A method for reconstructing time series vegetation index images based on comprehensive temporal and spatial characteristics
By combining the HANTS model and the spatiotemporal regression model, the time-dimensional VI image reconstruction method is solved, and the problem of low accuracy when processing large continuous missing values is achieved is achieved.
Patent Information
- Application Number
- CN202111424679.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-11-26
- Publication Date
- 2025-03-25
- Estimated Expiration
- 2041-11-26
AI Technical Summary
The time-dimensional VI image reconstruction method has low reconstruction accuracy when processing pixels with large continuous missing pixels.
The time series vegetation index image reconstruction method with comprehensive spatiotemporal features is used to reconstruct smaller continuous missing values through the HANTS model, and the larger continuous missing values are reconstructed using the spatiotemporal regression model between similar pixels.
Effectively improve the accuracy of the time-dimensional reconstruction method, especially when dealing with large continuous missing values, it significantly improves the real-time and usability of image quality and data.
Smart Images

Figure CN114283073B_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of image processing, and in particular relates to a time series vegetation index image reconstruction method integrating temporal and spatial characteristics. Background Art
[0002] Vegetation coverage affects the surface accessibility and concealment in off-road maneuvers. Remote sensing technology is an important means to obtain vegetation information over a large area. Vegetation Index (VI) images calculated based on satellite remote sensing images can effectively reflect the growth status of vegetation. However, in the process of acquiring remote sensing images, the influence of factors such as aerosols, clouds / cloud shadows on the reflected radiation of ground objects leads to low-quality pixels (hereinafter referred to as missing values) containing noise and missing information on VI images, which reduces the image quality and limits the real-time and availability of data. By analyzing the historically acquired time series vegetation index images and establishing a regional vegetation change model, we can better carry out analysis work such as interpreting vegetation cover types and predicting vegetation cover conditions, and thus provide more scientific auxiliary decision-making for off-road maneuvering.
[0003] The problem that needs to be solved in the analysis of time series VI images is the reconstruction of missing values. To address this problem, the reconstruction methods of time series VI images have been studied. At present, the reconstruction methods based on the time dimension are the most widely studied. Such methods only use the time series VI values in a single pixel to build a reconstruction model. HANTS (Harmonic ANalysis of TimeSeries) is a representative VI image reconstruction method based on the time dimension. Its basic principle is Fourier transform. It represents the periodic changes of VI values during vegetation growth as the superposition of sine and cosine functions of different frequencies. By setting the number of sine and cosine waves, the HANTS model can represent complex vegetation changes and has high flexibility. Using the valid VI values in the time series within a single pixel, the HANTS model parameters are obtained by fitting, and then the VI values at any time in the cycle can be calculated. However, when there are many missing values in a single pixel, especially when there are time-continuous missing values, there is a defect that the established HANTS model has low accuracy. Summary of the invention
[0004] Aiming at the problem that the VI image reconstruction method based on time dimension only uses the time series VI value in a single pixel to build a reconstruction model, and has low reconstruction accuracy for pixels with large continuous missing, the present invention proposes a time series vegetation index image reconstruction method with comprehensive temporal and spatial characteristics.
[0005] In order to achieve the above object, the present invention adopts the following technical solutions:
[0006] A time series vegetation index image reconstruction method integrating temporal and spatial characteristics, comprising:
[0007] Step 1: Determine the length of time-continuous missing values according to the position of time-continuous missing values in the time series vegetation index image, and set the threshold l th As a reconstruction standard for time-continuous missing values of smaller length, the HANTS model is used to reconstruct time-continuous missing values of smaller length by pixel-by-pixel processing;
[0008] Step 2: Reconstruct the long-term continuous missing values by integrating spatiotemporal features; including:
[0009] Step 2.1: For the pixels with large time-continuous missing values in the time series vegetation index image processed in step 1, take them as target pixels, set a search window with them as the center, and select pixels with similar vegetation index time variation characteristics as the target pixels from the window;
[0010] Step 2.2: Establish a spatiotemporal regression model between the target pixel and similar pixels, and use the vegetation index values of similar pixels that are valid but target pixels that are invalid at the same time to predict the time-continuous missing values of the target pixel through the spatiotemporal regression model;
[0011] Step 2.3: The prediction results of different similar pixels in the window are combined by weights to improve the stability of reconstruction and reduce the random errors contained in the prediction results of a single similar pixel;
[0012] Step 2.4: Smooth the time series vegetation index image again according to step 1;
[0013] Step 2.5: Repair all long time-continuous missing values in the time series vegetation index image in the manner of steps 2.1 to 2.4, save the repair results, and obtain a time series vegetation index image without missing values.
[0014] Furthermore, the step 1 comprises:
[0015] Step 1.1: For the i-th pixel in the time series vegetation index image, according to the missing condition P of the i-th pixel i Determine the missing position of the vegetation index value and the corresponding time continuous missing length l;
[0016] Step 1.2: Use the effective vegetation index value in the pixel to fit the HANTS model coefficients through linear least squares, and use the fitted HANTS model to calculate the vegetation index values corresponding to n dates to obtain the time series reconstructed by HANTS The missing case is Indicates that at this time All values of are 1, that is, there is no missing;
[0017] Step 1.3: For the missing position in the i-th pixel, if l>l th , then the corresponding position The value is set to 0, indicating that the positions of large continuous deletions are still invalid values;
[0018] Step 1.4: Iteratively process each pixel in the original time series vegetation index image according to steps 1.1 to 1.3 until all pixels are processed, and a time series vegetation index image with only large time continuity gaps is obtained.
[0019] Furthermore, the step 2.1 comprises:
[0020] Step 2.1.1: Set the initial value of the half window size h;
[0021] Step 2.1.2: Take any pixel with a large continuous missing value as the target pixel, and change the position (x c ,y c ) is the center, and the selection range is [(x c -h):(x c +h),(y c -h):(y c +h)], where the complete window size w = 2×h+1;
[0022] Step 2.1.3: Determine whether the pixel in the i-th window can be used as a candidate pixel for similar pixels, i = 1, 2, ..., w 2 , if the missing value distribution of the pixel in the i-th window satisfies the conditions in equations (2) and (3) at the same time, it can be used as a candidate pixel:
[0023]
[0024]
[0025] in Indicates the missing state of the target pixel to be reconstructed; Indicates the missing pixels in the ith window; p Indicates the number of common valid values between the pixels in the i-th window and the target pixel;
[0026] Through the above judgment, the candidate pixels and their number in the window are obtained;
[0027] Step 2.1.4: If the number of candidate pixels obtained is less than m, then expand h by a step size step, and repeat steps 2.1.2 to 2.1.4 until the number of candidate pixels is not less than m or h reaches the maximum value hmax ;
[0028] Step 2.1.5: Select similar pixels from candidate pixels:
[0029] For the i-th candidate pixel, use its common effective value with the target pixel to calculate its correlation coefficient CC with the target pixel i ; Then, calculate the ratio r of the valid values of the candidate pixels at the invalid position of the target pixel i ; Finally, all CC i × i Sort the values from large to small, and select the first m pixels as similar pixels;
[0030]
[0031] Furthermore, the step 2.2 includes:
[0032] For the i-th similar pixel, i = 1, 2, ..., m, use its common effective value with the target pixel to establish a linear spatiotemporal regression model and obtain the coefficient a i and b i ;
[0033] in,
[0034] in, Represents the effective vegetation index value of the i-th similar pixel; express missing conditions; Indicates the effective vegetation index value of the target pixel; express missing conditions;
[0035] Then, for the date t where the target pixel is invalid but similar pixels are valid, the coefficient a is used i and b i Predict the missing value of the target pixel:
[0036] in and
[0037] in, represents the result predicted by the i-th similar pixel on the date t when the target pixel is missing; Represents the effective vegetation index value of the i-th similar pixel on date t.
[0038] Furthermore, the step 2.3 includes:
[0039] The correlation coefficient between each similar pixel and the target pixel is used as the basis for determining the weight. The weight W of the i-th similar pixel is t i for:
[0040]
[0041] Among them, CC i is the correlation coefficient between the i-th similar pixel and the target pixel;
[0042] Finally, the prediction results of different similar pixels are integrated using formula (8) as the final prediction result of the missing value of the target pixel date t, and the corresponding Set to 1, which means the prediction result is valid:
[0043]
[0044] Compared with the prior art, the present invention has the following beneficial effects:
[0045] The present invention aims at the problem that the VI image reconstruction method based on time dimension only uses the time series vegetation index (VI) value in a single pixel to build a reconstruction model. For pixels with large continuous missing pixels, the reconstruction accuracy is low. A time series vegetation index image reconstruction method with comprehensive spatiotemporal characteristics is designed. The method divides the time series VI image reconstruction into two parts. First, the HANTS model is used to reconstruct smaller continuous missing pixels to ensure the reconstruction accuracy. Then, the correlation between the time series VI values between similar pixels is used to build a spatiotemporal regression model to reconstruct larger continuous missing pixels, which can effectively improve the accuracy of the reconstruction method based on time dimension. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] Figure 1 This is a flow chart of a method for reconstructing a time series vegetation index image with integrated temporal and spatial characteristics according to an embodiment of the present invention;
[0047] Figure 2 Schematic diagram of the results of reconstructing smaller time-continuous missing values using the HANTS model. DETAILED DESCRIPTION
[0048] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:
[0049] In order to introduce the technical solution of the present invention, the following introduction is first made:
[0050] On a VI image acquired on a certain date, pixels affected by factors such as clouds / cloud shadows, aerosols, etc. are missing pixels, and pixels not affected are valid pixels. For a time series VI image, the time series VI values contained in a pixel usually contain both valid values and missing values, and the missing values adjacent in time constitute continuous missing values. Assume that the time series VI value of the i-th pixel on the time series VI image is represented by the vector Z i Indicates that represents the VI value on the tth date, and n is the number of observations in the time series. For example, for MODIS 8-day and 16-day data products within a year, n is 46 and 23 respectively. i There are both valid values and missing values in the vector Indicates a date Is it effective? t i 1 means efficient, 0 means Invalid. For t∈[t1,t2] (where t2≥t1), if If all are 0, there is a missing length l = t2-t1+1. If l ≥ 2, it means that the time series VI has time-continuous missing values. When l is small, the HANTS method can achieve better reconstruction results, while when l is large, the accuracy of HANTS is low.
[0051] Since clouds are highly variable and random, the positions of clouds / cloud shadows on images of different dates may overlap but will not be exactly the same. Therefore, pixels with a large continuous missing length are usually the common overlapping areas of clouds / cloud shadows on images of consecutive dates. The number of these pixels and their spatial coverage are usually small. Therefore, in the consecutive missing dates, although these pixels have invalid values, their neighboring images are
[0052] The complete technical solution of the time series vegetation index image reconstruction method of the present invention is as follows: Figure 1As shown. First, according to the position of the missing value in the original time series VI image, the length of the continuous missing is determined, and the missing value with a smaller continuous missing length is reconstructed using the HANTS model to ensure a higher reconstruction accuracy and obtain a VI image with only a large time continuous missing. Then, for the pixel with a large time continuous missing, it is used as the target pixel, and a search window is set with it as the center. The pixel with similar VI time variation characteristics as the target pixel is selected from the window. A regression model is established between the target pixel and similar pixels, and the VI value of the similar pixel at the same time is valid but the target pixel is invalid. The missing value of the target pixel is predicted by the regression model. Finally, the prediction results of different similar pixels in the window are combined by weight to improve the stability of reconstruction and reduce the random error contained in the prediction result of a single similar pixel. Finally, the time series VI image is smoothed again. When all the missing values in the image are repaired, the repair results are saved to obtain a time series VI image without missing values.
[0053] The key of the present invention includes two parts. The first is to use the HANTS model to reconstruct the time continuous missing values of smaller length; the second is to reconstruct the time continuous missing values of larger length by integrating the spatiotemporal features, which specifically includes four steps: selecting similar pixels, establishing a spatiotemporal regression model, integrating spatiotemporal information based on weights, and smoothing the time series curve.
[0054] The specific implementation plans for the two key parts of our invention are as follows:
[0055] Step 1: Use the HANTS model to reconstruct the time-series missing values with a smaller length.
[0056] The HANTS model constructs the temporal variation characteristics of the surface by superimposing a series of trigonometric functions of different frequencies. The HANTS model can be expressed as follows:
[0057]
[0058] Among them, nf is the frequency number, that is, the frequency is f j The number of sine and cosine functions, and f j =j / n. a0, a j and b j is the coefficient of the model, which can be obtained by using Z i Then, the model coefficients can be used to calculate the VI value at any date t and reconstruct Z i Invalid values in , a smooth time series VI image is obtained.
[0059] For the original time series VI image, by setting the threshold l thAs the reconstruction standard for short continuous missing values, the HANTS model is used to reconstruct short time continuous missing values in a pixel-by-pixel manner. The specific steps are as follows:
[0060] Step 1.1: For the i-th pixel, according to P i Determine the missing position and the corresponding continuous missing length l of its VI value;
[0061] Step 1.2: Use the effective VI values in the pixels to fit the model coefficients a0, a j and b j , use the model coefficients to calculate the VI values corresponding to n dates, and obtain the time series reconstructed by HANTS The missing case is Indicates that at this time All values of are 1, that is, there is no missing;
[0062] Step 1.3: For the missing position in pixel i, if l>l th , then the corresponding position P H i The value is set to 0, indicating that the positions of large continuous deletions are still invalid values;
[0063] Step 1.4: Iteratively process each pixel in the original time series VI image according to steps 1.1 to 1.3 until all pixels are processed and a VI image with only large time continuity gaps is obtained.
[0064] In the reconstruction of smaller time-continuous missing values using the HANTS model, the processing results of steps 1.1 to 1.3 can be used Figure 2 express. Figure 2 The time series curve composed of the original VI values in the figure contains valid values (◆ points) and invalid values (× points). For positions with smaller continuous missing values, HANTS can achieve better reconstruction results, but for positions with larger continuous missing values, the reconstruction accuracy is lower. Therefore, the positions with larger continuous missing values in the HANTS reconstruction results are still regarded as invalid values (the darkened part in the solid line).
[0065] Step 2: Reconstruct larger time-continuous missing values by integrating spatiotemporal features.
[0066] Spatially adjacent vegetation of the same type usually has a similar growth cycle. The time series VI curves between corresponding pixels have similar trends and strong correlations. These pixels are called similar pixels. The relationship between the VI values of similar pixels can be represented by a linear model. Based on the above assumptions, for a pixel with a large continuous missing pixel, a linear model can be established first using the valid VI values of the pixel and similar pixels (common valid values), and then using the invalid VI values of the pixel but valid VI values of similar pixels to predict its missing value through the model.
[0067] For a pixel with a large time-continuous missing value, that is, the target pixel to be reconstructed, its position is (x c ,y c ), the time series VI value included is The missing The process of reconstructing large time-continuous missing values by integrating spatiotemporal features includes the following specific steps:
[0068] Step 2.1: Select similar pixels.
[0069] Selecting similar pixels includes the following 5 steps:
[0070] Step 2.1.1: Set the initial value of the half window size h;
[0071] Step 2.1.2: Take (x c ,y c ) as the center and select the range [(x c -h):(x c +h),(y c -h):(y c +h)], where the complete window size w = 2×h+1;
[0072] Step 2.1.3: Determine the i-th (i=1,2,…,w 2 ) whether the pixels in the ith window can be used as candidate pixels for similar pixels; if the distribution of missing values of the pixels in the ith window satisfies the conditions in equations (2) and (3) at the same time, they can be used as candidate pixels;
[0073]
[0074]
[0075] Formula (2) indicates that the number of common valid values between the pixels in the ith window and the target pixel should be no less than the threshold th p, if the number of common valid values is small, it will affect the accuracy of the subsequently established linear model; Formula (3) indicates that the number of values where the target pixel is invalid but the pixels in the i-th window are valid must be greater than 0, otherwise the pixels in the i-th window cannot be used to reconstruct the invalid value of the target pixel.
[0076] Through the above judgment, the candidate pixels and their number in the window are obtained;
[0077] Step 2.1.4: For a target pixel, it is usually necessary to select m similar pixels to improve the stability of the reconstruction result. If the number of candidate pixels is less than m, the window needs to be enlarged to enlarge h by a step size step. Repeat steps 2.1.2 to 2.1.4 until the number of candidate pixels is not less than m or h reaches the maximum value h. max ;
[0078] Step 2.1.5: Select similar pixels from candidate pixels:
[0079] For the i-th candidate pixel, use its common effective value with the target pixel to calculate the correlation coefficient CC between it and the target pixel i ; Then, calculate the proportion r of the valid values of the candidate pixels at the invalid position of the target pixel i (Formula (4)); Finally, all CC i × i Sort the values from large to small, and select the first m pixels as similar pixels;
[0080]
[0081] Step 2.2: Establish a spatiotemporal regression model.
[0082] For i, (i = 1, 2, ..., m) similar pixels, use their common effective values with the target pixel to establish a linear regression model (Formula (5)) and obtain the coefficient a i and b i ;
[0083] in,
[0084] in, Represents the effective vegetation index value of the i-th similar pixel; express missing conditions; Indicates the effective vegetation index value of the target pixel; express missing conditions;
[0085] Then, for the date t where the target pixel is invalid but similar pixels are valid, the coefficient a is used i and bi Predict the missing value of the target pixel:
[0086] in and
[0087] in, It represents the result predicted by the i-th similar pixel on the missing date t; Represents the effective vegetation index value of the i-th similar pixel on date t;
[0088] Step 2.3: Weight-based spatiotemporal information integration.
[0089] Since there are m similar pixels, the predicted value The number of is usually ≥ 1, and multiple prediction values are weighted Taken together, the final prediction result is obtained. The correlation coefficient between each similar pixel and the target pixel is used as the basis for determining the weight. The weight of the i-th similar pixel is calculated as shown in formula (7). Normalized to the range of 0 to 1.
[0090]
[0091] Among them, CC i is the correlation coefficient between the i-th similar pixel and the target pixel;
[0092] Finally, the prediction results of different similar pixels are combined using formula (8) as the final prediction result of the missing value of the target pixel date t, and the corresponding If set to 1, it means the prediction result is valid.
[0093]
[0094] Step 2.4: Smooth the time series curve.
[0095] Through the processing of the above steps, the reconstruction of time-continuous missing values when the target pixel is invalid but the similar pixel is valid can be completed. However, for the dates when the target pixel is invalid and the similar pixel is also invalid, the missing values still cannot be reconstructed. Moreover, the time series VI curve reconstructed by the above steps is not smooth. Therefore, in this step, the reconstruction result is smoothed. The method used is consistent with the method described in step 1 to reconstruct smaller time-continuous missing values using the HANTS model.
[0096] Through steps 2.1 to 2.4, the reconstruction of a large continuous missing value in a pixel is completed. For the time series VI image with large continuous missing values, first, the number of missing values contained in each pixel is sorted from small to large; then, starting from the pixel with the least number of missing values, the missing value reconstruction is completed according to the above four steps, and the reconstructed pixels can be used in the subsequent reconstruction process of other pixels; finally, when the entire time series VI image no longer contains missing values, the reconstruction is completed.
[0097] In summary, the present invention aims at the problem that the VI image reconstruction method based on the time dimension only uses the time series vegetation index (VI) value within a single pixel to construct a reconstruction model. For pixels with large continuous missing pixels, the reconstruction accuracy is low. A time series vegetation index image reconstruction method with comprehensive spatiotemporal characteristics is designed. This method divides the time series VI image reconstruction into two parts. First, the HANTS model is used to reconstruct smaller continuous missing pixels to ensure the reconstruction accuracy. Then, the correlation between the time series VI values between similar pixels is used to construct a spatiotemporal regression model to reconstruct larger continuous missing pixels, which can effectively improve the accuracy of the reconstruction method based on the time dimension.
[0098] The above is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.
Claims
1. A method for reconstructing a time series vegetation index image based on comprehensive temporal and spatial characteristics, characterized in that: include: Step 1: Determine the length of time-continuous missing values according to the position of time-continuous missing values in the time series vegetation index image, and set the threshold l th As a reconstruction standard for time-continuous missing values of smaller length, the HANTS model is used to reconstruct time-continuous missing values of smaller length by pixel-by-pixel processing; Step 2: Reconstruct the long-term continuous missing values by integrating spatiotemporal features; include: Step 2.1: For the pixels with large time-continuous missing values in the time series vegetation index image processed in step 1, take them as target pixels, set a search window with them as the center, and select pixels with similar vegetation index time variation characteristics as the target pixels from the window; The step 2.1 comprises: Step 2.1.1: Set the initial value of the half window size h; Step 2.1.2: Take any pixel with a large continuous missing value as the target pixel, and change the position (x c ,y c ) is the center, and the selection range is [(x c -h):(x c +h),(y c -h):(y c +h)], where the complete window size w = 2×h+1; Step 2.1.3: Determine whether the pixel in the i-th window can be used as a candidate pixel for similar pixels, i = 1, 2, ..., w 2 , if the missing value distribution of the pixel in the i-th window satisfies the conditions in equations (2) and (3) at the same time, it can be used as a candidate pixel: in Indicates the missing state of the target pixel to be reconstructed; Indicates the missing pixel in the ith window; p Indicates the number of common valid values between the pixels in the i-th window and the target pixel; Through the above judgment, the candidate pixels and their number in the window are obtained; Step 2.1.4: If the number of candidate pixels obtained is less than m, then expand h by a step size step, and repeat steps 2.1.2 to 2.1.4 until the number of candidate pixels is not less than m or h reaches the maximum value h max ; Step 2.1.5: Select similar pixels from candidate pixels: For the i-th candidate pixel, use its common effective value with the target pixel to calculate its correlation coefficient CC with the target pixel i ; Then, calculate the ratio r of the valid values of the candidate pixels at the invalid position of the target pixel i ; Finally, all CC i × i Sort the values from large to small, and select the first m pixels as similar pixels; Step 2.2: Establish a spatiotemporal regression model between the target pixel and similar pixels, and use the vegetation index values of similar pixels that are valid but target pixels that are invalid at the same time to predict the time-continuous missing values of the target pixel through the spatiotemporal regression model; The step 2.2 comprises: For the i-th similar pixel, i = 1, 2, ..., m, use its common effective value with the target pixel to establish a linear spatiotemporal regression model and obtain the coefficient a i and b i ; in, Represents the effective vegetation index value of the i-th similar pixel; express missing conditions; Indicates the effective vegetation index value of the target pixel; express missing conditions; Then, for the date t where the target pixel is invalid but similar pixels are valid, the coefficient a is used i and b i Predict the missing value of the target pixel: in, represents the result predicted by the i-th similar pixel on the date t when the target pixel is missing; Represents the effective vegetation index value of the i-th similar pixel on date t; Step 2.3: The prediction results of different similar pixels in the window are combined by weights to improve the stability of reconstruction and reduce the random errors contained in the prediction results of a single similar pixel; Step 2.4: Smooth the time series vegetation index image again according to step 1; Step 2.5: Repair all long time-continuous missing values in the time series vegetation index image in the manner of steps 2.1 to 2.4, save the repair results, and obtain a time series vegetation index image without missing values.
2. The method for reconstructing a time series vegetation index image based on comprehensive temporal and spatial characteristics according to claim 1, characterized in that: The step 1 comprises: Step 1.1: For the i-th pixel in the time series vegetation index image, according to the missing condition P of the i-th pixel i Determine the missing position of the vegetation index value and the corresponding time continuous missing length l; Step 1.2: Use the effective vegetation index value in the pixel to fit the HANTS model coefficients through linear least squares, and use the fitted HANTS model to calculate the vegetation index values corresponding to n dates to obtain the time series reconstructed by HANTS The missing case is Said that at this time All values of are 1, that is, there is no missing; Step 1.3: For the missing position in the i-th pixel, if l>l th , then the corresponding position The value is set to 0, indicating that the positions of large continuous deletions are still invalid values; Step 1.4: Iteratively process each pixel in the original time series vegetation index image according to steps 1.1 to 1.3 until all pixels are processed, and a time series vegetation index image with only large time continuity gaps is obtained.
3. The method for reconstructing a time series vegetation index image based on comprehensive temporal and spatial characteristics according to claim 1, characterized in that: The step 2.3 includes: The correlation coefficient between each similar pixel and the target pixel is used as the basis for determining the weight. The weight W of the i-th similar pixel is t i for: Among them, CC i is the correlation coefficient between the i-th similar pixel and the target pixel; Finally, the prediction results of different similar pixels are integrated using formula (8) as the final prediction result of the missing value of the target pixel date t, and the corresponding Set to 1, which means the prediction result is valid:
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