CN101825700A - Method for evaluating SAR image point target - Google Patents

Abstract

The invention discloses a method for evaluating an SAR (synthetic aperture radar) image point target, which comprises the following steps of: 1, setting two interpolation parameters, namely a two-dimensional interpolation multiple and a one-dimensional interpolation multiple, and initializing a two-dimensional matrix and a one-dimensional matrix; 2, carrying out two-dimensional interpolation by zero padding in an equivalent high-frequency area through two-dimensional Fourier transform; 3, extracting a range profile result and an azimuth profile result, and carrying out one-dimensional frequency domain interpolation respectively to obtain a range one-dimensional interpolation result and an azimuth one-dimensional interpolation result; and 4, acquiring a range resolution index and an azimuth resolution index according to the range one-dimensional interpolation result and the azimuth one-dimensional interpolation result. When an imaging result has residual linear phase, the position of an equivalent high-frequency point can be automatically determined according to frequency domain energy distribution and zero padding is performed in the equivalent high-frequency area, so a correct interpolation result and an accurate index result are obtained, the measuring precision is improved, an accurate evaluating index of the point target is provided, and the application range of the evaluated object is extended.

Description

A kind of SAR image point target appraisal procedure

Technical field

The present invention relates to a kind of SAR image point target appraisal procedure, specifically, be meant the interpolation method of the point target index evaluation of a kind of synthetic-aperture radar (being called for short SAR) image, belong to the Radar Technology field.

Background technology

SAR image property index is to weigh the important evidence of polarization sensitive synthetic aperture radar system performance, also is the quantitative basis of estimating imaging processing algorithm focusing effect.SAR image property index mainly comprises point target and appearance mark index two classes.SAR appearance mark index measurement only needs can finish through statistical study usually, the measuring process of point target index is than appearance mark index measurement complexity, need just to obtain the higher index of accuracy, thereby interpolation method has considerable influence to the measurement result of point target index through interpolation processing.The index measurement of point target is normally treated the frequency domain interpolation realization in two steps of assessment objective data, and wherein first step interpolation is a two-dimensional interpolation, and the second step interpolation is to adjust the distance respectively to carrying out the one dimension interpolation with the orientation to cross-sectional data.Existing frequency domain interpolation method is directly in the high-frequency region zero padding of frequency domain, this method has been ignored the influence of SAR point target time domain linear phase place, it is effective only not introduce the time domain linear phase place at SAR point target image, but for general SAR imaging processor, tend in the imaging processing process, introduce residual linear phase, thereby make the direct zero padding interpolation of frequency domain result mistake occur, can not obtain the correct measurement index.

Summary of the invention

The objective of the invention is in order to solve the interpolation Problem-Error that simple SAR point target frequency domain interpolation method is brought, frequency domain energy distribution characteristic according to point target, in the two-dimensional frequency interpolation process, adopt adaptive zero padding operation, promptly by the equivalent high frequency points of search, mode in equivalent high-frequency region zero padding obtains correct two-dimensional interpolation result, extract on this basis the orientation to the distance to cross-sectional data, and further do the one dimension interpolation processing, according to the cross-sectional data after the one dimension interpolation calculate respectively accurately the point target orientation to distance to index.

A kind of SAR image point target appraisal procedure of the present invention comprises following step:

Step 1: set two-dimensional interpolation multiple and two interpolation parameter of one dimension interpolation multiple, two-dimensional matrix and one dimension matrix are carried out initialization;

Step 2: carry out two-dimensional interpolation in the method for equivalent high-frequency region zero padding by two-dimensional Fourier transform;

Step 3: extract distance data matrix and orientation data matrix before the one dimension interpolation before the one dimension interpolation, and carry out the one dimension frequency domain interpolation respectively, obtain distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix;

Step 4, according to distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix obtain distance to the orientation to the resolution index.

The invention has the advantages that: when there is residual linear phase in the present invention in imaging results, automatically determine equivalent high frequency points position according to the frequency domain energy distribution, and in equivalent high-frequency region zero padding, thereby obtain correct interpolation result and index result of calculation accurately, improved measuring accuracy, point target evaluation index accurately can be provided, increase the scope of application of evaluation object.

Description of drawings

Fig. 1 is a method flow diagram of the present invention;

Fig. 2 is two-dimensional frequency matrix energy equivalence high frequency points synoptic diagram in the step 2 of the present invention;

Fig. 3 is two-dimensional interpolation matrix of consequence battle array assignment synoptic diagram in the step 2 of the present invention;

Fig. 4 for two-dimensional interpolation in the step 3 of the present invention as a result level line and distance to the orientation to diagrammatic cross-section;

Fig. 5 a is embodiment data matrix D ₁The power data three-dimensional plot;

Fig. 5 b is embodiment data matrix D ₁The frequency spectrum data three-dimensional plot;

Fig. 5 c is the contour map of two-dimensional interpolation matrix of consequence D_Interp2 among the embodiment;

Fig. 5 d be among the embodiment one-dimensional distance to the power normalization curve of interpolation result matrix D _ Interp1_R;

Fig. 5 e be among the embodiment one dimension orientation to the power normalization curve of interpolation result matrix D _ Interp1_A;

Fig. 6 a is the power contour map of the two-dimensional interpolation matrix of consequence D_Interp2 that the simple zero padding interpolation method of employing obtains among the embodiment;

Fig. 6 b is the one-dimensional distance that adopts simple zero padding interpolation method among the embodiment and the obtain power normalization curve to interpolation result matrix D _ Interp1_R;

Fig. 6 c is the one dimension orientation that adopts simple zero padding interpolation method among the embodiment and the obtain power normalization curve to interpolation result matrix D _ Interp1_A.

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention is a kind of SAR image point target appraisal procedure, and flow process comprises following step as shown in Figure 1:

Step 1: set two-dimensional interpolation multiple and two interpolation parameter of one dimension interpolation multiple, two-dimensional matrix and one dimension matrix are carried out initialization;

Be specially:

I: SAR view data to be assessed is the two-dimentional regional area complex data matrix D that contains point target to be assessed ₁, dimension is N * N, sets the interpolation multiple and comprises two-dimensional interpolation multiple N ₂, one dimension interpolation multiple N ₁, described N 〉=8, N ₂〉=16, N ₁〉=32;

Ii: according to SAR view data dimension to be assessed and interpolation multiple carry out two-dimensional interpolation matrix of consequence, distance before the one dimension interpolation data matrix, orientation before the one dimension interpolation data matrix, distance to one dimension interpolation result matrix and orientation to the initialization of one dimension interpolation result matrix;

Described two-dimensional interpolation matrix of consequence is D_Interp2, and matrix dimension is NN ₂* NN ₂Distance data matrix before the one dimension interpolation is D_R, and matrix dimension is NN ₂* 1; Orientation data matrix before the one dimension interpolation is D_A, and matrix dimension is NN ₂* 1; Distance is D_Interp1_R to one dimension interpolation result matrix, and matrix dimension is NN ₂N ₁* 1; The orientation is D_Interp1_A to one dimension interpolation result matrix, and matrix dimension is NN ₂N ₁* 1; The matrix element initial value of above-mentioned matrix is 0;

Step 2: carry out two-dimensional interpolation in the method for equivalent high-frequency region zero padding by two-dimensional Fourier transform;

With data matrix D ₁Carry out the original position two-dimensional Fourier transform, obtain the two-dimensional frequency result, the result is copied to data matrix D ₁, according to formula (2)～(5) search data matrix D ₁Equivalent high frequency points p ₁, cross p ₁Point is made level and apart from the separatrix, data matrix D ₁Be divided into 4 submatrixs, four corner matrixes of two-dimensional interpolation matrix of consequence D_Interp2 are used data matrix D respectively ₁4 submatrix assignment, two-dimensional interpolation matrix of consequence D_Interp2 is done the inverse Fourier transform of original position two dimension obtains the two-dimensional interpolation result, the result is copied to two-dimensional interpolation matrix of consequence D_Interp2, be specially:

(a) to the data matrix D ₁Carry out the original position two-dimensional Fourier transform, obtain the two-dimensional frequency result, the result is copied to matrix D ₁, realize the data matrix D ₁Renewal;

(b) obtain data matrix D after the renewal ₁Energy and S:

$S=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left|D_1(i,j)\right|}^2---\left(1\right)$

D wherein ₁(i, j) expression data matrix D ₁I capable, the element value of j row.

(c) to the data matrix D ₁Equivalent high frequency points p ₁Carry out two-dimensional search, establish equivalent high frequency points p ₁Volume coordinate be (i ₀, j ₀), then:

When

The time, establish i ₀Initial value is N, i ₀Subtract 1 successively, be met the i of formula (2) at last ₀

$\left\{\begin{array}{c}\underset{i=i_0-N/2}{\overset{i_0-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left|D_1(i,j)\right|}^2\≤0.5\·S\\ \underset{i=i_0-N/2-1}{\overset{i_0-2}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left|D_1(i,j)\right|}^2>0.5\·S\end{array}\right.---\left(2\right)$

When

The time, establish i ₀Initial value is 2, i ₀Add 1 successively, be met the i of formula (3) at last ₀

$\left\{\begin{array}{c}\underset{i=i_0}{\overset{i_0+N/2-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left|D_1(i,j)\right|}^2>0.5\·S\\ \underset{i=i_0-1}{\overset{i_0+N/2-2}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\left|D_1(i,j)\right|}^2\≤0.5\·S\end{array}\right.---\left(3\right)$

When

The time, establish j ₀Initial value is N, j ₀Subtract 1 successively, be met the j of formula (4) at last ₀

$\left\{\begin{array}{c}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=j_0-N/2}{\overset{j_0-1}{\mathrm{\Σ}}}{\left|D_1(i,j)\right|}^2\≤0.5\·S\\ \underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=j_0-N/2-1}{\overset{j_0-2}{\mathrm{\Σ}}}{\left|D_1(i,j)\right|}^2>0.5\·S\end{array}\right.---\left(4\right)$

When

The time, establish j ₀Initial value is 2, j ₀Add 1 successively, be met the j of formula (5) at last ₀

$\left\{\begin{array}{c}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{j=j_0}{\overset{{\mathrm{<figure-callout\; id="0"\; label="j"\; filenames="HSA00000090368800041.png,HSA00000090368800061.png"\; state="\{\{state\}\}">j</figure-callout>}}_0+N/2-1}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2>0.5\&CenterDot;S\\ \underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{j=j_0-1}{\overset{{\mathrm{<figure-callout\; id="0"\; label="j"\; filenames="HSA00000090368800041.png,HSA00000090368800061.png"\; state="\{\{state\}\}">j</figure-callout>}}_0+N/2-2}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2\&le;0.5\&CenterDot;S\end{array}\right.---\left(5\right)$

(d) according to (i ₀, j ₀) with data matrix D ₁Be divided into four sub-block matrix and be defined as S respectively ₁, S ₂, S ₃, S ₄, as shown in Figure 2, wherein four sub-block matrix juncture areas are equivalent high frequency region, four sub-block matrix satisfy formula (6):

$\left\{\begin{array}{c}{S}_1=D_1[1:(i_0-1),1:(j_0-1)]\\ S_2=D_1[1:(i_0-1),j_0:N]\\ S_3=D_1[i_0:N,1:(j_0-1)]\\ S_4=D_1[i_0:N,j_0:N]\end{array}\right.---\left(6\right)$

(e) with data matrix D ₁Four sub-block matrix S ₁, S ₂, S ₃, S ₄Compose to give four summit matrixes of two-dimensional interpolation matrix of consequence D_Interp2 successively, satisfy formula (7), as shown in Figure 3, simultaneously for guaranteeing that the amplitude of point target does not change before and after the interpolation, on amplitude, multiply by the two-dimensional interpolation multiple square:

$\left\{\begin{array}{c}D\_\mathrm{Interp}2[1:(i_0-1),1:(j_0-1)]=N_2\&CenterDot;N_2\&CenterDot;S_1\\ D\_\mathrm{Interp}2[1:(i_0-1),(N\&CenterDot;N_2-N+j_0):(N\&CenterDot;N_2)]=N_2\&CenterDot;N_2\&CenterDot;S_2\\ D\_\mathrm{Interp}2[(N\&CenterDot;N_2-N+i_0):(N\&CenterDot;N_2),1:(j_0-1)]=N_2\&CenterDot;N_2\&CenterDot;S_3\\ D\_\mathrm{Interp}2[(N\&CenterDot;N_2-N+i_0):(N\&CenterDot;N_2),(N\&CenterDot;N_2-N+j_0):(N\&CenterDot;N_2)]=N_2\&CenterDot;N_2\&CenterDot;S_4\end{array}\right.---\left(7\right)$

(f) two-dimensional interpolation matrix of consequence D_Interp2 is carried out the inverse Fourier transform of original position two dimension, obtain the two-dimensional interpolation result, the result is copied among the two-dimensional interpolation matrix of consequence D_Interp2 again, realize renewal two-dimensional interpolation matrix of consequence D_Interp2.

Step 3, extract distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix, and carry out the one dimension frequency domain interpolation respectively, obtain distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix;

The power maximal value coordinate of search two-dimensional interpolation matrix of consequence D_Interp2, extract distance data matrix D_R and orientation data matrix D_A before the one dimension interpolation before the one dimension interpolation, adjusting the distance respectively, data matrix D_R and orientation data matrix D_A before the one dimension interpolation carry out one dimension Fourier interpolation before the one dimension interpolation, obtain distance to one dimension interpolation result matrix D _ Interp1_R and orientation to one dimension interpolation result matrix D _ Interp1_A, be specially:

1. search for the coordinate (i of the power peak position correspondence of two-dimensional interpolation matrix of consequence D_Interp2 _p, j _p), set (i _p, j _p) initial value is (1,1), i _p, j _pAdd 1 successively, be met the coordinate (i of formula (8) at last _p, j _p), (i of this moment _p, j _p) be power maximal value coordinate;

${|D\_\mathrm{Interp}2(i_p,j_p)|}^2=\underset{i\&Element;[1,N\&CenterDot;N_2],j\&Element;[1,N\&CenterDot;N_2]}{\max }{|D\_\mathrm{Interp}2(i,j)|}^2---\left(8\right)$

2. in two-dimensional interpolation matrix of consequence D_Interp2, select i _pLine data is as distance data matrix D_R before the one dimension interpolation, shown in the horizontal linear among Fig. 4, that is:

D_R[j]＝D_Interp2[i _p，j]，j∈[1，N·N ₂] (9)

3. adjusting the distance, data matrix D_R carries out one dimension Fourier interpolation processing before the one dimension interpolation, and obtaining dimension is NN ₂N ₁Distance to one dimension interpolation result matrix D _ Interp1_R;

4. in two-dimensional interpolation matrix of consequence D_Interp2, select j _pRow are as orientation data matrix D_A before the one dimension interpolation, shown in the vertical line among Fig. 4, that is:

D_A[i]＝D_Interp2[i，j _p]，i∈[1，N·N ₂] (10)

5. orientation data matrix D_A before the one dimension interpolation is carried out one dimension Fourier interpolation processing, obtaining dimension is NN ₂N ₁The orientation to one dimension interpolation result matrix D _ Interp1_A.

Step 4, according to distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix obtain distance to the orientation to the resolution index;

Adjust the distance and make normalized to one dimension interpolation result matrix to one dimension interpolation result matrix and orientation, search for energy maximum value position and the half-power position, both sides of result after the normalized then respectively, utilize formula (11) and (12) obtain the distance to the orientation to resolution, be specially:

(1) adjust the distance and carry out the normalization log-transformation to one dimension interpolation result matrix D _ Interp1_R, the point of point by point search power maximal value correspondence is designated as Rp down; Search for left from Rp, record for the first time performance number is designated as Rl down less than the point of-3.0dB; Search for to the right from Rp, record for the first time is designated as Rr under the point of performance number less than-3.0dB again;

(2) according to the subscript Rr and the Rl that obtain in the step (1), through type (11) obtains distance to resolution δ _r, unit is apart from resolution element:

${\mathrm{\&delta;}}_r=\frac{\mathrm{Rr}-\mathrm{Rl}+1}{N_2{N}_1}---\left(11\right)$

(3) the normalization log-transformation is carried out to one dimension interpolation result matrix D _ Interp1_A in the orientation, the point of point by point search power maximal value correspondence is designated as Ap down; Search for left from Ap, record for the first time performance number is designated as Al down less than the point of-3.0dB; Search for to the right from Ap, record for the first time performance number is designated as Ar down less than the point of-3.0dB again;

(4) subscript Ar and the Al that obtains according to step (3), through type (12) obtains the orientation to resolution δ _a, unit is the azimuth discrimination unit:

${\mathrm{\&delta;}}_a=\frac{\mathrm{Ar}-\mathrm{Al}+1}{N_2{N}_1}---\left(12\right)$

The distance that obtains is the quantitative result of point target assessment to resolution to resolution and orientation.

Embodiment:

At a two-dimentional impulse response function is that F (m, assess by ideal point target n).

$F(m,n)=\sin c\left[\frac{n-0.5N}{{\mathrm{\&delta;}}_r^{\&prime;}}\right]\&CenterDot;\exp \{j\&CenterDot;2\mathrm{\&pi;}{f}_r\&CenterDot;(n-0.5N)\}$

$\&CenterDot;\sin c\left[\frac{m-0.5N}{{\mathrm{\&delta;}}_a^{\&prime;}}\right]\&CenterDot;\exp \{j\&CenterDot;2\mathrm{\&pi;}{f}_a\&CenterDot;(m-0.5N)\}---\left(13\right)$

$m,n\&Element;[1,N]$

Wherein the sinc function definition is N=32,

δ _a'=1.5, δ _r'=1.8, f _a=0.6, f _r=0.3.Exponential term exp{j2 π f in the above-mentioned function _rAnd exp{j2 π f (n-0.5N) } _a(m-0.5N) } show ideal point target in distance to contain residual linear phase to all existing with the orientation.Known F (16,16)=1,20lg F (16,16 ± 0.443 δ _r')=20lg 0.707=-3.0dB, then the range resolution theoretical value is δ _r=0.886 δ _r'=1.5948 apart from resolution element, in like manner 20lg F (16 ± 0.443 δ _a', 16)=20lg 0.707=-3.0dB, the azimuthal resolution theoretical value is δ _a=0.886 δ _a'=1.3290 azimuth discrimination unit.

Using appraisal procedure of the present invention is specially:

Step 1: set two-dimensional interpolation multiple and two interpolation parameter of one dimension interpolation multiple, two-dimensional matrix and one dimension matrix are carried out initialization, be specially:

I: (m, discrete sampling value n) is as the two-dimentional regional area complex data D that contains point target to be assessed with F ₁, dimension is 32 * 32, i.e. D[i, j]=F (i, j), i wherein, j ∈ [1,2 ..., 32], the 3-D display of its amplitude is shown in Fig. 5 a; Two-dimensional interpolation multiple N ₂=16, one dimension interpolation multiple N ₁=32;

Ii: carry out matrix initialization behind the matrix and one dimension interpolation before two-dimensional interpolation matrix of consequence, the one dimension interpolation according to SAR view data dimension to be assessed and interpolation multiple, establishing the two-dimensional interpolation matrix of consequence is D_Interp2, and matrix dimension is 512 * 512; Distance data matrix before the one dimension interpolation is D_R, and matrix dimension is 512 * 1; Orientation data matrix before the one dimension interpolation is D_A, and matrix dimension is 512 * 1; Distance is D_Interp1_R to one dimension interpolation result matrix, and matrix dimension is 16384 * 1; The orientation is D_Interp1_A to one dimension interpolation result matrix, and matrix dimension is 16384 * 1; The matrix element initial value of above-mentioned matrix is 0.

Step 2: carry out two-dimensional interpolation in the method for equivalent high-frequency region zero padding by two-dimensional Fourier transform;

Be specially:

(a) to the data matrix D ₁Carry out the original position two-dimensional Fourier transform, obtain the two-dimensional frequency result, the result is copied to matrix D ₁, realize the data matrix D ₁Renewal, the 3-D display of its amplitude is shown in Fig. 5 b;

(b) obtain data matrix D after the renewal ₁Energy and S:S=2706.786;

(c) to the data matrix D ₁Equivalent high frequency points p ₁Carry out two-dimensional search, obtain (i ₀, j ₀)=(5,28), be specially:

Because

So i ₀Initial value is made as 2, i ₀Add 1 successively until i ₀=5 satisfy formula (3), that is:

$\left\{\begin{array}{c}\underset{i=5}{\overset{20}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{32}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2=1401.63>0.5\&CenterDot;S=1353.39\\ \underset{i=4}{\overset{19}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{32}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2=1243.88\&le;0.5\&CenterDot;S=1353.39\end{array}\right.---\left(14\right)$

Because

So j ₀Initial value is made as 32, subtracts 1 successively until j ₀=28 satisfy formula (4), promptly satisfy:

$\left\{\begin{array}{c}\underset{i=1}{\overset{32}{\mathrm{\&Sigma;}}}\underset{j=12}{\overset{27}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2=1238.16\&le;0.5\&CenterDot;S=1353.39\\ \underset{i=1}{\overset{32}{\mathrm{\&Sigma;}}}\underset{j=11}{\overset{26}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2=1366.44>0.5\&CenterDot;S=1353.39\end{array}\right.---\left(15\right)$

(d) according to (i ₀, j ₀)=(5,28) with data matrix D ₁Be divided into four sub-block matrix S ₁, S ₂, S ₃, S ₄, be specially:

$\left\{\begin{array}{c}{S}_1=D_1[1:\mathrm{4,1}:27)]\\ S_2=D_1[1:\mathrm{4,28}:32]\\ S_3=D_1[5:\mathrm{32,1}:27]\\ S_4=D_1[5:\mathrm{32,28}:32]\end{array}\right.---\left(16\right)$

(e) with data matrix D ₁Four sub-block matrix S ₁, S ₂, S ₃, S ₄Compose four summit matrixes giving two-dimensional interpolation matrix of consequence D_Interp2 successively, other elements are initial value (equalling zero), that is:

$\left\{\begin{array}{c}D\_\mathrm{Interp}2[1:\mathrm{4,1}:27]=256\&CenterDot;S_1\\ D\_\mathrm{Interp}2[1:4,508:512]=256\&CenterDot;S_2\\ D\_\mathrm{Interp}2[485:\mathrm{512,1}:27]=256\&CenterDot;S_3\\ D\_\mathrm{Interp}2[485:\mathrm{512,508}:512]=256\&CenterDot;S_4\end{array}\right.---\left(17\right)$

(f) two-dimensional interpolation matrix of consequence D_Interp2 is carried out the inverse Fourier transform of original position two dimension, obtain the two-dimensional interpolation result, the result is copied to matrix D _ Interp2 again, realize renewal two-dimensional interpolation matrix of consequence D_Interp2.

Step 3, extract distance data matrix and orientation data matrix before the one dimension interpolation before the one dimension interpolation, and carry out the one dimension frequency domain interpolation respectively, obtain distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix;

Be specially:

1. search for the coordinate (i of the power peak position correspondence of two-dimensional interpolation matrix of consequence D_Interp2 _p, j _p)=(241,241), that is:

${|D\_\mathrm{Interp}2\left(\mathrm{241,241}\right)|}^2=\underset{i\&Element;\left[\mathrm{1,512}\right],j\&Element;\left[\mathrm{1,512}\right]}{\max }{|D\_\mathrm{Interp}2(i,j)|}^2---\left(18\right)$

2. in two-dimensional interpolation matrix of consequence D_Interp2, select the 241st line data as distance data matrix D_R before the one dimension interpolation, that is:

D_R[j]＝D_Interp2[241，j]，j∈[1，512] (19)

3. adjusting the distance, data matrix D_R carries out one dimension Fourier interpolation processing before the one dimension interpolation, obtains dimension and be 16384 distance to one dimension interpolation result matrix D _ Interp1_R, shown in Fig. 5 d;

4. in two-dimensional interpolation matrix of consequence D_Interp2, select the 241st row as orientation data matrix D_A before the one dimension interpolation, promptly

D_A[i]＝D_Interp2[i，241] (20)

5. orientation data matrix D_A before the one dimension interpolation is carried out one dimension Fourier interpolation processing, obtain dimension and be 16384 interpolation back side to one dimension interpolation result matrix D _ Interp1_A, shown in Fig. 5 e.

Step 4, according to distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix obtain distance to the orientation to the resolution index;

Be specially:

(1) adjust the distance and carry out the normalization log-transformation to one dimension interpolation result matrix D _ Interp1_R, the point of power maximal value correspondence after the point by point search normalization log-transformation is labeled as Rp=7682 down; Search for left from Rp, record for the first time performance number is designated as Rl=7341 down less than the point of-3.0dB; Search for to the right from Rp, record for the first time performance number is designated as Rr=8022 down, shown in Fig. 5 d less than the point of-3.0dB again;

(2) subscript Rr and the Rl that obtains according to step (1), through type (11) obtain distance to resolution δ _r, unit is apart from resolution element:

${\mathrm{\&delta;}}_r=\frac{\mathrm{Rr}-\mathrm{Rl}+1}{N_1{N}_2}=\frac{8022-7341+1}{32\&CenterDot;16}=1.3320---\left(21\right)$

(3) the normalization log-transformation is carried out to one dimension interpolation result matrix D _ Interp1_A in the orientation, the point of maximal value correspondence after the point by point search normalization log-transformation is labeled as Ap=7681 down; Search for left from Ap, record for the first time performance number is designated as Al=7273 down less than the point of-3.0dB; Search for to the right from Ap, record for the first time performance number is designated as Ar=8089 down, shown in Fig. 5 e less than the point of-3.0dB again;

(4) subscript Ar and the Al that obtains according to step (3), through type (12) obtains the orientation to resolution, and unit is the azimuth discrimination unit:

${\mathrm{\&delta;}}_a=\frac{\mathrm{Ar}-\mathrm{Al}+1}{N_1{N}_2}=\frac{8089-7273+1}{32\&CenterDot;16}=1.5957---\left(22\right)$

Obtain the distance to the resolution actual measured value be 1.3320 apart from resolution element, theoretical value be 1.3290 apart from resolution element, measuring relative errors is 0.225%; The orientation is 1.5957 azimuth discrimination unit to the resolution actual measured value, and then theoretical value is 1.5948 azimuth discrimination unit, and then measuring relative errors is 0.056%.The resultant error that the inventive method obtains is less than 5%, and error is very little, can be good at satisfying the engineering application need.

Data to be assessed and interpolation parameter at the implementation case, adopt the power contour map (shown in Fig. 6 a) of the two-dimensional interpolation matrix of consequence D_Interp2 that simple zero padding method obtains, the result produces more messy false target, further available one-dimensional distance is the power normalization curve (shown in Fig. 6 c) to interpolation result matrix D _ Interp1_A to the power normalization curve (shown in Fig. 6 b) of interpolation result matrix D _ Interp1_R and one dimension orientation, point target is smooth inadequately can find out interpolation qualitatively from above-mentioned contour map and power normalization figure after, quantitative calculation can apart to resolution be 0.8066 apart from resolution element, measuring relative errors is 39.31%; The orientation is 0.8066 azimuth discrimination unit to actual measurement, and measuring relative errors is 49.42%, thereby the assessment result that obtains of simple zero padding interpolation can not truly reflect the index of point target.

When the present invention is primarily aimed at the SAR point target and has residual linear phase, the problem of the interpolation result that direct two-dimensional frequency zero padding interpolation can make the mistake, frequency domain energy distribution characteristic according to point target, in the two-dimensional interpolation process, adopt adaptive zero padding operation, promptly by the equivalent high frequency points of search, mode in equivalent high-frequency region zero padding obtains correct two-dimensional interpolation result, extract on this basis distance to the orientation to cross-sectional data, finish the point target index evaluation by one dimension interpolation and search, describe implementation process of the present invention in detail in conjunction with concrete case study on implementation, measurement result shows that the present invention is the high SAR point target index evaluating method of a kind of precision, can provide point target evaluation index accurately.

Claims (2)

1. a SAR image point target appraisal procedure is characterized in that, comprises following step:

Step 1: set two-dimensional interpolation multiple and two interpolation parameter of one dimension interpolation multiple, two-dimensional matrix and one dimension matrix are carried out initialization;

Be specially:

I: SAR view data to be assessed is the two-dimentional regional area complex data matrix D that contains point target to be assessed ₁, dimension is N * N, sets the interpolation multiple and comprises two-dimensional interpolation multiple N ₂, one dimension interpolation multiple N ₁

Ii: according to SAR view data dimension to be assessed and interpolation multiple carry out two-dimensional interpolation matrix of consequence, distance before the one dimension interpolation data matrix, orientation before the one dimension interpolation data matrix, distance to one dimension interpolation result matrix and orientation to the initialization of one dimension interpolation result matrix;

Described two-dimensional interpolation matrix of consequence is D_Interp2, and matrix dimension is NN ₂* NN ₂Distance data matrix before the one dimension interpolation is D_R, and matrix dimension is NN ₂* 1; Orientation data matrix before the one dimension interpolation is D_A, and matrix dimension is NN ₂* 1; Distance is D_Interp1_R to one dimension interpolation result matrix, and matrix dimension is NN ₂N ₁* 1; The orientation is D_Interp1_A to one dimension interpolation result matrix, and matrix dimension is NN ₂N ₁* 1; The matrix element initial value of above-mentioned matrix is 0;

Step 2: carry out two-dimensional interpolation in the method for equivalent high-frequency region zero padding by two-dimensional Fourier transform;

Be specially:

(a) to the data matrix D ₁Carry out the original position two-dimensional Fourier transform, obtain the two-dimensional frequency result, the result is copied to matrix D ₁, realize the data matrix D ₁Renewal;

(b) obtain data matrix D after the renewal ₁Energy and S:

$S=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2---\left(1\right)$

D wherein ₁(i, j) expression data matrix D ₁I capable, the element value of j row;

(c) to the data matrix D ₁Equivalent high frequency points p ₁Carry out two-dimensional search, establish equivalent high frequency points p ₁Volume coordinate be (i ₀, j ₀), then:

When

The time, establish i ₀Initial value is N, i ₀Subtract 1 successively, be met the i of formula (2) at last ₀

$\left\{\begin{array}{c}\underset{i=i_0-N/2}{\overset{i_0-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2\&le;0.5\&CenterDot;S\\ \underset{i=i_0-N/2-1}{\overset{i_0-2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2>0.5\&CenterDot;S\end{array}\right.---\left(2\right)$

When

The time, establish i ₀Initial value is 2, i ₀Add 1 successively, be met the i of formula (3) at last ₀

$\left\{\begin{array}{c}\underset{i=i_0}{\overset{i_0+N/2-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2>0.5\&CenterDot;S\\ \underset{i=i_0-1}{\overset{i_0+N/2-2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2\&le;0.5\&CenterDot;S\end{array}\right.---\left(3\right)$

When

The time, establish j ₀Initial value is N, j ₀Subtract 1 successively, be met the j of formula (4) at last ₀

$\left\{\begin{array}{c}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{j=j_0-N/2}{\overset{j_0-1}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2\&le;0.5\&CenterDot;S\\ \underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{j=j_0-N/2-1}{\overset{j_0-2}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2>0.5\&CenterDot;S\end{array}\right.---\left(4\right)$

When The time, establish j ₀Initial value is 2, j ₀Add 1 successively, be met the j of formula (5) at last ₀

$\left\{\begin{array}{c}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{j=j_0}{\overset{j_0+N/2-1}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2>0.5\&CenterDot;S\\ \underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{j=j_0-1}{\overset{j_0+N/2-2}{\mathrm{\&Sigma;}}}{\left|D_1(i,j)\right|}^2\&le;0.5\&CenterDot;S\end{array}\right.---\left(5\right)$

(d) according to (i ₀, j ₀) with data matrix D ₁Be divided into four sub-block matrix and be defined as S respectively ₁, S ₂, S ₃, S ₄, wherein four sub-block matrix juncture areas are equivalent high frequency region, four sub-block matrix satisfy formula (6):

$\left\{\begin{array}{c}{S}_1=D_1[1:(i_0-1),1:(j_0-1)]\\ S_2=D_1[1:(i_0-1),j_0:N]\\ S_3=D_1[i_0:N,1:(j_0-1)]\\ S_4=D_1[i_0:N,j_0:N]\end{array}\right.---\left(6\right)$

(e) with data matrix D ₁Four sub-block matrix S ₁, S ₂, S ₃, S ₄Compose to give four summit matrixes of two-dimensional interpolation matrix of consequence D_Interp2 successively, and on amplitude, multiply by the two-dimensional interpolation multiple square, promptly satisfy formula (7):

$\left\{\begin{array}{c}D\_\mathrm{Interp}2[1:(i_0-1),1:(j_0-1)]=N_2\&CenterDot;N_2\&CenterDot;S_1\\ D\_\mathrm{Interp}2[1:(i_0-1),(N\&CenterDot;N_2-N+j_0):(N\&CenterDot;N_2)]=N_2\&CenterDot;N_2\&CenterDot;S_2\\ D\_\mathrm{Interp}2[(N\&CenterDot;N_2-N+i_0):(N\&CenterDot;N_2),1:(j_0-1)]=N_2\&CenterDot;N_2\&CenterDot;S_3\\ D\_\mathrm{Interp}2[(N\&CenterDot;N_2-N+i_0):(N\&CenterDot;N_2),(N\&CenterDot;N_2-N+j_0):(N\&CenterDot;N_2)]=N_2\&CenterDot;N_2\&CenterDot;S_4\end{array}\right.---\left(7\right)$

(f) two-dimensional interpolation matrix of consequence D_Interp2 is carried out the inverse Fourier transform of original position two dimension, obtain the two-dimensional interpolation result, the result is copied among the two-dimensional interpolation matrix of consequence D_Interp2 again, realize renewal two-dimensional interpolation matrix of consequence D_Interp2;

Step 3: extract distance data matrix and orientation data matrix before the one dimension interpolation before the one dimension interpolation, and carry out the one dimension frequency domain interpolation respectively, obtain distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix;

Be specially:

1. search for the coordinate (i of the power peak position correspondence of two-dimensional interpolation matrix of consequence D_Interp2 _p, j _p), set (i _p, j _p) initial value is (1,1), i _p, j _pAdd 1 successively, be met the coordinate (j of formula (8) at last _p, j _p), (j of this moment _p, j _p) be power maximal value coordinate;

${|D\_\mathrm{Interp}2(i_p,j_p)|}^2=\underset{i\&Element;[1,N\&CenterDot;N_2],j\&Element;[1,N\&CenterDot;N_2]}{\max }{|D\_\mathrm{Interp}2(i,j)|}^2---\left(8\right)$

2. in two-dimensional interpolation matrix of consequence D_Interp2, select i _pLine data is as distance data matrix D_R before the one dimension interpolation, that is:

D_R[j]＝D_Interp2[i _p，j]，j∈[1，N·N ₂] (9)

3. adjusting the distance, data matrix D_R carries out one dimension Fourier interpolation processing before the one dimension interpolation, and obtaining dimension is NN ₂N ₁Distance to one dimension interpolation result matrix D _ Interp1_R;

4. in two-dimensional interpolation matrix of consequence D_Interp2, select j _pRow are as orientation data matrix D_A before the one dimension interpolation, promptly

D_A[i]＝D_Interp2[i，j _p]，i∈[1，N·N ₂] (10)

5. orientation data matrix D_A before the one dimension interpolation is carried out one dimension Fourier interpolation processing, obtaining dimension is NN ₂N ₁The orientation to one dimension interpolation result matrix D _ Interp1_A;

Step 4, according to distance to one dimension interpolation result matrix and orientation to one dimension interpolation result matrix obtain distance to the orientation to the resolution index;

Be specially:

(1) adjust the distance and carry out the normalization log-transformation to one dimension interpolation result matrix D _ Interp1_R, the point of point by point search power maximal value correspondence is designated as Rp down; Search for left from Rp, record for the first time performance number is designated as Rl down less than the point of-3.0dB; Search for to the right from Rp, record for the first time is designated as Rr under the point of performance number less than-3.0dB again;

(2) according to the subscript Rr and the Rl that obtain in the step (1), through type (11) obtains distance to resolution δ _r, unit is apart from resolution element:

${\mathrm{\&delta;}}_r=\frac{\mathrm{Rr}-\mathrm{Rl}+1}{N_2{N}_1}---\left(11\right)$

(3) the normalization log-transformation is carried out to one dimension interpolation result matrix D _ Interp1_A in the orientation, the point of point by point search power maximal value correspondence is designated as Ap down; Search for left from Ap, record for the first time performance number is designated as Al down less than the point of-3.0dB; Search for to the right from Ap, record for the first time performance number is designated as Ar down less than the point of-3.0dB again;

(4) subscript Ar and the Al that obtains according to step (3), through type (12) obtains the orientation to resolution δ _a, unit is the azimuth discrimination unit:

${\mathrm{\&delta;}}_a=\frac{\mathrm{Ar}-\mathrm{Al}+1}{N_2{N}_1}---\left(12\right)$

The distance that obtains is the quantitative result of point target assessment to resolution to resolution and orientation.

2. a kind of SAR image point target appraisal procedure according to claim 1 is characterized in that, the N described in the step 1 〉=8, two-dimensional interpolation multiple N ₂〉=16, one dimension interpolation multiple N ₁〉=32.

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