Deep residual network-based geostationary satellite image super-resolution method and system

Abstract

The invention belongs to the technical field of satellite image super-resolution, and discloses a geostationary satellite image super-resolution method and system based on a deep residual network, and the method comprises the following steps: obtaining geostationary satellite image data which comprises a plurality of low-resolution and high-resolution images of different wavebands; performing up-sampling on the low-resolution image to obtain the same size as the high-resolution image by using a bicubic interpolation method so as to match images with different resolutions; cascading the up-sampled low-resolution image and the up-sampled high-resolution image to serve as the input of a deep residual network; performing feature extraction on the cascading result by using a plurality of depth residual blocks so as to obtain deep features; and combining the extracted deep features with the up-sampled low-resolution image in a residual information mode to obtain a super-resolution image. According to the method, super-resolution of all low-resolution images is unified, the problem of non-uniform resolution of geostationary satellite image data is effectively solved, and the reliability and utilization rate of satellite data are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite image super-resolution, and particularly relates to a method and system for super-resolving geostationary satellite images based on a deep residual network. Background Art

[0002] Thanks to the rapid development of geostationary orbit satellite technology, a new generation of meteorological satellites has formed a global observation network. These satellites are equipped with multi-spectral imagers and have the ability to cover a wide spectrum, and can obtain images of dozens of bands from visible light to infrared. In addition, the high-frequency observation data obtained (at intervals of 10-15 minutes) plays a key role in the field of meteorological monitoring, providing important support for earth observation tasks such as weather forecasting, forest fire warning, and typhoon path tracking. Despite these advantages, there are significant differences in the spatial resolution of satellite images in different bands. Specifically, the visible light band images have high spatial resolution, while the spatial resolution of infrared band images is usually 2 to 8 times lower than that of the visible light band. Taking the Fengyun-4B satellite of China as an example, it has ultra-high resolution imaging of 0.5 km in the visible light band, but due to the physical limitations of optical sensors, the resolution of its infrared channel drops to 4 km (a difference of 8 times).

[0003] The uneven spatial resolution of geostationary satellite images restricts the effectiveness and utilization rate of satellite observation data to a certain extent, especially for infrared band images. Therefore, how to super-resolution reconstruct low-resolution infrared band images to the resolution level of visible light band images so that all band images have the highest resolution has become a key problem to be solved urgently. In addition, although there are differences in resolution between different band images, how to effectively extract cross-band spectral information and combine the spatial features of high-resolution band images and transfer them to low-resolution images will be the core factor determining the super-resolution effect. Summary of the Invention

[0004] The main purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, and provide a method and system for super-resolving geostationary satellite images based on a deep residual network, which extracts the spectral features between different band images and the spatial features of high-resolution band images, and transfers the two features to low-resolution images, effectively restoring the missing image details and solving the technical problem of super-resolving all low-resolution images to the highest resolution.

[0005] The present invention is implemented as follows. A method for super-resolving geostationary satellite images based on a deep residual network, the method specifically includes:

[0006] S1. Obtain geostationary satellite image data, including multiple low-resolution and high-resolution images of different bands;

[0007] S2. Use bicubic interpolation to upsample the low-resolution image to the same size as the high-resolution image to match images of different resolutions;

[0008] S3. Concatenate the upsampled low-resolution image and the high-resolution image as the input to the deep residual network;

[0009] S4. Use multiple deep residual blocks to extract features from the concatenated result to obtain deep features;

[0010] S5. Combine the extracted deep features with the upsampled low-resolution image in the form of residual information to obtain a super-resolution image.

[0011] Further, S1 includes:

[0012] Obtain multiple satellite images of the same observation area collected by a geostationary satellite in the same time period. The bands involved in these images are visible light, near-infrared, short-wave infrared, mid-wave infrared, and long-wave infrared, and the resolutions of the images are uneven, showing that only a few short-wavelength images are of high resolution, and most of the remaining long-wavelength images are of low resolution.

[0013] Further, S2 includes:

[0014] If the size of the high-resolution image is W×H and the size of the low-resolution image is w×h, the bicubic interpolation method enlarges the low-resolution image to W×H to match the size of the high-resolution image.

[0015] Further, S3 includes:

[0016] Assume that there are N and n high-resolution and low-resolution images respectively. The high-resolution image set is represented as The set of upsampled low-resolution images is represented as The concatenated result of the high-resolution and low-resolution images is represented as At this time, the concatenated result C contains rich band information and high-resolution spatial details. In order to extract useful information in C to improve the super-resolution effect, C is used as the input to the deep residual network, and the final output result after super-resolution is output

[0017] Further, S4 includes:

[0018] The deep residual network F is composed of multiple deep residual blocks F b The input of the latter residual block is the output of the previous residual block. The deep residual network:

[0019]

[0020] Among them, I represents the deep features extracted after passing through multiple deep residual blocks F b M represents the number of deep residual blocks F b .

[0021] By stacking multiple residual blocks, features that fuse significant band information and high-definition texture details are progressively extracted, and the last residual block outputs the final deep features.

[0022] Furthermore, the deep residual block F b is composed of multiple deep residual groups F g and skip connections:

[0023]

[0024] Among them, O represents the input of the deep residual block F b K represents the number of deep residual groups F g , represents element-wise addition.

[0025] Furthermore, the deep residual group F g is composed of two consecutive convolutional layers, a Relu activation function, and a skip connection:

[0026]

[0027] Among them, L represents the input of the deep residual group F g F relu represents the Relu activation function, and F conv represents the convolutional layer.

[0028] Furthermore, the S5 includes:

[0029] By introducing a skip connection, the extracted deep features are used as residual information and added to the original upsampled low-resolution image to restore various details and textures missing in the original image, obtaining a super-resolution image such that all images of the geostationary satellite have the highest resolution:

[0030]

[0031] Another object of the present invention is to provide a geostationary satellite image super-resolution system based on the deep residual network of the geostationary satellite image super-resolution method based on the deep residual network. The system specifically includes:

[0032] A data acquisition module that acquires geostationary satellite image data, including multiple low-resolution and high-resolution images of different bands;

[0033] An image matching module, connected to the data acquisition module, uses bicubic interpolation to upsample the low-resolution image to the same size as the high-resolution image to match images of different resolutions;

[0034] A cascading module, connected to the image matching module, cascades the upsampled low-resolution image and the high-resolution image as the input to the deep residual network;

[0035] A feature extraction module, connected to the cascading module, uses multiple deep residual blocks to extract features from the cascaded result to obtain deep features;

[0036] A combination module, connected to the feature extraction module, combines the extracted deep features with the upsampled low-resolution image in the form of residual information to obtain a super-resolution image.

[0037] Another object of the present invention is to provide a computer device, the computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the super-resolution method of geostationary satellite images of the deep residual network.

[0038] Combined with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are:

[0039] The present invention proposes a super-resolution method for satellite images that combines band spectrum and spatial information. By jointly analyzing multi-band images obtained from geostationary meteorological satellites, the spectral correlation and spatial structure features between bands are fully exploited to obtain and fuse the hidden details in the low-resolution bands in a more refined manner. Specifically, this method uses the non-linear mapping ability of the deep residual network (ResNet) to layer by layer extract the deep features of the spectrum and space mixture from the low-resolution image to obtain a more abundant detailed representation.

[0040] In the process of feature extraction and transmission, this method adopts a residual connection mechanism (Residual Connection), and gradually feeds back the deep space-spectrum mixed features extracted in the high-level network to the low-resolution input image in the form of residuals. This way can effectively solve the problem of gradient disappearance in the training process of deep neural networks, strengthen the network's ability to recover the missing information in the low-resolution image, gradually restore the high-frequency details lost due to imaging conditions in the image, and significantly enhance the clarity and visual quality of satellite images.

[0041] This method unifies the super-resolution of each band image of geostationary satellites to the highest spatial resolution level. Specifically, it improves the spatial resolution of infrared band images to the same scale as that of visible light band images. This not only effectively alleviates the bottleneck of the observation ability caused by the uneven spatial resolution of the observation images of Fengyun meteorological satellites in China at present, but also improves the consistency of cross-band images and the reliability of data utilization, which helps the standardized processing and unified management of satellite remote sensing data.

[0042] During the training process of the deep residual network model, the end-to-end training method is adopted, and evaluation metrics such as pixel-based loss functions, such as peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM), are used to drive the optimization of model parameters to ensure that the super-resolution images have the consistency and visual authenticity of real image features. Through this training strategy, it is ensured that the deep features extracted by the network can accurately restore the key spatial details in satellite images of different bands, effectively improving the accuracy of super-resolution reconstructed images.

[0043] The super-resolution satellite images generated by the method of the present invention can significantly improve the refinement and accuracy of meteorological monitoring and forecasting work, especially in the fields of severe convective weather, typhoon prediction and heavy rain warning. High-resolution infrared band images can more accurately describe the subtle changes in the cloud top temperature field, cloud structure and meteorological elements, effectively improving the quality of the input data of subsequent weather forecasting models, and further enhancing the ability of the forecasting system to capture extreme weather events and the warning timeliness.

[0044] The present invention fills the gap in the field of super-resolution technology of geostationary satellites at home and abroad. It first proposes a multi-band image super-resolution method based on the fusion of spectral and spatial features of deep residual networks, realizes the unification of the spatial resolution of infrared band images to the visible light band, provides a simple, efficient and practical solution, effectively improves the utilization efficiency and reliability of satellite remote sensing data, and lays a solid foundation for subsequent related research and technological progress in the meteorological field. Description of the Drawings

[0045] Figure 1 is the flow chart of the super-resolution method for geostationary satellite images based on deep residual networks provided by the embodiment of the present invention;

[0046] Figure 2 is the structural diagram of the deep residual network provided by the embodiment of the present invention;

[0047] Figure 3 is the structural diagram of the deep residual group under the deep residual network provided by the embodiment of the present invention;

[0048] Figure 4It is a qualitative test chart before and after the super-resolution of the 4km band image of the deep residual network provided by the embodiment of the present invention to 0.5km. Detailed implementation manners

[0049] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0050] Figure 1 It is a flowchart of a super-resolution method for geostationary satellite images based on a deep residual network proposed by the present invention. The specific steps include:

[0051] First step, obtain multiple satellite images of the same observation area collected by a geostationary satellite within the same time period. The bands involved in these images are visible light, near-infrared, short-wave infrared, mid-wave infrared, and long-wave infrared, and the resolutions of the images are uneven, showing that only a few short-wavelength images are of high resolution, and most of the remaining long-wavelength images are of low resolution.

[0052] Second step, if the size of the high-resolution image is W×H and the size of the low-resolution image is w×h, the bicubic interpolation method is used to enlarge the low-resolution image to W×H to match the size of the high-resolution image.

[0053] Third step, assume that there are N and n high-resolution and low-resolution images respectively. The high-resolution image set is represented as The upsampled low-resolution image set is represented as The concatenation result of the high-resolution and low-resolution images is represented as At this time, the concatenation result C contains rich band information and high-resolution spatial details. In order to extract useful information in C to improve the super-resolution effect, C is used as the input of the deep residual network. The structure of the deep residual network is as Figure 2 shown, and finally the output result after super-resolution is output

[0054] Fourth step, the deep residual network F is composed of multiple deep residual blocks F b The input of the latter residual block is the output of the previous residual block. The described deep residual network:

[0055]

[0056] Among them, I represents the deep features extracted after passing through multiple deep residual blocks F b M represents the number of deep residual blocks F b

[0057] ​By stacking multiple residual blocks, features that integrate significant band information and high-definition texture details are progressively extracted, and the last residual block outputs the final deep features.

[0058] The depth residual block F b consists of multiple depth residual groups F g and skip connections:

[0059]

[0060] where O represents the input of the depth residual block F b and K represents the number of depth residual groups F g . represents element-wise addition.

[0061] The depth residual group F g consists of two consecutive convolutional layers, a Relu activation function, and a skip connection, as Figure 3 shown:

[0062]

[0063] where L represents the input of the depth residual group F g and F relu represents the Relu activation function, and F conv represents the convolutional layer.

[0064] In the fifth step, by introducing skip connections, the extracted deep features are used as residual information and added to the original upsampled low-resolution image to restore various details and textures missing in the original image, obtaining a super-resolution image such that all images of this geostationary satellite have the highest resolution:

[0065]

[0066] In the present invention, by introducing the bicubic interpolation method to preprocess the low-resolution image, an initial feature map with a size matching that of the high-resolution image is obtained. The mathematical significance of this interpolation strategy is that through a continuous and smooth cubic polynomial function, the obvious pixel staircase effect and detail loss generated by traditional interpolation methods are effectively suppressed, providing more accurate initial spatial information for the subsequent input of the deep residual network, thereby significantly improving the effectiveness and stability of the subsequent feature extraction of the network.

[0067] At the model input level, the present invention adopts a high-low resolution image cascaded fusion mechanism, that is, the high-resolution image set and the upsampled low-resolution image set are cascaded in the spatial dimension to form a unified input tensor. This operation not only increases the information content of the input data, but also fully preserves the rich band information and fine spatial details in the image. After the feature tensor after cascaded fusion is input into the deep residual network, it can significantly improve the network's ability to distinguish the differences between bands and image textures, and promote the collaborative recovery of the spatial information and spectral details of the super-resolution image.

[0068] The deep residual network designed by the present invention is composed of multiple deep residual blocks and residual groups. Inside each residual block, through continuous convolutional operations and ReLU non-linear activation functions, local feature extraction and enhancement are performed on the input features. Through this multi-level stacking method, each residual block gradually captures and enhances the subtle differences and deep feature expression capabilities in the input data, greatly improving the comprehensiveness, richness of feature extraction and the model generalization ability, thus effectively reconstructing the detailed features of the image.

[0069] Finally, the present invention introduces a residual skip connection in the model structure, taking the deep features extracted by the deep residual network as residual information and adding them to the original upsampled low-resolution image to realize the reconstruction process of the super-resolution image.

[0070] The mathematical significance of the residual skip connection is to avoid information loss during the feature transfer process in the network, and to achieve efficient feature backflow and enhancement, thereby significantly improving the image reconstruction effect, restoring a large number of high-frequency texture details, and ensuring that all geostationary satellite images can reach a unified and highest spatial resolution standard.

[0071] As Figure 2 shown, the overall structure of the deep residual network described in the present invention is formed by connecting multiple deep residual groups (ResidualGroup) in series. Each residual group contains several convolutional layers, batch normalization layers and non-linear activation layers, which are used to fully explore the spatial and spectral features of the multi-band image. At the input end of the network, the low-resolution image after bicubic interpolation is cascaded with the corresponding high-resolution image, and the end-to-end training method is used to realize the fusion extraction of the features of images with different resolutions.

[0072] Figure 3 This is the specific structure of the deep residual block inside the deep residual group. After the convolutional operation in each residual block, the direct connection path of the input signal is retained to solve the problems of gradient disappearance and information loss that may occur in the deep network. Through this residual connection method, the network can extract multi-scale features at a deeper level, enhance the ability to capture the difference information between high- and low-resolution images, and thus improve the accuracy and stability of super-resolution reconstruction.

[0073] At the network output end, the system fuses the residual information extracted by the deep residual block with the interpolated low-resolution image to generate a high-resolution prediction result. This residual fusion strategy can effectively utilize the prior knowledge of high-resolution images in terms of texture, edges, and other detailed information, compensating for the lack of details caused by insufficient resolution of low-resolution images, and significantly improving the reconstructed image in terms of visual effects and quantitative indicators.

[0074] Figure 4 It shows the qualitative comparison results when the embodiment of the present invention super-resolves the 4km resolution band data to 0.5km. It can be seen that the details of the image reconstructed by the deep residual network method of the present invention are presented more clearly in terms of target edges, cloud structures, and surface features, etc., and the visual difference from the real high-resolution image is significantly reduced, verifying the effectiveness and reliability of this network structure in the application of super-resolution of multi-band images of geostationary satellites.

[0075] To verify the feasibility of the method for super-resolving geostationary satellite images based on the deep residual network of the present invention, the following experiments were carried out:

[0076] The full-disk images of China's Fengyun-4B satellite were used for the experiment. The Fengyun-4B satellite has a total of 15 bands, and the resolutions of the bands are not uniform. One visible light band is 0.5km, two visible light bands are 1km, five infrared bands are 2km, and the remaining seven infrared bands are 4km. Three deep residual networks were respectively trained to super-resolve all bands of 1km, 2km, and 4km to 0.5km, and the only 0.5km band image was used as the high-resolution image A.

[0077] The Fengyun-4B satellite data at 3:00 UTC every day from January 2024 to June 2024 was selected, and the data was divided into non-overlapping training sets and test sets according to a ratio of 8:2. Since the full-disk images of the Fengyun-4B satellite are too large and the video memory of the graphics card is limited, it is not suitable to input the entire image into the neural network. Therefore, each low-resolution image was randomly divided into 50,000 images of 32×32 pixel points, and the high-resolution image was the same. Considering the lack of reference images, all the cut original images were downsampled according to the super-resolution multiple, that is, the 1km image was downsampled by 2 times, the 2km image was downsampled by 4 times, and the 4km image was downsampled by 8 times. The downsampled images were used as training data, and the original images were used as reference images to calculate the loss function.

[0078] The number of deep residual blocks and deep residual groups in the deep residual network was both set to 5, and the convolution kernel of each convolutional layer was 3×3 with a stride of 1. The training set data was input into the constructed deep residual network for training. Adam was used as the network optimizer, and 100 epochs were trained with the learning rate set to 1×10 -5。The loss function is selected as the absolute error loss function. After the model is trained, the test data is then input into the network for testing.

[0079] The testing is divided into quantitative testing and qualitative testing. Under quantitative testing, the root mean square error (RMSE) and peak signal-to-noise ratio (PSNR) of the image pixel values are selected as evaluation metrics. The root mean square error is the square root of the mean square error (MSE), which is used to measure the average error between the reconstructed image after super-resolution and the original reference image. It reflects the degree of difference between pixel values. The calculation formula for the root mean square error is:

[0080]

[0081] where n is the total number of pixels in the image, and D1 and D2 are the corresponding pixel values of the reconstructed image and the reference image respectively. The root mean square error is more sensitive to larger errors because it squares the errors. The lower the RMSE value, the smaller the difference between the reconstructed image and the reference image.

[0082] The peak signal-to-noise ratio is a metric for measuring image quality, which evaluates the image quality by comparing the maximum possible signal value and the error value between the reconstructed image and the reference image. The calculation formula for the peak signal-to-noise ratio is:

[0083]

[0084] where MAX is the maximum possible value of the image pixel values, and MSE is the mean square error. The unit of the peak signal-to-noise ratio is decibels (dB), and the higher the value, the better the quality of the reconstructed image.

[0085] By comparing with the traditional bicubic interpolation and the deep learning method Dsen2, the method proposed in the present invention has the best performance, as shown in the following table (all results are averaged).

[0086]

[0087] Under qualitative testing, the images before and after super-resolving the 4km band image to 0.5km are compared. As Figure 4 shown, the details of the image become richer and the image becomes clearer after super-resolution.

[0088] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated designed hardware. Those of ordinary skill in the art can understand that the above devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code is provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and their modules of the present invention can be implemented by hardware circuits of programmable hardware devices such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above hardware circuits and software such as firmware.

[0089] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be covered by the protection scope of the present invention.

Claims

1. A super-resolution method for geostationary satellite images based on a deep residual network, characterized in that The method includes: S1. Obtain geostationary satellite image data, including multiple low-resolution and high-resolution images in different bands; S2. Use bicubic interpolation to upsample the low-resolution image to the same size as the high-resolution image to match images with different resolutions; S3. Concatenate the upsampled low-resolution image and the high-resolution image as the input to the deep residual network; S4. Use multiple deep residual blocks to extract features from the concatenated result to obtain deep features; S5. Combine the extracted deep features with the upsampled low-resolution image in the form of residual information to obtain a super-resolution image.

2. The super-resolution method for geostationary satellite images based on a deep residual network according to claim 1, characterized in that The S1 includes: Obtain multiple satellite images of the same observation area collected by a geostationary satellite within the same time period. The bands involved in these images are visible light, near-infrared, short-wave infrared, mid-wave infrared, and long-wave infrared, and the resolutions of the images are uneven, with only a few short-wavelength images being high-resolution and most of the remaining long-wavelength images being low-resolution.

3. The method for super-resolution of geostationary satellite images based on a deep residual network according to claim 1, wherein The S2 includes: If the size of the high-resolution image is W×H and the size of the low-resolution image is w×h, the bicubic interpolation method enlarges the low-resolution image to W×H to match the size of the high-resolution image.

4. The super-resolution method for geostationary satellite images based on the deep residual network according to claim 1, wherein The S3 includes: Suppose there are N and n high-resolution and low-resolution images respectively, and the high-resolution image set is denoted as The upsampled low-resolution image set is denoted as The concatenation result of high-resolution and low-resolution images is denoted as At this time, the concatenation result C contains rich band information and high-resolution spatial details. To extract useful information from C to improve the super-resolution effect, C is used as the input of the deep residual network, and finally the output result after super-resolution is output 5. The super-resolution method for geostationary satellite images based on the deep residual network according to claim 1, wherein The S4 includes: The deep residual network F consists of multiple deep residual blocks F b The input of the subsequent residual block is the output of the previous residual block. The deep residual network described above: Among them, I represents the deep features extracted after passing through multiple depth residual blocks F b M represents the number of depth residual blocks F b ; By stacking multiple residual blocks, progressively extract features that integrate significant band information and high-definition texture details, and the last residual block outputs the final deep features.

6. The super-resolution method for geostationary satellite images based on the deep residual network according to claim 5, wherein The depth residual block F described above b consists of multiple depth residual groups F g and skip connections: Among them, O represents the input of the depth residual block F b , K represents the number of depth residual groups F g . denotes element-wise addition.

7. The method for super-resolution of geostationary satellite images based on a deep residual network according to claim 6, wherein The described deep residual group F g , which consists of two consecutive convolutional layers, a Relu activation function, and a skip connection: Among them, L represents the input of the depth residual group F g , F relu represents the Relu activation function, and F conv represents the convolutional layer.

8. The method for super-resolution of geostationary satellite images based on a deep residual network according to claim 1, wherein The S5 includes: By introducing skip connections, the extracted deep features are used as residual information and added to the original upsampled low-resolution image to restore various details and textures missing in the original image and obtain a super-resolution image so that all images of this geostationary satellite have the highest resolution:

9. The geostationary satellite image super-resolution system of the deep residual network for the geostationary satellite image super-resolution method according to any one of claims 1-8, characterized in that, The system specifically includes: A data acquisition module that obtains geostationary satellite image data, including multiple low-resolution and high-resolution images in different bands; An image matching module, connected to the data acquisition module, uses bicubic interpolation to upsample the low-resolution image to the same size as the high-resolution image to match images with different resolutions; A concatenation module, connected to the image matching module, concatenates the upsampled low-resolution image and the high-resolution image as the input to the deep residual network; A feature extraction module, connected to the concatenation module, uses multiple deep residual blocks to extract features from the concatenated result to obtain deep features; A combination module, connected to the feature extraction module, combines the extracted deep features with the upsampled low-resolution image in the form of residual information to obtain a super-resolution image.

10. A computer device, characterized in that, The computer device includes a memory and a processor. When the computer program stored in the memory is executed by the processor, the processor executes the steps of the method for super-resolving geostationary satellite images of the deep residual network according to any one of claims 1-8.

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