CN109829874A - SAR image fusion method based on Frame Theory - Google Patents
SAR image fusion method based on Frame Theory Download PDFInfo
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Abstract
The invention discloses the SAR image fusion methods based on Frame Theory, comprising the following steps: obtains the n width low resolution SAR image of Same Scene as image to be fused, treats blending image and carry out bilinear interpolation processing, obtain intermediate image；Piece image is chosen as benchmark image, all intermediate images are staggeredly merged according to pixel value deviation minimum principle, obtain the initial estimation image of high-resolution SAR image；Framework matrix H is constructed using point spread function；According to framework matrix H, restoration disposal is carried out to initial estimation image using the Tikhonov regularization method of threshold value iteration, obtains High Resolution SAR Images.The present invention uses Frame Theory, constructs more acurrate, more careful, more robust imaging device model, then carry out Pixel-level fusion to several low resolution SAR images, increases the Target scalar edge details of SAR image, improve the clarity of SAR image.
Description
Technical field
The invention belongs to technical field of image processing more particularly to a kind of SAR image fusion methods based on Frame Theory.
Background technique
Synthetic aperture radar (SAR) imaging is a kind of round-the-clock, round-the-clock microwave remote sensing imaging radar, due to SAR at
The characteristics such as picture has weatherproof, penetrability is strong, detection range is remote have extensive in national economy and Military Application field
Application, therefore, resulting SAR image is imaged with important researching value in SAR.
Since there are inevitable error components in acquisition process for SAR image, such as the non-ideal movement of platform, atmosphere
Disturbance, data acquisition errors, imaging algorithm error and system noise etc., these factors can make finally obtained SAR image clear
Clear degree is greatly affected.The quality of SAR image can seriously affect the subsequent applications efficiency of SAR image, and SAR image pixel is differentiated
Rate is higher, and image is more clear, and the target information that people therefrom obtain is abundanter, and subsequent application performance will be better, because
This promotes SAR image quality and has a very important significance.
With the development of a variety of SAR technologies, several SAR image data for obtaining areal have become possibility, due at
As the slight jitter of platform, certain sub-pix offset, and then sequence SAR can be generated between several SAR images of Same Scene
There are redundancies, complementary information between image.Image fusion technology can use redundancy between multiple image, complementary information,
By multiple image it is comprehensive at a width to scene have more comprehensively, the new images of apparent description.
It is rather mature in optical imagery that multiple image fusion promotes picture quality technology, but SAR area research compared with
Few, its research is concentrated on carry out increased quality to single width SAR image.Single image processing does not increase compared to multiple image
Add new image information, the edge details of ground object target are characterized by the high-frequency information of image in SAR image, and single image
Processing, merely add the low-frequency information of image, do not increase the high-frequency information of image, thus single image processing is for some
Distance farther out can not the ground object target of resolve minutiae do not improve ability.
Conventional images integration technology is mainly based upon the image interfusion method of small echo, and this method carrys out approximate retouch using wavelet basis
Imaging device model is stated, not fine enough to portraying for model, inadequate robust, making the imaging device model constructed, there are errors, lead
Cause restored image unintelligible.
Frame is a kind of extension of base in the space Hilbert, and energy has one group of vector of bound in the space Hilbert,
Referred to as frame.Frame Theory can describe the model of numerous signal/image procossings, and many numerous of signal/image procossing ask
Topic is inherently frame problem.
All linear transducers are illustrated as the translation and linear combination of a scattering function, frame to the perception of environment
It is exactly the set of all translation point scattering functions, in physical world, frame is most natural tool, is to imaging using frame
Construction in a systematic way mould is portrayed, and is modeled than using base more really, more finely, enhances robustness.
Summary of the invention
To solve the above-mentioned problems, the SAR image fusion method based on Frame Theory that the purpose of the present invention is to propose to a kind of,
Using Frame Theory, more acurrate, more careful, more robust imaging device model is constructed, on this basis to several low resolutions
SAR image carries out Pixel-level fusion, increases the Target scalar edge details of SAR image, improves the clarity of SAR image.
In order to achieve the above object, the present invention is resolved using following technical scheme.
SAR image fusion method based on Frame Theory, comprising the following steps:
Step 1, in SAR imaging system, the n width low resolution SAR image of Same Scene is obtained as image to be fused,
N ∈ N, and n >=2.
Step 2, bilinear interpolation processing is carried out to n image to be fused respectively, obtains n width intermediate image.
Step 3, piece image is chosen in n width intermediate image as benchmark image Iref, remaining n-1 width intermediate image
It is denoted as Ik, k=1 ..., n-1 are minimum according to pixel value deviation to n width intermediate image using the pixel value of benchmark image as benchmark
Principle is staggeredly merged, and a width blending image, i.e. the initial estimation image g of high-resolution SAR image are obtained.
Step 4, the point spread function of SAR imaging system is obtained, Frame Theory is based on, constructs SAR using point spread function
The framework matrix H of imaging system.
Step 5, according to framework matrix H, using threshold value iteration Tikhonov regularization method to initial estimation image g into
Row restoration disposal, obtains High Resolution SAR Images.
Compared with prior art, the invention has the benefit that
First, the present invention passes through frame square using the framework matrix of the point spread function building imaging model of imaging system
Battle array realize imaging model it is more acurrate, it is more careful, more robustly portray, missed to solve during regularization deconvolution model
The not high problem of restored image clarity caused by difference.
Second, the present invention uses the Tikhonov regularization method of threshold value iteration, can effectively inhibit in image restoration process
Influence of the middle system noise to image definition.
Detailed description of the invention
The present invention is described in further details in the following with reference to the drawings and specific embodiments.
Fig. 1 is the flow diagram of the SAR image fusion method of the invention based on Frame Theory.
Fig. 2 (a)-(d) is four images to be fused in the embodiment of the present invention.
Fig. 3 is that resulting intermediate image after bilinear interpolation is carried out to Fig. 2 (a).
Fig. 4 is initial estimation image obtained in the embodiment of the present invention.
Fig. 5 is the template three-dimensional figure of the point spread function of the SAR imaging system simulated in the embodiment of the present invention.
Fig. 6 is the resulting High Resolution SAR Images of the embodiment of the present invention.
Specific embodiment
Embodiment of the present invention is described in detail below in conjunction with embodiment, but those skilled in the art will
It will be appreciated that following embodiment is merely to illustrate the present invention, and it is not construed as limiting the scope of the invention.
The process that Fig. 1 show a kind of SAR image fusion method based on Frame Theory provided in an embodiment of the present invention is shown
It is intended to.Referring to Fig.1, realization step of the invention includes the following:
Step 1, in SAR imaging system, the n width low resolution SAR image of Same Scene is obtained as image to be fused,
N ∈ N, and n >=2.
Wherein, used n image to be fused is kinematic error and characterization Same Scene area between having had corrected that image
The low resolution SAR image in domain.
Step 2, bilinear interpolation processing is carried out to n image to be fused respectively, obtains n width intermediate image.Every width is waited for
The pixel of blending image carries out operation as the following formula:
Wherein, F (x, y) indicates the pixel value after pixel (x, y) interpolation processing, F (x0, y0)、F(x0, y1)、F(x1,
y0)、F(x1, y1) indicate the four pixel (xs nearest with point (x, y) distance0, y0)、(x0, y1)、(x1, y0)、(x1, y1) picture
Element value.
Step 3, piece image is chosen in n width intermediate image as benchmark image Iref, remaining n-1 width intermediate image
It is denoted as Ik, k=1 ..., n-1 are minimum according to pixel value deviation to n width intermediate image using the pixel value of benchmark image as benchmark
Principle is staggeredly merged, and a width blending image, i.e. the initial estimation image g of high-resolution SAR image are obtained；Comprising following
Sub-step:
Sub-step 3.1, any width intermediate image of choosing is as benchmark image Iref, remaining n-1 width intermediate image is denoted as
Ik, sequence number k=1 ..., n-1.
Sub-step 3.2, by benchmark image IrefWith remaining n-1 width intermediate image IkPiecemeal is carried out respectively:
Using every 2 × 2 pixels as one group of block of pixels (p, q), (p, q) is (p, q) a 2 × 2 block of pixels, (p, q)
Four pixels in a block of pixels are respectively (m0, n0), (m1, n1), (m2, n2), (m3, n3)；Wherein, (m0, n0)=(2p,
2q), (m1, n1)=(2p, 2q+1), (m2, n2)=(2p+1,2q), (m3, n3)=(2p+1,2q+1), p=0,1 ..., M-1, q
=0,1 ..., N-1, M × N are the size of low resolution SAR image.
Sub-step 3.3, to each pixel value in the block of pixels (p, q) of benchmark image respectively and among remaining n-1 width
The pixel value of the corresponding position of image is compared, and obtains the sequence number of the smallest intermediate image of difference；
Wherein, k1, k2, k3For the sequence number of intermediate image respectively, Iref(m1, n1) indicate (p, q) a picture in benchmark image
Pixel (m in plain block1, n1) corresponding pixel value, Ik(m1, n1) indicate (p, q) a picture in remaining n-1 width intermediate image
Pixel (m in plain block1, n1) corresponding pixel value, Iref(m2, n2) indicate in benchmark image in (p, q) a block of pixels
Pixel (m2, n2) corresponding pixel value, Ik(m1, n1) indicate in remaining n-1 width intermediate image in (p, q) a block of pixels
Pixel (m2, n2) corresponding pixel value, Iref(m3, n3) indicate pixel (m in benchmark image in (p, q) a block of pixels3,
n3) corresponding pixel value, Ik(m1, n1) indicate pixel (m in remaining n-1 width intermediate image in (p, q) a block of pixels3,
n3) corresponding pixel value.
Sub-step 3.4, according to the sequence number of the smallest intermediate image of difference, by the pixel value in the block of pixels of benchmark image
With remaining n-1 width intermediate image IkBlock of pixels in pixel value staggeredly merged:
Obtain the initial estimation image g of a width high-resolution SAR image.
Step 4, the point spread function of SAR imaging system is obtained, Frame Theory is based on, constructs SAR using point spread function
The framework matrix H of imaging system；Include following sub-step:
Sub-step 4.1 obtains the point spread function of SAR imaging system, the pattern matrix h of point spread function is determined, to point
The pattern matrix h of spread function carries out zero padding, makes the dimension of the pattern matrix h of point spread function and the dimension of initial estimation image
Identical, pattern matrix h ', h ' after obtaining zero padding are that R × T ties up matrix；Wherein, R × T is the size of initial estimation image.
Sub-step 4.2 constructs the frame of SAR imaging system to the pattern matrix h ' carry out cyclic shift processing after zero padding
Frame matrix H.
Specific cyclic shift processing includes following sub-step:
Sub-step 4.2.1 obtains the row vector of 1 R × T to the pattern matrix h ' carry out matrix expansion processing after zero padding,
The 1st row as framework matrix H；To the column of the pattern matrix h ' after zero padding 1 list position of cyclic shift backward, then carry out matrix
Expansion processing, obtains the 2nd row of framework matrix H；Successively to the column of the pattern matrix h ' after zero padding, cyclic shift j-1 is single backward
Position, j=3 ..., R, j often take a value, carry out 1 submatrix expansion processing, obtain 1 row of framework matrix H；J gets R from 1, i.e.,
Obtain the preceding R row of framework matrix H.
Sub-step 4.2.2 carries out matrix exhibition to the row of the pattern matrix h ' after zero padding 1 row unit of downward cyclic shift
Processing is opened, the row vector of 1 R × T is obtained, the R+1 row as framework matrix H；1 list of cyclic shift backward will be arranged again
Position, then matrix expansion processing is carried out, obtain the R+2 row of framework matrix H；Successively backward to the column of the pattern matrix h ' after zero padding
J-1 list position of cyclic shift, j=3 ..., R, j often take a value, carry out matrix expansion processing, obtain framework matrix H
1 row；J gets R from 1, obtains the 2nd R row of framework matrix H.
Sub-step 4.2.3, to i-1 row unit of row downward cyclic shift of the pattern matrix h ' after zero padding, i=3 ...,
T, 1 row unit of every cyclic shift, obtains the R row of framework matrix H；I gets T from 1, obtains R × T R × T row vector, i.e. RT
× RT square matrix, as the framework matrix H of SAR imaging system.
Further, after the 2nd row of matrix is successively is moved sequentially to the 1st row to last 1 row by the matrix expansion processing
It is arranged.R × T is the size of initial estimation image.
Step 5, according to framework matrix H, using threshold value iteration Tikhonov regularization method to initial estimation image into
Row restoration disposal, obtains High Resolution SAR Images.
Specific Tikhonov threshold value alternative manner is as follows:
The Tikhonov regularization method of the threshold value iteration are as follows:
Iteration function is set as f, enables f0=0, then Tikhonov threshold value iterative formula are as follows:
Wherein, S is the high fdrequency component in initial estimation image, and Γ is soft-threshold operator,For the transposition of H；
I indicate withThe identical unit diagonal matrix of dimension, sgn (x) are sign function, and th is threshold value,γ is threshold coefficient, 0 < γ < 1；σnFor the noise variance of initial estimation image；
The termination condition of iterative algorithm are as follows:
Wherein, δ > 0 and δ are the constants to go to zero, | | | |2Indicate 2- norm.
Illustratively, fusion experiment is carried out to the four width low resolution SAR images that somewhere is surveyed using method of the invention,
N=4 is taken, detailed process is as follows for experiment:
(1) low resolution SAR image is obtained as image to be fused
The actual measurement low resolution SAR image of the characterization Same Scene of kinematic error between four corrected images of selection, i.e.,
In Fig. 2 a), b), c), d) four width images are as image to be fused.
(2) intermediate image is obtained
Bilinear interpolation is carried out respectively to four width actual measurement low resolution SAR image:
Wherein, F (x, y) indicates the pixel value after pixel (x, y) interpolation processing, F (x0, y0)、F(x0, y1)、F(x1,
y0)、F(x1, y1) indicate the four pixel (xs nearest with point (x, y) distance0, y0)、(x0, y1)、(x1, y0)、(x1, y1) picture
Element value.Four width intermediate images are obtained, as shown in figure 3, Fig. 3 is the figure that a) figure obtains after bilinear interpolation processing in Fig. 2
Picture.
Comparison diagram 2a) and Fig. 3, it is found that the pixel of obtained intermediate image becomes more, in fact, by two-wire
Property interpolation processing after the pixel of image will increase 1 times, support can be provided in this way for subsequent staggeredly fusion；It can from Fig. 3
To see, the intermediate image after bilinear interpolation fogs, this is mainly due to single image interpolation merely add it is low
Frequency information does not increase high-frequency information, and therefore, the corresponding edge definition of image high frequency section is not greatly improved.
(3) the initial estimation image of high-resolution SAR image is obtained
Piece image is arbitrarily chosen in four width intermediate images as benchmark image, to its excess-three width intermediate image according to most
The different fusion method of small pixel value difference is merged with benchmark image, and obtained blending image is as high-resolution SAR image
Initial estimation image.
Specifically, a width intermediate image is arbitrarily chosen as benchmark image Iref, remaining 3 width intermediate image is denoted as Ik；It will
Benchmark image IrefPiecemeal is carried out respectively with remaining 3 width intermediate image Ik: i.e. using every 2 × 2 pixels as one group of block of pixels
(p, q), (p, q) are (p, q) a 2 × 2 block of pixels, and four pixels in (p, q) a block of pixels are respectively (m0, n0), (m1,
n1), (m2, n2), (m3, n3)；Wherein, (m0, n0)=(2p, 2q), (m1, n1)=(2p, 2q+1), (m2, n2)=(2p+1,2q),
(m3, n3)=(2p+1,2q+1), p=0,1 ..., M-1, q=0,1 ..., N-1, M × N are the size of low resolution SAR image.
Then, to each pixel in the block of pixels (p, q) of benchmark image respectively with the corresponding position of remaining n-1 width intermediate image
Pixel is compared, and obtains the smallest middle image sequence number of difference；
Wherein, k1, k2, k3The respectively sequence number of intermediate image, Iref(m1, n1) indicate (p, q) a picture in benchmark image
Pixel (m in plain block1, n1) corresponding pixel value, Ik(m1, n1) indicate (p, q) a picture in remaining n-1 width intermediate image
Pixel (m in plain block1, n1) corresponding pixel value, Iref(m2, n2) indicate in benchmark image in (p, q) a block of pixels
Pixel (m2, n2) corresponding pixel value, Ik(m1, n1) indicate in remaining n-1 width intermediate image in (p, q) a block of pixels
Pixel (m2, n2) corresponding pixel value, Iref(m3, n3) indicate pixel (m in benchmark image in (p, q) a block of pixels3,
n3) corresponding pixel value, Ik(m1, n1) indicate pixel (m in remaining n-1 width intermediate image in (p, q) a block of pixels3,
n3) corresponding pixel value；
Finally, according to the smallest middle image sequence number of difference, by the pixel value and residue in the block of pixels of benchmark image
3 width intermediate image IkBlock of pixels in pixel value staggeredly merged:
The initial estimation image of a width high-resolution SAR image is obtained, R × T is the size of initial estimation image.
It is the initial estimation image that four width intermediate images are obtained after staggeredly merging shown in Fig. 4.It can be seen that by
There is the offset of sub-pix, thus the information with redundancy complementation in the SAR image of four width Same Scenes, staggeredly merged
Afterwards, complementary information is fused to a high-resolution grid, improves resolution ratio to a certain degree.But image still have by
Image caused by the point spread function of SAR imaging system is fuzzy.
(4) framework matrix of SAR imaging system is obtained
The point spread function of SAR imaging system is obtained, Frame Theory is based on, utilizes point spread function building SAR imaging system
The framework matrix of system.Include following sub-step:
Sub-step 4.1 obtains the point spread function of SAR imaging system, the pattern matrix h of point spread function is determined, to point
The pattern matrix h of spread function carries out zero padding, makes the dimension of the pattern matrix h of point spread function and the dimension of initial estimation image
Identical, pattern matrix h ', h ' after obtaining zero padding are that R × T ties up matrix；Wherein, R × T is the size of initial estimation image；
Sub-step 4.2 constructs the frame of SAR imaging system to the pattern matrix h ' carry out cyclic shift processing after zero padding
Frame matrix H.
Specific cyclic shift processing are as follows: sub-step 4.2.1, at the pattern matrix h ' carry out matrix expansion after zero padding
Reason, obtains the row vector of 1 R × T, the 1st row as framework matrix H；The column of pattern matrix h ' after zero padding are recycled backward
1 list position is shifted, then carries out matrix expansion processing, obtains the 2nd row of framework matrix H；Successively to the pattern matrix after zero padding
J-1 unit of cyclic shift, j=3 ..., R, j often take a value to the column of h ' backward, carry out 1 submatrix expansion processing, obtain frame
1 row of frame matrix H；J gets R from 1 to get to the preceding R row of framework matrix H；
Sub-step 4.2.2 carries out matrix exhibition to the row of the pattern matrix h ' after zero padding 1 row unit of downward cyclic shift
Processing is opened, the row vector of 1 R × T is obtained, the R+1 row as framework matrix H；1 list of cyclic shift backward will be arranged again
Position, then matrix expansion processing is carried out, obtain the R+2 row of framework matrix H；Successively backward to the column of the pattern matrix h ' after zero padding
J-1 list position of cyclic shift, j=3 ..., R, j often take a value, carry out matrix expansion processing, obtain framework matrix H
1 row；J gets R from 1, obtains the 2nd R row of framework matrix H；
Sub-step 4.2.3, to i-1 row unit of row downward cyclic shift of the pattern matrix h ' after zero padding, i=3 ...,
T, 1 row unit of every cyclic shift, obtains the R row of framework matrix H；I gets T from 1, obtains R × T R × T row vector, i.e. RT
× RT square matrix, as the framework matrix H of SAR imaging system.
During above-mentioned cyclic shift, downward cyclic shift 1 time every to the row of the pattern matrix h ' after zero padding, backward to column
Cyclic shift R times；It arranges every cyclic shift 1 time, carries out 1 submatrix expansion processing, obtain 1 row of framework matrix H；Every circulation at once
Displacement 1 time obtains the row vector of R R × T to get the T row of framework matrix H is arrived；Successively to the row of the pattern matrix h ' after zero padding
Downward cyclic shift T times, R × T R × T row vector, i.e. RT × RT square matrix, as the frame square of SAR imaging system can be obtained
Battle array H.
The present invention program needs to construct the frame of SAR imaging system models using the point spread function of SAR imaging system
Matrix, the corresponding point spread function of different SAR imaging systems are different.The point spread function of SAR imaging system in the present embodiment
The point target data that number is emulated by the radar parameter of practical SAR imaging system are Lai approximate acquisition.It is this implementation shown in Fig. 5
The point spread function for the SAR imaging system that example simulates.
(5) High Resolution SAR Images are obtained
According to comprehensive framework matrix, initial estimation Image Iterative is asked using the Tikhonov regularization method of threshold value iteration
Solution, removal image as caused by system point spread function obscure, and finally obtain a fused High Resolution SAR Images.
The Tikhonov regularization method of specific threshold value iteration are as follows:
Iteration function is set as f, enables f0=0, then Tikhonov threshold value iterative formula are as follows:
Wherein, S is the high fdrequency component in initial estimation image, and Γ is soft-threshold operator,For the transposition of H；
I indicate withThe identical unit diagonal matrix of dimension, sgn (x) are sign function, and th is threshold value,γ is threshold coefficient, 0 < γ < 1；σnFor the noise variance of initial estimation image；
The termination condition of iterative algorithm are as follows:
Wherein, δ > 0 and δ are the constants to go to zero, | | | |2Indicate 2- norm.
It should be further noted that the specific iterative step of the Tikhonov threshold value alternative manner of the present embodiment is as follows:
Firstly, given δ=10-5, enable f0=0；
Secondly, according to Tikhonov threshold value iterative formulaCalculate fr+1；
Finally, working asWhen, iteration is terminated, is enabled As utilize Tikhonov threshold value iteration
Method carries out obtained High Resolution SAR Images after restoration disposal.
It is resulting High Resolution SAR Images after merging shown in Fig. 6, comparison diagram 6 and Fig. 1 can be seen that the mesh in Fig. 6
The edge details for marking atural object are more richer than the edge details of the same Target scalar of figure each in figure Fig. 1, and image is apparent, with back
The contrast of scape becomes apparent from, and illustrates to may be implemented to obtain by the low fusion for differentiating SAR image sequence using the method for the present invention high
The clear SAR image of pixel resolution realizes being obviously improved for SAR image quality.
To each image obtained in the above embodiment of the present invention, by comparing image to be fused and final resulting fusion
The Brenner gradient function and entropy of High Resolution SAR Images after reconstruction illustrates this method to the effect of SAR image increased quality
Fruit.
1Brenner gradient function
Brenner gradient function is a kind of common Image Definition.In SAR image, clear image
Target scalar has more sharp edge, and edge details are richer, thus Brenner gradient function value is bigger.
The Brenner gradient function value D (f) of image:
D (f)=∑y∑x| f (x+2, y)-f (x, y) |2
Wherein, f (x, y) indicates that the gray value of image f corresponding pixel points (x, y), f (x+2, y) indicate image f respective pixel
The gray value of point (x+2, y).
2 entropys statistics
For SAR image, the entropy of image is smaller, illustrates that image object is more obvious with background differentiation, image is more clear.
The entropy H of image:
Wherein, piOccurs the probability for the pixel that gray value is i for image.
The Brenner gradient letter of image to be fused and final resulting High Resolution SAR Images in the embodiment of the present invention
Several and entropy calculated result is as shown in table 1.
The calculated result of 1 embodiment of table
| Index | Image to be fused | High Resolution SAR Images |
| Brenner gradient function | 1751.23 | 2517.72 |
| Entropy | 6.97 | 6.68 |
As it can be seen from table 1 the method merges image through the invention, the Brenner gradient function of image
Value is significant to be increased, and illustrates that the method for the present invention can significantly improve the marginal definition of SAR image, and entropy reduces, and illustrates present invention side
Method can enhance the differentiation of image and background, and therefore, the method for the present invention is remarkably improved the clarity of image.
Those of ordinary skill in the art will appreciate that: realize that all or part of the steps of above method embodiment can pass through
The relevant hardware of program instruction is completed, and program above-mentioned can be stored in a computer readable storage medium, the program
When being executed, step including the steps of the foregoing method embodiments is executed；And storage medium above-mentioned includes: ROM, RAM, magnetic disk or light
The various media that can store program code such as disk.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (8)
1. the SAR image fusion method based on Frame Theory, which comprises the following steps:
Step 1, in SAR imaging system, the n width low resolution SAR image of Same Scene is obtained as image to be fused, n ∈
N, and n >=2；
Step 2, bilinear interpolation processing is carried out to n image to be fused respectively, obtains n width intermediate image；
Step 3, piece image is chosen in n width intermediate image as benchmark image Iref, remaining n-1 width intermediate image is denoted as
Ik, k=1 ..., n-1, using the pixel value of benchmark image as benchmark, to n width intermediate image according to pixel value deviation minimum principle
It is staggeredly merged, obtains a width blending image, i.e. the initial estimation image g of high-resolution SAR image；
Step 4, the point spread function of SAR imaging system is obtained, Frame Theory is based on, is imaged using point spread function building SAR
The framework matrix H of system；
Step 5, according to framework matrix H, initial estimation image g is answered using the Tikhonov regularization method of threshold value iteration
Original place reason, obtains High Resolution SAR Images.
2. the SAR image fusion method according to claim 1 based on Frame Theory, which is characterized in that in step 1, institute
State the image of image to be fused kinematic error between corrected image.
3. the SAR image fusion method according to claim 1 based on Frame Theory, which is characterized in that in step 2, institute
State bilinear interpolation processing are as follows: operation is carried out as the following formula to the pixel of every image to be fused:
Wherein, F (x, y) indicates the pixel value after pixel (x, y) interpolation processing, F (x0, y0)、F(x0, y1)、F(x1, y0)、F
(x1, y1) indicate the four pixel (xs nearest with point (x, y) distance0, y0)、(x0, y1)、(x1, y0)、(x1, y1) pixel value.
4. the SAR image fusion method according to claim 1 based on Frame Theory, which is characterized in that step 3 include with
Lower sub-step:
Sub-step 3.1, any width intermediate image of choosing is as benchmark image Iref, remaining n-1 width intermediate image is denoted as Ik, sequence
Row number k=1 ..., n-1；
Sub-step 3.2, by benchmark image IrefWith remaining n-1 width intermediate image IkPiecemeal is carried out respectively；
Using every 2 × 2 pixels as one group of block of pixels (p, q), (p, q) is (p, q) a 2 × 2 block of pixels, (p, q) a picture
Four pixels in plain block are respectively (m0, n0), (m1, n1), (m2, n2), (m3, n3)；Wherein, (m0, n0)=(2p, 2q),
(m1, n1)=(2p, 2q+1), (m2, n2)=(2p+1,2q), (m3, n3)=(2p+1,2q+1), p=0,1 ..., M-1, q=0,
1 ..., N-1, M × N are the size of low resolution SAR image；
Sub-step 3.3, to each pixel in the block of pixels (p, q) of benchmark image respectively with remaining n-1 width intermediate image
The pixel value of corresponding position is compared, and obtains the sequence number of the smallest intermediate image of difference；
Wherein, k1, k2, k3The respectively sequence number of intermediate image, Iref(m1, n1) indicate (p, q) a block of pixels in benchmark image
In pixel (m1, n1) corresponding pixel value, Ik(m1, n1) indicate (p, q) a block of pixels in remaining n-1 width intermediate image
In pixel (m1, n1) corresponding pixel value, Iref(m2, n2) indicate pixel in benchmark image in (p, q) a block of pixels
Point (m2, n2) corresponding pixel value, Ik(m1, n1) indicate pixel in remaining n-1 width intermediate image in (p, q) a block of pixels
Point (m2, n2) corresponding pixel value, Iref(m3, n3) indicate pixel (m in benchmark image in (p, q) a block of pixels3, n3)
Corresponding pixel value, Ik(m1, n1) indicate pixel (m in remaining n-1 width intermediate image in (p, q) a block of pixels3, n3)
Corresponding pixel value；
Sub-step 3.4 by the pixel value in the block of pixels of benchmark image and is remained according to the sequence number of the smallest intermediate image of difference
Remaining n-1 width intermediate image IkBlock of pixels in pixel value staggeredly merged:
Obtain the initial estimation image g of a width high-resolution SAR image.
5. the SAR image fusion method according to claim 1 based on Frame Theory, which is characterized in that step 4 include with
Lower sub-step:
Sub-step 4.1 obtains the point spread function of SAR imaging system, determines the pattern matrix h of point spread function, to a diffusion
The pattern matrix h of function carries out zero padding, makes the dimension of the pattern matrix h of point spread function with the dimension phase of initial estimation image
Together, pattern matrix h ', h ' after obtaining zero padding are that R × T ties up matrix；Wherein, R × T is the size of initial estimation image；
Sub-step 4.2 constructs the frame square of SAR imaging system to the pattern matrix h ' carry out cyclic shift processing after zero padding
Battle array H.
6. the SAR image fusion method according to claim 5 based on Frame Theory, which is characterized in that in step 4, institute
It states cyclic shift processing and includes following sub-step:
Sub-step 4.2.1 obtains the row vector of 1 R × T to the pattern matrix h ' carry out matrix expansion processing after zero padding, as
The 1st row of framework matrix H；To the column of the pattern matrix h ' after zero padding 1 list position of cyclic shift backward, then carry out matrix expansion
Processing, obtains the 2nd row of framework matrix H；Successively to the column of the pattern matrix h ' after zero padding j-1 unit of cyclic shift backward, j
=3 ..., R, j often take a value, carry out 1 submatrix expansion processing, obtain 1 row of framework matrix H；
J gets R from 1 to get to the preceding R row of framework matrix H；
Sub-step 4.2.2 carries out at matrix expansion the row of the pattern matrix h ' after zero padding 1 row unit of downward cyclic shift
Reason, obtains the row vector of 1 R × T, the R+1 row as framework matrix H；1 list position of cyclic shift backward will be arranged again, then
Matrix expansion processing is carried out, the R+2 row of framework matrix H is obtained；Successively the column of the pattern matrix h ' after zero padding are recycled backward
J-1 list position, j=3 ..., T are shifted, j often takes a value, carries out matrix expansion processing, obtains the 1 of framework matrix H
Row；J gets R from 1, obtains the 2nd R row of framework matrix H；
Sub-step 4.2.3, to i-1 row unit of row downward cyclic shift of the pattern matrix h ' after zero padding, i=3 ..., T, often
1 row unit of cyclic shift, obtains the R row of framework matrix H；I gets T from 1, obtains R × T R × T row vector, i.e. RT × RT
Square matrix, as the framework matrix H of SAR imaging system.
7. the SAR image fusion method according to claim 6 based on Frame Theory, which is characterized in that sub-step
4.2.1, in sub-step 4.2.2 and sub-step 4.2.3, matrix expansion processing for by the 2nd row of matrix to last 1 row successively
It is arranged after being moved sequentially to the 1st row.
8. the SAR image fusion method according to claim 4 based on Frame Theory, which is characterized in that in step 5, institute
State the Tikhonov regularization method of threshold value iteration are as follows:
Iteration function is set as f, enables f0=0, then Tikhonov threshold value iterative formula are as follows:
Wherein, S is the high fdrequency component in initial estimation image, and Γ is soft-threshold operator,For the transposition of H；
I indicate withThe identical unit diagonal matrix of dimension, sgn (x) are sign function, and th is threshold value,γ is threshold coefficient, 0 < γ < 1；σnFor the noise variance of initial estimation image；
The termination condition of iterative algorithm are as follows:
Wherein, δ > 0 and δ are the constants to go to zero, | | | |2Indicate 2- norm.
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