CN111915519B - Strip repairing method based on spatial spectrum radial basis function interpolation - Google Patents
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Abstract
The invention relates to a band repairing method based on spatial spectrum radial basis function interpolation, which comprises the steps of firstly carrying out global histogram matching on a known auxiliary image to obtain a known image which is closer to an image to be repaired in a characteristic space; then interpolation calculation is carried out on the reflectivity change of the pixels to be repaired in time by using a spatial spectrum radial basis function, and the reflectivity change between the pixels of the known images in each wave band and the pixels to be repaired is obtained; and finally, adding the predicted change value to the data of the corresponding missing pixel position on the known image to obtain a final predicted result of the missing pixel. Compared with the prior art, the method and the device can effectively integrate the useful information of the known image and the image to be repaired, and have better repairing effect.
Description
Technical Field
The invention relates to the technical field of remote sensing image processing, in particular to a band repairing method based on spatial spectrum radial basis function interpolation.
Background
Landsat series satellites, including Landsat 7, provide very effective data for surface monitoring. The etm+ linear scan corrector (the scan-line corrector, SLC) of the Landsat 7 satellite is permanently disabled on 31 th year of 2003, such that an unscanned stripe gap appears on the image it acquires. These unscanned portions account for approximately 22% of the entire image, severely impacting the use of Landsat 7 satellite data in all aspects. The image acquired before SLC failure is generally referred to as an SLC-on image, and the image acquired after SLC failure is referred to as an SLC-off image. In order to solve the SLC-off problem, so that the application of etm+ is more reliable, it is necessary to develop a corresponding theory and method to estimate the data of the non-scanned pixels. The basic principle of SLC-off data restoration is as follows: and filling the numerical value into the position corresponding to the SLC-off data by adopting an interpolation method, so that the whole image is complete and the tone is as consistent as possible. The currently used methods of repairing a strip mainly include the following categories. The first category is interpolation methods using the SLC-off image itself information, which use the active pixels in the same scene image to fill in the non-scanned pixels, for example, the Gapfill plug-in ENVI was developed based on this principle. The method is widely applied because of being simple and easy to realize without any auxiliary data. However, the repaired strip is usually obviously different from the surrounding ground, and the repairing effect is usually poor. In order to obtain a better repair effect, researchers have developed methods for repairing strips by means of other sensor data, i.e. methods of the second type. The auxiliary image (also known image) used by the method has complete space coverage although the acquisition time is inconsistent with that of the SLC-off image, and the data of the missing value corresponding to the geographic position on the SLC-off image at other time points is provided, so that the use of the data can obtain more accurate prediction results. Among them, the local linear histogram matching (Localized Linear Histogram Match, LLHM) method mentioned in an official report by the united states geological exploration agency (USGS) compiled in 2004 is one of the most used methods. The method uses one or more known images, establishes a linear transformation function in a moving window of each missing pixel according to the effective pixel and the known image data of the corresponding position, and then uses the function to convert the data of the corresponding position of the missing pixel in the known image into the data of SLC-off missing pixel. The method is simple and easy to implement, and has higher precision in a homogeneous region. In addition, the neighborhood similar pel interpolation method (Neighborhood Similar Pixel Interpolater, NSPI) is also a more classical and common interpolation method. The NSPI method is used for a region with strong heterogeneity to obtain a better effect, but for a known image with a far acquired time interval SLC-off image, the accuracy of a prediction result is obviously reduced.
In recent years, various interpolation methods are applied to repairing SLC-off image strips, particularly in areas with uniform coverage of ground features, the method has good repairing effect, and larger prediction deviation is generated in areas with strong heterogeneity. In addition, most interpolation methods require using images that are closer in time to the SLC-off images as known images to obtain a more optimal prediction result. However, due to the effect of cloud, available known images close enough in time are often not available in many areas, which sometimes makes the application of the aforementioned method less effective. For this reason, it is necessary to develop a more stable, higher-precision interpolation method to predict the missing pixels.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a strip repairing method based on spatial spectrum radial basis function interpolation.
The aim of the invention can be achieved by the following technical scheme:
A band repairing method based on spatial spectrum radial basis function interpolation is used for repairing SLC-off band images, and comprises the following steps:
S1: according to the SLC-off stripe image to be repaired, performing global histogram matching (GLHM, global Linear Histogram Match) on the known image to obtain a matched known image;
S2: and (3) predicting the missing pixels of the SLC-off band image to be repaired by using the known image obtained in the step (S1) after carrying out GLHM and adopting a spatial spectrum radial basis function method.
Further, the specific content of step S1 is:
The acquisition time of the known image and the SLC-off strip image to be repaired is respectively marked as t k and t p, linear regression modeling is carried out on the set of effective pixels corresponding to the acquisition time of the known image and the SLC-off strip image to be repaired, a linear model is constructed on data of each wave band, and the known image is integrally transformed into a new known image which is closer to the SLC-off strip image to be repaired in a characteristic space by using coefficients obtained by the constructed linear model. Specifically:
11 Linear regression modeling is carried out according to the set of the effective pixels of the known image at the moment t k and the effective pixels of the SLC-off strip image to be repaired at the moment t p, a linear relation model between the SLC-off strip image to be repaired at the moment t p and the known image at the moment t k is constructed, and a linear coefficient is obtained;
the expression of the linear model constructed for the data of each band is:
L(x,y,b,tp)＝Ab×L(x,y,b,tk)+Bb
Where L (x, y, B, t p) and L (x, y, B, t k) are the reflectivity of band B at the location (x, y) of the SLC-off image to be repaired and the known image, respectively, and A b and B b are linear coefficients, respectively. And the linear coefficients A b and B b are solved by adopting least square fitting according to the effective data sets corresponding to the SLC-off image to be repaired and the known image.
12 The known image at the time t k is subjected to integral linear transformation through the linear coefficient, and a new known image at the time t k is obtained.
Further, the step S2 specifically includes the following steps:
21 Selecting similar pixels of the known image and the SLC-off stripe image to be repaired, for any missing pixel of the SLC-off stripe image to be repaired, finding out the positions of neighboring pixels similar to the known image based on the pixels in the same geographic position in the known image, and selecting N similar pixels for each missing pixel to participate in subsequent calculation;
22 Acquiring a space radial basis function between similar neighborhood pixels selected by each missing pixel, and defining a space radial basis function between a center pixel and the similar pixels in a known image window; the expression of the spatial radial basis function between the center pixel and the effective pixel is:
Where (x 0,y0) is the coordinates of the center pixel, delta 1 is the spatial radial basis parameter, and (x i,yi) is the coordinates of the ith and jth valid pixels within the window.
23 Constructing a spectrum radial basis function of spectrum similarity between similar pixels in a known image window and spectrum similarity between a center pixel and adjacent similar pixels; spectral radial basis function of known spectral similarity between similar pixels in image windowAnd the spectral radial basis function/>, of the spectral similarity of the central pixel and its neighboring similar pixelsThe expression of (2) is:
Where δ 2 is the spectral radial basis parameter, RMSD i is the RMSD value between the center pixel and the i-th similar pixel in the window, and RMSD ij is the RMSD value between the i-th pixel and the j-th similar pixel in the window.
24 Multiplying the spatial radial basis function obtained according to step 22) with the spectral radial basis function obtained according to step 23) to obtain a spatial spectral radial basis function; the expression of the spatial radial basis function is:
In the method, in the process of the invention, As a spatial radial basis function,/>As a spatial radial basis function between the center pixel and the active pixel,As a spectral radial basis function of spectral similarity between similar pixels in an SLC-off strip image window to be repaired,/>Is a spectral radial basis function of the spectral similarity of the center pixel of the known image window and its neighboring similar pixels.
25 Using the selected N similar pixels, calculating radial basis weights based on reflectivity changes between pixels in the known image and pixels of the SLC-off stripe image to be repaired;
Specifically, using the selected N similar pixels, regarding the change in reflectivity between the known image and the SLC-off stripe image to be repaired, as ΔL(xi,yi,b)＝L(xi,yi,b,tp)-L′(xi,yi,b,tk),, where L (x, y, b, t p) is the reflectivity of the SLC-off stripe image to be repaired and the known image at the position (x, y) in the band b, L' (x, y, b, t k) is the integral transformation of the known image in step 1) to a new known image that is closer to the SLC-off stripe image to be repaired in the feature space, and t k and t p are the acquisition moments of the known image and the SLC-off stripe image to be repaired, respectively, then the radial basis weights are denoted as ω bi (i=1, 2, the term, N), and then the calculation formula of the radial basis weights is as follows:
26 Based on step 25) obtaining radial basis weights of each band, calculating the reflectivity change between the pixels of the known image of the corresponding band and the pixels of the SLC-off band image to be repaired;
27 Superposing the known image subjected to GLHM in the step 1) and the reflectivity change in the step 26) to obtain a final prediction result.
Compared with the prior art, the method expands a classical spatial radial basis interpolation method, innovatively adds a spectrum radial basis and builds a spatial radial basis interpolation model, and fully excavates the spectrum information of adjacent pixels; meanwhile, the GLHM pretreatment transforms the whole known image to a new known image which is closer to the image to be repaired in the characteristic space, so that the influence of large difference between the known image and the image to be repaired caused by large time span and more obvious change of the ground feature can be reduced to a certain extent, and the method can obtain a better repairing effect under the condition of larger time interval of the known image.
Drawings
FIG. 1 is a schematic flow chart of a band repairing method based on spatial spectrum radial basis function interpolation in an embodiment;
FIG. 2 is a graph showing the results of region 1 in an exemplary simulation experiment, wherein (a) is a simulated SLC-off image, (b) through (e) are SLC-off image restoration results of Gapfill plug-ins, LLHM, NSPI, and the SSRBF method of the present invention, respectively, and (f) is a reference image;
FIG. 3 is a graph showing the results of region 2 in an exemplary simulation experiment, wherein (a) is a simulated SLC-off image, (b) to (e) are SLC-off image restoration results of Gapfill plug-ins, LLHM, NSPI, and the SSRBF method of the present invention, respectively, and (f) is a reference image.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
Examples
The invention relates to a band repairing method based on spatial spectrum radial basis function interpolation, which is used for repairing an SLC-off band image, and a known image which is closer to an image to be repaired in a characteristic space is obtained by carrying out GLHM (Global Linear Histogram Match) pretreatment on the known auxiliary image; then interpolation calculation is carried out on the reflectivity change of the pixels to be repaired in time by using a spatial spectrum radial basis function, and the reflectivity change between the pixels of the known images in each wave band and the pixels to be repaired is obtained; and finally, adding the predicted change value to the data of the corresponding missing pixel position on the known image to obtain a final predicted result of the missing pixel. As shown in fig. 1, the repairing method of the present invention specifically includes the following steps:
Step 1, implementing GLHM on the known image. The acquisition times of the known image and the SLC-off stripe image to be repaired are respectively marked as t k and t p. And (3) carrying out linear regression modeling according to the set of the effective pixels of the images at the moments t k and t p, and constructing a linear model shown in the formula (1) for the data of each wave band.
L(x,y,b,tp)＝Ab×L(x,y,b,tk)+Bb (1)
Wherein L (x, y, b, t p) and L (x, y, b, t k) are the reflectivity of band b at position (x, y) of the image to be repaired and the known image in the strip, respectively. A b and B b are two linear coefficients that can be solved using least squares fitting based on the effective dataset corresponding to the image to be repaired and the known image. The known image as a whole can be transformed to a new known image (denoted as L' (x, y, b, t k)) that is closer to the image to be repaired in the feature space using the resulting coefficients.
Specifically, the known image after GLHM is implemented and the image to be repaired are more approximate in the feature space through mathematical derivation. The magnitude of the difference between the images is quantified by the expected value of the difference image between the same bands. To simplify the expression, the following formulas are each based on a single band representation of the image.
Performing linear regression modeling according to a set of known images at time t k and effective pixels of the SLC-off image at time t p, wherein the relation between the two images is shown as a formula (A1):
Lp＝ALk+B+γ (A1)
Where L p and L k are the reflectance matrices of the image to be repaired and the known image in the strip, respectively. A and B are two linear coefficients, and a least square fitting solution is used according to the effective data set corresponding to the image to be repaired and the known image. Gamma is the residual of the regression model. Thus, when GLHM is not implemented, the difference Δl between the effective pixels of the image at times t k and t p can be represented by formula (A2):
after GLHM is performed, the new known image is subjected to overall linear transformation by the coefficients A and B to obtain L' k
L′k＝ALk+B (A3)
Therefore, the difference DeltaL' between the image at time t p and the known image at time t k after GLHM conversion can be represented by formula (A4)
ΔL′＝Lp-L′k＝γ (A4)
The desired squares of E (ΔL 2) and E [ (ΔL ') 2 ] for ΔL before GLHM and ΔL' after GLHM, respectively, are calculated below.
1) E (Δl 2) without GLHM:
according to the relationship between expectations and variances:
E(ΔL2)＝Var(ΔL)+E2(ΔL) (A5)
For the first term in (A5), substituting (A2), since B is a constant, by the fundamental property of the variance
In the equation "·" represents the inner product between the two matrices. For Cov (L k ·γ) in (A6), it is expanded according to the desired basic properties:
Cov(Lk·γ)＝E(Lk·γ)-E(Lk)E(γ) (A7)
for the classical least squares linear regression model, there are two important properties: 1) The expectation of the residual is 0; 2) The product of the argument and the residual is expected to be 0. As shown in formula (A8):
from the properties of formula (A8), formula (A7) is equal to 0, so formula (A6) can be simplified as:
Var(ΔL)＝Var[(A-1)Lk]+Var(γ) (A9)
Namely, the formula (A5) can be represented as:
E(ΔL2)＝Var[(A-1)Lk]+Var(γ)+E2(ΔL) (A10)
2) E [ (DeltaL') 2 ] after GLHM was carried out
E [ (DeltaL') 2]＝E(γ2) is known from formula (A4). For E (gamma 2), the relationship between the expectations and the variances is:
E(γ2)＝Var(γ)+E2(γ) (A11)
from the formula (A8), the second term in (A11) is 0, so (A11) can be simplified as:
E(γ2)＝Var(γ) (A12)
As can be seen by comparing formulas (a 10) and (a 12): e [ (DeltaL') 2]＜E(ΔL2) (both the first term and the third term on the right side of equation (A10) are greater than 0). Thus, it is demonstrated that the known image after GLHM is closer to the SLC-off image in the feature space than the known image without GLHM.
And 2, predicting the missing pixels by using a Spatial Spectrum Radial Basis Function (SSRBF) method by using the GLHM known image obtained in the step 1. The method comprises the following specific steps:
And 2.1, selecting similar pixels. And for any missing pixel, the positions of similar neighborhood pixels are found out based on pixels in the same geographic position in the known image. The similarity of the neighborhood pixels is measured by the root mean square deviation (Root Mean Square Deviation, RMSD) value of the spectrum. The root mean square deviation is defined as shown in formula (2):
Wherein L (x i,yi, b, t) and L (x j,yj, b, t) are the i-th and j-th (i, j=1, 2, …, M being the number of active pixels in the window) pixels in the image window at time t (the acquisition time of the SLC-off image or the known image), the image window being paired and present on both the SLC-off image and the known image. n is the number of bands. According to equation (2), based on the known image, RMSD values between the center pixel and its neighborhood pixels may be calculated within a window, and the first N pixels in the window that are most similar to the center pixel are selected. The RMSD value between the center pixel and the i-th similar pixel in the window is denoted RMSD i.
And 2.2, constructing a space radial basis function. Defining spatial radial basis functions using commonly used Gaussian functionsAs shown in formula (3).
Wherein (x i,yi) and (x j,yj) are the coordinates of the ith and jth effective pixels in the image window, respectively, and δ 1 is a spatial radial basis parameter. The value of the parameter delta 1 is defined in terms of a value that is 2 times the maximum distance of the central picture element from the other picture elements within the image window in which it is located. Similarly, a spatial radial basis function between the center pixel and the effective pixel may be definedAs shown in formula (2).
Wherein (x 0,y0) is the coordinates of the center pixel.
And 2.3, constructing a spectrum radial basis function. Defining a spectral radial basis function based on spectral similarity between similar pixels in a windowAnd a spectral radial basis function/>, based on the spectral similarity of the center pixel and its neighboring similar pixelsAs shown in formula (5):
Wherein δ 2 is the spectral radial basis parameter. The value of the parameter delta 2 is determined from the set of RMSD values between the pels in each window, i.e. taking 2 times the maximum value in the set. For example, if the vast majority of the RMSD values in the statistics do not exceed 0.05, then the value of δ 2 is set to 0.1.RMSD ij is the RMSD value between the i-th pel and the j-th similar pel in the window.
And 2.4, constructing a spatial spectrum radial basis function. On the basis of considering the space distance between pixels, the influence of the spectrum similarity of adjacent pixels is considered. Multiplying the spatial radial basis function by the spectral radial basis function to obtain a spatial spectral radial basisAnd/>As shown in formula (6):
And 2.5, calculating radial basis weights. The reflectance variation of the center missing pixel over time is estimated using SSRBF. First, using the selected N similar pixels, note that its radial basis weight is ω bi (i=1, 2,..n) for a change in reflectivity between the known image and the image to be repaired of ΔL(xi,yi,b)＝L(xi,yi,b,tp)-L′(xi,yi,b,tk),. The weight is calculated as shown in formula (7):
For N similar pixels in a window, a unique set of weight values ω bi can be solved using the above equation.
Step 2.6, calculate SSRBF interpolation. Substituting the weight omega bi calculated by each wave band into the (8) to obtain the reflectivity change between the known image pixel (the pixel on the known image position corresponding to the position of the pixel to be filled) of the corresponding wave band and the pixel to be repaired (the pixel to be filled) in the strip
And 2.7, adding the pixel value of the known image center with the predicted change value to obtain a final prediction result. As shown in the formula (9),
In order to verify the effectiveness of the invention, the embodiment adopts the method to repair the SLC-off image generated by using the Landsat OLI image simulation, and compares the repair result with the existing classical algorithm. The comparison method is ENVI GAPFILL plug-in method, local linear histogram matching method published by USGS authorities (Localized Linear Histogram Match, LLHM) and classical neighborhood similar pel interpolation (Neighborhood Similar Pixel Interpolator, NSPI) for repair. The two test areas were located in the Vironat city of Italy (area 1) and Zhejiang province of China (area 2), respectively. The repair results for the two regions are shown in fig. 2 and 3, respectively. In each of the two sets of plots (e.g., fig. 2 (a)), the left large plot is an image of the entire experimental region, and the corresponding right small plot is an enlarged two sub-regions, so as to more intuitively compare the difference between the results of repairing SLC-off image bands using the methods.
As can be seen from fig. 2 and 3, the area where the image to be repaired is located has strong heterogeneity as a whole. The Gapfill plug-in repair results are generally consistent in hue with the original image, but have distinct banding edges. The LLHM and NSPI methods can both predict the reflectivity data of the ground object better, but the repair results have larger prediction errors in areas with stronger heterogeneity, for example, when the strip is positioned in the center of the complete ground object, the prediction of the ground object has the problem of incomplete edge and obvious deviation of the spectrum prediction information of the pixels in the ground object. The method reduces the influence caused by the difference of the acquisition time of the known data and the data to be repaired by using global histogram matching, and fully excavates more information of the data based on the high-precision advantage of SSRBF interpolation model, so that the complete contour of the ground object and the spectrum information of the missing pixels in the ground object can be predicted more accurately.
The repair results of each method were evaluated for accuracy using root mean square error (Root Mean Square Error, RMSE) and correlation coefficient (Correlation Coefficient, CC) evaluation index, as shown in table 1. The first row in the table is from left to right, 6 wave bands related to experiments are respectively arranged in the last column, the average value of experimental results of the 6 wave bands is shown in the last column, and the 6 wave bands are sequentially blue wave bands, green wave bands, red wave bands, near infrared wave bands, short wave infrared wave bands 1 and short wave infrared wave bands 2. Wherein the RMSE measures the difference between the repair information and the real information, the larger the value of the RMSE indicates that the predicted information deviates from the real information; CC reflects the correlation between the predicted information and the real information, and the larger the value thereof, the closer the predicted information and the real information are.
Table 1 evaluation of repair result accuracy
As can be seen from the objective evaluation results in Table 1, the method of the present invention is superior to other 3 conventional methods, and various indexes indicate that the method of the present invention can obtain a repair image closer to the real situation.
In conclusion, the strip repairing method has obvious advantages in vision and precision evaluation, and the obtained repairing image can better keep the information of the ground object, so that the method is a feasible SLC-off image repairing method.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions may be made without departing from the spirit and scope of the invention as defined by the appended claims. Therefore, the protection scope of the invention is subject to the protection scope of the claims.
Claims (6)
1. A band repairing method based on spatial spectrum radial basis function interpolation is used for repairing SLC-off band images, and is characterized by comprising the following steps:
1) According to the SLC-off stripe image to be repaired, performing global histogram matching on the known image to obtain a matched known image;
2) Predicting missing pixels of the SLC-off band image to be repaired by using the known image after the global histogram matching obtained in the step 1) and adopting a spatial spectrum radial basis function method;
Step 2) comprises the following steps:
21 Selecting similar pixels of the known image and the SLC-off stripe image to be repaired, for any missing pixel of the SLC-off stripe image to be repaired, finding out the positions of neighboring pixels similar to the known image based on the pixels in the same geographic position in the known image, and selecting N similar pixels for each missing pixel to participate in subsequent calculation;
22 Acquiring a space radial basis function between similar neighborhood pixels selected by each missing pixel, and defining a space radial basis function between a center pixel and the similar pixels in a known image window;
23 Constructing a spectrum radial basis function of spectrum similarity between similar pixels in an SLC-off strip image window to be repaired, and constructing a spectrum radial basis function of spectrum similarity between a center pixel of a known image window and adjacent similar pixels;
24 Multiplying the spatial radial basis function obtained according to step 22) with the spectral radial basis function obtained according to step 23) to obtain a spatial spectral radial basis function;
25 Using the selected N similar pixels, calculating radial basis weights based on reflectivity changes between pixels in the known image and pixels of the SLC-off stripe image to be repaired;
26 Based on step 25) obtaining radial basis weights of each band, calculating the reflectivity change between the pixels of the known image of the corresponding band and the pixels of the SLC-off band image to be repaired;
27 Superposing the known image matched with the global histogram in the step 1) and the reflectivity change in the step 26) to obtain a final prediction result;
in step 22), the expression of the spatial radial basis function between the center pixel and the effective pixel is:
Wherein, (x 0,y0) is the coordinate of the central pixel, delta 1 is the spatial radial base parameter, and (x i,yi) is the coordinate of the ith and jth effective pixels in the window;
In step 23), the spectral radial basis function of the spectral similarity between similar pixels in the SLC-off strip image window to be repaired And the spectral radial basis function/>, which knows the spectral similarity of the center pixel of the image window and its neighboring similar pixelsThe expression of (2) is:
Wherein delta 2 is a spectrum radial base parameter, RMSD i is a RMSD value between a central pixel and an ith similar pixel in a window, and RMSD ij is a RMSD value between the ith pixel and a jth similar pixel in the window;
in step 24), the expression of the spatial radial basis function is:
In the method, in the process of the invention, As a spatial radial basis function,/>Is a spatial radial basis function between the center pixel and the effective pixel,/>As a spectral radial basis function of spectral similarity between similar pixels in an SLC-off strip image window to be repaired,/>Is a spectral radial basis function of the spectral similarity of the center pixel of the known image window and its neighboring similar pixels.
2. The method for band restoration based on spatial spectrum radial basis function interpolation according to claim 1, wherein the specific contents of step 1) are as follows:
The acquisition time of the known image and the SLC-off strip image to be repaired is respectively marked as t k and t p, linear regression modeling is carried out on the set of effective pixels corresponding to the acquisition time of the known image and the SLC-off strip image to be repaired, a linear model is constructed on data of each wave band, and the known image is integrally transformed into a new known image which is closer to the SLC-off strip image to be repaired in a characteristic space by using coefficients obtained by the constructed linear model.
3. The band repairing method based on spatial spectrum radial basis function interpolation according to claim 2, wherein the specific contents of transforming the known image as a whole into a new known image closer to the SLC-off band image to be repaired in the feature space are:
11 Linear regression modeling is carried out according to the set of the effective pixels of the known image at the moment t k and the effective pixels of the SLC-off strip image to be repaired at the moment t p, a linear relation model between the SLC-off strip image to be repaired at the moment t p and the known image at the moment t k is constructed, a linear coefficient is obtained, and the difference between the two is obtained;
12 Global histogram matching is carried out, and the known image at the time t k is subjected to integral linear transformation through linear coefficients, so that a new known image at the time t k is obtained;
13 The linear relation model and the new known image are subjected to difference, and a new difference between the SLC-off stripe image to be repaired at the moment t p and the new known image at the moment t k after transformation is obtained after global histogram matching is implemented;
14 Calculating expected values of the two differences before and after the change, and judging, if the expected value of the difference before the change is smaller than the expected value of the difference after the change, the known image subjected to global histogram matching is closer to the SLC-off stripe image to be repaired in the characteristic space.
4. The method for band repair based on spatial spectral radial basis function interpolation according to claim 1, wherein the specific contents of step 25) are:
Using the selected N similar pixels, the change in reflectivity between the known image and the SLC-off stripe image to be repaired is denoted ΔL(xi,yi,b)＝L(xi,yi,b,tp)-L′(xi,yi,b,tk),, where L (x, y, b, t p) is the reflectivity of the SLC-off stripe image to be repaired and the known image at the position (x, y) for the band b, L' (x, y, b, t k) is the step 1) of transforming the known image as a whole to a new known image that is closer to the SLC-off stripe image to be repaired in the feature space, t k and t p are the acquisition moments of the known image and the SLC-off stripe image to be repaired, respectively, and then the radial basis weight is denoted ω bi (i=1, 2,..n), the calculation formula of the radial basis weight is as follows:
5. the method for band repair based on spatial spectral radial basis function interpolation according to claim 2, wherein in step 1), the expression of the linear model constructed for the data of each band is:
L(x,y,b,tp)＝Ab×L(x,y,b,tk)+Bb
Where L (x, y, B, t p) and L (x, y, B, t k) are the reflectivity of band B at the location (x, y) of the SLC-off image to be repaired and the known image, respectively, and A b and B b are linear coefficients, respectively.
6. The method for band restoration based on spatial-spectral radial basis function interpolation according to claim 5, wherein the linear coefficients a b and B b are solved by least square fitting according to the effective data sets corresponding to the complex SLC-off image to be restored and the known image.
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