CN102608576B - A Geometric Correction Method for Large Forward Slope Synthetic Aperture Radar Echo Images - Google Patents

Abstract

The invention discloses a two-dimensional Sinc interpolation method for geometric correction of large forward oblique synthetic aperture radar (SAR), belonging to the technical field of SAR imaging. The invention constructs a new two-dimensional Sinc interpolation function according to the asymmetric characteristic of the side lobe of the point spread function, which is used for the geometric correction of the large forward oblique SAR image. The present invention also introduces two parameters to the interpolation function, which can realize low-pass filtering while interpolating, can eliminate the spatial variability of image resolution, and can avoid under-sampling when the distance between the ground and image pixels is large.

Description

A kind of geometric correction method for oblique synthetic-aperture radar echo before large

Technical field

The present invention relates to synthetic-aperture radar (SAR) imaging field, specifically, is a kind of geometric correction method for oblique synthetic-aperture radar echo before large.

Background technology

In oblique SAR, front bevel angle is violent along with oblique distance changes, thereby makes Doppler center and doppler frequency rate with the oblique distance significant change, when carrying out imaging processing, must consider the space-variant of these Doppler parameters before large.Due to the space-variant of having considered the Doppler center, the point spread function that imaging algorithm is derived has asymmetrical two-dimentional secondary lobe, and this asymmetrical sidelobe structure can cause its frequency spectrum to be distorted, thereby no longer about the frequency axis symmetry.Because sampling rate is limited, the distortion of frequency spectrum often can develop into the folding of frequency spectrum.

Before large tiltedly the SAR slant-range image under pattern serious geometric distortion is arranged, after must carrying out geometry correction to it, just can be further for identification and the coupling of target.Geometry correction need to be carried out interpolation to two dimensional image, and traditional two-dimensional interpolation method is all realized by two separable one dimension interpolation, and these one dimension interpolation all are equivalent to about the axisymmetric window function of frequency at frequency domain.But before large tiltedly the frequency spectrum of the point spread function of SAR slant-range image about frequency axis, be asymmetric, and often fold, thereby traditional two-dimensional interpolation method is carrying out before large can introducing obvious distortion during oblique SAR geometry correction.

Before large, tiltedly the space-variant of SAR distance image resolution ratio is larger, when pixel separation is larger, just may owes sampling and makes some track rejections, therefore need to before geometry correction, carry out low-pass filtering to slant-range image, eliminates the space-variant of resolution.But increase by a step low pass operation, will certainly increase operand.If low-pass filtering and interpolation can be combined, just can realize low-pass filtering in the situation that do not increase calculated amount.

So need a kind of energy adapt to large front tiltedly SAR point spread function characteristic and be easy to the two-dimensional interpolation method combined with low-pass filtering.

Summary of the invention

In view of this, the invention provides a kind of geometric correction method for oblique synthetic-aperture radar echo before large, can carry out geometry correction to large front tiltedly SAR slant-range image, and can be in conjunction with low-pass filtering, eliminate the space-variant of resolution, avoid simultaneously the generation of owing to sample.

A kind of geometric correction method for oblique synthetic-aperture radar echo before large of the present invention, utilizing spectrum analysis SPECAN imaging algorithm to during before large, tiltedly the slant-range image of the echo of synthetic-aperture radar carries out the step of geometry correction, adopt function h (t, τ) slant-range image is carried out to the two-dimensional interpolation processing, then obtain the distance image;

The expression formula of described function h (t, τ) is:

h(t，τ)＝sinc(F _r·τ)sinc[F _a·(t+Kτ)]

F wherein _rSlant-range image distance to sampling rate, F _aFor slant-range image in orientation to sampling rate, t is the orientation time, τ is Distance Time, $K=\frac{2\mathrm{vc}}{\mathrm{\&lambda;}}\&CenterDot;\cos \mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2\sqrt{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2-h^2}}/[-2f_{\mathrm{dr}}\left(r_0\right)],$ C is the light velocity, and v is the movement velocity of Texas tower, and λ is the carrier wavelength of radar, α be the velocity of Texas tower at ground projection and the wave beam direction of visual lines angle in the ground projection, h be large before the oblique height of Texas tower in polarization sensitive synthetic aperture radar system, r ₀For the oblique distance of imaging scene center, f _Dr(r ₀) for the doppler frequency rate at imaging scene center place.

A kind of geometric correction method for oblique synthetic-aperture radar echo before large of the present invention, utilizing spectrum analysis SPECAN imaging algorithm to during before large, tiltedly the slant-range image of the echo of synthetic-aperture radar carries out the step of geometry correction, adopt function h _LP(t, τ) carries out the two-dimensional interpolation processing to slant-range image, then obtains the distance image;

Described function h _LPThe expression formula of (t, τ) is: $h_{\mathrm{LP}}(t,\mathrm{\&tau;})=\sin c(\frac{F_r}{{\mathrm{\&gamma;}}_r}\&CenterDot;\mathrm{\&tau;})\sin c[\frac{F_a}{{\mathrm{\&gamma;}}_a}\&CenterDot;(t+\mathrm{K\&tau;})];$

F wherein _rSlant-range image distance to sampling rate, F _aFor slant-range image in orientation to sampling rate, t is the orientation time, τ is Distance Time, $K=\frac{2\mathrm{vc}}{\mathrm{\&lambda;}}\&CenterDot;\cos \mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2\sqrt{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2-h^2}}/[-2f_{\mathrm{dr}}\left(r_0\right)],$ C is the light velocity, and v is the movement velocity of Texas tower, and λ is the carrier wavelength of radar, α be the velocity of Texas tower at ground projection and the wave beam direction of visual lines angle in the ground projection, h be large before the oblique height of Texas tower in polarization sensitive synthetic aperture radar system, r ₀For the oblique distance of imaging scene center, f _Dr(r ₀) for the doppler frequency rate at imaging scene center place;

For the distance to the sampling rate coefficient, For orientation to the sampling rate coefficient, ρ wherein _rFor distance range resolution, the ρ required _aFor the distance azimuthal resolution required, μ _rFor slant range resolution to ground range resolution apart from conversion factor and μ _aFor the orientation conversion factor of slant range resolution to ground range resolution.

The present invention is a kind of method that adopts two dimension coupling interpolation to carry out geometry correction, than traditional geometric correction method method, non-perpendicular sidelobe performance and the distortion spectral characteristic of the point spread function that the space-variant due to Doppler parameter causes have been taken into full account, can realize well the large front tiltedly geometry correction of SAR image, and can with low-pass filtering, combine at an easy rate, eliminate the space-variant of resolution, avoid owing sampling, improved the image quality of distance image.

The accompanying drawing explanation

Fig. 1 is the large front tiltedly geometric relationship schematic diagram of SAR imaging system of the present invention.

Fig. 2 is that classic method and two kinds of methods of the present invention are carried out 4 times of frequency spectrums after rising sampling to the oblique distance point target image respectively.

Fig. 3 is that classic method and two kinds of methods of the present invention are respectively to the oblique distance point target image after the geometry correction of SAR slant-range image before large.

Embodiment

The invention provides a kind ofly for the oblique geometric correction method of synthetic-aperture radar echo before large, below in conjunction with the accompanying drawing embodiment that develops simultaneously, describe the present invention:

As shown in Figure 1, OXYZ is rectangular coordinate system in space, and wherein the OXY plane is on ground level, and Z axis makes progress perpendicular to ground level; Texas tower O _r0 of distance is high on Z axis be the h place, is parallel to Y-axis and moves, and speed is v; P is imaging scene center point, and θ is the front bevel angle of target, and α is the Texas tower velocity at ground projection and wave beam direction of visual lines at the angle of ground projection, is called position angle, and β is the angle on wave beam direction of visual lines and ground, is called the angle of pitch.Adopt spectrum analysis (Spectral Analysis, SPECAN) to become algorithm to carry out imaging processing, sub-aperture length is elected 1024 PRT as.Ka wave band SAR system is adopted in this experiment, and experiment parameter is as shown in table 1:

Table 1 experiment parameter

At first according to the above large front tiltedly two-dimensional interpolation function of parametric configuration in the geometry correction step of SAR system, detailed process is as follows:

According to the oblique geometric relationship of SAR system before large, can obtain the front bevel angle θ of target and the pass of oblique distance r and be:

$\sin \mathrm{\&theta;}=\cos \mathrm{\&alpha;}\&CenterDot;\sqrt{1-{\left(\frac{h}{r}\right)}^2}---\left(1\right)$

According to computing formula the convolution (1) at Doppler center, can obtain the Doppler center f of scene _Dc(r) with the relational expression of oblique distance r, be:

$f_{\mathrm{dc}}\left(r\right)=\frac{2v}{\mathrm{\&lambda;}}\cos \mathrm{\&alpha;}\&CenterDot;\sqrt{1-{\left(\frac{h}{r}\right)}^2}---\left(2\right)$

Formula (2) is at scene center oblique distance r ₀Place carries out the single order Taylor expansion, by Doppler center f _Dc(r) be approximately the linear function of oblique distance r:

$f_{\mathrm{dc}}\left(r\right)=f_{\mathrm{dc}}\left(r_0\right)+{f_{\mathrm{dc}}}^{\&prime;}\left(r_0\right)\&CenterDot;(r-r_0)$

$=f_{\mathrm{dc}}\left(r_0\right)+\frac{2v}{\mathrm{\&lambda;}}\&CenterDot;\cos \mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2\sqrt{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2-h^2}}\&CenterDot;(r-r_0)---\left(3\right)$

Order

$\frac{2v}{\mathrm{\&lambda;}}\&CenterDot;\cos \mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2\sqrt{{{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA0000145069240000012.png,HDA0000145069240000021.png"\; state="\{\{state\}\}">r</figure-callout>}}_0}^2-h^2}}=k---\left(4\right)$

With the altering a great deal of oblique distance, so imaging algorithm must be considered the space-variant of Doppler center with oblique distance due to Doppler center in whole imaging scene.For compensating for doppler center space-variant, spectrum analysis goes oblique function to adopt following expression as the orientation in algorithm:

h _dechirp(t；r)＝exp[-j2πf _dc(r)t-jπf _dr(r)t ²] (5)

Can derive and obtain point spread function expression formula s (t, τ; r ₀):

s(t，τ；r ₀)＝sinc[B _r(τ-τ ₀)·sinc{B _a[t+K(τ-τ ₀)]} (6)

Wherein, t and τ are respectively orientation time and Distance Time, K=ck/[-2f _Dr(r ₀)] be defined as the distortion factor;

Utilize two-dimensional Fourier transform, obtain the 2-d spectrum expression formula S (f of point spread function _t, f _τr ₀):

$S(f_t,f_{\mathrm{\&tau;}};r_0)=\mathrm{rect}\left(\frac{f_t}{B_a}\right)\mathrm{rect}\left(\frac{f_{\mathrm{\&tau;}}-{\mathrm{Kf}}_t}{B_r}\right)\exp (-j2\mathrm{\&pi;}{f}_{\mathrm{\&tau;}}{\mathrm{\&tau;}}_0)---\left(7\right)$

Wherein, f _tFor frequency variable corresponding to point spread function orientation time, f _τFor frequency variable corresponding to point spread function Distance Time.

Making the frequency spectrum supporting domain of two-dimensional interpolation function and the frequency spectrum supporting domain of point spread function is similar parallelogram, in the situation that ignore the linear phase impact, can construct the spectrum expression formula H (f of two-dimensional interpolation function _t, f _τ):

$H(f_t,f_{\mathrm{\&tau;}})=\mathrm{rect}\left(\frac{f_t}{F_a}\right)\mathrm{rect}\left(\frac{f_{\mathrm{\&tau;}}-{\mathrm{Kf}}_t}{F_r}\right)---\left(8\right)$

Wherein, F _rBe according to radar return process the slant-range image obtain target distance to sampling rate, F _aFor according to radar return, process obtain target slant-range image in orientation to sampling rate.

Finally utilize two-dimentional inverse Fourier transform, obtain two-dimensional interpolation function h (t, τ) by the frequency spectrum of two-dimensional interpolation function:

h(t，τ)＝sinc(F _r·τ)sinc[F _a·(t+Kτ)] (9)

Based on two-dimensional interpolation function h (t, τ), obtained considering the two-dimensional interpolation function of low-pass filtering:

$h_{\mathrm{LP}}(t,\mathrm{\&tau;})=\sin c(\frac{F_r}{{\mathrm{\&gamma;}}_r}\&CenterDot;\mathrm{\&tau;})\sin c[\frac{F_a}{{\mathrm{\&gamma;}}_a}\&CenterDot;(t+\mathrm{K\&tau;})]---\left(10\right)$

Wherein

For the distance to the sampling rate coefficient,

For orientation to the sampling rate coefficient, ρ _rAnd ρ _aBe respectively distance range resolution and the distance azimuthal resolution of requirement, μ _rAnd μ _aBe respectively slant range resolution to ground range resolution apart from conversion factor and orientation conversion factor.

In Fig. 2, (a) utilizes traditional two-dimensional interpolation function to process the frequency spectrum of the interruption obtained in geometry correction, can see that this frequency spectrum folds, and in Fig. 3, (a) is corresponding point target distance image,

By in correlation parameter substitution formula (2) and (4) in table 1, calculate f _Dc(r ₀)=17.81kHz, k=2.23Hz/m, i.e. the every increase of oblique distance 1m, the Doppler center will change 2.23Hz; Then calculate distortion factor K=1.0625 * 10 ⁶, obtain F according to calculation of parameter in table 1 _a=71.6Hz, by K, F _a, F _rBe updated in formula (9), obtain h (t, τ)=sinc (1 * 10 ⁸τ) sinc[71.6 (t+1.0625 * 10 ⁶τ)], utilize this two-dimensional interpolation function to carry out 4 times to the frequency spectrum of the slant-range image of point target and rise sampling processing, obtain complete parallelogram frequency spectrum, (b) as shown in Figure 2, and then obtain corresponding point target distance image as shown in (b) in Fig. 3.

Base area is apart from 4 meters resolution requirement of image, and the decrease of the passband width of design two-dimensional interpolation function, realize low-pass filtering.According to the computing formula of ground range resolution calculate distance to orientation to the sampling rate coefficient be respectively γ _r=2 and γ _a=3.3, by γ _rAnd γ _aBe updated to the two-dimensional interpolation function that has obtained considering low-pass filtering in formula (10): h _LP(t, τ)=sinc (5 * 10 ⁷τ) sinc[21.7 (t+1.0625 * 10 ⁶τ)], utilize this two-dimensional interpolation function of having considered low-pass filtering to carry out 4 times to the frequency spectrum of the slant-range image of point target and rise sampling processing, obtain Fig. 2 (c), with respect to (b) figure in Fig. 2, frequency spectrum reduces to some extent, and namely resolution descends, and has realized low-pass filtering, in Fig. 3 (c), be corresponding point target distance image, table 2 has provided the assessment result of each distance point target.

Table 2 distance image point target assessment result

From Fig. 3 and table 2, finding out, use classic method to carry out the geometry correction meeting to oblique SAR slant-range image before large and make significantly target distortion, interpolation method of the present invention has obtained good distance image, and the interpolation method that combines low pass has arrived desired value by decrease resolution.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (2)

1. the geometric correction method for oblique synthetic-aperture radar echo before large, is characterized in that,

Utilize spectrum analysis SPECAN imaging algorithm to carry out in the step of geometry correction the slant-range image of the echo of oblique synthetic-aperture radar before large, adopt function h (t, τ) to carry out the two-dimensional interpolation processing to slant-range image, then obtain the distance image;

The expression formula of described function h (t, τ) is:

h(t,τ)＝sinc(F _r·τ)sinc[F _a·(t+Kτ)]

F wherein _rSlant-range image distance to sampling rate, F _aFor slant-range image in orientation to sampling rate, t is the orientation time, τ is Distance Time, $K=\frac{2\mathrm{vc}}{\mathrm{\&lambda;}}\&CenterDot;\cos \mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{r_0}^2\sqrt{{r_0}^2-h^2}}/\&lsqb;-2f_{\mathrm{dr}}\left(r_0\right)\&rsqb;,$ C is the light velocity, and v is the movement velocity of Texas tower, and λ is the carrier wavelength of radar, α be the velocity of Texas tower at ground projection and the wave beam direction of visual lines angle in the ground projection, h be large before the oblique height of Texas tower in polarization sensitive synthetic aperture radar system, r ₀For the oblique distance of imaging scene center, f _Dr(r ₀) for the doppler frequency rate at imaging scene center place.

2. the geometric correction method for oblique synthetic-aperture radar echo before large, is characterized in that,

Utilize spectrum analysis SPECAN imaging algorithm to carry out in the step of geometry correction the slant-range image of the echo of oblique synthetic-aperture radar before large, adopt function h _LP(t, τ) carries out the two-dimensional interpolation processing to slant-range image, then obtains the distance image;

Described function h _LPThe expression formula of (t, τ) is: $h_{\mathrm{LP}}(t,\mathrm{\&tau;})=\sin c(\frac{F_r}{{\mathrm{\&gamma;}}_r}\&CenterDot;\mathrm{\&tau;})\sin c\&lsqb;\frac{F_a}{{\mathrm{\&gamma;}}_a}\&CenterDot;(t+\mathrm{K\&tau;})\&rsqb;;$

F wherein _rSlant-range image distance to sampling rate, F _aFor slant-range image in orientation to sampling rate, t is the orientation time, τ is Distance Time, $K=\frac{2\mathrm{vc}}{\mathrm{\&lambda;}}\&CenterDot;\cos \mathrm{\&alpha;}\&CenterDot;\frac{h^2}{{r_0}^2\sqrt{{r_0}^2-h^2}}/\&lsqb;-2f_{\mathrm{dr}}\left(r_0\right)\&rsqb;,$ C is the light velocity, and v is the movement velocity of Texas tower, and λ is the carrier wavelength of radar, α be the velocity of Texas tower at ground projection and the wave beam direction of visual lines angle in the ground projection, h be large before the oblique height of Texas tower in polarization sensitive synthetic aperture radar system, r ₀For the oblique distance of imaging scene center, f _Dr(r ₀) for the doppler frequency rate at imaging scene center place;

For the distance to the sampling rate coefficient,

For orientation to the sampling rate coefficient, ρ wherein _rFor distance range resolution, the ρ required _aFor the distance azimuthal resolution required, μ _rFor slant range resolution to ground range resolution apart from conversion factor, μ _aFor the orientation conversion factor of slant range resolution to ground range resolution.

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