A method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images

Abstract

The present application relates to a kind of based on satellite remote sensing image super-resolution reconstruction fine water body identification method, construct pre-sampling super-resolution network pre-EDSR and the pre-sampling diffusion probability super-resolution reconstruction model ED-DDIM of improved DDIM diffusion probability model in series, for remote sensing image is introduced including NDWI water body index channel in multiple channel image, obtain super-resolution reconstruction model, can effectively restore the detail in image, reduce distortion problem, and through diffusion iteration denoising mechanism, combined with the multiscale feature extraction capability of UNet jump connection, it realizes from low resolution to high resolution image gradual reconstruction, then apply pre-training water body identification model, obtain the binary image of high resolution under the multiple channel image restored remote sensing image about water body area and non-water body area, realize water body area identification, make contribution for the monitoring under increasingly changing environment and arid region water resource protection.

Description

Technical Field

[0001] This invention relates to a method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images, belonging to the fields of super-resolution reconstruction technology and surface water extraction technology. Background Technology

[0002] Water, as a non-renewable resource, is not only the basic material basis for sustaining life, but also the key to important functions such as climate regulation and material transportation on Earth. Therefore, it is essential to monitor water resources in arid areas.

[0003] Satellite remote sensing technology, with its advantages of wide coverage, high monitoring frequency, and low cost, provides effective technical support for the dynamic monitoring of surface water resources. Especially in arid regions where ground hydrological observation conditions are scarce, satellite imagery can accurately obtain surface water information, helping local areas to rationally optimize water resource allocation, making it an irreplaceable and important tool for water resource management. Many scholars have used remote sensing technology to obtain water resource information in arid regions, but most have relied on foreign satellite imagery such as MODIS, Landsat, and Sentinel. Paper 1, "Surface water monitoring in small waterbodies: potential and limits of multi-sensor Landsat time series," analyzes the changes in multiple reservoirs in the Merguelier watershed from 1999 to 2014 using Landsat series imagery, demonstrating the advantages of long-term remote sensing imagery. Paper 2, "Seasonal inundation dynamics and water balance of the MaraWetland, Tanzania based on multi-temporal Sentinel-2 image classification," uses multi-temporal Sentinel-2 imagery to monitor the bimodal nature of seasonal expansion and contraction of wetlands in Tanzania, confirming the importance of river flow and local precipitation to water resources during the dry season. Paper 3, "Water Body Extraction Method in Arid Zones Based on Sentinel-2 Super-Resolution Imagery," provides a feasible method for rapidly and accurately extracting small water bodies in the Heihe River Basin of Northwest China under complex environments using Sentinel-2 imagery. Paper 4, "Developing a High-Resolution Seamless Surface WaterExtent Time-Series over Lake Victoria by Integrating MODIS and Landsat Data," integrates MODIS and Landsat imagery to generate a seamless surface water extent time series with a spatial resolution of 30m, obtaining the long-term dynamic changes of the super-large lake Victoria from 2000 to 2020. Paper 5, “Impact of climate change and human activities on the spatiotemporal dynamics of surface water area in Gansu Province, China”, uses long-term Landsat images to obtain large-scale spatiotemporal changes in arid inland areas of my country.

[0004] In recent years, the successive launches of domestically produced Gaofen series satellites have made high-frequency, large-scale monitoring of surface water possible, providing services and decision support for major fields such as modern agriculture, environment, and public safety. However, wide-swath satellite imagery with high temporal resolution, such as GF-1 WFV and GF-6 WFV, typically has low spatial resolution, with obvious mixed pixels at the water body edges; while high-resolution imagery, such as GF-1 PMS and GF-6 PMS, has high spatial resolution but insufficient temporal resolution and high cost. In 2024, Kang Hui et al. used the domestically produced GF-1 WFV to monitor surface water changes in Miyun District from 2013 to 2022, meeting the accuracy requirements for regional-level monitoring of spatial changes in water bodies. Paper 6, "High spatio-temporal resolution dynamic water monitoring using multi-source Chinese Gaofen imagery: a case study in the Eastern Nile Basin," combined with domestically produced GF-1 / 6 WFV imagery, achieved time-series monitoring of large lakes in the Eastern Nile River Basin from 2020 to 2024. Most of these studies based on domestically produced imagery use free and open-source 16m resolution wide-span imagery as their data source. This typically only meets the extraction accuracy requirements for regional surface water and large lakes, making it difficult to identify small water bodies. Water scarcity results in numerous small water bodies on the surface, which 16m resolution wide-span imagery cannot clearly reveal. Therefore, using domestically produced wide-span imagery to achieve precise water body extraction in arid regions presents a significant challenge. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images, which optimizes multi-scale information extraction and fusion, improves the resolution of wide-span images, enriches image information, and enables efficient identification of small water bodies.

[0006] To solve the aforementioned technical problems, this invention adopts the following technical solution: This invention designs a method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images. Steps A to D are performed to obtain the super-resolution reconstruction model corresponding to the target area. Then, for the first-resolution remote sensing image to be analyzed corresponding to the target area, steps A to D are performed. To the steps To achieve the identification of water bodies in the first-resolution remote sensing image of the target area;

[0007] Step A. Obtain a preset number of spatiotemporally synchronized first-resolution remote sensing images and second-resolution remote sensing images corresponding to the target area, perform preprocessing and updates, then construct a single master sample using the spatiotemporally synchronized first-resolution remote sensing images and second-resolution remote sensing images, obtain each master sample, and proceed to Step B; wherein, the first resolution is lower than the second resolution.

[0008] Step B. For the first-resolution remote sensing image and the second-resolution remote sensing image in each master sample, obtain the channel images corresponding to each preset channel, including the NDWI water index channel, and then proceed to step C.

[0009] Step C. Construct the pre-sampling diffusion probability super-resolution reconstruction model ED-DDIM, which is a cascaded pre-sampling super-resolution network pre-EDSR and an improved DDIM diffusion probability model, and then proceed to step D;

[0010] Step D. Based on each master sample, take the channel images corresponding to the first resolution remote sensing image in the master sample as input and the channel images corresponding to the second resolution remote sensing image in the master sample as output, train the presampled diffusion probability super-resolution reconstruction model ED-DDIM to obtain the trained model, which is used as the super-resolution reconstruction model.

[0011] step First, following step B, obtain the images of each channel to be analyzed corresponding to the first-resolution remote sensing image to be analyzed. Then, apply the super-resolution reconstruction model to obtain the images of each channel to be analyzed at the second resolution corresponding to the first-resolution remote sensing image to be analyzed. Then proceed to step [further steps]. ;

[0012] step For each channel image to be analyzed at the second resolution, a pre-trained water body recognition model is applied to obtain binary classification images of the remote sensing images of water body areas and non-water body areas restored by each channel image to be analyzed at the second resolution, thereby determining the water body areas in the first resolution remote sensing image to be analyzed for the target area.

[0013] As a preferred technical solution of the present invention: In step A, based on obtaining a preset number of spatiotemporally synchronized medium-resolution GF-1 16m WFV remote sensing images and high-resolution GF-1 8m / 2m PMS remote sensing images corresponding to the target area, the following steps A1 to A3 are specifically performed for each set of spatiotemporally synchronized medium-resolution GF-1 16m WFV remote sensing images and high-resolution GF-1 8m / 2m PMS remote sensing images to achieve preprocessing update;

[0014] Step A1. For the 16m WFV remote sensing image of medium resolution GF-1 and the 8m / 2m PMS remote sensing image of high resolution GF-1, respectively, perform radiometric calibration, atmospheric correction and orthorectification in sequence to complete the processing update, and then proceed to step A2.

[0015] Step A2. Using the NNDiffuse tool, perform image fusion on the 8m PMS remote sensing image of the updated high-resolution GF-1 image processed in Step A1 and the 2m PMS remote sensing image of the updated high-resolution GF-1 image processed in Step A1 to obtain a fused 2m PMS remote sensing image, and then proceed to Step A3.

[0016] Step A3. For the updated 16m WFV remote sensing image of medium resolution GF-1 processed in step A1 and the fused PMS remote sensing image, perform pixel registration to update and obtain the WFV remote sensing image and PMS remote sensing image.

[0017] In step B, the preset channels include the NDWI water index channel, the blue band channel, the green band channel, the red band channel, and the near-infrared band channel.

[0018] As a preferred technical solution of the present invention: in the presampled diffusion probability super-resolution reconstruction model ED-DDIM constructed in step C, the input end of the presampled super-resolution network pre-EDSR constitutes the input end of the presampled diffusion probability super-resolution reconstruction model ED-DDIM, the output end of the presampled super-resolution network pre-EDSR is connected to the input end of the improved DDIM diffusion probability model, and the output end of the improved DDIM diffusion probability model constitutes the output end of the improved DDIM diffusion probability model.

[0019] The pre-EDSR pre-sampling super-resolution network consists of several components connected in series from the input to the output. Convolutional layers, residual modules, Convolutional layers, upsampling modules, Convolutional layers, where the first one in sequence The input of the convolutional layer forms the input of the pre-EDSR pre-sampling super-resolution network, the third one in sequence. The output of the convolutional layer constitutes the output of the pre-EDSR pre-sampling super-resolution network; the residual module consists of at least two cascaded residual blocks from input to output, wherein the input of the first residual block constitutes the input of the residual module, and the output of the last residual block constitutes the output of the residual module; each residual block has the same structure, and each residual block consists of cascaded residual blocks from input to output. Convolutional layers, ReLU activation function layers, The first convolutional layer in the residual block. The input of the convolutional layer forms the input of the residual block, which is the second input in sequence within the residual block. The output of the convolutional layer forms the output of the residual block;

[0020] The improved DDIM diffusion probability model includes a noise extraction layer, a splicing layer, and a first... Convolutional layer, downsampling encoder group, upsampling decoder group, second The convolutional layer has an input terminal of the noise extraction layer connected to one input terminal of the concatenation layer, with the connection point forming the input terminal of the improved DDIM diffusion probability model. The output terminal of the noise extraction layer is connected to the other input terminal of the concatenation layer. The noise extraction layer is used to extract the corresponding noise map from the feature map output by the pre-EDSR network. The output terminal of the concatenation layer is connected to the first... The input of the convolutional layer, the concatenation layer is used to concatenate the feature map output by the pre-EDSR network with the corresponding noise map output by the noise extraction layer, and the output feature concatenation map is obtained; first The output of the convolutional layer is sequentially connected in series with the downsampled encoding group, the upsampled decoding group, and the second... Convolutional layer, consisting of the second The output of the convolutional layer constitutes the output of the improved DDIM diffusion probability model, and a skip connection is established between the downsampled coding group and the upsampled decoding group.

[0021] As a preferred embodiment of the present invention: the upsampling module includes a main road, and Convolution kernel 4x upsampling layer and The convolutional kernel is an 8x upsampling layer, where the main path first connects two concatenated layers from the input to the output. The convolutional kernel is upsampled by 2 times, then connected in series with one of the inputs of the first fusion layer, and finally connected to a... The input of the convolutional kernel is twice that of the upsampling layer, where the first one in sequence... The input of the convolution kernel, which is twice the size of the upsampling layer, forms the input of the main circuit, and is the third in sequence. The output of the convolution kernel, which is twice the output of the upsampling layer, constitutes the output of the main circuit.

[0022] The input of the convolution kernel is 4 times that of the upsampling layer. The input terminals of the convolution kernel 8x upsampling layer, the main circuit input terminal, and the connection point constitute the input terminal of the upsampling module; The output of the convolutional kernel is upsampled by 4 times and then connected to the other input of the first fusion layer. The output of the 8x upsampling layer and the output of the main circuit are respectively connected to the two inputs of the second fusion layer, and the output of the second fusion layer constitutes the output of the upsampling module.

[0023] As a preferred embodiment of the present invention: the upsampling decoding group includes a predetermined number of decoding layers connected in series from the input end to the output end, wherein the input end of the first sequential decoding layer constitutes the input end of the upsampling decoding group, and the output end of the last sequential decoding layer constitutes the output end of the upsampling decoding group; the structures of each decoding layer are identical, and each decoding layer includes an upsampling decoding layer and a third fusion layer, wherein the input end of the upsampling decoding layer constitutes the input end of the decoding layer, the output end of the upsampling decoding layer is connected to one of the input ends of the corresponding third fusion layer, and the output end of the third fusion layer constitutes the output end of the decoding layer;

[0024] The downsampling coding group consists of sequentially connected downsampling coding layers from input to output. The number of downsampling coding layers is equal to the number of decoding layers in the upsampling decoding group. The input of the first sequential downsampling coding layer constitutes the input of the downsampling coding group, and the output of the last sequential downsampling coding layer constitutes the output of the downsampling coding group.

[0025] The upsampling decoder group is ordered from input to output in the following order: In the third fusion layer of the decoding layer, the other input of the downsampled coding group is sequentially connected from the input to the output direction. The input skip connections of each downsampling coding layer are as follows: Indicates the number of decoding layers in the upsampled decoding group. Indicates 1 to Integers;

[0026] Each downsampling encoding layer and each upsampling decoding layer performs sampling operations according to a preset time step T.

[0027] As a preferred embodiment of the present invention: the structures of each downsampling coding layer are identical, and each downsampling coding layer includes a fourth fusion layer, an SE self-attention layer, and a preset step size. The system consists of a stride convolutional layer and two branches. The first branch, from the input to the output, comprises a dilated convolutional layer, a normalization layer, and a SiLU activation layer connected in series. The kernel size of the dilated convolutional layer is [missing information]. The expansion factor is 2. The input of the dilated convolutional layer forms the input of the first branch, and the output of the SiLU activation layer forms the output of the first branch. The second branch consists of sequentially cascaded layers from the input to the output. Convolutional layers, normalization layers, and SiLU activation layers, among which, The input of the convolutional layer forms the input of the second branch, and the output of the SiLU activation layer forms the output of the second branch. The input of the first branch is connected to the input of the second branch, and the connection point forms the input of the downsampling coding layer. The output of the first branch is connected to the output of the second branch, and the connection point is connected to the input of the fourth fusion layer. The output of the fourth fusion layer is connected in series with the SE after the attention layer. The input end of the stride convolutional layer, The output of the stride convolutional layer constitutes the output of the downsampling coding layer.

[0028] As a preferred embodiment of the present invention: the structures of each upsampling decoding layer are identical, and each upsampling decoding layer comprises sequentially connected components from the input end to the output end. Convolutional layer, normalization layer, SiLU activation layer, fifth fusion layer Convolutional layer, normalization layer, SiLU activation layer, sixth fusion layer, SE self-attention layer, Upsampling convolutional layers, where the first one is in sequence The input of the convolutional layer is connected to the other input of the fifth fusion layer, and the connection point forms the input of the upsampling decoding layer. The output of the fifth fusion layer is simultaneously connected to the other input of the sixth fusion layer. The output of the upsampling convolutional layer constitutes the output of the upsampling decoding layer.

[0029] As a preferred technical solution of the present invention: Step B further includes slicing the channel images corresponding to each remote sensing image in each master sample according to a preset pixel size and a preset overlap rate between slices to obtain each slice image corresponding to the channel image, and then constructing a single subsample with each spatiotemporally synchronized slice image to obtain each subsample.

[0030] In step D, based on each subsample, the slice images of different channels at the first resolution in the subsample are taken as input, and the slice images of different channels at the second resolution in the subsample are taken as output. The presampled diffusion probability super-resolution reconstruction model ED-DDIM is trained to obtain the trained model, which is used as the super-resolution reconstruction model.

[0031] The steps First, following step B, obtain the corresponding slice images for each channel of the remote sensing image to be analyzed at the first resolution. Then, based on each spatial sub-region under the target region slice, apply a super-resolution reconstruction model to process the slice images for different channels within the same spatial sub-region under the first resolution remote sensing image to obtain the slice images for different channels of the corresponding spatial sub-region at the second resolution corresponding to the first resolution remote sensing image. Finally, following the inverse operation of step B, restore the slice images for different channels of each spatial sub-region at the second resolution to obtain the images for each channel of the remote sensing image to be analyzed at the second resolution corresponding to the first resolution remote sensing image, and then proceed to step [further steps]. .

[0032] As a preferred technical solution of the present invention: the steps The pre-trained water body identification model is based on a random forest classification model. It takes the images of each channel at the second resolution as input and the binary classification images of the remote sensing images of water areas and non-water areas restored by the images of each channel at the second resolution as output, and is obtained through training.

[0033] As a preferred technical solution of the present invention: In step D, during the training of the presampled diffusion probability super-resolution reconstruction model ED-DDIM, the predicted label and the real label corresponding to the image pixel position are combined according to a preset weight, and the peak signal-to-noise ratio PSNR and structural similarity SSIM obtained by the following formula are weighted and calculated, and the quality of model application is evaluated by the obtained weighted result.

[0034] (1);

[0035] (2);

[0036] (3);

[0037] (4);

[0038] (5);

[0039] (6);

[0040] (7);

[0041] (8);

[0042] in, and These represent the height and width of the image processed by the presampled diffusion probability super-resolution reconstruction model ED-DDIM, respectively. and These represent the pixel positions in the image. Predicted labels and true labels , , , This indicates a preset constant value, and , L represents the dynamic range of image pixel values, L=2 bits per pixel -1, bits per pixel, indicates the number of bits per pixel in the image. This represents the number of bits per pixel in the image. This represents the mean of the predicted labels for pixel locations in the image. This represents the mean of the true labels for pixel locations in the image. This represents the variance of the predicted labels for pixel locations in the image. This represents the variance of the true labels at pixel locations in an image. This represents the covariance between the predicted label and the true label at the pixel location in the image.

[0043] The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images described in this invention has the following technical advantages compared with existing technologies:

[0044] This invention designs a method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images. It constructs a pre-sampled diffusion probability super-resolution reconstruction model, ED-DDIM, which combines a cascaded pre-sampled super-resolution network (pre-EDSR) and an improved DDIM diffusion probability model. Multi-channel images, including the NDWI water index channel, are introduced into the remote sensing imagery. The model is trained by fully utilizing the spatial features of the water boundary lines to obtain a super-resolution reconstruction model that effectively restores details in the image and reduces distortion. Through a diffusion iterative denoising mechanism combined with the multi-scale feature extraction capabilities of UNet skip connections, it achieves gradual reconstruction from low-resolution to high-resolution images. Furthermore, in practical applications, the pre-trained water body identification model is used to obtain binary classification images of water and non-water areas from the remote sensing imagery reconstructed from the high-resolution multi-channel images, enabling water body area identification and contributing to monitoring in an increasingly changing environment and protecting water resources in arid regions. Attached Figure Description

[0045] Figure 1 This is a flowchart of the method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images designed in this invention;

[0046] Figure 2This is a schematic diagram of the presampled diffusion probability super-resolution reconstruction model ED-DDIM in the design of this invention;

[0047] Figure 3 This is a schematic diagram of the downsampling coding layer in the design of this invention;

[0048] Figure 4 This is a schematic diagram of the upsampling decoding group in the design of this invention;

[0049] Figure 5 These are the test set reconstructed images and water extraction results provided in the embodiments of the present invention;

[0050] Figure 6 This is the water extraction result from the GF-1 WFV image to be analyzed, provided in an embodiment of the present invention. Detailed Implementation

[0051] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0052] This invention designs a method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images. In practical applications, such as... Figure 1 As shown, the specific design involves performing steps A to D to obtain the super-resolution reconstruction model corresponding to the target region.

[0053] Step A. Based on domestic satellites, obtain a preset number of spatiotemporally synchronized first-resolution remote sensing images and second-resolution remote sensing images corresponding to the target area, and perform preprocessing and updating. Then, construct a single master sample using the spatiotemporally synchronized first-resolution remote sensing images and second-resolution remote sensing images, obtain each master sample, and proceed to Step B; wherein, the first resolution is lower than the second resolution.

[0054] In actual implementation, in step A above, based on the preset number of spatiotemporally synchronized medium-resolution GF-1 16m WFV remote sensing images and high-resolution GF-1 8m / 2m PMS remote sensing images corresponding to the target area obtained by domestic satellites, the following steps A1 to A3 are specifically executed for each set of spatiotemporally synchronized medium-resolution GF-1 16m WFV remote sensing images and high-resolution GF-1 8m / 2m PMS remote sensing images to achieve preprocessing and updating.

[0055] Step A1. For the 16m WFV remote sensing image of medium resolution GF-1 and the 8m / 2m PMS remote sensing image of high resolution GF-1, respectively, perform radiometric calibration, atmospheric correction and orthorectification in sequence to complete the processing update, and then proceed to step A2.

[0056] Step A2. Using the NNDiffuse tool, perform image fusion on the 8m PMS remote sensing image of high-resolution GF-1 after processing and updating in Step A1 and the 2m PMS remote sensing image of high-resolution GF-1 after processing and updating in Step A1 to obtain a fused 2m PMS remote sensing image, and then proceed to Step A3.

[0057] Step A3. Perform pixel registration on the updated 16m WFV remote sensing image of medium resolution GF-1 and the fused PMS remote sensing image processed in step A1, and update to obtain the WFV remote sensing image and PMS remote sensing image.

[0058] Step B. For the first-resolution and second-resolution remote sensing images in each master sample, obtain the corresponding NDWI water index channel, blue band channel, green band channel, red band channel, and near-infrared band channel, and then proceed to step C.

[0059] The formula is as follows:

[0060] ;

[0061] Calculate the NDWI water index, where, Indicates the green band. Indicates the near-infrared band.

[0062] Step C. Construct a presampled diffusion probability super-resolution reconstruction model ED-DDIM, which consists of a cascaded presampled super-resolution network pre-EDSR and an improved DDIM diffusion probability model. The first-stage presampled super-resolution network pre-EDSR is used to fully extract various features from the low-resolution image to achieve presampled super-resolution magnification. The second-stage improved DDIM diffusion probability model is used to iteratively refine the output image of the first stage and restore high-frequency details in the image. Then proceed to step D.

[0063] Regarding the constructed presampled diffusion probability super-resolution reconstruction model ED-DDIM, as follows: Figure 2 As shown, the input of the pre-sampling super-resolution network pre-EDSR constitutes the input of the pre-sampling diffusion probability super-resolution reconstruction model ED-DDIM, the output of the pre-sampling super-resolution network pre-EDSR is connected to the input of the improved DDIM diffusion probability model, and the output of the improved DDIM diffusion probability model constitutes the output of the improved DDIM diffusion probability model.

[0064] In actual implementation, such as Figure 2 As shown, the specific design of the pre-EDSR pre-sampling super-resolution network includes, from the input to the output, the following components connected in series. Convolutional layers, residual modules, Convolutional layers, upsampling modules, Convolutional layers, where the first one in sequence The input of the convolutional layer forms the input of the pre-EDSR pre-sampling super-resolution network, the third one in sequence. The output of the convolutional layer constitutes the output of the pre-EDSR pre-sampling super-resolution network; the residual module consists of at least two cascaded residual blocks from input to output, wherein the input of the first residual block constitutes the input of the residual module, and the output of the last residual block constitutes the output of the residual module; each residual block has the same structure, and each residual block consists of cascaded residual blocks from input to output. Convolutional layers, ReLU activation function layers, The first convolutional layer in the residual block. The input of the convolutional layer forms the input of the residual block, which is the second input in sequence within the residual block. The output of the convolutional layer constitutes the output of the residual block.

[0065] like Figure 2 As shown, the upsampling module in the pre-EDSR pre-sampling super-resolution network is specifically designed including the backbone and... Convolution kernel 4x upsampling layer and The convolutional kernel is an 8x upsampling layer, where the main path first connects two concatenated layers from the input to the output. The convolutional kernel is upsampled by 2 times, then connected in series with one of the inputs of the first fusion layer, and finally connected to a... The input of the convolutional kernel is twice that of the upsampling layer, where the first one in sequence... The input of the convolution kernel, which is twice the size of the upsampling layer, forms the input of the main circuit, and is the third in sequence. The output of the convolution kernel, which is twice the output of the upsampling layer, constitutes the output of the main circuit. The input of the convolution kernel is 4 times that of the upsampling layer. The input terminals of the convolution kernel 8x upsampling layer, the main circuit input terminal, and the connection point constitute the input terminal of the upsampling module; The output of the convolutional kernel is upsampled by 4 times and then connected to the other input of the first fusion layer. The output of the 8x upsampling layer and the output of the main path are respectively connected to the two inputs of the second fusion layer. The output of the second fusion layer constitutes the output of the upsampling module. This forms a multi-level feature pyramid, which enhances the ability to reconstruct details at different scales, reduces the network burden, and enhances the network's expressiveness. It can effectively restore details in the image and, compared with traditional triple convolutional upsampling, can effectively capture key structural information.

[0066] like Figure 2As shown, the specific design of the improved DDIM diffusion probability model includes a noise extraction layer, a splicing layer, and a first... Convolutional layer, downsampling encoder group, upsampling decoder group, second The convolutional layer has an input terminal of the noise extraction layer connected to one input terminal of the concatenation layer, with the connection point forming the input terminal of the improved DDIM diffusion probability model. The output terminal of the noise extraction layer is connected to the other input terminal of the concatenation layer. The noise extraction layer is used to extract the corresponding noise map from the feature map output by the pre-EDSR network. The output terminal of the concatenation layer is connected to the first... The input of the convolutional layer, the concatenation layer is used to concatenate the feature map output by the pre-EDSR network with the corresponding noise map output by the noise extraction layer, and the output feature concatenation map is obtained; first The output of the convolutional layer is sequentially connected in series with the downsampled encoding group, the upsampled decoding group, and the second... Convolutional layer, consisting of the second The output of the convolutional layer constitutes the output of the improved DDIM diffusion probability model, and a skip connection is established between the downsampled coding group and the upsampled decoding group.

[0067] In practical applications, such as Figure 2 As shown, the specific design of the upsampling decoding group includes a predetermined number of decoding layers connected in series from the input end to the output end. The input end of the first decoding layer in sequence constitutes the input end of the upsampling decoding group, and the output end of the last decoding layer in sequence constitutes the output end of the upsampling decoding group. The structures of each decoding layer are the same, and each decoding layer includes an upsampling decoding layer and a third fusion layer. The input end of the upsampling decoding layer in the decoding layer constitutes the input end of the decoding layer, and the output end of the upsampling decoding layer is connected to one of the input ends of the corresponding third fusion layer. The output end of the third fusion layer constitutes the output end of the decoding layer.

[0068] The specific design of the downsampling coding group includes sequentially connected downsampling coding layers from the input to the output. The number of downsampling coding layers is equal to the number of decoding layers in the upsampling decoding group. The input of the first downsampling coding layer in sequence constitutes the input of the downsampling coding group, and the output of the last downsampling coding layer in sequence constitutes the output of the downsampling coding group.

[0069] In the application of the downsampling coding group, the input is composed of a 5-channel low-resolution image upsampled and a 5-channel noisy image concatenated to form a 10-channel input. The number of channels is expanded to 32 dimensions through 3x3 convolution while keeping the spatial resolution of 256x256 unchanged. The downsampling coding group contains 4 downsampling coding layers, with the number of channels increasing sequentially from 32 to 64, 128, 256, and 512 dimensions.

[0070] In the application of the upsampling decoding group, the upsampling decoding group contains 4 decoding layers. With skip connections, transposed convolution is used to achieve 2x upsampling, reducing the number of channels from 512 to 256, 128, 64, and 32 dimensions.

[0071] like Figure 2 As shown, the upsampling decoding group is sequentially arranged from the input to the output end. In the third fusion layer of the decoding layer, the other input of the downsampled coding group is sequentially connected from the input to the output direction. The input skip connections of each downsampling coding layer are used to learn the residual mapping from the first resolution to the second resolution. Indicates the number of decoding layers in the upsampled decoding group. Indicates 1 to Integers.

[0072] In practical applications, the various downsampling coding layers and the various upsampling decoding layers, such as Figure 2 As shown, sampling operations are performed according to the preset time step T.

[0073] like Figure 3 As shown, the structures of each downsampling coding layer are identical. Specifically, each downsampling coding layer includes a fourth fusion layer, an SE self-attention layer, and a preset stride. The system consists of a stride convolutional layer and two branches. The first branch, from the input to the output, comprises a dilated convolutional layer, a normalization layer, and a SiLU activation layer connected in series. The kernel size of the dilated convolutional layer is [missing information]. The dilated convolutional layer, with a scaling factor of 2, forms the input of the first branch. The application of the dilated convolutional layer expands the receptive field. The output of the SiLU activation layer forms the output of the first branch. The second branch, from input to output, includes sequentially cascaded... Convolutional layers, normalization layers, and SiLU activation layers, among which, The input of the convolutional layer forms the input of the second branch, and the output of the SiLU activation layer forms the output of the second branch. The input of the first branch is connected to the input of the second branch, and the connection point forms the input of the downsampling coding layer. The output of the first branch is connected to the output of the second branch, and the connection point is connected to the input of the fourth fusion layer. The output of the fourth fusion layer is connected in series with the SE after the attention layer. The input end of the stride convolutional layer, The output of the stride convolutional layer constitutes the output of the downsampling coding layer.

[0074] like Figure 4 As shown, the structures of each upsampling decoding layer are identical. Specifically, each upsampling decoding layer, from input to output, comprises sequentially connected components. Convolutional layer, normalization layer, SiLU activation layer, fifth fusion layer Convolutional layer, normalization layer, SiLU activation layer, sixth fusion layer, SE self-attention layer, Upsampling convolutional layers, where the first one is in sequence The input of the convolutional layer is connected to the other input of the fifth fusion layer, and the connection point forms the input of the upsampling decoding layer. The output of the fifth fusion layer is simultaneously connected to the other input of the sixth fusion layer. The output of the upsampling convolutional layer constitutes the output of the upsampling decoding layer.

[0075] Step D. Based on each master sample, take the channel images corresponding to the first resolution remote sensing image in the master sample as input and the channel images corresponding to the second resolution remote sensing image in the master sample as output, train the presampled diffusion probability super-resolution reconstruction model ED-DDIM to obtain the trained model, which is the super-resolution reconstruction model.

[0076] Regarding the training of the presampled diffusion probability super-resolution reconstruction model ED-DDIM, the predicted label and the real label corresponding to the image pixel position are combined according to the preset weights. The peak signal-to-noise ratio PSNR and structural similarity SSIM obtained by the following formula are weighted and calculated. The quality of model application is evaluated by the weighted result.

[0077] (1);

[0078] (2);

[0079] (3);

[0080] (4);

[0081] (5);

[0082] (6);

[0083] (7);

[0084] (8);

[0085] in, and These represent the height and width of the image processed by the presampled diffusion probability super-resolution reconstruction model ED-DDIM, respectively. and These represent the pixel positions in the image. Predicted labels and true labels , , , This indicates a preset constant value, and , L represents the dynamic range of image pixel values, L=2 bits per pixel -1, bits per pixel, indicates the number of bits per pixel in the image. This represents the number of bits per pixel in the image. This represents the mean of the predicted labels for pixel locations in the image. This represents the mean of the true labels for pixel locations in the image. This represents the variance of the predicted labels for pixel locations in the image. This represents the variance of the true labels at pixel locations in an image. This represents the covariance between the predicted label and the true label at the pixel location in the image.

[0086] In applications, PSNR mainly assesses the similarity of images based on the difference in pixel values ​​between two images. The higher the PSNR value, the better the image quality. SSIM is based on the assumption that the human eye can extract structured information from images. It examines the similarity of images from three aspects: brightness, contrast, and structure. The higher the SSIM value, the better the image quality. The accuracy evaluation of actual application examples is shown in Table 1 below.

[0087] Table 1. Accuracy Evaluation in the Examples

[0088] Reconstruction methods PSNR SSIM Bicubic interpolation 29.76 0.8937 SwinR 31.85 0.9191 EDSR 31.80 0.9193 SRGAN 28.77 0.9075 ED-DDIM 33.88 0.9851

[0089] As shown in Table 1, the present invention improves the image reconstruction quality in the embodiments.

[0090] Based on steps A to D above, a super-resolution reconstruction model corresponding to the target region is obtained. Then, for the first-resolution remote sensing image to be analyzed corresponding to the target region, the following steps are performed. To the steps This enables the identification of water bodies in the remote sensing image to be analyzed at the first resolution for the target area.

[0091] step First, following step B, obtain the images of each channel to be analyzed corresponding to the first-resolution remote sensing image to be analyzed. Then, apply the super-resolution reconstruction model to obtain the images of each channel to be analyzed at the second resolution corresponding to the first-resolution remote sensing image to be analyzed. Then proceed to step [further steps]. .

[0092] step For each channel image to be analyzed at the second resolution, a pre-trained water body recognition model is applied to obtain binary classification images of the remote sensing images of water body areas and non-water body areas restored by each channel image to be analyzed at the second resolution, thereby determining the water body areas in the first resolution remote sensing image to be analyzed for the target area.

[0093] In practical applications, the pre-trained water body recognition model is based on a random forest classification model. It takes the images of each channel at the second resolution as input and the binary classification images of the remote sensing images of water areas and non-water areas restored by the images of each channel at the second resolution as output, and is obtained through training.

[0094] The above technical solution includes steps A to D, and step... To the steps In practical applications, the design further incorporates image slicing, first executing step A to obtain each master sample, and then proceeding to step B.

[0095] Step B involves obtaining channel images for each of the first-resolution and second-resolution remote sensing images in each master sample, including preset channels such as the NDWI water index channel. Then, for each channel image corresponding to each remote sensing image in each master sample, slices are made according to preset pixel size and preset overlap rate to obtain slice images corresponding to each channel image. For example, PMS images are cropped into 256x256 slices with 16 pixels overlap between slices, and WFV images are cropped into 32x32 slices with 2 pixels overlap between slices. Then, a single subsample is constructed using the spatiotemporally synchronized slice images to obtain each subsample, and then proceeds to step C.

[0096] Based on step C, the presampled diffusion probability super-resolution reconstruction model ED-DDIM is constructed. In step D, based on each subsample, each slice image of different channels at the first resolution in the subsample is used as input, and each slice image of different channels at the second resolution in the subsample is used as output. The presampled diffusion probability super-resolution reconstruction model ED-DDIM is trained to obtain the trained model, which is used as the super-resolution reconstruction model.

[0097] Then, for the first-resolution remote sensing image to be analyzed corresponding to the target area, the following steps are performed. To the steps During the process, the steps First, following step B, obtain the corresponding slice images for each channel of the remote sensing image to be analyzed at the first resolution. Then, based on each spatial sub-region under the target region slice, apply a super-resolution reconstruction model to process the slice images for different channels within the same spatial sub-region under the first resolution remote sensing image to obtain the slice images for different channels of the corresponding spatial sub-region at the second resolution corresponding to the first resolution remote sensing image. Finally, following the inverse operation of step B, restore the slice images for different channels of each spatial sub-region at the second resolution to obtain the images for each channel of the remote sensing image to be analyzed at the second resolution corresponding to the first resolution remote sensing image, and then proceed to step [further steps]. The target area is determined by identifying the water body region in the first-resolution remote sensing image to be analyzed.

[0098] In practical applications, the above design scheme produces local images after super-resolution reconstruction, such as... Figure 5 As shown, the image reconstructed according to the design scheme better reconstructs and reveals the small rivers, and the rivers are extracted more completely, resulting in better extraction effects compared to WFV imagery. Figure 6 The image shown is the WFV image of the area to be analyzed and the water extraction results.

[0099] This invention constructs a pre-sampled diffusion probability super-resolution reconstruction model, ED-DDIM, which combines a cascaded pre-sampled super-resolution network (pre-EDSR) with an improved DDIM diffusion probability model. It incorporates multi-channel images, including the NDWI water index channel, into remote sensing imagery, fully utilizing the spatial features of water edges for model training. This results in a super-resolution reconstruction model that effectively restores image details and reduces distortion. Through a diffusion-iterative denoising mechanism combined with the multi-scale feature extraction capabilities of UNet skip connections, it achieves gradual reconstruction from low-resolution to high-resolution images. Furthermore, in practical applications, a pre-trained water body identification model is used to obtain binary classification images of water and non-water areas from the multi-channel images at high resolution, enabling water area identification and contributing to monitoring in increasingly changing environments and water resource protection in arid regions.

[0100] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images, characterized in that: Perform steps A through D to obtain the super-resolution reconstruction model corresponding to the target area. Then, for the first-resolution remote sensing image to be analyzed corresponding to the target area, perform the following steps... To the steps To achieve the identification of water bodies in the first-resolution remote sensing image of the target area; Step A. Obtain a preset number of spatiotemporally synchronized first-resolution remote sensing images and second-resolution remote sensing images corresponding to the target area, perform preprocessing and updates, then construct a single master sample using the spatiotemporally synchronized first-resolution remote sensing images and second-resolution remote sensing images, obtain each master sample, and proceed to Step B; wherein, the first resolution is lower than the second resolution. Step B. For the first-resolution remote sensing image and the second-resolution remote sensing image in each master sample, obtain the channel images corresponding to each preset channel, including the NDWI water index channel, and then proceed to step C. Step C. Construct the pre-sampling diffusion probability super-resolution reconstruction model ED-DDIM, which is a cascaded pre-sampling super-resolution network pre-EDSR and an improved DDIM diffusion probability model, and then proceed to step D; Step D. Based on each master sample, take the channel images corresponding to the first resolution remote sensing image in the master sample as input and the channel images corresponding to the second resolution remote sensing image in the master sample as output, train the presampled diffusion probability super-resolution reconstruction model ED-DDIM to obtain the trained model, which is used as the super-resolution reconstruction model. step First, following step B, obtain the images of each channel to be analyzed corresponding to the first-resolution remote sensing image to be analyzed. Then, apply the super-resolution reconstruction model to obtain the images of each channel to be analyzed at the second resolution corresponding to the first-resolution remote sensing image to be analyzed. Then proceed to step [further steps]. ; step For each channel image to be analyzed at the second resolution, a pre-trained water body recognition model is applied to obtain binary classification images of the remote sensing images of water body areas and non-water body areas restored by each channel image to be analyzed at the second resolution, thereby determining the water body areas in the first resolution remote sensing image to be analyzed for the target area.

2. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 1, characterized in that: In step A, based on the acquisition of a preset number of spatiotemporally synchronized 16m WFV remote sensing images of medium resolution GF-1 and 8m / 2m PMS remote sensing images of high resolution GF-1 corresponding to the target area, the following steps A1 to A3 are specifically executed for each set of spatiotemporally synchronized 16m WFV remote sensing images of medium resolution GF-1 and 8m / 2m PMS remote sensing images of high resolution GF-1 to achieve preprocessing update; Step A1. For the 16m WFV remote sensing image of medium resolution GF-1 and the 8m / 2m PMS remote sensing image of high resolution GF-1, respectively, perform radiometric calibration, atmospheric correction and orthorectification in sequence to complete the processing update, and then proceed to step A2. Step A2. Using the NNDiffuse tool, perform image fusion on the 8m PMS remote sensing image of the updated high-resolution GF-1 image processed in Step A1 and the 2m PMS remote sensing image of the updated high-resolution GF-1 image processed in Step A1 to obtain a fused 2m PMS remote sensing image, and then proceed to Step A3. Step A3. For the updated 16m WFV remote sensing image of medium resolution GF-1 processed in step A1 and the fused PMS remote sensing image, perform pixel registration to update and obtain the WFV remote sensing image and PMS remote sensing image. In step B, the preset channels include the NDWI water index channel, the blue band channel, the green band channel, the red band channel, and the near-infrared band channel.

3. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 1, characterized in that: In the presampled diffusion probability super-resolution reconstruction model ED-DDIM constructed in step C, the input of the presampled super-resolution network pre-EDSR constitutes the input of the presampled diffusion probability super-resolution reconstruction model ED-DDIM, the output of the presampled super-resolution network pre-EDSR is connected to the input of the improved DDIM diffusion probability model, and the output of the improved DDIM diffusion probability model constitutes the output of the improved DDIM diffusion probability model. The pre-EDSR pre-sampling super-resolution network consists of several components connected in series from the input to the output. Convolutional layers, residual modules, Convolutional layers, upsampling modules, Convolutional layers, where the first one in sequence The input of the convolutional layer forms the input of the pre-EDSR pre-sampling super-resolution network, the third one in sequence. The output of the convolutional layer constitutes the output of the pre-EDSR pre-sampling super-resolution network; the residual module consists of at least two cascaded residual blocks from input to output, wherein the input of the first residual block constitutes the input of the residual module, and the output of the last residual block constitutes the output of the residual module; each residual block has the same structure, and each residual block consists of cascaded residual blocks from input to output. Convolutional layers, ReLU activation function layers, The first convolutional layer in the residual block. The input of the convolutional layer forms the input of the residual block, which is the second input in sequence within the residual block. The output of the convolutional layer forms the output of the residual block; The improved DDIM diffusion probability model includes a noise extraction layer, a splicing layer, and a first... Convolutional layer, downsampling encoder group, upsampling decoder group, second The convolutional layer has an input terminal of the noise extraction layer connected to one input terminal of the concatenation layer, with the connection point forming the input terminal of the improved DDIM diffusion probability model. The output terminal of the noise extraction layer is connected to the other input terminal of the concatenation layer. The noise extraction layer is used to extract the corresponding noise map from the feature map output by the pre-EDSR network. The output terminal of the concatenation layer is connected to the first... The input of the convolutional layer, the concatenation layer is used to concatenate the feature map output by the pre-EDSR network with the corresponding noise map output by the noise extraction layer, and the output feature concatenation map is obtained; first The output of the convolutional layer is sequentially connected in series with the downsampled encoding group, the upsampled decoding group, and the second... Convolutional layer, consisting of the second The output of the convolutional layer constitutes the output of the improved DDIM diffusion probability model, and a skip connection is established between the downsampled coding group and the upsampled decoding group.

4. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 3, characterized in that: The upsampling module includes the main circuit and... Convolution kernel 4x upsampling layer and The convolutional kernel is an 8x upsampling layer, where the main path first connects two concatenated layers from the input to the output. The convolutional kernel is upsampled by 2 times, then passed through one of the inputs of the first fusion layer in series, and finally connected to a... The input of the convolutional kernel is twice that of the upsampling layer, where the first one in sequence... The input of the convolution kernel, which is twice the size of the upsampling layer, forms the input of the main circuit, and is the third in sequence. The output of the convolution kernel, which is twice the output of the upsampling layer, constitutes the output of the main circuit. The input of the convolution kernel is 4 times that of the upsampling layer. The input terminals of the convolution kernel 8x upsampling layer, the main circuit input terminal, and the connection point constitute the input terminal of the upsampling module; The output of the convolutional kernel is upsampled by 4 times and then connected to the other input of the first fusion layer. The output of the 8x upsampling layer and the output of the main circuit are respectively connected to the two inputs of the second fusion layer, and the output of the second fusion layer constitutes the output of the upsampling module.

5. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 3, characterized in that: The upsampling decoding group comprises a predetermined number of decoding layers connected in series from the input to the output. The input of the first decoding layer in sequence constitutes the input of the upsampling decoding group, and the output of the last decoding layer in sequence constitutes the output of the upsampling decoding group. Each decoding layer has the same structure, and each decoding layer includes an upsampling decoding layer and a third fusion layer. The input of the upsampling decoding layer in the decoding layer constitutes the input of the decoding layer, and the output of the upsampling decoding layer is connected to one of the inputs of the corresponding third fusion layer. The output of the third fusion layer constitutes the output of the decoding layer. The downsampling coding group consists of sequentially connected downsampling coding layers from input to output. The number of downsampling coding layers is equal to the number of decoding layers in the upsampling decoding group. The input of the first sequential downsampling coding layer constitutes the input of the downsampling coding group, and the output of the last sequential downsampling coding layer constitutes the output of the downsampling coding group. The upsampling decoder group is ordered from input to output in the following order: In the third fusion layer of the decoding layer, the other input of the downsampled coding group is sequentially connected from the input to the output direction. The input skip connections of each downsampling coding layer are as follows: Indicates the number of decoding layers in the upsampled decoding group. Indicates 1 to Integers; Each downsampling encoding layer and each upsampling decoding layer performs sampling operations according to a preset time step T.

6. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 5, characterized in that: The structures of each downsampling coding layer are identical, and each downsampling coding layer includes a fourth fusion layer, an SE self-attention layer, and a preset step size. The system consists of a stride convolutional layer and two branches. The first branch, from the input to the output, comprises a dilated convolutional layer, a normalization layer, and a SiLU activation layer connected in series. The kernel size of the dilated convolutional layer is [missing information]. The expansion factor is 2. The input of the dilated convolutional layer forms the input of the first branch, and the output of the SiLU activation layer forms the output of the first branch. The second branch consists of sequentially cascaded layers from the input to the output. Convolutional layers, normalization layers, and SiLU activation layers, among which, The input of the convolutional layer forms the input of the second branch, and the output of the SiLU activation layer forms the output of the second branch. The input of the first branch is connected to the input of the second branch, and the connection point forms the input of the downsampling coding layer. The output of the first branch is connected to the output of the second branch, and the connection point is connected to the input of the fourth fusion layer. The output of the fourth fusion layer is connected in series with the SE after the attention layer. The input end of the stride convolutional layer, The output of the stride convolutional layer constitutes the output of the downsampling coding layer.

7. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 5, characterized in that: The structures of each upsampling decoding layer are identical, and each upsampling decoding layer consists of sequentially connected components from the input to the output. Convolutional layer, normalization layer, SiLU activation layer, fifth fusion layer Convolutional layer, normalization layer, SiLU activation layer, sixth fusion layer, SE self-attention layer, Upsampling convolutional layers, where the first one is in sequence The input of the convolutional layer is connected to the other input of the fifth fusion layer, and the connection point forms the input of the upsampling decoding layer. The output of the fifth fusion layer is simultaneously connected to the other input of the sixth fusion layer. The output of the upsampling convolutional layer constitutes the output of the upsampling decoding layer.

8. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 1, characterized in that: Step B further includes slicing the channel images corresponding to each remote sensing image in each master sample according to a preset pixel size and a preset overlap rate between slices to obtain each slice image corresponding to the channel image. Then, a single subsample is constructed using the spatiotemporally synchronized slice images to obtain each subsample. In step D, based on each subsample, the slice images of different channels at the first resolution in the subsample are taken as input, and the slice images of different channels at the second resolution in the subsample are taken as output. The presampled diffusion probability super-resolution reconstruction model ED-DDIM is trained to obtain the trained model, which is used as the super-resolution reconstruction model. The steps First, following step B, obtain the corresponding slice images for each channel of the remote sensing image to be analyzed at the first resolution. Then, based on each spatial sub-region under the target region slice, apply a super-resolution reconstruction model to process the slice images for different channels within the same spatial sub-region under the first resolution remote sensing image to obtain the slice images for different channels of the corresponding spatial sub-region at the second resolution corresponding to the first resolution remote sensing image. Finally, following the inverse operation of step B, restore the slice images for different channels of each spatial sub-region at the second resolution to obtain the images for each channel of the remote sensing image to be analyzed at the second resolution corresponding to the first resolution remote sensing image, and then proceed to step [further steps]. .

9. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 1, characterized in that: The steps The pre-trained water body identification model is based on a random forest classification model. It takes the images of each channel at the second resolution as input and the binary classification images of the remote sensing images of water areas and non-water areas restored by the images of each channel at the second resolution as output, and is obtained through training.

10. The method for identifying small water bodies based on super-resolution reconstruction of satellite remote sensing images according to claim 1, characterized in that: In step D, during the training of the presampled diffusion probability super-resolution reconstruction model ED-DDIM, the predicted label and the real label corresponding to the image pixel position are combined according to a preset weight. The peak signal-to-noise ratio PSNR and structural similarity SSIM obtained by the following formula are weighted and calculated. The weighted result is used to evaluate the quality of model application. （1）； （2）； （3）； （4）； （5）； （6）； （7）； （8）； in, and These represent the height and width of the image processed by the presampled diffusion probability super-resolution reconstruction model ED-DDIM, respectively. and These represent the pixel positions in the image. Predicted labels and true labels , , , This indicates a preset constant value, and , L represents the dynamic range of image pixel values, L=2 bits per pixel -1, bits per pixel, indicates the number of bits per pixel in the image. This represents the number of bits per pixel in the image. This represents the mean of the predicted labels for pixel locations in the image. This represents the mean of the true labels for pixel locations in the image. This represents the variance of the predicted labels for pixel locations in the image. This represents the variance of the true labels at pixel locations in an image. This represents the covariance between the predicted label and the true label at the pixel location in the image.

Images