CN113671499A - SAR and optical image matching method based on extraction of echo matrix map - Google Patents

SAR and optical image matching method based on extraction of echo matrix map Download PDF

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CN113671499A
CN113671499A CN202110900414.XA CN202110900414A CN113671499A CN 113671499 A CN113671499 A CN 113671499A CN 202110900414 A CN202110900414 A CN 202110900414A CN 113671499 A CN113671499 A CN 113671499A
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zernike
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phase
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王博
李惠堂
田思净
陈建强
盛庆红
陈梓昂
张玥杰
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Nanjing University of Aeronautics and Astronautics
Xian Institute of Space Radio Technology
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Xian Institute of Space Radio Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9021—SAR image post-processing techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9021—SAR image post-processing techniques
    • G01S13/9023—SAR image post-processing techniques combined with interferometric techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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Abstract

The invention discloses an SAR and optical image matching method based on extraction of an echo matrix diagram, which comprises the steps of firstly, simulating SAR image echoes by adopting an RD imaging algorithm, extracting phase characteristics by a four-wave transverse shearing interference method, and performing phase unwrapping by using a branch cutting method; secondly, a least square method based on Zernike polynomials is used for fitting the fitted SAR echo characteristics, and the phase characteristics extracted from the SAR echo are represented by Zernike polynomial coefficients; then, respectively extracting the characteristics of the real optical image and the complex SAR echo data by using the Zernike moment, and obtaining an initial matching point pair by comparing Euclidean distances of the Zernike moment in each characteristic point field in combination with a constant moment matching method; and finally, eliminating the pseudo matching point pairs by utilizing a simplified RANSAC algorithm, establishing affine between images, and realizing fusion registration of optical and SAR image characteristics. The invention is beneficial to the registration of the SAR and the optical image by utilizing the high-order characteristics extracted by the echo of the SAR complex image, and improves the identification capability of the SAR target and the scene.

Description

SAR and optical image matching method based on extraction of echo matrix map
Technical Field
The invention belongs to the field of multi-source information fusion and analysis application, and particularly relates to an SAR and optical image matching method based on extraction of an echo matrix image.
Background
The registration of SAR and optical images is a popular subject of multi-source remote sensing image registration research nowadays. There is a great difference between SAR and optical images. For example, the SAR image is sensitive to the fine roughness, physical material property, and reflection number of the photographed target, whereas the optical image is not easily determined but is sensitive to the reflectivity, color, and the like of the photographed target compared to the SAR image. The SAR is imaging all day long and all weather, is not influenced by interference of any environment, weather and natural disasters, has ground structures penetrating cloud and fog, vegetation and the like, and the optical sensor is extremely easy to be influenced by cloud, rain and snow weather and cannot perform uninterrupted imaging all day long. In order to fuse different images and collect different information of the same ground object and realize continuous and uninterrupted observation of the ground object, the information in the SAR and the optical image can be fused to obtain the ground object. However, because the two images have different imaging mechanisms in the shooting process, the registration of the SAR and the optical image can determine the effective fusion of information to a certain extent in the information fusion process, and therefore, the registration of the SAR and the optical image becomes an urgent problem to be solved.
Due to the fact that SAR adopts oblique distance imaging, speckle multiplicative noise is obvious, the SAR scattering intensity and the characteristic difference shown by optical image reflected radiation are large, and difficulty is caused to the registration of the SAR and the optical image. The existing SAR information extraction method is mainly based on image level characteristics, namely the SAR information is obtained through SAR image gray data, the SAR image has rich phase information, echo level characteristics obtained from the phase are not subjected to coherent processing, and error transfer on the phase is reduced; the SAR image has a large imaging range and complex target scattering characteristics, and the dynamic range of data can be reduced by processing the SAR image by using a phase; and the Zernike moment is a high-order moment with direction scale invariance, and particularly has outstanding performances in the aspects of information redundancy, image description capacity, noise sensitivity and the like.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problems and the defects in the prior art, the invention provides the SAR and optical image matching method based on the extraction of the echo matrix diagram, the method achieves higher precision, and the identification capability of the SAR target and the scene is improved.
The technical scheme is as follows: the invention relates to a SAR and optical image matching method based on extraction of an echo matrix map, which specifically comprises the following steps:
(1) simulating SAR image echoes by using an RD imaging algorithm, extracting phase characteristics by using a four-wave transverse shearing interference method, and performing phase unwrapping by using a branch cutting method;
(2) fitting the fitted SAR echo characteristics by a least square method based on a Zernike polynomial, wherein the phase characteristics extracted from the SAR echo are represented by Zernike polynomial coefficients;
(3) respectively extracting the characteristics of the real optical image and the complex SAR echo data by using the Zernike moment, and obtaining an initial matching point pair by comparing Euclidean distances of the Zernike moment in each characteristic point field in combination with an invariant moment matching method;
(4) and eliminating the pseudo matching point pairs by utilizing a simplified RANSAC algorithm, establishing affine between images, and realizing fusion registration of optical and SAR image characteristics.
Further, the RD imaging algorithm in step (1) includes distance direction compression, distance motionless correction, and orientation direction compression, and the specific implementation process is as follows:
the distance direction compression processing is represented by the matched filtering of a fast time domain, the time domain convolution is equivalent to a frequency domain product, and the matched output obtained by the matched filtering is as follows:
sτ(τ,t)＝IFFT{FFT[s0(τ,t)]·FFT[hr(τ)]}；
in the formula, the amplitude S of the target after distance compressionτ(τ, t), target in echo is S0(τ, t) differing by τ times the pulse duration t, the function of the matched filtering in the range direction being hr(tau), performing distance migration correction by adopting sinc function interpolation, wherein the result of one point target after interpolation operation is as follows:
Figure BDA0003199583220000021
wherein the distance between the radar and the target point is RcThe propagation speed of the pulse is c, the wavelength of the pulse signal is lambda, the motion speed of the radar platform is V, and the azimuth matching filter parameter is omegaa(t) the second exponential term represents t2A function of (a); the azimuth direction also conforms to the linear frequency modulation, and the frequency modulation is as follows:
Figure BDA0003199583220000022
after the range migration is completed, the echo is converted into a straight line from a hyperbola, the azimuth compression is carried out, the straight line is converted into a point, the imaging of the target is realized, and the output is as follows:
sa(τ,t)＝IFFT{FFT[srcmc(τ,t)]·FFT[ha(t)]}
in the formula, the amplitude S of the target after azimuth compressiona(τ, t) as a function of azimuth matched filtering ha(τ)。
Further, the phase feature extraction by the four-wave transverse shear interference method in the step (1) is implemented as follows:
superposing four levels of sub wave fronts on the original wave to obtain interference intensity information:
Figure BDA0003199583220000031
in the formula, A0Is (x, y) amplitude, W is (x, y) phase value, and the filtered spectrum carrier frequency is mu0And v0；
Fourier transform is carried out on the equation, a 5 x 5 filtering window is selected, carrier frequency is removed through translation, the frequency spectrum is moved to the center, inverse Fourier transform is carried out in the X, Y direction, and the shear difference phase in the two directions is extracted through an arc tangent function.
Further, the step (2) is realized by the following formula:
Figure BDA0003199583220000032
in the formula, the difference information obtained by the four-wave transverse shear interference method after unwrapping is delta omega, n is a fitting coefficient of Zernike polynomial, m is the number of difference pixels, ai、εiRepresenting the Zernike ith term coefficients and error; arbitrarily taking m and n, and adopting generalized inverse delta Z as a least square solution in the expression+Expressed as:
A＝△Z+△W+(I-△Z+△Z)Y
in the case where Y is 0, the equation has a least squares solution, and the target wavefront fitting coefficient a is calculated:
A＝(△Z+△Z)-1·△ZT·△W
calculating a phase value corresponding to any coordinate of the target wavefront to acquire SAR target phase characteristics:
Figure BDA0003199583220000041
in the formula, akIs the coefficient of the Zernike polynomial of the K term, ZkIs a Zernike polynomial of the K-th term.
Further, the step (3) is realized as follows:
drawing a circle of r for the reference image and the corresponding matching point in the image to be registered corresponding to the reference image, and solving the Zernike matrix of the characteristic neighborhood formed by the circle for multiple times by using the characteristic points(ii) a Method for establishing descriptor vector P by adopting Zernike momentdFor each feature point neighborhood, the geometric moment m00Performing an operation of Pd＝(|Z′11|,…,|Z′pq|),Z′pqRepresents the magnitude of a nonnegative integer p-order Zernike moment, expressed as:
Figure BDA0003199583220000042
in the formula, p- | q | is an even number, and | q | is less than or equal to p;
when the Zernike moment operation of the circular neighborhood is carried out on each pair of feature points, the feature points to be calculated are taken as the original points during calculation, and simultaneously, coordinates expressed by all pixel points in the circular neighborhood are corresponding to the same circle expressed by a unit circle; namely satisfy
Figure BDA0003199583220000043
Wherein ZpqIs a moment of Zernike of order p;
constructing a distance matrix C, establishing initial matching through Euclidean distance, and writing elements i in the matrix into:
Figure BDA0003199583220000044
in the formula (I), the compound is shown in the specification,
Figure BDA0003199583220000045
and
Figure BDA0003199583220000046
are respectively
Figure BDA0003199583220000047
And
Figure BDA0003199583220000048
the element in (1), i ═ 1,2,. K, K and K' represent the number of feature points in the two images, respectively; determining a minimum value of the distance by the rows and columns of the distance matrix C; in rows and columnscijWhen all can satisfy the minimum value, P is adjustediAnd Pj' two points are considered to be in one-to-one correspondence.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: the invention extracts the phase characteristics of the high-order Zernike moment by utilizing the echo of the SAR complex image, more accurately registers the SAR and the optical image, and has important theoretical significance and practical value in the field of remote sensing.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides an SAR and optical image matching method based on an extraction echo matrix diagram, which is characterized in that phase characteristics of real optical images and complex SAR echo data are respectively extracted by utilizing Zernike moments, initial matching is established through Euclidean distance, and finally, RANSAC is utilized to remove corresponding pseudo matching points of the initial matching of the two images, so that more accurate SAR and optical images are registered. The high-order Zernike matrix phase characteristics are extracted by utilizing the echo of the SAR complex image, the SAR and the optical image can be accurately registered, and the method has important theoretical significance and practical value in the field of remote sensing. As shown in fig. 1, the method specifically comprises the following steps:
step 1: firstly, simulating SAR image echoes by using an RD algorithm, secondly, obtaining phase wavefront by using a shearing interference method, and then, carrying out phase unwrapping by using a branch cutting method.
The SAR image has rich phase information, echo level characteristics obtained from the phase information are not subjected to coherent processing, and error transfer is less. The Range Doppler (RD) imaging algorithm can be divided into several steps: the distance direction compression processing of the radar signals, the distance motionless correction through the statistics of the distance-doppler domain, and the azimuth direction compression processing of the radar signals are performed. The distance compression is convenient to calculate in the process of matched filtering, the calculation process in the frequency domain can be represented by matched filtering in a fast time domain, the time domain convolution is equal to the product of the frequency domain, and the matched output obtained by the matched filtering is as follows:
sτ(τ,t)＝IFFT{FFT[s0(τ,t)]·FFT[hr(τ)]}
amplitude S of distance compressed targetτ(τ, t), target in echo is S0(τ, t) differing by τ times the pulse duration t, the function of the matched filtering in the range direction being hrAnd (tau), under the condition that the two-dimensional echo generates migration due to the continuous change of the slant distance, carrying out distance migration correction by adopting sinc function interpolation. The result of a point target after the interpolation operation can be expressed as:
Figure BDA0003199583220000051
wherein the distance between the radar and the target point is RcThe propagation speed of the pulse is c, the wavelength of the pulse signal is lambda, the motion speed of the radar platform is V, and the azimuth matching filter parameter is omegaa(t) the second exponential term represents t2As a function of (c). The azimuth direction is thus considered to be also in accordance with the chirp, which is expressed as:
Figure BDA0003199583220000052
after completing range migration, the echo is converted from hyperbolic to linear for subsequent azimuth compression processing.
After the azimuth compression, the straight line is converted into a point, so that the imaging of the target is completely realized, and the output is as follows:
sa(τ,t)＝IFFT{FFT[srcmc(τ,t)]·FFT[ha(t)]}
in the formula, the amplitude S of the target after azimuth compressiona(τ, t) as a function of azimuth matched filtering ha(τ)。
And extracting phase characteristics by adopting a four-wave transverse shear interference method in the optical field. The method comprises the following steps of superposing original waves with four-level sub-wave fronts to obtain interference intensity information, and calculating:
Figure BDA0003199583220000061
in the formula, A0Is the (x, y) magnitude and W is the (x, y) phase value. Filtered spectrum carrier frequency of mu0And v0。
Fourier transform is carried out on the equation, a proper filtering window is selected, carrier frequency is removed through translation, the frequency spectrum is moved to the center, inverse Fourier transform is carried out in the X, Y direction, and the shear differential phase in the two directions is extracted through an arc tangent function.
And phase folding occurs in the range of the value range in the phase information obtained by the arctan function, folding phase unwrapping processing is carried out, and a branch cutting method is selected as a phase unwrapping algorithm.
Step 2: and closely fitting the SAR echo by using a Zernike polynomial obtained based on a least square method, and taking a Zernike polynomial coefficient obtained by the least square method as a phase characteristic extracted from the SAR echo.
Zernike is a high order moment with directional scale invariance with which images can be characterized in more dimensions. The original target wavefront is described using a set of Zernike polynomials and the matrix form can be expressed as:
Figure BDA0003199583220000062
where n is the fitting coefficient of Zernike polynomial, m is the number of difference pixels, ai、εiRepresenting the Zernike ith term coefficients and error. Arbitrarily taking m and n, and adopting generalized inverse delta Z as a least square solution in the expression+It can be expressed as:
A＝△Z+△W+(I-△Z+△Z)Y
in the case where Y is 0, the equation has a least squares solution, and the target wavefront fitting coefficient a can be calculated as:
A＝(△Z+△Z)-1·△ZT·△W
the phase value corresponding to any coordinate of the target wavefront can be calculated to obtain the SAR target phase characteristics by the following formula:
Figure BDA0003199583220000071
in the formula, akIs the coefficient of the Zernike polynomial of the K term, ZkIs a Zernike polynomial of the K-th term.
And step 3: and respectively extracting the characteristics of the real optical image and the complex SAR echo data by using the Zernike moment, combining with a constant moment matching method, and obtaining an initial matching point pair by comparing the Euclidean distances of the Zernike moment in each characteristic point field.
Drawing a circle with the radius r for a plurality of times aiming at the reference image and the corresponding registration point in the image to be registered corresponding to the reference image, and solving Zernike echo matrix graph points of the characteristic neighborhood formed by the circle for a plurality of times. Zernike moments are used to establish descriptor vectors PdFirstly, for each pair of corresponding feature point neighborhoods, the geometric moment m00Performing an operation of Pd＝(|Z′11|,…,|Z′pq|),Z′pqThe magnitude of a Zernike moment, representing the p-order of a non-negative integer, can be expressed as:
Figure BDA0003199583220000072
in the formula, p- | q | is an even number, and | q | is less than or equal to p.
When the Zernike moment operation of the circular neighborhood is carried out on each pair of feature points, the pair of feature points to be calculated is taken as the origin point during calculation, and simultaneously, the coordinates expressed by all the pixel points of the circular neighborhood are all corresponding to the same circle expressed by the unit circle. Namely satisfy
Figure BDA0003199583220000073
Wherein ZpqIs the Zernike moment of the p-order.
And constructing a distance matrix C, and establishing initial matching through Euclidean distance. The element i in the matrix can be written as:
Figure BDA0003199583220000074
in the formula
Figure BDA0003199583220000075
And
Figure BDA0003199583220000076
are respectively
Figure BDA0003199583220000077
And
Figure BDA0003199583220000078
the element in (1), (2) · K, and K' represents the number of feature points in the two images, respectively. In matrix C, the distance minimum is found by row and column search. c. CijWhen the minimum values are satisfied on both the row and column, the point P is setiAnd Pj' matching can be considered.
And 4, step 4: and finally, removing the pseudo matching point pairs of the two images by using a simplified RANSAC algorithm, and establishing affine between the images so as to realize information fusion and registration of the characteristics of the two images.
The RANSAC algorithm is able to maximize the estimation of the total data given and then combine an allowable error to separate the measured data into two categories, including interior and exterior. The mismatched point pairs are typically called outliers and the algorithm can accurately eliminate outliers. The main idea of the algorithm is as follows: firstly, two points are arbitrarily selected from all data sets as an initial point set, and an initialization model is obtained. Secondly, solving the supporting point set of the initial model, namely the effective point or the inner point, based on the bearable error in the experimental range of the traditional SAR image amplitude method. This model is re-quantized by combining the interior points of the solution. The above process is repeated until the number of interior points is unchanged.
As shown in table 1, the effectiveness of the proposed method was verified by three sets of SAR images and optical image registration experiments, and compared with the conventional SAR image amplitude feature based method. Experimental data as used herein, SAR images, which were provided by eurodr co-funded ISPRS scientific project "multi-platform high resolution photogrammetry" (2014-2015), all derived from the isps published data set, were employed with the C-band synthetic aperture radar satellite images of sentinel-1.
TABLE 1 registration refinement
Figure BDA0003199583220000081
And extracting phase characteristics based on the echoes of the SAR complex image. In SAR imaging, the echo phase directly reflects the SAR imaging process and is the most important information in SAR imaging, so that the available characteristics can be better reserved based on phase processing, and error transfer caused by operations such as subsequent coherent processing and the like is avoided; in addition, due to the fact that the SAR image imaging range is large, the scattering characteristic of the target is complex, the dynamic range of data can be reduced by utilizing the phase to process, and follow-up processing is facilitated.
And (5) performing feature extraction by using Zernike moments. The Zernike moment is a high-order polynomial fitting method with scale invariance, and the Zernike moment utilizes the information of adjacent points in calculation to obtain coefficients in 16 dimensions, so that point characteristics in more dimensions can be reflected. Even if the scattering intensity is the same, the different feature points still have large difference in coefficient, namely the Zernike echo moment feature maps are obviously different. The high-dimensional feature information ensures the effectiveness of the method, namely the Zernike expands the one-dimensional feature vector of the original echo phase into a 16-dimensional feature matrix, and the matching precision is improved.

Claims (5)

1. A SAR and optical image matching method based on extraction of an echo matrix map is characterized by comprising the following steps:
(1) simulating SAR image echoes by using an RD imaging algorithm, extracting phase characteristics by using a four-wave transverse shearing interference method, and performing phase unwrapping by using a branch cutting method;
(2) fitting the fitted SAR echo characteristics by a least square method based on a Zernike polynomial, wherein the phase characteristics extracted from the SAR echo are represented by Zernike polynomial coefficients;
(3) respectively extracting the characteristics of the real optical image and the complex SAR echo data by using the Zernike moment, and obtaining an initial matching point pair by comparing Euclidean distances of the Zernike moment in each characteristic point field in combination with an invariant moment matching method;
(4) and eliminating the pseudo matching point pairs by utilizing a simplified RANSAC algorithm, establishing affine between images, and realizing fusion registration of optical and SAR image characteristics.
2. The method for calibrating the SAR and optical image based on the extracted echo matrix map as claimed in claim 1, wherein the RD imaging algorithm in step (1) includes a distance-direction compression process, a distance-motionless correction and an orientation-direction compression process, and the method is implemented as follows:
the distance direction compression processing is represented by the matched filtering of a fast time domain, the time domain convolution is equivalent to a frequency domain product, and the matched output obtained by the matched filtering is as follows:
sτ(τ,t)＝IFFT{FFT[s0(τ,t)]·FFT[hr(τ)]}；
in the formula, the amplitude S of the target after distance compressionτ(τ, t), target in echo is S0(τ, t) differing by τ times the pulse duration t, the function of the matched filtering in the range direction being hr(tau), performing distance migration correction by adopting sinc function interpolation, wherein the result of one point target after interpolation operation is as follows:
Figure FDA0003199583210000011
wherein the distance between the radar and the target point is RcThe propagation speed of the pulse is c, the wavelength of the pulse signal is lambda, the motion speed of the radar platform is V, and the azimuth matching filter parameter is omegaa(t) the second exponential term represents t2A function of (a); the azimuth direction also conforms to the linear frequency modulation, and the frequency modulation is as follows:
Figure FDA0003199583210000012
after the range migration is completed, the echo is converted into a straight line from a hyperbola, the azimuth compression is carried out, the straight line is converted into a point, the imaging of the target is realized, and the output is as follows:
sa(τ,t)＝IFFT{FFT[srcmc(τ,t)]·FFT[ha(t)]}
in the formula, the amplitude S of the target after azimuth compressiona(τ, t) as a function of azimuth matched filtering ha(τ)。
3. The method for calibrating SAR and optical image phase based on echo matrix image extraction according to claim 1, characterized in that the phase feature extraction by four-wave transversal shear interferometry in step (1) is implemented as follows:
superposing four levels of sub wave fronts on the original wave to obtain interference intensity information:
Figure FDA0003199583210000021
in the formula, A0Is (x, y) amplitude, W is (x, y) phase value, and the filtered spectrum carrier frequency is mu0And v0；
Fourier transform is carried out on the equation, a 5 x 5 filtering window is selected, carrier frequency is removed through translation, the frequency spectrum is moved to the center, inverse Fourier transform is carried out in the X, Y direction, and the shear difference phase in the two directions is extracted through an arc tangent function.
4. The method for calibrating SAR to optical image based on echo matrix image extraction according to claim 1, characterized in that the step (2) is realized by the following formula:
Figure FDA0003199583210000022
in the formula, the difference information obtained by the four-wave transverse shear interference method after unwrapping is delta omega, n is a fitting coefficient of Zernike polynomial, and m is a difference imageNumber of elements, ai、εiRepresenting the Zernike ith term coefficients and error; arbitrarily taking m and n, and adopting generalized inverse delta Z as a least square solution in the expression+Expressed as:
A＝△Z+△W+(I-△Z+△Z)Y
in the case where Y is 0, the equation has a least squares solution, and the target wavefront fitting coefficient a is calculated:
A＝(△Z+△Z)-1·△ZT·△W
calculating a phase value corresponding to any coordinate of the target wavefront to acquire SAR target phase characteristics:
Figure FDA0003199583210000031
in the formula, akIs the coefficient of the Zernike polynomial of the K term, ZkIs a Zernike polynomial of the K-th term.
5. The method for calibrating SAR and optical image based on echo matrix image extraction according to claim 1, characterized in that the step (3) is implemented as follows:
drawing a circle of r aiming at the reference image and the corresponding matching points in the image to be registered corresponding to the reference image, and solving the Zernike matrix of the characteristic neighborhood formed by the circle for multiple times; method for establishing descriptor vector P by adopting Zernike momentdFor each feature point neighborhood, the geometric moment m00Performing an operation of Pd＝(|Z′11|,…,|Z′pq|),Z′pqRepresents the magnitude of a nonnegative integer p-order Zernike moment, expressed as:
Figure FDA0003199583210000032
in the formula, p- | q | is an even number, and | q | is less than or equal to p;
when performing Zernike matrix operation of circular neighborhood for each pair of feature points, the pair of feature points to be calculatedThe feature point is used as an original point during calculation, and coordinates which are used for representing all pixel points in the circle neighborhood are corresponding to the same circle which is represented by the unit circle; namely satisfy
Figure FDA0003199583210000033
Wherein ZpqIs a moment of Zernike of order p;
constructing a distance matrix C, establishing initial matching through Euclidean distance, and writing elements i in the matrix into:
Figure FDA0003199583210000034
in the formula (I), the compound is shown in the specification,
Figure FDA0003199583210000035
and
Figure FDA0003199583210000036
are respectively
Figure FDA0003199583210000037
And
Figure FDA0003199583210000038
the element in (1), i ═ 1,2,. K, K and K' represent the number of feature points in the two images, respectively; determining a minimum value of the distance by the rows and columns of the distance matrix C; in rows and columns cijWhen all can satisfy the minimum value, P is adjustediAnd P'jTwo points are regarded as corresponding one to one.
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