after image area residual delta X nth iteration；

4.5) by initial target sceneIt is converted into a column vector, takes its range valueObtainIn every Each amplitude element sum shared by one amplitude elementRatioObtain range value's Amplitude is expectedWherein m is column vectorLength；

4.6) expect according to amplitudeObtain initial target scene amplitudeMultiplicative noise:Root Obey the characteristic of Gamma distribution according to sparse target scene scattering coefficient, obtain initial target scene amplitudeTake advantage of The statistical distribution Probability p of property noise Z_z(Z)；

4.7) according to the statistical distribution Probability p of multiplicative noise Z_z(Z), p is obtained_z(Z) maximum index Index, By initial target scene amplitudeValue corresponding for middle Index is as the threshold parameter σ's in iteration hard threshold algorithm Value；

4.8) according to step 4.7) threshold value σ that obtains, utilize iteration hard-threshold formula To initial target sceneProcessing, reconstruct obtains target image X；

4.9) nth iteration result X of target image X is calculated_nWith the (n-1)th iteration result X_n-1Between error delta_n, By this error delta_nCompare with error threshold ε, if δ_nMore than or equal to ε, then return step 4.1), if δ_nLittle In ε, then terminate iteration, and by X_nFinal iteration result as X.

The present invention has the advantage that compared with prior art

1, the present invention to orientation to distance to observing respectively and carrying out the most down-sampled, efficiently reduce observation square The memory space that battle array takies；

2, the present invention uses the iteration hard-threshold restructing algorithm of compressed sensing, wherein regularization parameter ask for use new Self adaptation acquiring method, observation scene degree of rarefication the unknown in the case of still can reconstruct target figure accurately Picture, parameter arranges and asks for simple；

3, point target emulation and measured data imaging results show, the present invention can preferably suppress the secondary lobe of target with And background clutter and noise, and more traditional compressed sensing formation method speed is faster.

Accompanying drawing explanation

Fig. 1 be the present invention realize schematic flow sheet；

Fig. 2 is the present invention simulation imaging result figure to point target；

Fig. 3 is the present invention imaging results figure to measured data；

Fig. 4 is the present invention axis information comparison diagram to measured data；

Detailed description of the invention

Below in conjunction with accompanying drawing, the solution of the present invention and effect are described in further detail.

With reference to Fig. 1, the present invention to implement step as follows:

Step one, to original echoed signals S_eCarry out two-dimensional Fourier transform and range migration correction and secondary range Compression, obtains pretreated two-dimensional frequency echo-signal S_r。

1.1) to original echoed signals S_eCarry out two-dimensional Fourier transform, obtain S_e2-d spectrum S_f；

1.2) according to 2-d spectrum S_fObtain original echoed signals S_eThe phase theta of 2-d spectrum_a(f_τ,f_η) and distance Migration factor D (f_η,V_r):

${\mathrm{\θ}}_a(f_{\mathrm{\τ}},f_{\mathrm{\η}})=-\frac{4\mathrm{\π}{R}_0{f}_0}{c}\sqrt{D^2(f_{\mathrm{\η}},V_r)+\frac{2f_{\mathrm{\τ}}}{f_0}+\frac{f_{\mathrm{\τ}}^2}{f_0^2}}-\frac{\mathrm{\π}{f}_{\mathrm{\τ}}^2}{K_r}---\left(1\right)$

$D(f_{\mathrm{\η}},V_r)=\sqrt{1-\frac{c^2{f}_{\mathrm{\η}}^2}{4V_r^2{f}_0^2}}---\left(2\right)$

Wherein, K_rFor distance to frequency modulation rate, R₀For the beeline of target to radar, f₀For radar center frequency, c is The light velocity, f_τFor distance to sample frequency, f_ηFor orientation to sample frequency, V_rFor radar effective speed, D (f_η,V_r) For the range migration factor；

1.3) by the phase theta of 2-d spectrum_a(f_τ,f_η) press f_τTaylor series expansion, and retain extremely, obtain θ_a(f_τ,f_η) approximate expression be:

${\mathrm{\θ}}_a^{\′}(f_{\mathrm{\τ}},f_{\mathrm{\η}})=-\frac{4\mathrm{\π}{R}_0{f}_0}{c}[D(f_{\mathrm{\η}},V_r)+\frac{f_{\mathrm{\τ}}}{f_{0}D(f_{\mathrm{\η}},V_r)}-\frac{f_{\mathrm{\τ}}^2}{2f_0^2{D}^3(f_{\mathrm{\η}},V_r)}\frac{c^2{f}_{\mathrm{\τ}}^2}{4V_r^2{f}_0^2}]-\frac{{\mathrm{\πf}}_{\mathrm{\τ}}^2}{K_r}---\left(3\right)$

Wherein, in formula (3) bracket Section 1 be orientation to modulation item, Section 2 is range migration item, Section 3 be distance to With orientation to cross-couplings item；

1.4) obtain performing range migration correction and the wave filter H of secondary range compression according to formula (3)_f:

$H_f=\exp \left(j\frac{4\mathrm{\π}{R}_0{f}_0}{c}\right[\frac{f_{\mathrm{\τ}}}{f_{0}D(f_{\mathrm{\η}},V_r)}-\frac{f_{\mathrm{\τ}}^2}{2f_0^2{D}^3(f_{\mathrm{\η}},V_r)}\frac{c^2{f}_{\mathrm{\τ}}^2}{4V_r^2{f}_0^2}\left]\right)---\left(4\right)$

Wherein, K_rFor distance to frequency modulation rate, R₀For the beeline of target to radar, f₀For radar center frequency, c is The light velocity, f_τFor distance to sample frequency, f_ηFor orientation to sample frequency, V_rFor radar effective speed, D (f_η,V_r) For the range migration factor；

1.5) by the wave filter H of range migration correction and secondary range compression_fWith S_e2-d spectrum S_fCarry out a little Take advantage of, obtain pretreated two-dimensional frequency echo-signal S_r。

Step 2, to pretreated two-dimensional frequency echo-signal S_rCarry out two-dimensional random down-sampled.

2.1) original echoed signals S is set_eDistance to orientation to umber of pulse be respectively N_aAnd N_r, randomly select Size is N_a×N_rThe M of unit matrix_aRow and M_rRow, obtaining size is M_a×N_aOrientation to stochastical sampling Matrix Φ_aAnd N_r×M_rDistance to stochastical sampling matrix Φ_r；

2.2) by orientation to stochastical sampling matrix Φ_aWith distance to stochastical sampling matrix Φ_r, respectively with pretreated Two-dimensional frequency echo-signal S_rOrientation to distance to being multiplied, obtain down-sampled after echo-signal Y_s=Φ_aS_rΦ_r。

Step 3, structure distance to orientation to observing matrix.

3.1) original echoed signals S is calculated_eSpectral phase after range migration correction and secondary range compression is:

${\mathrm{\θ}}_{\mathrm{arc}}(f_{\mathrm{\τ}},f_{\mathrm{\η}})=-\frac{4\mathrm{\π}{R}_{0}D(f_{\mathrm{\η}},V_r)f_0}{c}-\frac{\mathrm{\π}{f}_{\mathrm{\τ}}^2}{K_r}---\left(5\right)$

Wherein, θ_arc(f_τ,f_η) Section 1 be azimuth match filter item, Section 2 is that distance is to matched filtering item.

3.2) by θ_arc(f_τ,f_η) Section 1 and Section 2 respectively as orientation to the phase place of dictionary and distance to dictionary Phase place, thus obtain orientation to dictionary A_aWith distance to dictionary A_r:

$A_a=\exp (-j\frac{4\mathrm{\π}{R}_{0}D(f_{\mathrm{\η}},V_r)f_0}{c})---\left(6\right)$

$A_r=\exp (-j\frac{f_{\mathrm{\τ}}^2}{K_r})---\left(7\right)$

3.3) according to step 2.1) distance that obtains is to stochastical sampling matrix Φ_rWith orientation to stochastical sampling matrix Φ_aWith And distance is to dictionary A_rWith orientation to dictionary A_a, obtain distance to orientation to observing matrix:

Θ_r=A_rΦ_r (8)

Θ_a=Φ_aA_a (9)

Step 4, according to compressed sensing mathematical model and iteration hard threshold algorithm, reconstruct target image X.

Mathematical model according to compressed sensing obtains the optimization aim expression formula of imaging:

Wherein 0 ＜ p≤1, | | | |_FRepresent Frobenius norm, | | | |_pRepresent l_pNorm, λ is regularization parameter, and X is target Image.According to iteration hard threshold algorithm, obtain the goal expression of iteration:

X_n=S_p,σ(X_n-1+μΔX_n-1), (11)

Wherein S_p,σIteration threshold operator, σ is threshold value, X_nFor the target image after nth iteration, X_n-1For target figure As the target image after (n-1)th iteration of X, Δ X_nFor the result after image area residual delta X nth iteration, μ is ladder Degree parameter, μ value is a constant.For the first time during iteration, target image X is initialized as one and original echo Signal S_eThe null matrix that size is identical, and specification error threshold epsilon is the positive number between 0 to 1；

4.1) according to the distance obtained of step 3 to observing matrix Θ_rWith orientation to observing matrix Θ_a, obtain The observation echo-signal of target image X

Y_x=Θ_aXΘ_r (12)

4.2) according to step 2.2) down-sampled echo-signal Y that obtains_sWith step 4.1) the observation echo-signal that obtains Y_x, obtain echo territory residual error Ω_x

Ω_x=Y_s-Y_x (13)

4.3) according to step 4.2) echo territory residual error Ω that obtains_x, obtain image area residual error:

WhereinWithIt is respectively Θ_aAnd Θ_rPseudoinverse；

4.4) utilize above-mentioned parameter, decline step according to the gradient in iteration hard threshold algorithm and obtain initial target scene B_xResult after nth iteration

$B_{x_n}=X_n+\mathrm{\μ\Δ}{X}_n---\left(15\right)$

Wherein, μ is gradient parameter, and μ value is a constant, X_nFor the nth iteration result of target image X, ΔX_nFor the result after image area residual delta X nth iteration；

4.5) by initial target sceneIt is converted into a column vector, takes its amplitudeCalculateIn every The accounting of individual amplitude element:

4.6) according to accounting p of each amplitude element_nAmplitude with initial target sceneUtilize mathematic expectaion Computing formula, obtain amplitude expectation

${E_x}_n=\underset{n=1}{\overset{m}{\mathrm{\Σ}}}{p}_n\left|B_{x_n}\right|---\left(16\right)$

Wherein m is column vectorLength；

4.7) expect according to amplitudeWith the characteristic that noise is multiplicative noise of SAR image, obtain initial target Scene amplitudeNoise:

4.8) according to step 4.7) the noise Z that obtains and sparse target scene scattering coefficient obey Gamma distribution Characteristic, obtain initial target sceneThe statistical distribution probability of noise Z:

$p_z\left(Z\right)=\frac{{2L}^L}{\mathrm{\Γ}\left(L\right)}\exp \left({-\mathrm{LZ}}^2\right)Z^{2L-1}---\left(17\right)$

Wherein, L is that imaging regards number, and Γ is Gamma function；

4.9) according to the statistical distribution Probability p of noise Z_z(Z), p is obtained_z(Z) maximum index Index, will Initial target scene amplitudeAmplitude corresponding for middle Index is as regularization parameter λ in iteration hard threshold algorithm Value, thus obtains the threshold parameter σ=λ in iteration hard threshold algorithm；

4.10) according to step 4.9) the threshold parameter σ that obtains, utilize iteration hard-threshold formula to (n-1)th iteration After initial target sceneIt is reconstructed, obtains nth iteration result X of target image X_n:

4.11) nth iteration result X of target image X is calculated_nWith (n-1)th iteration result X_n-1Between Error:

${\mathrm{\δ}}_n=\frac{{\left|\right|\left|X_n\right|-\left|X_{n-1}\right|\left|\right|}_2^2}{{\left|\right|\left|X_{n-1}\right|\left|\right|}_2^2}---\left(19\right).$

Wherein, | | for modulo operator, | | | |₂It is two norm operators,

4.12) by described error delta_nCompare with error threshold ε, if δ_nMore than or equal to ε, then return step 4.1), if δ_nLess than ε, then terminate iteration, and by X_nFinal iteration result as target image X.

The effect of the present invention can be further illustrated by the emulation of following point target and measured data imaging:

1. emulation and actual measurement condition

The target simulator scene that sets up an office is 5 point targets, and measured data scene is six ships.Evaluation index is by peak value Lobe is than PSLR, and unit is decibel (dB), main lobe width IRW, and unit is hits (sample), and integration secondary lobe Ratio ISLR, unit is decibel (dB), and as shown in table 1, wherein main lobe width IRW is when calculating, and chooses one piece 16 × 16 The section of size, and use the interpolation of 16 times.

Table 1

2. emulation content

Be respectively adopted RANGE-DOPPLER IMAGING method RDA, based on orientation to the formation method ACS of compressed sensing and The inventive method FCS, carries out imaging experiment, wherein range Doppler RD formation method to point target simulating scenes Use fully sampled raw radar data, all use to formation method and the inventive method of compressed sensing based on orientation Sample rate is the raw radar data of 25%, and the imaging results of three kinds of methods is respectively such as Fig. 2 (a), Fig. 2 (b) and Fig. 2 (c) Shown in.

3. actual measurement content

Be respectively adopted RANGE-DOPPLER IMAGING method RDA, based on orientation to the formation method ACS of compressed sensing and The inventive method FCS carries out imaging experiment to measured data scene, and result is as it is shown on figure 3, the detail section of result As shown in Figure 4, wherein:

It is under 25% that Fig. 3 (a) and Fig. 3 (d) is respectively RANGE-DOPPLER IMAGING method RDA in fully sampled and sample rate Imaging results；

It is 25% He that Fig. 3 (b) and Fig. 3 (e) are respectively based on orientation to the formation method ACS of compressed sensing in sample rate Imaging results under 6%；

Fig. 3 (c) and Fig. 3 (f) is respectively the inventive method FCS imaging results under sample rate is 25% and 6%；

By the amplification of white frame portion in Fig. 3 (a), Fig. 3 (b) and Fig. 3 (c), enlarged drawing picture is respectively such as Fig. 4 (a), figure Shown in 4 (b) and Fig. 4 (c).

From Fig. 2, Fig. 3 and Fig. 4 and table 1 it can be seen that the present invention can preferably suppress target secondary lobe and Background clutter and noise, improve the resolution of target, and the sampled data of needs is less.By contrast, how general distance is Strangling RD imaging results and yet suffer from higher secondary lobe after windowing process, resolution is relatively low, and needs fully sampled Data.There is more background clutter and noise in conventional compression perception imaging results.

Claims (4)

1. the sparse target imaging method of two-dimensional SAR based on compressed sensing, comprises the steps:

1) by original echoed signals S_eCarry out two-dimensional Fourier transform, obtain echo-signal S of two-dimensional frequency_f, to S_fCarry out range migration correction and secondary range compression obtains echo-signal S of pretreatment_r；

2) randomly select partial row and the part row of unit matrix, obtain distance to stochastical sampling matrix Φ_rWith orientation to stochastical sampling matrix Φ_a, echo-signal S to pretreatment_rCarry out distance to orientation to the most down-sampled, obtain down-sampled echo-signal Y_s=Φ_aS_rΦ_r；

3) according to echo-signal S after range migration correction_r2-d spectrum, structure distance to dictionary A_rWith orientation to dictionary A_a, obtain distance to observing matrix: Θ_r=A_rΦ_rWith orientation to observing matrix: Θ_a=Φ_aA_a；

4) according to down-sampled echo-signal Y_sAnd distance to observing matrix Θ_rWith orientation to observing matrix Θ_aAnd the optimization aim expression formula of imaging, reconstruct target image by iteration hard threshold algorithm:

4.1) set X as target image, obtain the optimization aim expression formula of imaging according to the mathematical model of compressed sensing:

Wherein 0 < p≤1, | | | |_FRepresent Frobenius norm, | | | |_pRepresent l_pNorm, λ is regularization parameter, according to iteration hard threshold algorithm, obtains the goal expression of iteration:

X_n=S_{p, σ}(X_n-1+μΔX_n-1),

Wherein S_{p, σ}Iteration threshold operator, σ is threshold value, X_nFor the target image after nth iteration, X_n-1For the target image after (n-1)th iteration of target image X, Δ X_nFor the result after image area residual delta X nth iteration, μ is gradient parameter, and μ value is a constant ；For the first time during iteration, target image X is initialized as one and original echoed signals S_eThe null matrix that size is identical, and specification error threshold epsilon is the positive number between 0 to 1；

4.2) it is iterated computing: for the first time during iteration, X is set to one and original echoed signals matrix S_rThe null matrix that size is identical, and specification error threshold epsilon is the positive number between 0 to 1；By step 3) distance to observing matrix Θ_rWith orientation to observing matrix Θ_a, obtain observing echo-signal Y_x=Θ_aXΘ_r；

4.3) according to step 2) in down-sampled echo-signal Y that obtains_sWith step 4.2) in observation echo-signal Y that obtains_x, obtain residual error Ω in echo territory_x=Y_s-Y_x；

4.4) according to echo territory residual error Ω_x, obtain image area residual errorWhereinFor orientation to observing matrix Θ_aPseudoinverse,For distance to observing matrix Θ_rPseudoinverse；

4.5) decline step according to the gradient in iteration hard threshold algorithm and obtain initial target scene Β_xResult after nth iterationWherein, μ is gradient parameter, and μ value is a constant, X_nFor target image X nth iteration result, Δ X_nFor the result after image area residual delta X nth iteration；

4.6) by initial target sceneIt is converted into a column vector, takes its range valueObtainIn each amplitude element sum shared by each amplitude elementRatioObtain range valueAmplitude expectationWherein m is column vectorLength；

4.7) expect according to amplitudeObtain initial target scene amplitudeMultiplicative noise:Obey the characteristic of Gamma distribution according to sparse target scene scattering coefficient, obtain initial target scene amplitudeThe statistical distribution Probability p of multiplicative noise Z_z(Z)；

4.8) according to the statistical distribution Probability p of multiplicative noise Z_z(Z), p is obtained_z(Z) maximum index Index, by initial target scene amplitudeValue corresponding for middle Index is as the value of the threshold parameter σ in iteration hard threshold algorithm；

4.9) according to step 4.8) threshold value σ that obtains, utilize iteration hard-threshold formulaTo initial target sceneProcessing, reconstruct obtains target image X；

4.10) nth iteration result X of target image X is calculated_nWith the (n-1)th iteration result X_n-1Between error delta_n, by this error delta_nCompare with error threshold ε, if δ_nMore than or equal to ε, then return step 4.2), if δ_nLess than ε, then terminate iteration, and by X_nFinal iteration result as X.

The sparse target imaging method of two-dimensional SAR based on compressed sensing the most according to claim 1, wherein said step 4.6) in statistical distribution Probability p_z(Z), it is expressed as follows:

Wherein, L is that imaging regards number, and Γ is Gamma function.

The sparse target imaging method of two-dimensional SAR based on compressed sensing the most according to claim 1, wherein said step 3) in distance to dictionary A_rWith orientation to dictionary A_a, it is expressed as follows:

Wherein, K_rFor distance to frequency modulation rate, R₀For the beeline of target to radar, f₀For radar center frequency, c is the light velocity, f_τFor distance to sample frequency, f_ηFor orientation to sample frequency, V_rFor radar effective speed, D (f_η,V_r) it is the range migration factor, j is imaginary symbols.

The sparse target imaging method of two-dimensional SAR based on compressed sensing the most according to claim 1, wherein said step 4.9) in error delta_n, it is expressed as follows:

Wherein, | | for modulo operator, | | | |₂It is two norm operators.