Spectral image sub-pixel localization method based on bias information measurement

Abstract

This invention proposes a method for sub-pixel localization of spectral images based on bias information measurement. The method includes the following steps: 1. Upsampling the coarse abundance image using a dual-scale spatial attraction model (DSAM) to obtain a predicted abundance image. 2. Measuring the biased abundance image with DI (Discretionary Indicator) based on fine-grained prior images captured from the same field of view at different times using a geographically weighted regression (GWR) model. 3. Fusing the predicted abundance image and the biased abundance image to generate an optimal abundance image. Based on the proportion information of sub-pixels in the optimal abundance image, a label assignment method is used to generate the final mapping result.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing image processing technology, and particularly relates to a method for sub-pixel localization of spectral images based on deviation information measurement. Background Technology

[0002] With the rapid development of imaging systems, land cover mapping information obtained from spectral images (i.e., multispectral or hyperspectral images) has been widely applied in medicine, forestry, geology, military, and other fields. To ensure photosensitivity and imaging quality, the physical size of the photosensitive element has been increased, resulting in a large number of mixed pixels in the spectral images of the imaging system. These mixed pixels reduce the spatial resolution of the imaging system, thus affecting the accuracy of class localization information extraction. To analyze these mixed pixels, spectral demixing has been developed to generate abundance images with a certain scale information on the mixed pixels. These abundance images are named coarse abundance images because they are directly generated from the original spectral image. However, class localization information still cannot be measured definitively. To address this problem, sub-pixel mapping (SPM) technology is proposed. In SPM, the coarse abundance image is optimized for upsampling to obtain an upsampled abundance image through a scaling factor. These abundance images, named predicted abundance images, will have information gain (IG). Based on these IG in the predicted abundance images, class labels are assigned to sub-pixels using a label assignment method to obtain land cover mapping results. SPM (Spatial Presence Mapping) technology has been applied in many fields, such as flood inundation mapping, change detection, fire zone mapping, and forest vegetation detection. Based on whether or not auxiliary data is used, current SPM methods can be divided into two types. Due to their simple structure, most SPM methods are based on the spatial dependency assumption, i.e., the closer the spatial distance, the more likely sub-pixels belong to the same land cover class. In these methods based on the spatial dependency assumption, a spatial dependency-based mathematical model is used to improve the coarse abundance image, thereby generating a predicted abundance image using IG (Inductively Coupled Geographical Indication). Then, a label assignment method is used to assign class labels according to maximizing spatial dependency. Typical methods include spatial attraction models, Hopfield neural networks, indicative co-kriging, and radial basis function interpolation. Recently, the reduction of the point spread function effect in SPM methods has been validated, and the final localization results can be further improved. Furthermore, because traditional SPM methods often lack prior information on the true geographic distribution, the uncertainty of the mapping results is limited, affecting the accuracy of the results. To address this issue, SPM methods based on auxiliary data have been proposed in recent years. These methods improve the final localization results by using prior knowledge from auxiliary data. Typical auxiliary data include panchromatic images, light detection and ranging multi-displacement images, and deep learning network training data. In particular, spatiotemporal SPM (SSPM) shows greater potential than traditional SPM methods by utilizing spatiotemporal information from fine prior images of the same region. Proposed SSPM based on spatiotemporal dependencies typically establish a spatiotemporal objective using spatiotemporal dependencies, and then optimize the objective to obtain reasonable results.In addition, Wang Peng et al. used the point spread function effect to improve the SSPM model, patent number CN202011572383.1.

[0003] From the above description of SPM, we can see that achieving the optimal solution for the predicted abundance image using IG is key to obtaining good localization results. However, SPM represents an ill-posed problem; many reasonable results for predicting the abundance image can lead to the same coherent reproduction of the optimal abundance image. Therefore, in the SPM solution, there exists deviation information (DI), defined opposite to IG in the predicted abundance image; it refers to the gain of the SPM solution on the coarse abundance image. Although the goal of SPM is to minimize DI, this loss always exists and will never be zero. If DI could be measured, it could be used to compensate for the SPM solution to obtain more accurate localization results. However, existing SPM methods rarely measure DI, which hinders further improvements in the accuracy of localization results. Summary of the Invention

[0004] The purpose of this invention is to provide a sub-pixel localization method for spectral images based on deviation information measurement, to address the issue that deviation information (DI) exists in the SPM solution. Although the goal of SPM is to minimize DI, this loss always exists and will never be zero. If DI can be measured, it can be used to compensate for the SPM solution to obtain more accurate localization results. However, existing SPM methods rarely measure DI, which hinders further improvements in the accuracy of localization results.

[0005] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0006] A method for sub-pixel localization of spectral images based on deviation information measurement includes the following steps:

[0007] Step 1: Upsample the roughness abundance image using the dual-scale spatial attraction model (DSAM) to obtain the predicted abundance image;

[0008] Step 2: Using a geographically weighted regression (GWR) model, measure the bias abundance image with bias information (DI) based on fine prior images captured from the same field of view at different times;

[0009] Step 3: Fuse the predicted abundance image with the biased abundance image to generate the optimal abundance image; based on the proportion information of sub-pixels in the optimal abundance image, use the label assignment method to generate the final localization result.

[0010] Furthermore, in step 1, the specific steps for obtaining the predicted abundance image are as follows: setting a... 1 pixel and The original coarse spectral images of each category were demixed to obtain A roughness abundance image ,in =1,2, ..., Roughness abundance image It is used as input to the Deviation Information Measurement Based SPM (DIM) method for spectral image sub-pixel localization; in the DIM method, the Dual-scale Spatial Attraction Model (DSAM) is used to determine the scale factor. Comparative example Roughness abundance image Upsampling is performed to obtain the predicted abundance image. The central sub-pixel No. The prediction ratio of the class is ,in =1,2, ..., In the predicted abundance image In the middle, the central sub-pixel No. Class prediction ratio The calculation is shown in formula (1):

[0011] (1)

[0012] Where parameters These are empirical values ​​obtained through multiple experiments;

[0013] Represents the central sub-pixel and 8 adjacent pixels The pixel scale dependency between them, where =1, 2, ...,8, defined as formula (2);

[0014] (2)

[0015] in, The first adjacent pixel Class ratio; yes and Euclidean distance between them; parameters These are empirical values ​​obtained through multiple experiments; Represents the central sub-pixel and 8 adjacent sub-pixels Sub-pixel scale dependency between them, where =1, 2, ..., 8, and expressed as equation (3);

[0016] (3)

[0017] in yes and Euclidean distance between them; parameters These are empirical values ​​obtained through multiple experiments; Represents the central sub-pixel and adjacent sub-pixels Whether they belong to the same category is defined by formula (4). If the central sub-pixel and adjacent sub-pixels If they belong to the same category, then =1, otherwise =0;

[0018] (4).

[0019] Furthermore, in step 2, the module for measuring deviation information DI includes the following specific steps: In this work, selecting images captured from the same field of view at different times... 1 pixel and Fine prior images for each category As training images, =1,2,..., ;

[0020] Step 2.1, Prior Abundance Image Generation: This involves generating a refined prior image. Demix to obtain Prior abundance image of time ,in =1, 2, ..., ; Provide center sub-pixel No. Prior proportion of the class Information;

[0021] Step 2.2, Simulate roughness abundance image generation: Each with prior proportion Prior abundance images Through point spread function filter Downsampling is performed to obtain a priori proportions. Simulated roughness abundance image , defined as formula (5):

[0022] (5)

[0023] in This is a convolution operation;

[0024] Point spread function filter It is assumed to follow a Gaussian distribution model, expressed as formula (6):

[0025] (6)

[0026] Where parameters The width of the point spread function filter; Indicates the spatial location of a subpixel;

[0027] Step 2.3, Generating a simulated fine abundance image: Using the proposed dual-scale spatial attraction model (DSAM), the rough abundance image is generated using formulas (1)-(4). Upsampling is performed to generate simulated fine-grained abundance images. At this point, simulated fine abundance images Includes sub-pixels No. Class proportion ;

[0028] Step 2.4, Prior Bias Abundance Image Generation: This involves generating an image containing prior proportions. Prior abundance images With proportion Simulated fine abundance images The difference between them yields a proportion with prior bias. Prior bias abundance image , expressed as formula (7):

[0029] (7)

[0030] Step 2.5, Biased Abundance Image Generation: All prior biased abundance images Both are used to measure proportions with deviation. Biased abundance image The deviation information DI is implemented using a linear combination as shown in formula (8):

[0031] (8)

[0032] Where parameters It is time Upper prior bias abundance image The weights; these weights are based on the bias abundance image. Abundance image with prior bias The relationship between pixels is determined; the geographic weighted regression (GWR) model is used to characterize the distance between pixels by predicting the weights in equation (8) here; the geographic weighted regression (GWR) model is expressed as equation (9):

[0033] (9)

[0034] Where parameters Indicates the initial value;

[0035] set up It consists of all simulated roughness abundance images in a local window. Prior proportion The size of the composition is The matrix, including pixels; It is the size of Vectors, including roughness abundance images in local windows. proportion ; It has spatial weights. Diagonal matrix; then, weights constitute a vector It can be expressed by formula (10):

[0036] (10)

[0037] in, and Indicates spatial nonstationarity; diagonal elements in Defined as equation (11);

[0038] (11)

[0039] in Represents the center pixel The Euclidean distance between it and its neighboring pixel i. It's the core bandwidth.

[0040] Furthermore, in step 3, the specific steps for obtaining the optimal abundance image are as follows: including the proportion Predicted abundance image and including proportion Biased abundance image By fusing the data, the optimal abundance image can be obtained. sub-pixels The The optimal ratio of classes is , expressed as formula (12):

[0041] (12)

[0042] Using the best abundance image The best ratio obtained The final output is generated using a label assignment method; the objective function is maximized. The goal of the label assignment method is to determine if the central sub-pixel belongs to the first... Class, then =1, otherwise The value is 0; the method is given by equations (13) and (14);

[0043] (13)

[0044] (14)

[0045] The constraints in formula (15) must be met for convergence to be achieved and the final positioning result obtained:

[0046] (15)

[0047] in Indicated to The rounding function for the nearest integer; the first term in equation (15) indicates that each sub-pixel belongs to only one class, and the second term in equation (15) indicates that the number of sub-pixels in each class conforms to the rounding function. The constraints provided.

[0048] The sub-pixel localization method for spectral images based on deviation information measurement of the present invention has the following advantages:

[0049] The method of this invention improves existing sub-pixel localization methods by considering bias information to enhance the accuracy of sub-pixel localization. Compared with six common SPM methods, the proposed new method (DIM) outperforms existing state-of-the-art methods, significantly improving localization results in terms of class classification accuracy, overall accuracy (OA), and Kappa coefficient. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the principle of the spectral image sub-pixel localization method based on deviation information measurement according to the present invention.

[0051] Figure 2 (a) is a diagram showing the positioning results obtained using PSAM in this invention;

[0052] Figure 2 (b) is a diagram showing the positioning results obtained using DSAM in this invention;

[0053] Figure 2 (c) is a localization result diagram obtained by using HNNP in this invention;

[0054] Figure 2 (d) is a diagram showing the positioning results obtained using RPSFE in this invention;

[0055] Figure 2 (e) is a diagram showing the positioning results obtained using STD in this invention;

[0056] Figure 2 (f) is a diagram showing the positioning results obtained using CPSFE in this invention;

[0057] Figure 2 (g) is a diagram showing the positioning results obtained using DIM in this invention;

[0058] Figure 3 (a) is a reference image of the salient region;

[0059] Figure 3 (b) is a salient region map obtained using PSAM in this invention;

[0060] Figure 3 (c) is a salient region map obtained using DSAM in this invention;

[0061] Figure 3 (d) is a salient region map obtained using HNNP in this invention;

[0062] Figure 3 (e) is a salient region map obtained using RPSFE in this invention;

[0063] Figure 3 (f) is a salient region map obtained using STD in this invention;

[0064] Figure 3 (g) is a salient region map obtained using CPSFE in this invention;

[0065] Figure 3 (h) is a salient region map obtained using DIM in this invention; Detailed Implementation

[0066] To better understand the purpose, structure, and function of this invention, the following detailed description of a spectral image sub-pixel localization method based on deviation information measurement is provided in conjunction with the accompanying drawings.

[0067] This invention proposes a sub-pixel localization method for spectral images based on deviation information measurement (DIM). The basic idea of ​​DIM is to use a geographically weighted regression (GWR) model to compute auxiliary spatiotemporal information from refined previous images in order to measure the deviation abundance of the image using DI.

[0068] In DIM, a coarse abundance image is upsampled using a dual-scale spatial attraction model (DSAM) to obtain a predicted abundance image. Then, a biased abundance image with DIM is measured using a GWR model based on previous fine images captured from the same field of view at different times. The predicted abundance image and the biased abundance image are fused to generate the optimal abundance image. The final localization result is generated using a label assignment method based on the sub-pixel proportions in the optimal abundance image. The proposed DIM-based method is tested using three spectral images, and the results show that it improves the localization results compared to existing SPM methods.

[0069] A method for sub-pixel localization of spectral images based on deviation information measurement includes the following steps:

[0070] Step 1: Upsample the roughness abundance image using the dual-scale spatial attraction model (DSAM) to obtain the predicted abundance image;

[0071] The specific steps to obtain the predicted abundance image are as follows: assuming that there are 1 pixel and The original coarse spectral images of each category were demixed to obtain A roughness abundance image ( =1,2, ..., Roughness abundance images are used as input to DIM. In the spectral image sub-pixel localization method DIM, the dual-scale spatial attraction model DSAM is used based on the scaling factor. Comparative example Roughness abundance image Upsampling is performed to obtain the predicted abundance image. The central sub-pixel No. The proportion of classes is ,in =1,2, ..., In the predicted abundance image In the middle, the central sub-pixel No. Class prediction ratio The calculation is shown in formula (1):

[0072] (1)

[0073] Where parameters This is an empirical value obtained through multiple experiments, and it is set to 0.4 in this work;

[0074] Represents the central sub-pixel and 8 adjacent pixels The pixel scale dependency between them, where =1, 2, ...,8, defined as formula (2);

[0075] (2)

[0076] in, The first adjacent pixel Class ratio; yes and Euclidean distance between them; parameters This is an empirical value obtained through multiple experiments, and it is set to 0.5 in this work; Represents the central sub-pixel and 8 adjacent sub-pixels Sub-pixel scale dependency between them, where =1, 2, ..., 8, and expressed as equation (3);

[0077] (3)

[0078] in yes and Euclidean distance between them; parameters This is an empirical value obtained through multiple experiments, and it is set to 0.5 in this work; Represents the central sub-pixel and adjacent sub-pixels Whether they belong to the same category is defined by formula (4). If the central sub-pixel and adjacent sub-pixels If they belong to the same category, then =1, otherwise =0;

[0079] (4).

[0080] Step 2: Using a geographically weighted regression (GWR) model, measure the bias abundance images with bias information (DI) based on fine-grained prior images captured from the same field of view at different times; in this work, images with bias information (DI) captured from the same field of view at different times are selected. 1 pixel and Fine prior images for each category As training images, =1,2,..., ;

[0081] The module for measuring deviation information (DI) includes the following specific steps:

[0082] Step 2.1, Prior Abundance Image Generation: This involves generating a refined prior image. Demix to obtain Prior abundance image of time ,in =1, 2, ..., ; Provide center sub-pixel No. Prior proportion of the class Information;

[0083] Step 2.2, Simulate roughness abundance image generation: Each with prior proportion Prior abundance images Through point spread function filter Downsampling is performed to obtain a priori proportions. Simulated roughness abundance image , defined as formula (5):

[0084] (5)

[0085] in This is a convolution operation;

[0086] Point spread function filter It is assumed to follow a Gaussian distribution model, expressed as formula (6):

[0087] (6)

[0088] Where parameters The width of the point spread function filter; Indicates the spatial location of a subpixel;

[0089] Step 2.3, Generating a simulated fine abundance image: Using the proposed dual-scale spatial attraction model (DSAM), the rough abundance image is generated using formulas (1)-(4). Upsampling is performed to generate simulated fine-grained abundance images. At this point, simulated fine abundance images Includes sub-pixels No. Class proportion ;

[0090] Step 2.4, Prior Bias Abundance Image Generation: This involves generating an image containing prior proportions. Prior abundance images With proportion Simulated fine abundance images The difference between them yields a proportion with prior bias. Prior bias abundance image , expressed as formula (7):

[0091] (7)

[0092] Step 2.5, Biased Abundance Image Generation: All prior biased abundance images Both are used to measure proportions with deviation. Biased abundance image The deviation information DI is implemented using a linear combination as shown in formula (8):

[0093] (8)

[0094] Where parameters It is time Upper prior bias abundance image The weights; these weights are based on the bias abundance image. Abundance image with prior bias The relationship between pixels is determined; the geographic weighted regression (GWR) model is used to characterize the distance between pixels by predicting the weights in equation (8) here; the geographic weighted regression (GWR) model is expressed as equation (9):

[0095] (9)

[0096] Where parameters Indicates the initial value;

[0097] set up It consists of all simulated roughness abundance images in a local window. Prior proportion The size of the composition is The matrix, including pixels; It is the size of Vectors, including roughness abundance images in local windows. proportion ; It has spatial weights. Diagonal matrix; then, weights constitute a vector It can be expressed by formula (10):

[0098] (10)

[0099] in, and Indicates spatial nonstationarity; diagonal elements in Defined as equation (11);

[0100] (11)

[0101] in Represents the center pixel The Euclidean distance between it and its neighboring pixel i. It's the core bandwidth.

[0102] Step 3: Fuse the predicted abundance image with the biased abundance image to generate the optimal abundance image; based on the proportion information of sub-pixels in the optimal abundance image, use the label assignment method to generate the final localization result.

[0103] The specific steps to obtain the optimal abundance image are as follows: including the proportion Predicted abundance image and including proportion Biased abundance image By fusing the data, the optimal abundance image can be obtained. sub-pixels The The optimal ratio of classes is , expressed as formula (12):

[0104] (12)

[0105] Using the best abundance image The best ratio obtained The final output is generated using a label assignment method; the objective function is maximized. The goal of the label assignment method is to determine if the central sub-pixel belongs to the first... Class, then =1, otherwise The value is 0. This method is given by equations (13) and (14);

[0106] (13)

[0107] (14)

[0108] The constraints in formula (15) must be met for convergence to be achieved and the final positioning result obtained:

[0109] (15)

[0110] in Indicated to The rounding function for the nearest integer; the first term in equation (15) indicates that each sub-pixel belongs to only one class, and the second term in equation (15) indicates that the number of sub-pixels in each class conforms to the rounding function. The constraints provided.

[0111] The principle flowchart of the spectral image sub-pixel localization method based on deviation information measurement proposed in this invention is shown in Figure 1.

[0112] The dataset used in this method consists of images captured by NLCD in 2011 and 2006, obtained through raster-based classification with a spatial resolution of 30 m. Image NLCD 2011 was selected as the original image to be processed. Image NLCD 2006 was considered a fine prior image to aid in the proposed DIM measurement DI. Following the general SPM experimental procedure, the reference fine classification image was downsampled using mean filtering to generate a simulated coarse abundance image. In this experiment, the scale was set to 5, and image NLCD 2011 with a spatial resolution of 30 m was downsampled using an average filter to obtain a coarse abundance image with a spatial resolution of 150 m. Although the coarse abundance image can provide information on the proportion of mixed pixels, the specific spatial distribution of categories remains uncertain. Therefore, SPM technology was employed to address this issue.

[0113] Figure 2The localization results of seven SPM methods on the NLCD 2011 image are shown. The seven SPM methods are: the SPM method based on a pixel-scale spatial attraction model (PSAM), the SPM method based on a dual-scale spatial attraction model (DSAM), the SPM method based on a Hopfield neural network with rich prior information (HNNP), the SPM method based on the point spread function effect reduction (RPSFE), the spatiotemporal SPM method based on a spatio-temporal dependence (STD), the spatiotemporal SPM method considering the point spread function effect (CPSFE), and the dual-scale spatial attraction model (DIM).

[0114] For ease of observation, Figure 3 middle, Figure 2 The significant subregions marked in (a) are magnified. According to Figure 3 The proposed DIM localization result is closest to the reference image among all methods. Compared with the reference image, Figure 3 (b)-3(e) contain many boundaries and regions with discontinuous shapes and jagged edges. This is because these methods lack prior knowledge about the actual geographical distribution. However, by utilizing the auxiliary spatiotemporal information provided by the NLCD 2001 imagery, the mapping results of STD and CPSFE alleviate the above phenomena, such as... Figure 3As shown in (f) and 3(g). Nevertheless, the class regions are not sufficiently continuous, and the class boundaries are not smooth enough. Nevertheless, the proposed DIM can accurately measure the DI between the predicted SPM results and the reference image. It improves the accuracy of ill-posed conditions and mapping results. Boundaries become smoother, and more continuous regions are generated, such as... Figure 3 As shown in (h).

[0115] Table 1 shows the accuracy for each category (%), OA (%), and Kappa. The proposed DIM achieves higher evaluation metrics than the other six SPM methods. For example, compared to the evaluation metrics in CPSFE, the accuracy of the proposed DIM is improved by approximately 4.98%, 8.40%, and 4.82% for developed, moderate intensity, poor soil (rock / sand / clay), and grassland / herbaceous types, respectively. Furthermore, among all methods, the proposed DIM has the highest values ​​for OA (%) and Kappa. Experimental results confirm that DIM significantly improves localization results.

[0116] Table 1 Evaluation Indicators for Localization Results of Seven Methods

[0117] PSAM DSAM HNNP RPSFE STD CPSFE DIM 1. Developed, High Intensity (%) 47.51 49.67 39.10 56.60 89.94 94.02 97.04 2. Developed, Medium Intensity (%) 36.24 38.54 35.54 45.05 82.21 90.73 95.71 3. Evergreen Forest (%) 65.82 67.90 64.42 72.13 95.75 96.41 97.78 4. Open Water (%) 51.73 54.21 48.37 61.81 94.94 95.54 96.26 5. Cultivated Crops (%) 74.38 75.96 71.05 79.90 96.55 97.21 98.17 6. Deciduous Forest (%) 54.40 56.49 54.51 62.67 94.90 95.61 96.63 7. Emergent Herbaceous Wetlands (%) 29.91 36.41 15.10 43.82 91.59 91.95 94.76 8. Developed, Low Intensity (%) 45.23 48.29 40.89 53.33 87.83 94.18 96.82 9. Barren Land (Rock / Sand / Clay) (%) 56.15 57.59 51.49 62.01 85.35 87.18 95.58 10. Shrub / Scrub (%) 64.08 66.22 65.50 70.85 78.20 81.50 96.59 11. Mixed Forest (%) 45.36 46.94 51.34 53.27 95.08 94.47 94.87 12. Pasture / Hay (%) 62.86 64.47 70.53 69.40 96.03 96.51 96.94 13. Developed, Open Space (%) 60.45 61.41 77.07 66.00 90.50 95.04 96.98 14. Woody Wetlands (%) 96.11 95.55 96.64 96.35 98.38 98.91 99.04 15. Grassland / Herbaceous (%) 60.08 61.11 67.03 66.49 89.02 90.90 95.72 OA (%) 65.51 66.92 67.79 71.12 93.82 95.55 97.26 Kappa 0.6015 0.6185 0.6311 0.6686 0.9296 0.9493 0.9689

[0118] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for sub-pixel localization of spectral images based on deviation information measurement, characterized in that, Includes the following steps: Step 1: Upsample the roughness abundance image using the dual-scale spatial attraction model (DSAM) to obtain the predicted abundance image; Step 2: Using a geographic weighted regression (GWR) model, measure the bias abundance image with bias information (DI) based on fine prior images captured from the same field of view at different times; Step 3: Fuse the predicted abundance image with the biased abundance image to generate the optimal abundance image; based on the proportion information of sub-pixels in the optimal abundance image, use the label assignment method to generate the final localization result; In step 1, the specific steps for obtaining the predicted abundance image are as follows: Set the image with... 1 pixel and The original coarse spectral images of each category were demixed to obtain A roughness abundance image ,in =1,2, ..., Roughness abundance image Used as input for the spectral image sub-pixel localization method DIM; in the spectral image sub-pixel localization method DIM, the dual-scale spatial attraction model DSAM is used based on the scale factor. Comparative example Roughness abundance image Upsampling is performed to obtain the predicted abundance image. The central sub-pixel No. The prediction ratio of the class is ,in =1,2, ..., In the predicted abundance image In the middle, the central sub-pixel No. Class prediction ratio The calculation is shown in formula (1): （1） Where parameters These are empirical values ​​obtained through multiple experiments; Represents the central sub-pixel and 8 adjacent pixels The pixel scale dependency between them, where =1,2, ...,8, defined as formula (2); （2） in, The first adjacent pixel Class ratio; yes and Euclidean distance between them; parameters These are empirical values ​​obtained through multiple experiments; Represents the central sub-pixel and 8 adjacent sub-pixels Sub-pixel scale dependency between them, where =1, 2, ..., 8, and expressed as equation (3); （3） in yes and Euclidean distance between them; parameters These are empirical values ​​obtained through multiple experiments; Represents the central sub-pixel and adjacent sub-pixels Whether they belong to the same category is defined by formula (4). If the central sub-pixel and adjacent sub-pixels If they belong to the same category, then =1, otherwise =0; （4）； In step 2, the module for measuring deviation information (DI) includes the following specific steps: In this work, images captured from the same field of view at different times are selected. 1 pixel and Fine prior images for each category As training images, =1,2,..., ; Step 2.1, Prior Abundance Image Generation: This involves generating a refined prior image. Demix to obtain Prior abundance image of time ,in =1, 2, ..., ; Provide center sub-pixel No. Prior proportion of the class Information; Step 2.2, Simulate roughness abundance image generation: Each with prior proportion Prior abundance images Through point spread function filter Downsampling is performed to obtain a priori proportions. Simulated roughness abundance image , defined as formula (5): （5） in This is a convolution operation; Point spread function filter It is assumed to follow a Gaussian distribution model, expressed as formula (6): （6） Where parameters The width of the point spread function filter; Indicates the spatial location of a subpixel; Step 2.3, Generating a simulated fine abundance image: Using the proposed dual-scale spatial attraction model (DSAM), the rough abundance image is generated using formulas (1)-(4). Upsampling is performed to generate simulated fine-grained abundance images. At this point, simulated fine abundance images Includes sub-pixels No. Class proportion ; Step 2.4, Prior Bias Abundance Image Generation: This involves generating an image containing prior proportions. Prior abundance images With proportion Simulated fine abundance images The difference between them yields a proportion with prior bias. Prior bias abundance image , expressed as formula (7): （7） Step 2.5, Biased Abundance Image Generation: All prior biased abundance images Both are used to measure proportions with deviation. Biased abundance image The deviation information DI is implemented using a linear combination as shown in formula (8): （8） Where parameters It is time Upper prior bias abundance image The weights; these weights are based on the bias abundance image. Abundance image with prior bias The relationship between pixels is determined; the geographic weighted regression (GWR) model is used to characterize the distance between pixels by predicting the weights in equation (8) here; the geographic weighted regression (GWR) model is expressed as equation (9): （9） Where parameters Indicates the initial value; set up It consists of all simulated roughness abundance images in a local window. Prior proportion The size of the composition is The matrix, including Pixels; It is the size of Vectors, including roughness abundance images in local windows. proportion ; It has spatial weights. Diagonal matrix; then, weights constitute a vector It can be expressed by formula (10): （10） in, and Indicates spatial nonstationarity; diagonal elements in Defined as equation (11); （11） in Represents the center pixel The Euclidean distance between it and its neighboring pixel i. It's the core bandwidth.

2. The method for sub-pixel localization of spectral images based on deviation information measurement according to claim 1, characterized in that, In step 3, the specific steps to obtain the optimal abundance image are as follows: including the proportion Predicted abundance image and including proportion Biased abundance image By fusing the data, the optimal abundance image can be obtained. sub-pixels The The optimal ratio of classes is , expressed as formula (12): （12） Using the best abundance image The best ratio obtained The final output is generated using a label assignment method; the objective function is maximized. The goal of the label assignment method is to determine if the central sub-pixel belongs to the first... Class, then =1, otherwise =0; given by equations (13) and (14); （13） （14） The constraints in formula (15) must be met for convergence to be achieved and the final positioning result obtained: （15） in Indicated to The rounding function for the nearest integer; the first term in equation (15) indicates that each sub-pixel belongs to only one class, and the second term in equation (15) indicates that the number of sub-pixels in each class conforms to the rounding function. The constraints provided.

Images