CN104793195B - Near-field planar scanning three-dimensional imaging and phase error compensating method - Google Patents

Abstract

The invention provides a near-field planar scanning three-dimensional imaging and phase error compensating method. The near-field planar scanning three-dimensional imaging and phase error compensating method comprises the following steps of acquiring sparse three-dimensional imaging echo data; performing discretization on an imaging scene; establishing a target dictionary; and performing imaging solution to obtain a focused high-resolution target image after establishing a signal model with phase errors. Limitation on the traditional Nyquist sampling is broken by a compressed sensing imaging theory, problems caused by planar scanning imaging large-scale data are solved, the imaging resolution ration is improved, interferences of the phase errors on imaging are avoided effectively, the testing efficiency is improved while a three-dimensional target image with high focusing effect is obtained, and according to a simulation result, target echo data with phase errors can be imaged accurately by an algorithm.

Description

A kind of filed-close plane scanning three-dimensional imaging and phase error compensation method

Technical field

The present invention relates to microwave Imaging Technique field, especially filed-close plane scanning three-D imaging method.

Background technology

Microwave near-field is imaged as a kind of effective non-damaged data and evaluation measures, to aircraft coating, spacecraft It is estimated, plays important work to hiding article and carrying out the fields such as safety detection with the important feature such as the bonding of combined material With.Because it has higher spatial resolution capability, the relative positioning between sensor and target, and system can be realized It is easily achieved, thus with extensive engineering application value.

Typical near-field flat scanning 3-D imaging system obtains high-resolution target by obtaining substantial amounts of echo data Picture, it is based on conventional Nyquist sampling and matched filtering technique, and the key step of imaging is as follows：

1) wave-number domain is transformed to by echo data is received first with two-dimensional Fourier transform；

2) wave number numeric field data is carried out by phase shift process by matched filter；

3) the wave number numeric field data of non-uniform Distribution is carried out by Interpolating transform using Stolt interpolation, is transformed to meet in Fu The data form of leaf transformation；

4) target three-dimensional image is obtained through three-dimensional Fourier transform process；

Due to large-scale data big etc. the asking that will cause that system testing efficiency is low, data storage takes up room in tradition imaging Topic, to the engineer applied of near field imaging system huge challenge is brought；It is constrained to as dividing based on the imaging method of traditional sampling law The raising of resolution；Because kinematic error, the echo-signal phase error brought such as unstable of test system destroy the phase of signal Dryness, and then cause imaging results to occur defocusing, can not be imaged when serious, affect extraction and the target identification of target signature.

The content of the invention

In order to overcome the shortcomings of existing imaging technique, the present invention proposes that a kind of filed-close plane based on compressed sensing scans three Dimension imaging and phase error compensation method, the phase error that the method can have edge scanning moving direction to echo is effectively estimated Meter compensation, improves the resolution ratio of imaging, while reducing systematic sampling rate, simplifies system.

A kind of filed-close plane scanning three-dimensional imaging is as follows with phase error compensation method key step：

Step 1：Obtain the echo data of sparse three-dimensional imaging：In L_x×L_yThe plane of scanning motion on randomly select partial scan Point is N_aPoint carries out echo data admission, wherein L_x、L_yRepresent the number of scan points in bidimensional aperture respectively, measure respectively empty darkroom and Darkroom containing measured target, the sparse observation signal obtained after Jing background cancels is s', and its dimension is N_a×N_f, wherein N_a ＜ L_x×L_y, N_fRepresent frequency sampling points, by s' by row pull into one-dimensional vector, be expressed as s, its dimension be N × 1, wherein N= N_aN_f；

Step 2：Image scene discretization：Imaging region is carried out into 3 d-dem, its X to, Y-direction and Z-direction it is corresponding from Scattered grid number is respectively N_x、N_yAnd N_z, reflectance factor matrix by rows three-dimensional in scene or row are conspired to create into an one-dimensional vector, table It is shown asWherein g_kRepresent the backscattering coefficient of k-th scattering point；

Step 3：Build target dictionary：Target dictionary A is built according to test parameter and target scene, its dimension be N × N_xN_yN_z, each element of dictionary A is：

N=1,2 ..., N_aN_f；P=1,2 ..., N_xN_yN_z

Wherein, A_npRepresent line n, the element of pth row in dictionary A；Represent the unit of imaginary number, k_nRepresent the mod(n/N_a) individual space variable, mod () be complementation, (x '_n,y′_n,z₀) it is abs ((n/N_a)+1) individual aperture location sits Mark, abs () is to round, as mod (n/N_aDuring)=0, (x '_n,y′_n,z₀) it is abs (n/N_a) individual aperture location coordinate, (x_p,y_p,z_p) for p-th scattering point position coordinates in discrete scene；

Step 4：Signal model of the construction containing phase error：The signal observation model affected by phase error is expressed as：

s_ε=Φ Ag+ θ

Wherein s_εThe echo-signal with phase error is represented, Φ represents phase error term, and size is N_aN_f×N_aN_fIt is right Angular moment battle array, Wherein, φ (i) (i=1,2 ..., N_a) the phase of echo error at i aperture location is represented, θ represents making an uproar in echo-signal Sound；

Step 5：Imaging is solved, and is concretely comprised the following steps：

Step 5-1：Set up solving model：Φ A=A (φ) in step 4 is made, following solving model is set up：

Wherein λ is the regularization parameter of majorized function, can be by being tried to achieve using Generalized Cross Validation (GCV) method；

Step 5-2：Scene scatters coefficient is estimated：Scattering coefficient estimates in by solving following cost function to obtain scene Evaluation：

Error in dictionary is converted into into the noise item of observation model, by Separable Surrogate Functionals (SSF) Optimization MethodWherein,Represent estimating for (t+1) secondary iteration scene reflectivity coefficient Evaluation；A(φ^(t)) represent the t time iteration when the dictionary matrix containing phase error；φ^(t)The phase error of the t time iterative estimate Value, in first iteration, φ⁽⁰⁾Value takes zero；

Step 5-3：Phase error estimation and phase error：Because the phase error at each sampling location is differed, in echo-signal Each data sampling point be both needed to be estimated, i.e., by solve following formula carry out phase estimation：

s_εM () represents the echo-signal obtained at the m of sampling location,Represent in (t+1) secondary iteration, adopting Phase error estimation and phase error value at the m of sample position,Represent at the m of position, after the t time phase error estimation and phase error more New dictionary, φ^(t+1)M () represents the phase error to be estimated at m positions in (t+1) secondary iteration, solve above formula, can obtain To estimation error expression formula：

Wherein, Im { } represents the imaginary part of plural number, and Re { } represents real, the conjugate transposition of H representing matrixs；

Step 5-4：Update observation model：Imaging observation is updated using the phase error estimation and phase error value at each sampling for obtaining Model matrix is：

Step 5-5：Repeat step 5-2 to step 5-4, until meetingWhen iteration stop Only, ε values are that imaging effect is chosen with the compromise of iteration efficiency, can be 10^-6-10^-3In the range of arrange, after iteration stopping will To the high resolution target picture for focusing on.

The invention has the beneficial effects as follows as a result of a kind of filed-close plane scanning three-dimensional imaging based on compressed sensing with Phase error compensation method, the method has been broken conventional Nyquist sampling and has been limited using compressed sensing imaging theory, solves The problem that flat scanning imaging large-scale data brings, while improve imaging resolution.Joined using phase error estimation and phase error compensation Combined pressure contracting perceives imaging technique and phase error in echo is compensated, and efficiently solves phase error dry to imaging belt Disturb, for comparing traditional imaging method for not considering estimation error compensation, imaging method of the present invention is good in acquisition focusing effect Good objective as while improve testing efficiency.Find that the algorithm can effectively to there is phase error by simulation result Target echo data carry out accurately image.

Description of the drawings

Fig. 1 is Irnaging procedures figure of the present invention.

Fig. 2 is emulation point target model.

Fig. 3 is tradition RMA imaging effect figures when data defect 90% has phase error.

Fig. 4 is that conventional compression perceives imaging effect figure when data defect 90% has same phase error.

Fig. 5 is the imaging effect figure of present invention when data defect 90% has same phase error.

Specific embodiment

With reference to the accompanying drawings and examples the present invention is further described.

Fig. 1 is the flow chart of imaging method of the present invention, on this basis, to using the object module institute shown in Fig. 2 The step of flat scanning echo data of generation is imaged be：

Step 1：Obtain the echo data of sparse three-dimensional imaging：In L_x×L_yThe plane of scanning motion on randomly select partial scan Point is N_aPoint carries out echo data admission, wherein L_x、L_yRepresent the number of scan points in bidimensional aperture respectively, measure respectively empty darkroom and Darkroom containing measured target, the sparse observation signal obtained after Jing background cancels is s', and its dimension is N_a×N_f, wherein N_a ＜ L_x×L_y, N_fRepresent frequency sampling points, by s' by row pull into one-dimensional vector, be expressed as s, its dimension be N × 1, wherein N= N_aN_f；

Microwave dark room obtains flat scanning target echo data.Sweep limits in antenna scanning plane is 1m × 1m, is sent out It is 8G-12G to penetrate signal bandwidth, and frequency step is 40MHz, randomly selects N_aIndividual aperture (complete situation is 2601 apertures) is respectively Echo data admission is carried out to empty darkroom and the darkroom for being placed with target to be measured, the sparse observation signal obtained after Jing background cancels For s', its dimension is N_a×N_f(N_a＜ (L_x×L_y)), N_fRepresent frequency sampling points.Each aperture location is added and obeyed in s' The random phase error of [- 3/4 π, 3/4 π].The s' for adding phase error is pulled into into one-dimensional vector by row, s is expressed as, its dimension For N × 1, wherein N=N_aN_f.In this example, N_a=324, N_f=101, L_x=L_y=51.

Step 2：Image scene discretization：Imaging region is carried out into 3 d-dem, its X to, Y-direction and Z-direction it is corresponding from Scattered grid number is respectively N_x、N_yAnd N_z, reflectance factor matrix by rows three-dimensional in scene or row are conspired to create into an one-dimensional vector, table It is shown asWherein g_kRepresent the backscattering coefficient of k-th scattering point；

By three-dimensional imaging discrete region, the corresponding discrete grid block number of wherein X, Y, Z-direction is respectively N_x、N_y、N_z, by field Scape three-dimensional reflection coefficient matrix G is expressed as one-dimensional vectorIn this example, N_x=N_y= N_z=41, each size of mesh opening is Δ δ=0.025m.

Step 3：Build target dictionary：Target dictionary A is built according to test parameter and target scene, its dimension be N × N_xN_yN_z, each element of dictionary A is：

N=1,2 ..., N_aN_f；P=1,2 ..., N_xN_yN_z

Wherein, A_npRepresent line n, the element of pth row in dictionary A；Represent the unit of imaginary number, k_nRepresent the mod(n/N_a) individual space variable, mod () be complementation, (x '_n,y′_n,z₀) it is abs ((n/N_a)+1) individual aperture location sits Mark, abs () is to round, as mod (n/N_aDuring)=0, (x '_n,y′_n,z₀) it is abs (n/N_a) individual aperture location coordinate, (x_p,y_p,z_p) for p-th scattering point position coordinates in discrete scene；

Target dictionary is built, dictionary A is built according to test parameter and target scene, its size is

(324 × 101) × (41 × 41 × 41), each element of dictionary A is

N=1,2 ..., N_aN_f；I=1,2 ..., N_xN_yN_z

In this example, total aperture number N_a=18 × 18, N_f=101, k_nThe span of=- 2 π f/c, f for [8GHz, 12GHz。]

Step 4：Signal model of the construction containing phase error：The signal observation model affected by phase error is expressed as：

s_ε=Φ Ag+ θ

Wherein s_εThe echo-signal with phase error is represented, Φ represents phase error term, and size is N_aN_f×N_aN_fIt is right Angular moment battle array, Wherein, φ (i) (i=1,2 ..., N_a) the phase of echo error at i aperture location is represented, θ represents making an uproar in echo-signal Sound；

Step 5：Imaging is solved, and is concretely comprised the following steps：

Step 5-1：Set up solving model：Φ A=A (φ) in step 4 is made, following solving model is set up：

Wherein λ is the regularization parameter of majorized function, can be by being tried to achieve using Generalized Cross Validation (GCV) method；

Step 5-2：Scene scatters coefficient is estimated：Scattering coefficient estimates in by solving following cost function to obtain scene Evaluation：

Error in dictionary is converted into into the noise item of observation model, by Separable Surrogate Functionals (SSF) Optimization MethodWherein,Represent estimating for (t+1) secondary iteration scene reflectivity coefficient Evaluation；A(φ^(t)) represent the t time iteration when the dictionary matrix containing phase error；φ^(t)The phase error of the t time iterative estimate Value, in first iteration, φ⁽⁰⁾Value takes zero；

Step 5-3：Phase error estimation and phase error：Because the phase error at each sampling location is differed, in echo-signal Each data sampling point be both needed to be estimated, i.e., by solve following formula carry out phase estimation：

s_εM () represents the echo-signal obtained at the m of sampling location,Represent in (t+1) secondary iteration, adopting Phase error estimation and phase error value at the m of sample position,Represent at the m of position, after the t time phase error estimation and phase error more New dictionary, φ^(t+1)M () represents the phase error to be estimated at m positions in (t+1) secondary iteration, solve above formula, can obtain To estimation error expression formula：

Wherein, Im { } represents the imaginary part of plural number, and Re { } represents real, the conjugate transposition of H representing matrixs；

Step 5-4：Update observation model：Imaging observation is updated using the phase error estimation and phase error value at each sampling for obtaining Model matrix is：

Step 5-5：Repeat step 5-2 to step 5-4, until meetingWhen iteration stop Only, ε values are that imaging effect is chosen with the compromise of iteration efficiency, can be 10^-6-10^-3In the range of arrange, after iteration stopping will To the high resolution target picture for focusing on.

Totally according to this and in the case of no phase error interference, the resolution ratio being imaged using conventional imaging method is low, As shown in Figure 3.When there is phase error interference in echo, conventional imaging method failure, it is impossible to be imaged to target is such as schemed Shown in 4.And using the method for the present invention while realizing that target is focused on, the high-precision target picture of high-resolution is obtained, such as Fig. 5 institutes Show.In addition the inventive method only carries out imaging using 10% data, obtains target more measured than conventional imaging method matter Picture, while illustrating that the inventive method can greatly improve testing efficiency image quality is improved.

Claims (1)

1. a kind of filed-close plane scans three-dimensional imaging and phase error compensation method, it is characterised in that comprise the steps：

Step 1：Obtain the echo data of sparse three-dimensional imaging：In L_x×L_yThe plane of scanning motion on randomly select partial scan point i.e. N_aPoint carries out echo data admission, wherein L_x、L_yThe number of scan points in bidimensional aperture is represented respectively, empty darkroom is measured respectively and is contained The darkroom of measured target, the sparse observation signal obtained after Jing background cancels is s', and its dimension is N_a×N_f, wherein N_a＜ L_x ×L_y, N_fRepresent frequency sampling points, by s' by row pull into one-dimensional vector, be expressed as s, its dimension be N × 1, wherein N=N_aN_f；

Step 2：Image scene discretization：Imaging region is carried out into 3 d-dem, its X is to, Y-direction and the corresponding discrete net of Z-direction Lattice number is respectively N_x、N_yAnd N_z, reflectance factor matrix by rows three-dimensional in scene or row are conspired to create into an one-dimensional vector, it is expressed asWherein g_kRepresent the backscattering coefficient of k-th scattering point；

Step 3：Build target dictionary：Target dictionary A is built according to test parameter and target scene, its dimension is N × N_xN_yN_z, Each element of dictionary A is：

$\begin{array}{c}{A}_{np}=\exp \[-j2k_n\sqrt{{(x_n^{\′}-x_p)}^2+{(y_n^{\′}-y_p)}^2+{(z_0-z_p)}^2}\]\\ n=1,2,...,N_a{N}_f;p=1,2,...,N_x{N}_y{N}_z\end{array}$

Wherein, A_npRepresent line n, the element of pth row in dictionary A；Represent the unit of imaginary number, k_nRepresent mod (n/ N_a) individual space variable, mod () be complementation, (x '_n,y′_n,z₀) it is abs ((n/N_a)+1) individual aperture location coordinate, abs () is to round, as mod (n/N_aDuring)=0, (x '_n,y′_n,z₀) it is abs (n/N_a) individual aperture location coordinate, (x_p,y_p,z_p) P-th scattering point position coordinates in for discrete scene；

Step 4：Signal model of the construction containing phase error：The signal observation model affected by phase error is expressed as：

s_ε=Φ Ag+ θ

Wherein s_εThe echo-signal with phase error is represented, Φ represents phase error term, and size is N_aN_f×N_aN_fTo angular moment Battle array,Wherein, φ (i) (i=1,2 ..., N_a) the phase of echo error at i aperture location is represented, θ represents the noise in echo-signal；

Step 5：Imaging is solved, and is concretely comprised the following steps：

Step 5-1：Set up solving model：Φ A=A (φ) in step 4 is made, following solving model is set up：

$J(g,\mathrm{\φ})=\left|\right|s_{\mathrm{\ϵ}}-A\left(\mathrm{\φ}\right)g|{|}_2^2+\mathrm{\λ}|\left|g\right|{|}_1$

Wherein λ is the regularization parameter of majorized function, can be by being tried to achieve using Generalized Cross Validation (GCV) method；

Step 5-2：Scene scatters coefficient is estimated：The estimation of scattering coefficient in by solving following cost function to obtain scene Value：

${\hat{g}}^{(t+1)}=\arg \underset{g}{min}\left|\right|s_{\mathrm{\ϵ}}-A\left({\mathrm{\φ}}^{\left(t\right)}\right)g|{|}_2^2+\mathrm{\λ}|\left|g\right|{|}_1$

Error in dictionary is converted into into the noise item of observation model, by Separable Surrogate Functionals (SSF) Optimization MethodWherein,Represent the estimate of (t+1) secondary iteration scene reflectivity coefficient；A(φ^(t)) Dictionary matrix containing phase error when representing the t time iteration；φ^(t)The phase error of the t time iterative estimate, in first iteration When, φ⁽⁰⁾Value takes zero；

Step 5-3：Phase error estimation and phase error：Because the phase error at each sampling location is differed, in the every of echo-signal Individual data sampled point is both needed to be estimated, i.e., carry out phase estimation by solving following formula：

$\begin{array}{cc}{\widehat{\mathrm{\φ}}}^{(t+1)}\left(m\right)=\arg \underset{{\mathrm{\φ}}^{(t+1)}\left(m\right)}{\min }\left|\right|s_{\mathrm{\ϵ}}\left(m\right)-e^{\left({\mathrm{j\φ}}^{(t+1)}\right(m\left)\right)}{A}_m\left({\widehat{\mathrm{\φ}}}^{\left(t\right)}\right(m\left)\right){\hat{g}}^{(t+1)}|{|}_2^2& \∀m=1,2,...,N_a\end{array}$

s_εM () represents the echo-signal obtained at the m of sampling location,Represent in (t+1) secondary iteration, in sample bits The phase error estimation and phase error value at m is put,Represent at the m of position, update after the t time phase error estimation and phase error Dictionary, φ^(t+1)M () represents the phase error to be estimated at m positions in (t+1) secondary iteration, solve above formula, can be missed Difference estimates expression formula：

${\widehat{\mathrm{\φ}}}^{(t+1)}\left(m\right)=-arctan\left(\frac{-\mathrm{Im}\left\{{\left({\hat{g}}^{(t+1)}\right)}^H{A}_m^H\left({\widehat{\mathrm{\φ}}}^{\left(t\right)}\right(m)\right)s_{\mathrm{\ϵ}}\left(m\right)\}}{\mathrm{Re}\left\{{\left({\hat{g}}^{(t+1)}\right)}^H{A}_m^H\left({\widehat{\mathrm{\φ}}}^{\left(t\right)}\right(m)\right)s_{\mathrm{\ϵ}}\left(m\right)\}}\right)$

Wherein, Im { } represents the imaginary part of plural number, and Re { } represents real, the conjugate transposition of H representing matrixs；

Step 5-4：Update observation model：It is updated to as observation model using the phase error estimation and phase error value at each sampling for obtaining Matrix is：

$\begin{array}{cc}{A}_m\left({\widehat{\mathrm{\φ}}}^{(t+1)}\right(m\left)\right)=e^{\left(j{\widehat{\mathrm{\φ}}}^{(t+1)}\right(m\left)\right)}{A}_m\left({\widehat{\mathrm{\φ}}}^{\left(t\right)}\right(m\left)\right)& \∀m=1,2,...,N_a\end{array}$

Step 5-5：Repeat step 5-2 to step 5-4, until meetingWhen iteration stopping, ε takes Value is that imaging effect is chosen with the compromise of iteration efficiency, can be 10^-6-10^-3In the range of arrange, will be focused on after iteration stopping High resolution target picture.