CN102879777B - Sparse ISAR (Inverse Synthetic Aperture Radar) imaging method based on modulation frequency-compressive sensing - Google Patents

Abstract

The invention discloses a sparse ISAR (Inverse Synthetic Aperture Radar) imaging method based on modulation frequency-compressive sensing, and mainly solves the problems that a model is inaccurate and a target distance-azimuth range ISAR image cannot be obtained in the conventional imaging method. The sparse ISAR imaging method comprises the steps as follows: (1) carrying out translation compensation on echoes; (2) fixing the value of the modulation frequency alpha, constructing a modulation frequency dictionary T, and calculating to obtain an ISAR signal vector w; (3) fixing the ISAR signal vector w, and calculating the modulation frequency alpha; (4) calculating a rotation parameter omega by utilizing the obtained modulation frequency alpha; (5) carrying out ISAR imaging by using the ISAR signal vector, and carrying out azimuth dimensioning by utilizing the calculated rotation parameter omega; and (6) outputting and finally obtaining the target distance-azimuth range ISAR image. Compared with the conventional sparse imaging method, the model is more accurate, the parameter is accurately calculated, the target distance-azimuth range sparse ISAR image can be obtained, and feature extraction and classifier design of subsequent target identification are better facilitated.

Description

Sparse ISAR formation method based on frequency modulation rate-compressed sensing

Technical field

The invention belongs to Radar Technology field, relate to ISAR formation method, by dictionary learning, obtain moving target range-azimuth Range Profile, be more conducive to follow-up target identification.

Background technology

ISAR imaging has round-the-clock, round-the-clock advantage, be the effective means of target detection and identification, so ISAR imaging becomes the study hotspot in Radar Technology field.

ISAR imaging obtains apart from high resolving power by transmitting broadband signal, by the coherent accumulation of target echo is obtained to high azimuthal resolution, thereby obtains distance-Doppler image.Because noncooperative target is unknown with respect to radar line of sight rotating speed, obtain ISAR image aspect dimension Doppler frequency and do not represent the full-size(d) of target, thereby bring certain difficulty to the target identification based on ISAR image.Because real system possibility echo-pulse number is limited or partial pulse is subject to stronger interference, the range-doppler algorithm of tradition based on Fourier transform will lose efficacy.For this reason, Chinese scholars is applied to super-resolution parametrization spectrum method of estimation in ISAR imaging, as [lazarov A D.Iterative MMSE method and recurrent kalman procedure for ISAR image reconstruction[J] .IEEE Transations on Aerospace and Electronic System, 2001,37 (4): 1432-1440].Compare with traditional nonparametric technique, parametrization spectrum method of estimation can obtain the ISAR image of super-resolution.Owing to not utilizing sparse prior imformation, solution out of true and convergence that said method obtains are not proven.Super-resolution imaging is actually an interpolation process, from the signal of a low dimension, recovers high-dimensional signal, because equation owes fixed, therefore its solution has uncertainty.Compressive sensing theory has obtained broad research at home and abroad in recent years, and compressive sensing theory is pointed out can go out high-dimensional sparse signal by L1 norm optimization Exact recovery in certain condition.Because imageable target scattering point has sparse characteristic, for the application of compressed sensing in SAR/ISAR imaging provides good condition.The research that at present existing compressed sensing is applied in ISAR imaging, as [L.Zhang, M.D.Xing, C.W.Qiu, J.Li, Z.Bao, " Achieving higher resolution ISAR imaging with limited pulses via compressed sensing, " IEEE Trans.Geosci.Remote Sens.Lett., vol.6, no.3, pp.567-571, Jul.2009].In literary composition, by single order that target is rotatablely moved, launch, obtain Fourier dictionary, then by protruding Optimization Solution, finally obtain the ISAR picture of target.

Although above-mentioned compressed sensing ISAR formation method can obtain the sparse ISAR image of target under certain condition, because it utilizes fixing Fourier dictionary, thereby do not there is adaptivity.In addition, because compressed sensing ISAR formation method does not have rotary speed information, what obtain is distance-Doppler ISAR image, can not represent real goal size, is unfavorable for follow-up target identification.

Summary of the invention

Fundamental purpose of the present invention is for above-mentioned existing methods not enough, proposes a kind of sparse ISAR formation method based on frequency modulation rate-compressed sensing.To obtain the range-azimuth of target apart from ISAR image, be beneficial to follow-up target identification.

Realizing the object of the invention technical thought is: on the basis of Fourier basis, by introducing scattering point, adjust frequency information, construct the frequency modulation rate dictionary that reflects more accurately target state, utilize the frequency modulation rate of scattering point can carry out rotating speed estimation.

The core concept that realizes the object of the invention is: by target is rotatablely moved and carries out second order expansion, obtain echo signal model.By iterative estimate parameter, and then obtain the estimation of rotating speed, finally obtain the range-azimuth of target apart from ISAR image.Its technical step comprises as follows:

(1) radar return is carried out to translation compensation, obtain the signal model of ISAR imaging;

(2) according to obtaining ISAR imaging model, the frequency modulation rate dictionary T of structure ISAR imaging;

(3) radar return is arranged in to the column vector y of a MN, wherein M and N are respectively distance by radar unit number and umber of pulse;

(4), according to frequency modulation rate dictionary T and echo column vector signal y, utilize protruding optimization tool bag CVX to solve the vector signal w of sparse ISAR;

(5) according to the sparse ISAR vector signal w obtaining, utilize Newton Algorithm frequency modulation rate vector α;

(6), according to obtaining frequency modulation rate vector α, calculate target rotational parameters ω:

$\mathrm{\ω}=\sqrt{\frac{{\mathrm{\α}}^T{y}_{R}c}{2{y_R}^T{y}_R{f}_c}}$

Wherein c represents the light velocity, f _cfor radar carrier frequency, () ^trepresent matrix transpose operation;

(7) sparse ISAR vector signal w is arranged in to M * N matrix, obtains the distance-Doppler image of sparse ISAR;

(8) utilize target rotational parameters ω, the ISAR distance-Doppler obtaining is carried out to direction ruler scale note, the sparse ISAR image of range-azimuth distance of export target.

As preferably, the sparse ISAR formation method based on frequency modulation rate-compressed sensing according to claim 1, the frequency modulation rate dictionary T of the structure ISAR imaging described in step 2 wherein, carries out as follows:

2a) according to radar ISAR signal model, be constructed as follows Doppler's dictionary T _fand with the dictionary T that adjusts frequency dependence _α:

$T_f=\left[\begin{array}{cccc}\exp (-j2{\mathrm{\πf}}_1{t}_1)& \exp (-j2{\mathrm{\πf}}_2{t}_1)& \·\·\·& \exp (-j2\mathrm{\π}{f}_M{t}_1)\\ \exp (-j2{\mathrm{\πf}}_1{t}_2)& \exp (-j2{\mathrm{\πf}}_2{t}_2)& & \exp (-j2\mathrm{\π}{f}_M{t}_2)\\ \·& \·& & \·\\ \·& \·& & \·\\ \·& \·& & \·\\ \exp (-j2\mathrm{\π}{f}_1{t}_M)& \exp (-j2{\mathrm{\πf}}_2{t}_M)& \·\·\·& \exp (-j2\mathrm{\π}{f}_M{t}_M)\end{array}\right]$

$T_{\mathrm{\&alpha;}}=\left[\begin{array}{cccc}\exp \left(j{\mathrm{\&pi;\&alpha;}}_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002149988200021.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2\right)& \exp \left(j{\mathrm{\&pi;\&alpha;}}_2{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002149988200021.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp \left(j\mathrm{\&pi;}{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="1"\; label="M\; t"\; filenames="HDA00002149988200021.png"\; state="\{\{state\}\}">M</figure-callout>}}{t}_{}^{}{}_1^2\right)\\ \exp \left(j{\mathrm{\&pi;\&alpha;}}_1{t}_2^2\right)& \exp \left(j{\mathrm{\&pi;\&alpha;}}_2{t}_2^2\right)& & \exp \left(j\mathrm{\&pi;}{\mathrm{\&alpha;}}_M{t}_2^2\right)\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \exp \left(j\mathrm{\&pi;}{\mathrm{\&alpha;}}_1{t}_N^2\right)& \exp \left(j{\mathrm{\&pi;\&alpha;}}_2{t}_N^2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp \left(j\mathrm{\&pi;}{\mathrm{\&alpha;}}_N{t}_N^2\right)\end{array}\right]$

F wherein _irepresent i Frequency point, t _irepresent i moment point, a _irepresent that i is adjusted Frequency point, exp () and j to represent respectively to take exponential function and the imaginary unit that natural logarithm e is the end;

2b) with T _ffor MN * MN matrix of diagonal matrix expansion, be designated as T _f'; With T _αmiddle element obtains MN * MN matrix along classifying diagonal element as, is designated as T _α', calculate frequency modulation rate dictionary:

T=T _α′×T _f′。

As preferably, the sparse ISAR formation method based on frequency modulation rate-compressed sensing according to claim 1, the Newton Algorithm frequency modulation rate vector α described in step 5 wherein, carry out as follows:

5a) set frequency modulation rate initial value α ¹=1, iterations n=1, convergence threshold δ=10 ^-5;

5b) utilize

gradient f _αand Hessian matrix H _α, calculate and adjust frequency vector:

$\mathrm{\&alpha;}={\mathrm{\&alpha;}}^n-H_{{\mathrm{\&alpha;}}^n}^{-1}{f}_{{\mathrm{\&alpha;}}^n}$

α wherein ⁿrepresent the value of n step frequency, () ^-1represent matrix inversion operation;

5c) as α and α ⁿmeet

time, obtain frequency modulation rate vector α, otherwise n=n+1, α ⁿ=α, enters step 5b).

The present invention has the following advantages:

1) the present invention, owing to being based upon on more accurate ISAR imaging signal model basis, is embodied rotary speed parameter in dictionary, utilizes the rotary speed parameter of adjusting frequency parameter to obtain target, obtains the range-azimuth of target apart from ISAR image.

2) the present invention, owing to estimating to adjust frequency parameter by Newton method, can obtain adjusting more accurately frequency parameter, and rotating speed estimates to have higher precision;

3) the present invention, owing to adopting sparse method for solving, therefore can carry out the imaging of ISAR orientation in the situation that of a few pulses, and the range-azimuth that finally obtains target is apart from ISAR image, is conducive to feature extraction and the classifier design of succeeding target identification.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the ISAR model that the present invention uses;

Result after the radar data translation compensation of Fig. 3 outfield;

The ISAR image that Fig. 4 outfield radar data utilization tradition fourier method obtains;

The ISAR image that Fig. 5 outfield radar data utilizes existing compression sensing method to obtain;

The ISAR image that Fig. 6 outfield radar data utilizes the inventive method to obtain.

Embodiment

With reference to Fig. 1, specific implementation step of the present invention is as follows:

Step 1, carries out translation compensation to radar return data, obtains the signal model of ISAR imaging.

1.1) radar return is carried out to translation compensation, eliminate the impact of translation on radar return envelope, hypothetical target at X-Y plane with rotational parameters ω uniform rotation, as shown in Figure 2, ignore more Range cell migration of the target scattering point that caused by rotation, obtain distance and to the radar echo signal after pulse pressure be:

$y\left(1\right)=\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i\exp (-j\frac{4\mathrm{\&pi;}{f}_c}{c}(y_i\cos \mathrm{\&theta;}\left(t\right)+x_i\sin \mathrm{\&theta;}\left(t\right)))---<1>$

Wherein K is that range unit inscattering is counted out, σ _ifor the signal complex magnitude after pulse compression, f _cfor radar carrier frequency, c is the light velocity, and 5 is the slow time, and exp () and j represent respectively take exponential function and the imaginary unit that natural logarithm e is the end.

As shown in Figure 2, target with respect to the angle θ (t) of radar line of sight is:

θ(5)=θ ₀+ωt <2>

θ wherein ₀for initial observation angle, ω is rotational parameters;

1.2) by cos θ (t) and sin θ (5) second order Taylor series expansion, formula <1> can be expressed as

$y\left(t\right)=\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{w}_i\&times;\exp [-j2\mathrm{\&pi;}(f_{d}t-\frac{1}{2}\mathrm{\&alpha;}{t}^2)],---<3>$

Wherein $w_i={\mathrm{\&sigma;}}_i\exp (-j\frac{4\mathrm{\&pi;}{f}_c}{c}{y}_i)$ For signal complex magnitude,

for Doppler frequency,

for frequency modulation rate;

1.3) consider observation noise, write radar return data as matrix form along range unit, ISAR signal model is as follows:

y=Tw+ε，

Wherein y is radar return data vector, and T is frequency modulation rate dictionary, and w is ISAR signal phasor, and ε is observation noise vector.

Step 2, according to signal model, constructs frequency modulation rate dictionary T.

2.1), according to above-mentioned ISAR signal model, be constructed as follows Doppler's dictionary T _fand with the dictionary T that adjusts frequency dependence _α:

$T_f=\left[\begin{array}{cccc}\exp (-j2{\mathrm{\&pi;f}}_1{t}_1)& \exp (-j2{\mathrm{\&pi;f}}_2{t}_1)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp (-j2\mathrm{\&pi;}{f}_M{t}_1)\\ \exp (-j2{\mathrm{\&pi;f}}_1{t}_2)& \exp (-j2{\mathrm{\&pi;f}}_2{t}_2)& & \exp (-j2\mathrm{\&pi;}{f}_M{t}_2)\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \exp (-j2\mathrm{\&pi;}{f}_1{t}_M)& \exp (-j2{\mathrm{\&pi;f}}_2{t}_M)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp (-j2\mathrm{\&pi;}{f}_M{t}_M)\end{array}\right],$

$T_{\mathrm{\&alpha;}}=\left[\begin{array}{cccc}\exp \left(j{\mathrm{\&pi;\&alpha;}}_1{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002149988200021.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2\right)& \exp \left(j{\mathrm{\&pi;\&alpha;}}_2{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA00002149988200021.png"\; state="\{\{state\}\}">t</figure-callout>}}_1^2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp \left(j\mathrm{\&pi;}{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="1"\; label="M\; t"\; filenames="HDA00002149988200021.png"\; state="\{\{state\}\}">M</figure-callout>}}{t}_{}^{}{}_1^2\right)\\ \exp \left(j{\mathrm{\&pi;\&alpha;}}_1{t}_2^2\right)& \exp \left(j{\mathrm{\&pi;\&alpha;}}_2{t}_2^2\right)& & \exp \left(j\mathrm{\&pi;}{\mathrm{\&alpha;}}_M{t}_2^2\right)\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \exp \left(j\mathrm{\&pi;}{\mathrm{\&alpha;}}_1{t}_N^2\right)& \exp \left(j{\mathrm{\&pi;\&alpha;}}_2{t}_N^2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp \left(j\mathrm{\&pi;}{\mathrm{\&alpha;}}_N{t}_N^2\right)\end{array}\right],$

F wherein _irepresent i Frequency point, t _irepresent i moment point, a _irepresent that i is adjusted Frequency point.

Doppler's dictionary T _fbe actually Fourier basis matrix, be at ISAR signal model and ignore the dictionary after frequency modulation rate; Frequency modulation rate dictionary T _αit is follow-up key of carrying out rotating speed estimation.

2.2) with T _ffor MN * MN matrix of diagonal matrix expansion, be designated as T _f'; With T _αmiddle element obtains MN * MN matrix along classifying diagonal element as, is designated as T _α', calculate frequency modulation rate dictionary:

T=T _α′×T _f′

Wherein, M and N are respectively distance by radar unit number and umber of pulse.

Step 3, by radar return vector arranged in columns.

Because radar return is matrix form, be unfavorable for follow-up Optimization Solution ISAR signal phasor, therefore radar return is arranged as to the column vector of a MN along orientation.

Step 4, according to frequency modulation rate dictionary T and echo column vector signal y, utilizes protruding optimization tool bag CVX to solve sparse ISAR vector signal w.

4.1) according to frequency modulation rate dictionary T and echo column vector signal y, to ISAR signal, w carries out a norm constraint, can change into and solves optimization problem below solving sparse ISAR vector signal w:

$\underset{w}{\min }{|y-\mathrm{Tw}|}_2^2+\mathrm{\&lambda;}{\left|w\right|}_1^1$

Wherein

with

two norms and a norm of difference representation vector, λ is regularization parameter;

4.2) utilize protruding optimization CVX kit to solve above formula optimization problem, obtain ISAR vector signal w.

Step 5, the sparse ISAR vector signal w according to obtaining, utilizes Newton Algorithm frequency modulation rate vector α.

5.1) set frequency modulation rate initial value α ¹=1, iterations n=1, convergence threshold δ=10 ^-5;

5.2) utilize

gradient f _αand Hessian matrix H _α, calculate and adjust frequency vector:

$\mathrm{\&alpha;}={\mathrm{\&alpha;}}^n-H_{{\mathrm{\&alpha;}}^n}^{-1}{f}_{{\mathrm{\&alpha;}}^n},$

Wherein, α ⁿrepresent the value of n step frequency, () ^-1represent matrix inversion operation;

5.3) as α and α ⁿmeet

time, obtain frequency modulation rate vector α, otherwise n=n+1, α ⁿ=α, returns and enters step 2).

Step 6, according to obtaining frequency modulation rate vector α, calculates target rotational parameters ω.

According to frequency modulation rate, with linear this character of range unit, solve rotational parameters ω, the frequency modulation rate vector α substitution following formula that soon step 2 obtains solves rotational parameters ω:

$\mathrm{\&omega;}=\sqrt{\frac{{\mathrm{\&alpha;}}^T{y}_{R}c}{2{y_R}^T{y}_R{f}_c}},$

Wherein () ^trepresent matrix transpose operation, y _rcan be calculated by following formula:

$y_R=[-\frac{M}{2}:\frac{M}{2}-1]\&times;{\mathrm{\&rho;}}_r$

Range resolution ρ wherein _r=c/2B, B is signal bandwidth,

for arrive

the vector that forms of integer.

Step 7, is arranged in M * N matrix by sparse ISAR vector signal w, obtains the distance-Doppler image of sparse ISAR.

Because sparse ISAR vector signal is a column vector, in order to obtain final ISAR image, sparse ISAR vector signal is arranged in to M * N matrix.Owing to there is no rotary speed information, the image now obtaining is target ISAR distance-Doppler image.

Step 8, utilizes target rotational parameters ω, and the ISAR distance-Doppler obtaining is carried out to direction ruler scale note, the sparse ISAR image of range-azimuth distance of export target.

The rotational parameters ω being obtained by step 6, utilizes

try to achieve

f wherein _dfor orientation Doppler's resolution element, to sparse ISAR image orientation, to carrying out yardstick mark, the range-azimuth of export target is apart from sparse ISAR image.

Effect of the present invention can further illustrate by following measured data checking:

Experiment: the sparse range-azimuth that outfield radar data carries out is verified apart from ISAR formation method

Radar parameter: carrier frequency f _c=5520MHz, signal bandwidth B=400MHz, corresponding range resolution ρ _r=0.375m, pulse repetition rate prf=100Hz, gets 128 radar echo pulses for the data of experiment, and target is YAK-42 aircraft.Experimentation is as follows:

1) 128 radar echo pulse experimental datas are carried out translation compensation, and the result after compensation is as Fig. 3.As shown in Figure 3, radar return is after translation compensation, and target scattering point is located at same range unit, has eliminated the envelope of radar return data and has walked about.

2) utilize the radar echo pulse after traditional fourier method compensates the translation shown in Fig. 3 to carry out ISAR imaging, ISAR imaging results is as Fig. 4.

As shown in Figure 4, the ISAR that fourier method obtains is as smudgy, and there is many False Intersection Points, due to the ISAR picture being obtained by fourier method, do not there is rotational parameters, can not carry out the operation of direction ruler scale note to obtaining ISAR picture, ISAR picture image aspect is doppler information, the dimension information of target in can not therefrom extracting.

3) utilize the radar echo pulse after existing compression sensing method compensates the translation shown in Fig. 3 to carry out ISAR imaging, ISAR imaging results is as Fig. 5.

As shown in Figure 5, compare with fourier method, compression sensing method obtains ISAR picture quality and is better than the ISAR image that fourier method obtains.Equally, owing to not having target rotational parameters, resulting ISAR image orientation is still doppler information, can not obtain target azimuth full-size(d) information, and the feature extraction of succeeding target identification and the design of sorter have been brought to inconvenience.

4) utilize the radar echo pulse after the inventive method compensates the translation shown in Fig. 3 to carry out ISAR imaging, ISAR imaging results is as Fig. 6.

As shown in Figure 6, the ISAR image of gained can reflect the state of aircraft more clearly.

By the contrast of three kinds of methods, can find out and utilize ISAR picture quality that the inventive method obtains to be obviously better than the ISAR image that traditional Fourier and existing compression sensing method obtain.Because adopted ISAR signal model has target rotational parameters, resulting ISAR picture is the image that marked orientation yardstick, be range-azimuth apart from ISAR image, therefore can, directly from the dimension information of ISAR extracting target from images, be conducive to the feature extraction of follow-up target identification and the design of sorter.

Claims (2)

1. the sparse ISAR formation method based on frequency modulation rate-compressed sensing, comprises the following steps:

(1) radar return is carried out to translation compensation, obtain the signal model of ISAR imaging;

(2) signal model of the ISAR imaging obtaining according to step (1), the frequency modulation rate dictionary T of structure ISAR imaging:

2a) according to the signal model of radar ISAR imaging, be constructed as follows Doppler's dictionary T _fand with the dictionary T that adjusts frequency dependence _α:

$T_f=\left[\begin{array}{cccc}\exp (-j2\mathrm{\&pi;}{f}_1{t}_1)& \exp (-j2\mathrm{\&pi;}{f}_2{t}_1)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp (-j2\mathrm{\&pi;}{f}_M{t}_1)\\ \exp (-j2\mathrm{\&pi;}{f}_1{t}_2)& \exp (-j2\mathrm{\&pi;}{f}_2{t}_2)& & \exp (-j2\mathrm{\&pi;}{f}_M{t}_2)\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \exp (-j2\mathrm{\&pi;}{f}_1{t}_M)& \exp (-j2\mathrm{\&pi;}{f}_2{t}_M)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp (-j2\mathrm{\&pi;}{f}_M{t}_M)\end{array}\right]$

$T_{\mathrm{\&alpha;}}=\left[\begin{array}{cccc}\exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_1{t}_1^2\right)& \exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_2{t}_1^2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_N{t}_1^2\right)\\ \exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_1{t}_2^2\right)& \exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_2{t}_2^2\right)& & \exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_N{t}_2^2\right)\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_1{t}_N^2\right)& \exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_2{t}_N^2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& \exp \left(\mathrm{j\&pi;}{\mathrm{\&alpha;}}_N{t}_N^2\right)\end{array}\right]$

F wherein _irepresent i Frequency point, t _irepresent i moment point, α _irepresent that i is adjusted Frequency point, exp () and j to represent respectively to take exponential function and the imaginary unit that natural logarithm e is the end;

2b) with T _ffor MN * MN matrix of diagonal matrix expansion, be designated as T _f'; With T _αmiddle element obtains MN * MN matrix along classifying diagonal element as, is designated as T _α', calculate frequency modulation rate dictionary:

T＝T _α'×T _f'；

(3) radar return is arranged in to the column vector y of a MN, wherein M and N are respectively distance by radar unit number and umber of pulse;

(4), according to frequency modulation rate dictionary T and echo column vector signal y, utilize protruding optimization tool bag CVX to solve the vector signal w of sparse ISAR;

(5) according to the vector signal w of the sparse ISAR obtaining, utilize Newton Algorithm frequency modulation rate vector α;

(6), according to the frequency modulation rate vector α obtaining, calculate target rotational parameters ω:

$\mathrm{\&omega;}=\sqrt{\frac{{\mathrm{\&alpha;}}^T{y}_{R}c}{2{y_R}^T{y}_R{f}_c}}$

Wherein c represents the light velocity, f _cfor radar carrier frequency, () ^trepresent matrix transpose operation, y _rcan be calculated by following formula:

$y_R=[-\frac{M}{2}:\frac{M}{2}-1]\&times;{\mathrm{\&rho;}}_r$

Range resolution ρ wherein _r=c/2B, B is signal bandwidth,

for

arrive

the vector that forms of integer; ;

(7) sparse ISAR vector signal w is arranged in to M * N matrix, obtains the distance-Doppler image of sparse ISAR;

(8) utilize target rotational parameters ω, the ISAR distance-Doppler image obtaining is carried out to direction ruler scale note, the sparse ISAR image of range-azimuth distance of export target.

2. the sparse ISAR formation method based on frequency modulation rate-compressed sensing according to claim 1, the described Newton Algorithm frequency modulation rate vector α of step (5) wherein, carry out as follows:

5a) set frequency modulation rate initial value α ¹=1, iterations n=1, convergence threshold δ=10 ^-5;

5b) utilize

gradient f _αand Hessian matrix H _α, calculate and adjust frequency vector:

${\mathrm{\&alpha;}}^n-H_{{\mathrm{\&alpha;}}^n}^{-1}{f}_{{\mathrm{\&alpha;}}^n}$

α wherein ⁿrepresent the value of n step frequency, () ^-1represent matrix inversion operation;

5c) as α and α ⁿmeet

time, obtain frequency modulation rate vector α, otherwise n=n+1, α ⁿ=α, enters step 5b).

Images