CN101915943B - Joint inversion method of dielectric constant and concealed target parameters of homogeneous background media - Google Patents

Abstract

The invention provides a joint inversion method of dielectric constant and concealed target parameters of homogeneous background media, which is realized by the following ways: firstly setting an estimation interval of a dielectric constant, then computing each estimation value in the interval to generate dictionary matrixes, then arranging the dictionary matrixes in rows to generate a joint dictionary matrix, carrying out optimization solution by utilizing imaging algorithm based on compressed sensing on the basis of the joint dictionary matrix to obtain a joint target matrix, then segmenting and extracting the joint target matrix and simultaneously obtaining the dielectric constant and the imaging results of the detection regions of the background media, thus improving the real-time detecting and imaging capabilities of the ground penetrating radars to a greater extent.

Description

The specific inductive capacity of homogeneous background media and the joint inversion method of concealed target parameters

Technical field

The invention belongs to the high-resolution imaging technical field of GPR, relate to a kind of specific inductive capacity of homogeneous background media and the joint inversion method of concealed target parameters.

Technical background

GPR is a kind of effective lossless detection technology.It scans to the search coverage launching electromagnetic wave through the spatial domain and receives scatter echo; Can realize imaging processing to zone of ignorance inside; Obtain the concealed target parameters in the zone of ignorance; Be target distribution information and scattering strength information, effectively be applied to multiple occasions such as municipal works, archaeology, mine detection, anti-terrorism.The formation method of GPR has multiple; Imaging algorithm based on the compressed sensing technology is accomplished the high-resolution imaging processing to search coverage based on the sparse property of echoed signal, the randomness of measuring matrix and optimized Algorithm, has relaxed the requirement of GPR imaging to space peacekeeping time dimension high-density sampling to a great extent.Point scattering type target with in the even loss-free dielectric of the two dimension zone is an example, to given imaging region x ∈ [x ₁, x ₂]; Z ∈ [z ₁, z ₂], setting for as resolution element is δ _Xz, the grid number of its x direction and z direction is designated as L respectively _xAnd L _z, then can objective function be characterized by vector form

O＝[O _2D(1：L _z，1)；O _2D(1：L _z，2)；…；O _2D(1：L _z，L _x)] (1)

The length of this vector is L _o=L _xL _zO wherein _2DBe the matrix description form of two dimension target scattering strength, O _2D(m, n)=σ (m+ (n-1) * L _z), m ∈ [1, L _z], n ∈ [1, L _x], the scattering strength value of q resolution element of σ (q) expression.If this place driftlessness, then σ (q)=0.Spatial domain scanning is carried out along the x direction in this zone can obtain the scatter echo at some place, a plurality of aperture, and then can carry out imaging processing.Spatial domain sampling channel number scale is L _a, the time-sampling of per pass data is counted and is designated as N _tDIELECTRIC CONSTANTS when homogeneous background media _dWhen known, can set up from the objective function vector to the dictionary matrix the scattering data vector according to electromagnetic scattering mechanism, be designated as Ψ, it is of a size of L _aN _t* L _oThis matrix is by L _aSub-matrices is arranged by row, can be designated as:

Ψ＝[Ψ ₁；…；Ψ _s；…；Ψ _La] (2)

In this matrix, s the corresponding submatrix in aperture location place is designated as Ψ _s, it is of a size of N _t* L _oTheoretical according to electromagnetic scattering, the element value of this submatrix can be expressed as

${\mathrm{\Ψ}}_s={\left[{\mathrm{\Ψ}}_s\right]}_{N_t,q}=\frac{s(t_n-\mathrm{\τ}(s,q))}{{\left|\right|s(t_n-\mathrm{\τ}(s,q))\left|\right|}^2}---\left(3\right)$

Wherein, d (s; Q) s aperture location place of expression is to the space length at q resolution element place;

is the dielectric constant values in the vacuum, and c is the light velocity.Theoretical according to compressed sensing, when the stochastic sampling matrix Φ that selects satisfies Φ Ψ and has limited this condition of equidistance character, just can find the solution following equation realization finding the solution through optimized Algorithm to target vector O

$\hat{O}=\arg \min {\left|\right|O\left|\right|}_{1}s.t.{\mathrm{\χ}}_d=\mathrm{\Φ\ΨO}---\left(4\right)$

χ wherein _dExpression target echo stochastic sampling vector.

Need know the DIELECTRIC CONSTANTS of even nothing consumption background media in advance to the imaging processing of search coverage _dIf specific inductive capacity is unknown, then can't carry out the imaging processing in zone.Existing disposal route is to set a specific inductive capacity estimation interval, uses each the specific inductive capacity estimated value in this interval to carry out imaging processing respectively, confirms the specific inductive capacity of medium again according to the focus level of imaging results.This disposal route is based on the substep inverting, and operand is big, and estimated accuracy is not high, can't realize the joint inversion of medium electromagnetic parameter and target component, has restricted the application of GPR.

Summary of the invention

In order to overcome the deficiency of existing medium specific inductive capacity and concealed target parameters substep inverting; Improve the imaging inverting ability of GPR, the invention provides a kind of specific inductive capacity of homogeneous background media and the joint inversion method of concealed target parameters target in the unknown medium.Compressed sensing imaging algorithm with GPR is the basis, generate associating dictionary matrix through design, set up scatter echo the equation of constraint that will satisfy.Based on optimized Algorithm this equation of constraint is found the solution then, can obtain the electromagnetic parameter of medium and the parameter information of target simultaneously, improved the imaging inverting ability of GPR greatly target in the unknown medium of electromagnetic parameter.

Technical solution of the present invention is following:

A kind of specific inductive capacity of homogeneous background media and the joint inversion method of concealed target parameters may further comprise the steps:

Step 1: set initial specific inductive capacity estimated vector: evenly distribute according to interval D the value of setting in the initial specific inductive capacity estimated vector of an initial specific inductive capacity estimated vector of the specific inductive capacity of estimating;

Step 2: generate associating dictionary matrix: to each the estimated value ε in the initial specific inductive capacity estimated vector _m, m ∈ [1, D] calculates respectively and generates the dictionary matrix M ∈ [1, D]; Then this D dictionary matrix generated associating dictionary matrix by rows

Associating dictionary matrix Ψ _JOINTCorresponding objective function vector is O _JOINT, the form of objective function vector is:

Step 3: the estimated value of finding the solution objective function: according to

S.t. χ=Φ Ψ _JOINTO _JOINTAsk for the estimated value of objective function

χ representes that original GPR record section is through the data after the stochastic sampling; Wherein Φ is the stochastic sampling matrix of selection, and satisfies Φ Ψ _JOINTHas limited this condition of equidistance character; Form be:

Step 4: the imaging results and this regional dielectric constant values that obtain search coverage: because

S vector

Be non-zero vector, counter thus pushing away, initial specific inductive capacity estimated vector

Middle s corresponding numerical value ε _sBe the dielectric constant values of real background media;

In an only non-zero submatrices

Be the imaging results of search coverage.

The D value is the integer between 4～7.

Original GPR record section is as shown in Figure 2 through the data after the stochastic sampling, and laterally dimension is space dimension, i.e. each aperture sampled point in space; Vertically dimension is a time dimension, i.e. the time dimension variable of echo data.When utilization compressed sensing theory is handled, through selected suitable stochastic sampling matrix Φ original GPR section to be handled, the sectional view after the processing is as shown in Figure 9.Two-dimensional matrix shown in Figure 9 is the χ here, it comprised the objective function vector to separate

joint inversion be exactly the method that from 2-D data shown in Figure 9, proposes according to this patent that the specific inductive capacity and the concealed target parameters (being the scattering strength parameter of scattering point at location parameter He each scattering point of two-dimensional space) of background media carried out joint inversion.

Be equation of constraint

S.t. χ=Φ Ψ _JOINTO _JOINTSeparate the certain estimated value of our objective function that will obtain just.In this patent; Set up equation of constraint earlier; Purpose is exactly to try to achieve after wherein

try to achieve this matrix; Also just realize joint inversion, also just obtained the estimated value of objective function.

What

represented is vector, is for the ease of tectonic syntaxis dictionary matrix.Be referred to as " non-zero submatrices " here, can regard it as is the matrix of multirow one row.What in fact represented is the target distribution situation of a two-dimensional space, promptly required imaging results.

is the estimated value of

, and its essence also is the simulation of imaging results.As far as a two-dimensional imaging result, can be expressed as a two-dimensional matrix.Horizontal and vertically carry out grid dividing according to resolution element respectively.When certain grid place did not have target to exist, this position was exactly zero in the corresponding two-dimensional matrix.When having target to exist, just there is value this position, and the size of value is the scattering strength value of this target.In this patent,, such two-dimensional matrix is arranged by row, promptly suc as formula the statement of (1) for the ease of tectonic syntaxis dictionary matrix.After the method for employing this patent had realized joint inversion, what in fact obtain was a vector of arranging by row.Convert this vector into two-dimensional matrix again, just become the two-dimensional imaging result.

Beneficial effect:

Basic theories based on compressed sensing; Design generates objective function matrix and associating dictionary matrix; Optimization through to equation of constraint is found the solution; Can realize the joint inversion of target component in specific inductive capacity and the search coverage of homogeneous background media, reduced the operand of substep inverting to a great extent, improve GPR carries out imaging detection to search coverage processing capability in real time.

GPR carries out scanning probe to certain search coverage, can obtain a radar record section.If will obtain the imaging results of this search coverage, just need carry out imaging processing to record section.And the imaging processing needs the dielectric constant values of prevision background media.When the dielectric constant values of background media is unknown, just need estimate it.The estimated accuracy of specific inductive capacity can have influence on the focusing quality of imaging results.In traditional disposal route, have based on the form of the diffraction curve in the raw readings section and estimate, also have and to estimate based on the imaging computing.The former estimation is real-time estimation, but precision is relatively poor.The latter's estimated accuracy is higher, but operand is very big.When estimating based on the imaging computing; At first be to set a specific inductive capacity estimated vector, comprise a plurality of possible dielectric constant values, use each specific inductive capacity estimated value to carry out Polaroid computing then; Again a plurality of imaging results are calculated its focus value respectively; That imaging results of selective focus value maximum (focusing effect is best) is as the imaging results of search coverage, and the corresponding dielectric constant values specific inductive capacity of medium as a setting estimates that (document 2 sees reference: repair the will outstanding person, Chen Jie; Fang Guangyou, Li Fang.Based on F-K skew and minimum entropy ground Penetrating Radar Imaging, electronics and information journal, 2007,29 (4): 827-830).The operand of this method is very big, all will carry out Polaroid computing to each specific inductive capacity, calculates the focus value of imaging results separately then.This method can only off-line operation, obtains imaging results and specific inductive capacity estimation through handle afterwards.

The present invention is based on the basic theories of compressed sensing; Only need several sparse time-samplings and spatial sampling value; Can use and optimize the joint inversion of imaging results that the method find the solution realizes dielectric constant values and the search coverage of background media, promptly use equation of constraint dielectric constant values to imaging results and background media in the joint objective matrix that design generates to carry out associating optimizing estimation.This method has been avoided in the original disposal route each specific inductive capacity estimated value being carried out to the macrooperation amount processing as the focus value computing of computing and imaging results respectively; Greatly degree has reduced the operand of joint inversion; Can online in real time move, obtain imaging results and specific inductive capacity in real time and estimate.

Description of drawings

Fig. 1 shows three targets in the two-dimensional imaging zone; Among the figure, horizontal ordinate is represented the laterally spatial sampling vector of dimension, and ordinate is represented the spatial sampling vector of vertical dimension (depth dimension just).The vertical coordinate on the right is a color scale, has represented the color value corresponding shown in the figure.During this schemes, visible from the scale on the right, corresponding 0 value of black, light grey correspondence 0.25, white corresponding 0.5.Three resolution element non-zeros are only arranged in the key diagram, and its value is respectively 0.25,0.25 and 0.5.What here, in fact this value was represented is the scattering strength value of each scattering point.

Fig. 2 shows the spatial domain scatter echo of target shown in Figure 1;

Fig. 3 shows the corresponding associating dictionary matrix of imaging region shown in Figure 1;

Fig. 4 shows the corresponding submatrix of a certain specific inductive capacity estimated value in the associating dictionary matrix shown in Figure 3;

Fig. 5 shows the corresponding submatrix of a certain spatial aperture point in the submatrix shown in Figure 4;

Fig. 6 shows the transport function that corresponding a certain resolution element is put in aperture, space in the submatrix shown in Figure 5;

Fig. 7 shows all spatial aperture point corresponding random sampling matrixs;

Fig. 8 shows the corresponding submatrix of a certain spatial aperture point in the stochastic sampling matrix shown in Figure 7;

Fig. 9 shows and adopts stochastic sampling matrix shown in Figure 7 that scatter echo shown in Figure 2 is carried out the scattering data after the stochastic sampling;

Figure 10 shows the joint objective matrix that the utilization optimized Algorithm obtains;

Figure 11 shows the true imaging result after joint objective matrix shown in Figure 10 is cut apart.

Embodiment

Below combination figure and practical implementation process are explained further details to the present invention.

Be to confirm at first according to the diffraction curve form of target in the original radar record section and the empirical value of acquisition environment specific inductive capacity according to interval estimated vector

the valuation interval here of setting a specific inductive capacity of the specific inductive capacity of estimating.The number of this vector, promptly the value of D generally can be taken as 4～7.In this estimation interval, D value is equally distributed.Number is many more, and the subsequent operation amount is also big more, and estimated value is also accurate more, generally is taken as 4 to 7 and gets final product; Then to each the estimated value ε in the estimated vector _m, m ∈ [1, D] calculates respectively according to the method in the document [1] and generates the dictionary matrix

M ∈ [1; D] (document 1:AliC.Gurbuz; James H.McClellan; Waymond R.Scott Jr..Compressive sensing for subsurface imaging using ground penetrating radar.Signal Processing, 2009 (89): 1959-1972 :); [in the document, provided the imaging inversion method under the known situation of the specific inductive capacity of background media.Here, be that the method in certain the estimated value utilization document in the specific inductive capacity estimated vector is carried out to the picture inverting, the method in the document can directly be used herein.Chinese title: AliC.Gurbuz, James H.McClellan, Waymond R.Scott Jr.. is based on the underground imaging of the GPR of compressed sensing .Signal Processing, 2009 (89): 1959-1972.] then this D dictionary matrix generated associating dictionary matrix by rows and at last carry out finding the solution of objective function vector OJOINT based on the compressed sensing theory.

Associating dictionary matrix Ψ _JOINTBe of a size of L _aN _t* DL _oL _aBe spatial domain sampling channel number scale, N _tBe the time-sampling point number scale of per pass data, L _o=L _xL _z, L _xAnd L _zBe respectively the grid number of imaging resolution element in x direction and z direction.The difference of medium parameter causes the difference to each aperture point transport function of each resolution element in the dictionary matrix, just time delay value τ (s, difference q).With the two-dimensional imaging is example, along the one-dimensional space direction subsurface investigation zone is scanned.Scan mode has multiple, like synthetic aperture scanning, the scanning of real aperture, array antenna scanning etc.The aperture point is the spatial sampling point on this one-dimensional scanning direction, is generally even distribution form.For obtaining meticulous imaging results, spatial sampling will be satisfied nyquist sampling theorem, and promptly the spacing of two aperture points is less than certain numerical value.Spatial sampling is close more, and imaging results is good more, and certain data volume of gathering is also just big more, and the operand of data processing is also big more.

Imaging detection is carried out in certain zone, generally is the size of at first confirming the detection of a target of wanting, just is specified to the resolution element of picture; Confirm the density of spatial sampling then according to this resolution element, i.e. the aperture dot spacing; Carry out data acquisition and imaging processing again.

In the two-dimensional imaging, entire image can be represented with a two-dimensional matrix.The occupied space cell of each pixel is resolution element in the image, and each resolution element place numerical value separately is different, has represented the scattering strength value of position in the two-dimensional space respectively.Resolution element is the minimum unit that can differentiate adjacent two targets in the image.In between all block of air spaces in a resolution element, think that its scattering strength is identical.Ψ _JOINTA certain submatrix in the matrix Be of a size of L _aN _t* L _oThis submatrix comprises L again _aIn each self-corresponding submatrix of some place, individual aperture, the submatrix at s aperture location place is designated as

It is of a size of N _t* L _o, Ψ _JOINTMatrix comprises D submatrix, and wherein m submatrix is designated as And Matrix has comprised the information of all resolution elements of aperture point traversal.And aperture point one total L _aIndividual, therefore

Matrix has just comprised L _aIndividual submatrix.At this L _aIn the individual submatrix, s submatrix

Represent the matrix of s all resolution elements of aperture point traversal, it is of a size of N _t* L _o" s aperture location place " in the preceding text is " s aperture Dian Chu ".

Theoretical according to electromagnetic scattering, the element value of this submatrix can be expressed as

${\mathrm{\Ψ}}_{s,{\mathrm{\ϵ}}_m}={\left[{\mathrm{\Ψ}}_{s,{\mathrm{\ϵ}}_m}\right]}_{N_t,q}=\frac{s(t_n-\mathrm{\τ}(s,q))}{{\left|\right|s(t_n-\mathrm{\τ}(s,q))\left|\right|}^2}---\left(5\right)$

Wherein,

d-(s; Q) expression point place, s aperture is to the space length at q resolution element place; The aperture point is a sampled point of spatial sampling, and resolution element is the minimum unit that can differentiate adjacent two targets in the image.The distance that resolution element is put in said here aperture is meant that the aperture puts the distance at this regional center of resolution element.C is the light velocity, ε _mBe the estimated vector of specific inductive capacity

Middle corresponding dielectric constant values.O _JOINTVector is D and is of a size of L _oThe vector of * 1 (O is identical with vector) forms by the row arrangement, that is:

It is corresponding submatrix

non-zero of actual value that specific inductive capacity is wherein only arranged; This submatrix

is the form of formula (1), has characterized target distribution and the scattering coefficient information in the imaging region.Visible from above analysis: the estimation of specific inductive capacity is to lie in O _JOINTIn this vector, target location vector and scattering strength vector are included in O _JOINTA certain non-zero submatrices in, and O _JOINTIt is typical sparse vector.

Theoretical according to compressed sensing; When the stochastic sampling matrix Φ that selects (as far as

matrix of limited support with signal forms such as similar spike, sine, wavelet, Gabor functions; Have independent identically distributed Bernoulli stochastic variable or Gaussian stochastic variable and can be used for constructing stochastic sampling matrix Φ, shown in document 1.Each numerical value that is the stochastic sampling matrix all is a stochastic variable, and each stochastic variable satisfies independent identically distributed character.) satisfy Φ Ψ _JOINTWhen having limited this condition of equidistance character, just can find the solution following equation and realize target vector O through optimized Algorithm _JOINTFind the solution

${\hat{O}}_{\mathrm{JOINT}}=\arg \min {\left|\right|O_{\mathrm{JOINT}}\left|\right|}_{1}s.t.\mathrm{\χ}={\mathrm{\Φ\Ψ}}_{\mathrm{JOINT}}{O}_{\mathrm{JOINT}}---\left(7\right)$

The meaning of following formula is: at equality χ=Φ Ψ _JOINTO _JOINTConstraint under, select vector O with minimum 1-norm _JOINTEstimated value.Wherein, the variate-value when argmin representes to make objective function get minimum value, || O _JOINT|| ₁Expression vector O _JOINTThe 1-norm.The definition of 1-norm is following: make vector x=(x ₁, x ₂..., x _n), then the 1-norm of this vector is: || x|| ₁=| x ₁|+| x ₂|+...+| x _n|.Shown in Figure 9 be the χ in this example.

According to the structural form of above associating matrix, the inversion result of following formula has following form:

The meaning here is: under the model that formula 6 is confirmed, the method for using this patent to carry estimates that the estimated value of acquisition is identical with the initial value of master pattern.This formula also can be expressed as

That is: be L D length.The associating vector

that constitutes of vector in; It is real target vector O that s vector only arranged, and other D-1 vector is zero.And middle s the corresponding numerical value ε s of initial specific inductive capacity estimated vector is the dielectric constant values of real background media.After having obtained the estimated value

of target vector, an only non-zero submatrices

is the imaging results of search coverage in this estimated value.

Net result of the present invention is the imaging results and this regional dielectric constant values that can obtain search coverage simultaneously.The utilization GPR carries out scanning probe to search coverage and can obtain a record section.During some is used, be to be purpose with the imaging results that obtains this search coverage.During some is used, be to be purpose with the specific inductive capacity that obtains this background media.The application purpose that also has other.Under the different application requirements, also different to the disposal route of record section.This patent proposes to this problem of the specific inductive capacity joint inversion of concealed target parameters and background media (inverting of concealed target parameters is just to the imaging processing of radar record section).) and ε _dBe the dielectric constant values of background media, so just realized the joint inversion of the specific inductive capacity and the concealed target parameters of homogeneous background.

Embodiment 1:

This instance is to form images to two-dimensional detection, but present technique is not limited to 2 dimensional region, and is also suitable to the detection imaging of 3D region.

At first set an imaging region, establishing this regional specific inductive capacity is 16 ε ₀, should the zone being divided into 400 image-generating units along horizontal and vertical, horizontal and vertical number of unit all is 20.Fig. 1 provided should the zone in the spatial domain distribution situation of three scattering points.Each scattering point all is omnidirectional's scattering and is independent of each other that promptly scatter echo satisfies the linear superposition relation.The gray-scale value of each scattering point is represented its scattering strength value, and the scattering strength of these three scattering points is respectively 0.25,0.25 and 0.5.When imaging detection was carried out in this zone, the spatial domain was sampled as the form of stochastic sampling, laterally sampled along the x axle, and sampling number is 30.In each sample point, downward launching electromagnetic wave also receives scatter echo, and it is 256 that time-domain sampling is counted.Through the ray simulation calculation that tracks, the scatter echo in whole aperture is as shown in Figure 2.

During actual detection, can obtain similar record section shown in Figure 2 through space dimension x direction sampling.Radar imagery is this record section to be handled obtain the similar target distribution shown in Figure 1 and the scattering strength of each target.When the specific inductive capacity of background media is known, can adopt based on the theoretical imaging algorithm of compressed sensing.And when the specific inductive capacity of background media is unknown, carry out the joint inversion of the specific inductive capacity and the target scattering function of medium with regard to needing the associating dictionary matrix in the sampling this patent.

The estimated vector that at first defines specific inductive capacity is to judge selected estimation interval according to the curve form of raw readings section and to the experience of search coverage for

this estimated vector.In estimation interval, 5 numerical value that evenly distributed track based on ray then and generate associating dictionary matrix Ψ _JOINT, the two-dimentional display result of this matrix is as shown in Figure 3.This matrix has five sub-matrices by rows, and each submatrix is corresponding to the specific inductive capacity estimated vector

In a specific inductive capacity estimated value, providing the specific inductive capacity estimated value here is 12 ε ₀Submatrix

Two-dimentional display result, as shown in Figure 4.This submatrix has comprised the transport function between all horizontal aperture points and each resolution element of imaging region, and the transfer function matrix that each aperture point is corresponding is arranged by row.Provide the two-dimentional display result of the corresponding block matrix of first aperture point here, as shown in Figure 5.This matrix has 400 row, and the transport function of current scan point to arbitrary resolution element shown in each tabulation, and this transport function is a time domain signal, and it is 256 points that time-sampling is counted.Provide first aperture here and put the transport function form of first resolution element, as shown in Figure 6.

Theoretical according to compressed sensing, select stochastic sampling matrix Φ for obeying the stochastic matrix that N (0,1) distributes, as shown in Figure 7.This example is an example with the stochastic matrix of obeying N (0,1) distribution, but present technique is not limited to the stochastic matrix of this form, as long as satisfy Φ Ψ _JOINTStochastic matrix Φ with limited equidistance character is suitable for.This matrix is a broad sense diagonal matrix, i.e. the corresponding sub-stochastic matrix Φ in each some place, aperture _s, s ∈ [1, L _a] occupy a certain on the full stochastic matrix diagonal line.Provide the corresponding sub-stochastic matrix Φ of first aperture point here ₁, as shown in Figure 8.The size of this matrix is 10 * 256, and it is the time domain data of 10 stochastic samplings that raw scattered echo (256 time-domain samplings) is used this matrix conversion.Scatter echo to each aperture all uses stochastic matrix conversion, obtains the echo data of stochastic sampling, and is as shown in Figure 9.Radar Imaging Processing based on compressed sensing is an inverting target component information from stochastic sampling echo data as shown in Figure 9.Through setting up associating dictionary matrix, imaging processing can be converted into the optimization problem of formula (7) and find the solution.The utilization optimized Algorithm is carried out iterative processing to formula (7); This estimated value of estimated value

that can obtain the joint objective matrix is a column vector; It is carried out two dimension reset, the result is shown in figure 10.Visible from figure, obtained five two-dimensional imaging results that dielectric constant values is corresponding altogether, have only the corresponding imaging results non-zero of the 3rd dielectric constant values, other four imaging results are zero.Then the 3rd estimated value in the estimated vector

is real dielectric constant values; And corresponding imaging results is the inversion result of target component, and is shown in figure 11.Imaging results distributes identical with real goal shown in Figure 1.

Claims (2)

1. the joint inversion method of the specific inductive capacity of a homogeneous background media and concealed target parameters is characterized in that, may further comprise the steps:

Step 1: set initial specific inductive capacity estimated vector: evenly distribute according to interval D the value of setting in the initial specific inductive capacity estimated vector of an initial specific inductive capacity estimated vector

of the specific inductive capacity of estimating;

Step 2: generate associating dictionary matrix: to each the estimated value ε in the initial specific inductive capacity estimated vector _m, m ∈ [1, D] calculates respectively and generates the dictionary matrix

M ∈ [1, D]; Then this D dictionary matrix generated associating dictionary matrix by rows Associating dictionary matrix Ψ _JOINTCorresponding objective function vector is O _JOINT, the form of objective function vector is:

Step 3: the estimated value of finding the solution objective function: according to

S.t. χ=Φ Ψ _JOINTO _JOINTAsk for the estimated value of objective function

χ representes that original GPR record section is through the data after the stochastic sampling; Wherein Φ is the stochastic sampling matrix of selection, and satisfies Φ ψ _JOINTHas limited this condition of equidistance character; Form be:

Step 4: the imaging results and this regional dielectric constant values that obtain search coverage: because

S vector

Be non-zero vector, counter thus pushing away, initial specific inductive capacity estimated vector

Middle s corresponding numerical value ε _sBe the dielectric constant values of real background media;

In an only non-zero submatrices

Be the imaging results of search coverage.

2. the joint inversion method of the specific inductive capacity of homogeneous background media according to claim 1 and concealed target parameters is characterized in that, the D value is the integer between 4 ~ 7.

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