A multi-dimensional raster data compression method, system, device and storage medium

Abstract

The application relates to a multi-dimensional grid data compression method, system, device and storage medium, and relates to the field of data processing. The method is based on a Transformer super-resolution network, wherein the method comprises the following steps: after original floating-point scientific data is mapped into a grid image sequence, spatial downsampling preprocessing is performed; the down-sampled image sequence is subjected to time series compression coding based on inter-frame prediction to remove time redundancy; in the decoding stage, a super-resolution reconstruction model is used to restore the resolution of the compressed image; further, the error between the reconstructed data and the original data is calculated, the pixel points with errors exceeding a preset threshold are identified, and the corresponding pixel values are replaced with the original data values; meanwhile, the spatial positions and error information of the pixel points are subjected to entropy coding and stored together with the compressed data. The technical effect of the application is that the data compression rate is significantly improved, the reconstruction error is strictly constrained, and the application is suitable for the storage and transmission of remote sensing and scientific calculation data with high precision requirements.

Description

Technical Field

[0001] This application relates to the fields of data processing and remote sensing imagery, and in particular to a method, system, device, and storage medium for multidimensional raster data compression. Background Technology

[0002] Multidimensional raster data refers to a collection of scientific data that is highly correlated in both spatial and temporal dimensions, and is widely used in fields such as remote sensing monitoring, numerical weather prediction, and ocean dynamic simulation. With the improvement of remote sensing satellite resolution and the increase in monitoring frequency, spatiotemporal raster data is showing an exponential growth trend, which brings huge challenges to the storage and efficient transmission of large-scale data.

[0003] Traditional multidimensional data compression methods are generally divided into lossless compression and lossy compression. While lossless compression can completely preserve the numerical accuracy of the original data, its compression ratio is usually low (typically less than 3:1), making it difficult to meet the storage needs of massive amounts of data. Traditional lossy compression methods (such as those based on L-RDG transform or wavelet transform) can significantly improve the compression ratio, but often lead to blurred image edges or artifacts, and lack strict numerical error control mechanisms. In scientific research, even small numerical deviations can be amplified in subsequent modeling and analysis, causing the final inference results to fail.

[0004] In recent years, super-resolution reconstruction techniques based on deep learning have provided new insights into data compression. However, existing deep learning compression schemes often rely excessively on network inference when processing high-dimensional raster data, which can easily lead to oversmoothing reconstruction results.

[0005] This can lead to severe numerical distortion and blurring of details, and lacks strict constraints on the accuracy of scientific data. In particular, when dealing with multidimensional raster data with complex spatiotemporal relationships, it is difficult to balance storage efficiency and numerical fidelity. Summary of the Invention

[0006] In order to improve the compression efficiency of multidimensional raster data while effectively controlling the reconstruction accuracy, this application provides a multidimensional raster data compression method, system, device and storage medium.

[0007] Firstly, this application provides a method for compressing multidimensional raster data, employing the following technical solution: Receive a multidimensional raster data sequence to be compressed, and perform downsampling preprocessing on the multidimensional raster data sequence to obtain a low-resolution image sequence; The low-resolution image sequence is encoded and compressed to obtain the basic video bitstream; A lightweight super-resolution reconstruction model is constructed based on the Transformer super-resolution network. After decoding the basic video bitstream, the lightweight super-resolution reconstruction model is used to perform super-resolution reconstruction to obtain preliminary reconstructed raster data of the original resolution. By comparing the preliminary reconstructed raster data with the multidimensional raster data sequence, a pixel error distribution map is obtained; Abnormal pixel information is extracted from the pixel error distribution map according to a preset error tolerance threshold, and the abnormal pixel information is compressed a second time to obtain an auxiliary error correction bitstream. The base video bitstream and the auxiliary error correction bitstream are encapsulated to obtain the final compressed data packet.

[0008] Through the above technical solutions, this application adopts a multi-stage compression and reconstruction framework for general spatiotemporal data. By co-designing compression and reconstruction, it effectively controls reconstruction accuracy while improving data compression efficiency. Through the deep integration of MPEG temporal coding and L-DRCT spatial super-resolution reconstruction, the spatiotemporal redundancy of multidimensional raster data is fully exploited, maintaining excellent reconstruction quality even at extremely high compression ratios. In particular, the introduced adaptive error-aware correction module achieves strict hard control over the numerical accuracy of scientific data through lossless secondary compensation for a small number of outliers. Compared to traditional methods, this invention not only improves storage efficiency but also solves the pain point of "smooth transition" and unreliability in deep learning reconstruction results, significantly improving the reliability and fidelity of remote sensing big data processing.

[0009] This application introduces a Transformer-based super-resolution reconstruction network in the reconstruction decoding stage to perform spatial detail restoration processing on low-resolution raster images, thereby improving the spatial resolution and numerical reconstruction accuracy of the compressed raster image sequence. Furthermore, by introducing the aforementioned error-aware correction mechanism, this application can strictly constrain the worst-case reconstruction error while maintaining a high compression ratio. This constraint directly corresponds to the physical error tolerance and is suitable for scientific data compression and reconstruction scenarios with high numerical accuracy requirements.

[0010] In one specific implementation, the downsampling preprocessing of the multidimensional raster data sequence to obtain a low-resolution image sequence includes: The multidimensional raster data sequence is denoised to obtain a first multidimensional raster data sequence; The resolution of the first multidimensional raster data sequence is reduced by using a bicubic interpolation algorithm to obtain a low-resolution image sequence.

[0011] The above technical solution performs spatial downsampling on the original multidimensional raster data sequence to reduce spatial resolution and data size, thereby reducing the redundancy of the multidimensional raster data in the spatial dimension and providing suitable data input for subsequent temporal compression processing. Through this spatial downsampling process, redundant spatial information in the image is removed while effectively reducing the data size, making the raster image sequence more suitable for subsequent temporal prediction-based compression coding.

[0012] In one specific implementation, the step of constructing a lightweight super-resolution reconstruction model based on the Transformer super-resolution network, decoding the basic video bitstream, and then using the lightweight super-resolution reconstruction model to perform super-resolution reconstruction to obtain preliminary reconstructed raster data at the original resolution includes: A lightweight super-resolution reconstruction model is constructed based on the Transformer super-resolution network. The lightweight super-resolution reconstruction model includes a shallow feature extraction module, a deep feature modeling module, and a reconstruction module. The deep feature modeling module includes several lightweight residual deep feature groups. Decoding the base video bitstream yields a reconstructed low-resolution image sequence; The shallow feature extraction module is used to extract shallow features from the low-resolution image sequence to obtain shallow features; The shallow features are sequentially input into several lightweight residual deep feature groups, and deep features are extracted from the several lightweight residual deep feature groups to obtain deep features. The deep features are then fed into the reconstruction module after being connected via global residuals to obtain preliminary reconstructed raster data at the original resolution.

[0013] In a specific feasible implementation, the shallow features are sequentially input into several lightweight residual deep feature groups, and deep features are extracted from these groups to obtain deep features. The calculation formula for the deep features is as follows:

[0014] in, For input features, The deep features are output. Presentation layer normalization operation, This indicates a multi-head self-attention mechanism based on a shift window. This represents a multilayer perceptron.

[0015] Through the above technical solution, the present invention introduces a super-resolution reconstruction network based on the Transformer structure in the decoding stage to perform spatial detail restoration processing on low-resolution raster images, effectively improving the spatial resolution and numerical reconstruction accuracy of the compressed raster image sequence.

[0016] In one specific implementation, comparing the initially reconstructed raster data with the multidimensional raster data sequence to obtain the pixel error distribution map includes: The preliminary reconstructed raster data is parsed to obtain several reconstructed values ​​for several pixels in the preliminary reconstructed raster data; The multidimensional raster data sequence is parsed to obtain several original values ​​of several pixels in the multidimensional raster data sequence; By comparing several reconstructed values ​​and several original values, several pixel error values ​​are obtained. The formula for calculating the pixel error value is as follows:

[0017] in, Representing coordinates Pixel error value at that location This represents the original value of the original multidimensional raster data at this point. This indicates the reconstructed value of the raster data at this point in the initial reconstruction. A pixel error distribution map is constructed based on several of the pixel error values.

[0018] In one specific implementation, the step of extracting abnormal pixel information from the pixel error distribution map according to a preset error tolerance threshold includes: Receive a preset error tolerance threshold and randomly determine any pixel in the pixel error distribution map as the target pixel; If the target pixel error value of the target pixel exceeds the error tolerance threshold, the target pixel is determined to be an abnormal pixel, and the pixel coordinate information of the target pixel is recorded. The numerical correction amount of the target pixel is obtained based on the reconstructed value of the target pixel and the original value of the target pixel; The abnormal feature vector of the target pixel is obtained by encapsulating the numerical correction amount and the pixel coordinate information; By analyzing each pixel in the pixel error distribution map, several abnormal feature vectors are obtained, and these abnormal feature vectors are arranged to form abnormal pixel information.

[0019] Through the above technical solution, the present invention introduces an explicit error control and correction mechanism after super-resolution reconstruction to ensure that the reconstructed data is within the user-preset physical error tolerance range, while taking into account the overall compression efficiency and visual continuity.

[0020] In one specific implementation, the secondary compression of the abnormal pixel information to obtain the auxiliary error correction bitstream includes: The probability distribution of several discrete coordinate values ​​corresponding to several pixel coordinate information in the abnormal pixel information is statistically analyzed, and a Huffman tree is constructed based on the probability distribution. The average code length of the discrete coordinate values ​​is calculated using the following formula:

[0021] in, The average code length of the discrete coordinate values. The size of the set of discrete coordinate values. For the first The probability of each discrete coordinate value occurring. The length of the binary code corresponding to this discrete coordinate value; Based on several discrete coordinate values ​​and several average code lengths, several pixel coordinate information are encoded in a Huffman tree using variable-length binary encoding to generate an auxiliary error correction bitstream.

[0022] Using the above technical solution, during the decoding process, the system traverses the decoding tree structure to sequentially decode the column coordinates, row coordinates, and error adjustment values ​​of pixels, and combines them into corresponding error correction vectors. Finally, based on the set of error correction vectors obtained from the decoding, the corresponding pixel positions in the super-resolution reconstructed image are corrected at specific points, thereby obtaining the final reconstruction result that satisfies the error constraints.

[0023] Secondly, this application provides a multi-dimensional raster data compression system, which is based on a Transformer super-resolution network and adopts the following technical solution: The system includes: The data receiving and processing module is used to receive the multidimensional raster data sequence to be compressed, and to downsample and preprocess the multidimensional raster data sequence to obtain a low-resolution image sequence. The encoding and compression module is used to encode and compress the low-resolution image sequence to obtain a basic video bitstream; The decoding and reconstruction module is used to construct a lightweight super-resolution reconstruction model based on the Transformer super-resolution network, decode the basic video bitstream, and then use the lightweight super-resolution reconstruction model to perform super-resolution reconstruction to obtain preliminary reconstructed raster data of the original resolution. The error analysis module is used to compare the preliminary reconstructed raster data with the multidimensional raster data sequence to obtain a pixel error distribution map; The secondary compression module is used to extract abnormal pixel information from the pixel error distribution map according to a preset error tolerance threshold, and to compress the abnormal pixel information to obtain an auxiliary error correction bitstream. The data integration module is used to encapsulate the basic video bitstream and the auxiliary error correction bitstream to obtain the final compressed data packet.

[0024] Thirdly, this application provides a computer device that adopts the following technical solution: it includes a memory and a processor, wherein the memory stores a computer program that can be loaded by the processor and executed as described above for a multidimensional raster data compression method.

[0025] Fourthly, this application provides a computer-readable storage medium that stores a computer program capable of being loaded by a processor and executing the aforementioned multidimensional raster data compression method.

[0026] In summary, this application has the following beneficial technical effects: (1) This application adopts a multi-stage compression and reconstruction framework for general spatiotemporal data. Through the collaborative design of compression and reconstruction, it achieves effective control of reconstruction accuracy while improving data compression efficiency. By deeply combining MPEG temporal coding and L-DRCT spatial super-resolution reconstruction, the spatiotemporal redundancy of multidimensional raster data is fully exploited, and excellent reconstruction quality can still be maintained under extremely high compression ratios. In particular, the introduced adaptive error-aware correction module achieves strict hard control of the numerical accuracy of scientific data through lossless secondary compensation for a small number of outliers. Compared with traditional methods, this invention not only improves storage efficiency, but also solves the pain point of "smooth transition" and unreliability of deep learning reconstruction results, significantly improving the reliability and fidelity of remote sensing big data processing.

[0027] (2) In the reconstruction decoding stage, this application introduces a super-resolution reconstruction network based on the Transformer structure to perform spatial detail restoration processing on low-resolution raster images, thereby improving the spatial resolution and numerical reconstruction accuracy of the compressed raster image sequence.

[0028] (3) By introducing the above-mentioned error perception correction mechanism, this application can strictly constrain the worst case of reconstruction error while maintaining a high compression ratio. It can directly correspond to the physical error tolerance and is suitable for scientific data compression and reconstruction scenarios with high numerical accuracy requirements. Attached Figure Description

[0029] Figure 1 This is a flowchart of a multidimensional raster data compression method according to an embodiment of this application.

[0030] Figure 2 This is a schematic diagram of the MPEG protocol.

[0031] Figure 3 This is a schematic diagram of the data compression method of this application.

[0032] Figure 4 This is a structural diagram of the super-resolution reconstruction model.

[0033] Figure 5 This is a structural block diagram of a multidimensional raster data compression method according to an embodiment of this application.

[0034] Reference numerals: 501, Data receiving and processing module; 502, Encoding and compression module; 503, Decoding and reconstruction module; 504, Error analysis module; 505, Secondary compression module; 506, Data integration module. Detailed Implementation

[0035] The following is in conjunction with the appendix Figures 1-5 This application will be described in further detail.

[0036] This application discloses a method, system, device, and storage medium for multidimensional raster data compression. The method aims to improve the compression efficiency of multidimensional raster data while effectively controlling the reconstruction accuracy. Multidimensional raster data refers to a collection of scientific data that is highly correlated in both spatial and temporal dimensions, and is widely used in fields such as remote sensing monitoring, numerical weather prediction, and ocean dynamic simulation. With the improvement of remote sensing satellite resolution and the increase in monitoring frequency, spatiotemporal raster data is showing an exponential growth trend, which brings huge challenges to the storage and efficient transmission of large-scale data.

[0037] Traditional multidimensional data compression methods are generally divided into lossless compression and lossy compression. While lossless compression can completely preserve the numerical accuracy of the original data, its compression ratio is usually low (typically less than 3:1), making it difficult to meet the storage needs of massive amounts of data. Traditional lossy compression methods (such as those based on L-RDG transform or wavelet transform) can significantly improve the compression ratio, but often lead to blurred image edges or artifacts, and lack strict numerical error control mechanisms. In scientific research, even small numerical deviations can be amplified in subsequent modeling and analysis, causing the final inference results to fail.

[0038] In recent years, super-resolution reconstruction techniques based on deep learning have provided new insights into data compression. However, existing deep learning compression schemes often rely excessively on network inference when processing high-dimensional raster data, which can easily lead to oversmoothing reconstruction results. This can lead to severe numerical distortion and blurring of details, and lacks strict constraints on the accuracy of scientific data. In particular, when dealing with multidimensional raster data with complex spatiotemporal relationships, it is difficult to balance storage efficiency and numerical fidelity.

[0039] Taking remote sensing applications as an example, remote sensing raster data is crucial scientific data for recording the physical properties of the Earth's surface. With the increasing resolution of sensors, the amount of data has exploded, posing serious challenges to storage and transmission. Traditional compression methods, such as JPEG or traditional video coding, often lead to a significant decrease in numerical accuracy, resulting in blurred edges or artifacts, failing to meet the high-fidelity requirements of scientific research. While lossless compression can maintain accuracy, its compression ratio is typically extremely low.

[0040] Therefore, this application proposes a multidimensional raster data compression method, which can improve the compression efficiency of multidimensional raster data while achieving effective control over reconstruction accuracy.

[0041] like Figure 1 As shown, the method includes: S10: Receive the multidimensional raster data sequence to be compressed, and perform downsampling preprocessing on the multidimensional raster data sequence to obtain a low-resolution image sequence.

[0042] Specifically, the system receives a multidimensional raster data sequence to be compressed. This sequence contains multiple floating-point raster frames with multiple time steps, and each frame contains multiple spatial pixel values. The multidimensional raster data sequence is first spatially downsampled to reduce spatial resolution and data size.

[0043] S20: Encode and compress the low-resolution image sequence to obtain the basic video bitstream.

[0044] Specifically, the low-resolution raster image sequence is input into the temporal compression coding module for compression processing. Preferably, the temporal compression coding module adopts a compression framework based on video coding standards. This framework has a clear hierarchical structure and configurable coding parameters, effectively removing temporal and spatial redundancy in multidimensional spatiotemporal data, making it suitable for the compressed storage and transmission of structured scientific data. Specifically, the downsampled low-resolution raster image sequence is encoded as temporal data, and a temporal compression mechanism based on inter-frame prediction is used to compress redundant information between adjacent time frames, thereby achieving effective utilization of temporal correlation.

[0045] In practical scenarios, low-resolution image sequences are input into video encoding modules based on the MPEG standard. For example... Figure 2 The diagram shown is a schematic of the MPEG protocol. Figure 2 The process is divided into two stages: Video Encoding and Video Decoding. The video sequence enters the Video Encoding stage, which includes RGB to YC encoding. b Cr (RGB to YCbCr color space conversion), Chroma subsampling, Macroblocks 16×16 (16×16 pixels), Block 8×8 / 4×4 (8×8 or 4×4 transform blocks), DCT (Discrete Cosine Transform), Q (Quantization), Motion Prediction, Motion Vectors, IDCT (Inverse Discrete Cosine Transform), Q - ¹ (Dequantization), Entropy coding; Video Decoding stage includes Entropy coding, Q... - ¹ (Inverse quantization), IDCT (Inverse Discrete Cosine Transform), Block 8×8 / 4×4 (Transform Block (8×8 or 4×4)), Motion vectors, Motion Prediction, Macroblocks 16×16 (Macroblocks (16×16 pixels)), YC b C r → RGB (YC) b C r (Conversion to RGB color space) and Chroma upsampling.

[0046] In this module, the image sequence is first divided into several grouped images (GOPs), and I-frames, P-frames, and B-frames are defined. Using a motion estimation algorithm, the macroblock position with the highest matching degree to the current block is searched in the reference frame to extract the motion vector. Further, the pixel residuals between the current frame and the predicted frame are calculated, and discrete cosine transform (DCT) and nonlinear quantization are performed on the residual data. By discarding high-frequency components that are insensitive to human vision or model reconstruction, the data volume is significantly reduced, generating a basic video bitstream that reflects redundant information in the temporal dimension.

[0047] S30 uses a lightweight super-resolution reconstruction model built on the Transformer super-resolution network. After decoding the basic video bitstream, the lightweight super-resolution reconstruction model is used to perform super-resolution reconstruction to obtain preliminary reconstructed raster data at the original resolution.

[0048] Specifically, a lightweight dense residual SwinTransformer (L-DRCT) model is constructed based on the Transformer super-resolution network with a window self-attention mechanism. This model achieves efficient modeling of multidimensional raster data through structurally lightweight design. The model as a whole adopts a shallow feature extraction module, a deep feature modeling module, and a reconstruction module.

[0049] In the data decoding and reconstruction stage, a super-resolution reconstruction model based on the Transformer structure is introduced for the low-resolution data obtained after temporal compression. By constructing multi-layer feature mapping and residual connection relationships, the spatial resolution of the low-resolution raster data is restored to enhance the spatial detail representation ability and numerical reconstruction accuracy of the reconstructed data.

[0050] S40. By comparing the preliminary reconstructed raster data with the multidimensional raster data sequence, a pixel error distribution map is obtained.

[0051] Specifically, the comparison process can be achieved by calculating the absolute difference or squared difference between the two pixels one by one. For example, the numerical difference of each corresponding pixel can be calculated and these differences can be organized into a two-dimensional or multi-dimensional map.

[0052] S50: Extract abnormal pixel information from the pixel error distribution map according to the preset error tolerance threshold, and compress the abnormal pixel information to obtain an auxiliary error correction bitstream.

[0053] Specifically, a preset error tolerance threshold is established; for example, a pixel is considered abnormal if its error value exceeds a certain fixed value. When a pixel's error exceeds this threshold, its coordinates and error correction value are recorded. This abnormal pixel information can then be compressed using simple run-length encoding or dictionary encoding.

[0054] S60 encapsulates the basic video bitstream and the auxiliary error correction bitstream to obtain the final compressed data packet.

[0055] Specifically, this encapsulation process can simply concatenate two bitstreams together, or package them using a container format. This data packet contains all the necessary compression information, which can be used for subsequent decompression and high-precision data recovery.

[0056] like Figure 3 The diagram shown is a schematic representation of the data compression method described in this application. Figure 3The process is divided into an encoding stage and a decoding and correction stage. In the encoding stage, the Group of Original Frames (GoF) is first downsampled to obtain the Group of Low-resolution Frames. After reconstruction, the Group of Reconstructed Frames is obtained, resulting in the reconstructed image frames. Among them, Downsampling is spatial downsampling, Group of Original Frames (GoF) is the original image frame group, Group of Low-resolution Frames is the low-resolution image frame group, Group of Reconstructed Frames is the reconstructed image frame group, Reconstructed Frame is the reconstructed image frame, CorrectedReconstructed Frame is the corrected reconstructed image frame, Original Frame is the original image frame, Compare is comparison, Diff_map is the error map, Error Points are error points, Huffman Encoding is Huffman coding, Huffman Decoding is Huffman decoding, Compressed Bitstream is compressed bitstream, Storage Data is stored data, Super-resolution (L-DRCT) is the super-resolution reconstruction module (a lightweight model based on Transformer), Correct is correction, Replace is replacement, MPEG Encoding is MPEG-based temporal compression coding, and MPEG Decoding is MPEG decoding.

[0057] This application employs a multi-stage compression and reconstruction framework for general spatiotemporal data. Through collaborative design of compression and reconstruction, it achieves effective control over reconstruction accuracy while improving data compression efficiency. By deeply integrating MPEG temporal coding with L-DRCT spatial super-resolution reconstruction, it fully exploits the spatiotemporal redundancy of multidimensional raster data, maintaining excellent reconstruction quality even at extremely high compression ratios. In particular, the introduced adaptive error-aware correction module achieves strict hard control over the numerical accuracy of scientific data through lossless secondary compensation for a small number of outliers. Compared with traditional methods, this invention not only improves storage efficiency but also solves the pain point of "smooth transition" and unreliability in deep learning reconstruction results, significantly enhancing the reliability and fidelity of remote sensing big data processing.

[0058] This application introduces a Transformer-based super-resolution reconstruction network in the reconstruction decoding stage to perform spatial detail restoration processing on low-resolution raster images, thereby improving the spatial resolution and numerical reconstruction accuracy of the compressed raster image sequence. Furthermore, by introducing the aforementioned error-aware correction mechanism, this application can strictly constrain the worst-case reconstruction error while maintaining a high compression ratio. This constraint directly corresponds to the physical error tolerance and is suitable for scientific data compression and reconstruction scenarios with high numerical accuracy requirements.

[0059] In one embodiment, to reduce the redundancy of multidimensional raster data in the spatial dimension and provide suitable data input for subsequent temporal compression processing, the step of downsampling preprocessing the multidimensional raster data sequence to obtain a low-resolution image sequence can be specifically performed as follows: The first multidimensional raster data sequence is obtained by denoising the multidimensional raster data sequence; the resolution of the first multidimensional raster data sequence is reduced by using a bicubic interpolation algorithm to obtain a low-resolution image sequence.

[0060] Specifically, for a high-resolution raster image frame at any given time point First, the image is smoothed by convolving it with a Gaussian kernel function to suppress high-frequency components and reduce aliasing effects that may occur during resampling. The standard deviation of the Gaussian kernel is preferably set to [value missing]. .

[0061] After smoothing, spatial downsampling is performed on the image frame, and bicubic interpolation is used to reduce the resolution according to a preset scaling factor to obtain the corresponding low-resolution raster image frame. Its expression is as follows:

[0062] in, Indicates the input image frame Perform Gaussian convolution operation. Indicates the scaling factor as Spatial downsampling operation, scaling factor The options are 2, 3, or 4.

[0063] Taking remote sensing applications as an example, remote sensing raster data, i.e., raw multidimensional raster data I_orig, is usually high-precision floating-point data. Because remote sensing data has extremely strong pixel correlation in spatial dimensions, direct encoding would lead to huge computational redundancy.

[0064] Therefore, a Gaussian smoothing filter is used to denoise the original data, eliminating random high-frequency noise generated by the sensor; subsequently, a bicubic interpolation algorithm is used to refine the original data to a resolution of [missing information]. The data was reduced to For low-resolution image sequences, the downsampling factor is preferably 2 or 4. , This represents the length and width of the original data. , This represents the length and width after downsampling. This process aims to initially eliminate spatial redundancy while mapping scientific data into smooth image features suitable for subsequent encoder processing.

[0065] By performing the spatial downsampling process described above, redundant spatial information in the image is removed while effectively reducing the data size, making the raster image sequence more suitable for subsequent compression coding based on time-series prediction.

[0066] In one embodiment, to improve the spatial resolution and numerical reconstruction accuracy of the compressed raster image sequence, a lightweight super-resolution reconstruction model is constructed based on the Transformer super-resolution network. After decoding the basic video bitstream, the lightweight super-resolution reconstruction model is used to perform super-resolution reconstruction to obtain preliminary reconstructed raster data at the original resolution. This step can be specifically performed as follows: First, a lightweight super-resolution reconstruction model is constructed based on the Transformer super-resolution network. The lightweight super-resolution reconstruction model includes a shallow feature extraction module, a deep feature modeling module, and a reconstruction module. The deep feature modeling module includes several lightweight residual deep feature groups. Specifically, a lightweight dense residual SwinTransformer (L-DRCT) model is constructed based on the Transformer super-resolution network with a window self-attention mechanism. This model achieves efficient modeling of multidimensional raster data through structurally lightweight design. The model as a whole adopts a shallow feature extraction module, a deep feature modeling module, and a reconstruction module.

[0067] The structural diagram of the super-resolution reconstruction model is as follows: Figure 4As shown in the figure, the shallow feature extraction module is constructed through a 3×3 convolutional layer; the deep feature modeling module consists of three lightweight residual deep feature groups (L-RDG) connected in series. Each L-RDG contains four lightweight Swing dense residual connection blocks (L-SDRCB), thereby compressing the structural depth of the six residual deep feature groups in the original dense residual Transformer network to half. While maintaining the feature expression level, the network depth and parameter scale are significantly reduced, thus achieving lightweighting. Inside each L-SDRCB, a lightweight Swing Transformer layer consisting of alternating window multi-head self-attention and window translation self-attention is adopted. The number of heads of multi-head self-attention is reduced from 6 to 4 to reduce the computational complexity of the attention matrix. At the same time, the feature concatenation depth in the dense connection is reduced from 5 layers to 4 layers, so that the input of the current layer is formed by concatenating the features of the previous four layers. This avoids the exponential growth of feature dimension while retaining multi-level feature reuse and gradient direct path.

[0068] During the model training phase, a loss function based on pixel differences is used to optimize the reconstruction results. The loss function is defined as follows:

[0069] in, Represents the training loss function. The number of training samples. This represents the luminance component obtained from super-resolution reconstruction. This represents the corresponding true high-resolution luminance component.

[0070] Then, the basic video bitstream is decoded to obtain the reconstructed low-resolution image sequence. Specifically, in order to restore and reconstruct the spatial dimension at the decoding end, the basic video bitstream needs to be restored first, for example, by performing entropy decoding, inverse quantization and inverse transform processing on the basic video bitstream.

[0071] Next, a shallow feature extraction module is used to extract shallow features from the low-resolution image sequence to obtain shallow features. Specifically, the super-resolution reconstruction network first processes the input low-resolution raster image... Shallow feature extraction is performed by obtaining the initial feature map through convolution operations, as shown in the following expression:

[0072] in, Indicates the kernel size as Convolution operation, This is the initial feature map; Then, the shallow features are sequentially input into several lightweight residual deep feature groups. Deep feature extraction is then performed within these lightweight residual deep feature groups to obtain deep features. Specifically, after completing the shallow feature extraction, the network enters the deep feature extraction stage. This stage includes multiple lightweight residual deep feature groups, each composed of several lightweight Transformer residual modules. By reducing the number of feature groups and attention heads, the network maintains its effective modeling ability for spatially relevant features while reducing model complexity.

[0073] In any lightweight Transformer residual module, the feature processing can be represented as:

[0074] in, Indicates the first An intermediate feature, This indicates a transitional convolution operation that includes the LeakyReLU activation function. This represents a lightweight Swing Transformer layer. This represents the feature concatenation operation. To enhance feature reuse capabilities and stabilize the network training process, a residual scaling connection is introduced at the module output, with the following expression:

[0075] in, This is the residual scaling factor, preferably set to 0.2. Indicates the module's input characteristics; Finally, the deep features are fed into the reconstruction module after passing through global residual connections to obtain preliminary reconstructed raster data at the original resolution. Specifically, after deep feature extraction, the network restores the spatial resolution of the feature map through a pixel-based upsampling module and generates the final high-resolution reconstructed image. Preferably, the upsampling module employs an adaptive block-based pixel rearrangement method to improve the continuity and stability of spatial reconstruction.

[0076] In one embodiment, to improve the spatial resolution and numerical reconstruction accuracy of the compressed raster image sequence, shallow features are sequentially input into several lightweight residual deep feature groups, and deep features are extracted from these lightweight residual deep feature groups to obtain deep features. This step can be specifically performed as follows: Shallow features are sequentially input into several lightweight residual deep feature groups. Deep features are then extracted from these lightweight residual deep feature groups. The formula for calculating deep features is as follows:

[0077] in, For input features, The deep features are output. Presentation layer normalization operation, This indicates a multi-head self-attention mechanism based on a shift window. This represents a multilayer perceptron.

[0078] like Figure 4 As shown, within each L-SDRCB, a lightweight Swin Transformer layer (L-STL) is used, consisting of alternating window multi-head self-attention and window translation self-attention. This includes a layer normalization layer and a window multi-head self-attention layer. ) and multilayer perceptron layer ( The formula for calculating deep features is:

[0079] in, For input features, The deep features are output. Presentation layer normalization operation, This indicates a multi-head self-attention mechanism based on a shift window. This represents a multilayer perceptron.

[0080] In one embodiment, a pre-trained lightweight dense residual Swing Transformer (L-DRCT) model was used for spatial dimension super-resolution reconstruction.

[0081] Specifically, low-resolution image frame sequences Input to the L-DRCT network, first through Convolutional layers extract shallow features. The core reconstruction part consists of cascaded lightweight dense residual connective blocks (L-SDRCB).

[0082] In each L-SDRCB, a shifted window MS-Attention mechanism is used to capture long-range spatial dependencies. Unlike traditional CNNs, the Transformer structure can establish global relationships between pixels. At the same time, through a dense residual connection structure, all feature outputs from previous layers are concatenated along the channel dimension and fed back to the current layer, effectively mitigating the feature degradation problem in deep networks.

[0083] Finally, the feature maps are upsampled to the original resolution using global residual connections and sub-pixel convolutional layers (PixelShuffle). Preliminary reconstructed raster data was obtained. The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

[0084] This application introduces a super-resolution reconstruction network based on the Transformer structure in the reconstruction decoding stage to perform spatial detail restoration processing on low-resolution raster images, thereby improving the spatial resolution and numerical reconstruction accuracy of the compressed raster image sequence.

[0085] Although deep learning-based super-resolution reconstruction models can effectively recover the spatial structure information of compressed images, numerical errors exceeding the allowable range may still occur in local regions. In some scientific computing and engineering applications, such as geophysical simulation and marine environmental modeling, there are usually clear and strict physical constraints on the numerical accuracy of data. Even if local pixel-level errors are not visually obvious, they may be amplified during subsequent numerical calculations, differencing operations, or model assimilation, thus affecting the reliability of the analysis results.

[0086] In practical applications, physical quantities usually have a definite dynamic range of change within the original numerical domain. When they are mapped to a data representation with a finite bit depth (such as a grayscale image), a small physical deviation can correspond to a change in intensity at multiple pixel levels.

[0087] In one embodiment, to improve the compression efficiency of multidimensional raster data while effectively controlling the reconstruction accuracy, the step of comparing the preliminary reconstructed raster data with the multidimensional raster data sequence to obtain a pixel error distribution map can be specifically performed as follows: The process involves analyzing the initial reconstructed raster data to obtain several reconstructed values ​​for several pixels; analyzing the multidimensional raster data sequence to obtain several original values ​​for several pixels; and comparing the reconstructed values ​​with the original values ​​to obtain several pixel error values. The formula for calculating the pixel error value is as follows:

[0088] in, Representing coordinates Pixel error value at that location This represents the original value of the original multidimensional raster data at this point. This represents the reconstructed value of the raster data at this point; a pixel error distribution map is constructed based on several pixel error values.

[0089] Specifically, the initial reconstructed raster data typically exists in the form of multidimensional arrays or tensors. The parsing process involves traversing these data structures to extract the specific values ​​at each spatial or spatiotemporal coordinate point. The original multidimensional raster data sequence is uncompressed data that serves as the true value; its parsing process is similar to that of the initial reconstructed raster data, aiming to extract the original values ​​at each corresponding coordinate point. Compared with the original raster data Perform pixel-by-pixel comparison and calculate the error distribution map. The formula for calculating pixel error values ​​is:

[0090] in, Representing coordinates Pixel error value at that location This represents the original value of the original multidimensional raster data at this point. This indicates the initial reconstruction value of the raster data at this point.

[0091] In one embodiment, in order to improve the compression efficiency of multidimensional raster data while effectively controlling the reconstruction accuracy, this step can be specifically performed as follows: The system receives a preset error tolerance threshold and randomly selects any pixel in the pixel error distribution map as the target pixel. If the target pixel error value exceeds the error tolerance threshold, the target pixel is determined to be an abnormal pixel, and its pixel coordinate information is recorded. The system obtains the numerical correction amount of the target pixel based on its reconstructed value and original value. The system encapsulates the numerical correction amount and pixel coordinate information to obtain the abnormal feature vector of the target pixel. The system analyzes all pixels in the pixel error distribution map one by one to obtain several abnormal feature vectors, and arranges these abnormal feature vectors to form abnormal pixel information.

[0092] Specifically, the preset error tolerance threshold Iterate through all pixels in the error distribution map; if If the pixel is not found to be an abnormal pixel, its corresponding spatiotemporal coordinates are recorded. Calculate the numerical correction amount for the abnormal pixel. The coordinate information and numerical correction value of each abnormal pixel are encapsulated into a vector. ,in Indicates the number of times within the current frame The abnormal points are identified, and all vectors are arranged in coordinate order to form an abnormal information sequence, i.e., abnormal pixel information.

[0093] This invention introduces an explicit error control and correction mechanism after super-resolution reconstruction to ensure that the reconstructed data is within the user-preset physical error tolerance range, while taking into account overall compression efficiency and visual continuity.

[0094] In one embodiment, to improve the compression efficiency of multidimensional raster data while effectively controlling the reconstruction accuracy, the step of obtaining an auxiliary error correction bitstream by secondary compression of abnormal pixel information can be specifically performed as follows: The probability distribution of discrete coordinate values ​​corresponding to several pixel coordinates in the abnormal pixel information is analyzed, and a Huffman tree is constructed based on the probability distribution. The average code length of the discrete coordinate values ​​is calculated using the following formula:

[0095] in, The average code length of the discrete coordinate values. The size of the set of discrete coordinate values. For the first The probability of each discrete coordinate value occurring. The length of the binary code corresponding to the discrete coordinate value is given; based on several discrete coordinate values ​​and several average code lengths, several pixel coordinate information is encoded in a Huffman tree using variable-length binary encoding to generate an auxiliary error correction bitstream.

[0096] Specifically, abnormal pixel information typically includes the pixel coordinates of multiple abnormal pixels. These pixel coordinates may exhibit a certain spatial distribution pattern, meaning some coordinate values ​​appear more frequently than others. To achieve efficient compression, this application first performs statistical analysis on the discrete coordinate values ​​appearing in these pixel coordinates to obtain the frequency of each discrete coordinate value in the abnormal pixel information, and then calculates its probability distribution. Based on this probability distribution, a Huffman tree can be constructed. A Huffman tree is an optimal prefix coding tree, and its construction process assigns codes based on the frequency of characters (here, discrete coordinate values). Characters with higher frequencies have shorter codes, and vice versa, thereby achieving overall data compression.

[0097] After constructing the Huffman tree, in order to evaluate the coding efficiency, it is necessary to calculate the average code length of several discrete coordinate values. The formula for calculating the average code length is:

[0098] in, The average code length of the discrete coordinate values. The size of the set of discrete coordinate values. For the first The probability of each discrete coordinate value occurring. This is the binary code length corresponding to the discrete coordinate value; this average code length can intuitively reflect the average number of bits required for each discrete coordinate value after Huffman coding, and is an important indicator for measuring compression efficiency. For each pixel coordinate in the abnormal pixel information, its corresponding binary code is looked up in the Huffman tree based on its discrete coordinate value. Since the Huffman code is variable-length, frequently occurring coordinate values ​​are assigned shorter codes, while infrequently occurring coordinate values ​​are assigned longer codes. In this way, all pixel coordinate information is converted into a compact binary sequence, thus generating an auxiliary error correction bitstream.

[0099] By introducing the aforementioned error-aware correction mechanism, this invention can strictly constrain the worst-case scenario of reconstruction errors while maintaining a high compression ratio. Compared to methods that rely on loss function adjustment or model regularization, this method has a clear structure, strong interpretability, and can directly correspond to physical error tolerance, making it suitable for scientific data compression and reconstruction scenarios with high numerical accuracy requirements.

[0100] Based on the above method, this application also discloses a multi-dimensional raster data compression system. For example... Figure 5 The system includes the following modules: The data receiving and processing module 501 is used to receive the multidimensional raster data sequence to be compressed and to downsample and preprocess the multidimensional raster data sequence to obtain a low-resolution image sequence. The encoding and compression module 502 is used to encode and compress low-resolution image sequences to obtain a basic video bitstream; The decoding and reconstruction module 503 is used to build a lightweight super-resolution reconstruction model based on the Transformer super-resolution network. After decoding the basic video bitstream, the lightweight super-resolution reconstruction model is used to perform super-resolution reconstruction to obtain preliminary reconstructed raster data of the original resolution. Error analysis module 504 is used to compare the preliminary reconstructed raster data with the multidimensional raster data sequence to obtain a pixel error distribution map; The secondary compression module 505 is used to extract abnormal pixel information from the pixel error distribution map according to the preset error tolerance threshold, and to compress the abnormal pixel information to obtain an auxiliary error correction bit stream. The data integration module 506 is used to encapsulate the basic video bitstream and the auxiliary error correction bitstream to obtain the final compressed data packet.

[0101] In one embodiment, the data receiving and processing module 501 is specifically used to denoise the multidimensional raster data sequence to obtain a first multidimensional raster data sequence; and to reduce the resolution of the first multidimensional raster data sequence using a bicubic interpolation algorithm to obtain a low-resolution image sequence.

[0102] In one embodiment, the decoding and reconstruction module 503 is specifically used to construct a lightweight super-resolution reconstruction model based on the Transformer super-resolution network. The lightweight super-resolution reconstruction model includes a shallow feature extraction module, a deep feature modeling module, and a reconstruction module. The deep feature modeling module includes several lightweight residual deep feature groups. Decoding the base video bitstream yields a reconstructed low-resolution image sequence; Shallow features are obtained by using a shallow feature extraction module to extract shallow features from low-resolution image sequences; Shallow features are sequentially input into several lightweight residual deep feature groups, and deep features are extracted from these lightweight residual deep feature groups to obtain deep features. The deep features are fed into the reconstruction module after being connected via global residuals to obtain preliminary reconstructed raster data at the original resolution.

[0103] In one embodiment, the decoding and reconstruction module 503 is specifically used to sequentially input shallow features into several lightweight residual deep feature groups, and extract deep features from these groups to obtain deep features. The calculation formula for the deep features is as follows:

[0104] in, For input features, The deep features are output. Presentation layer normalization operation, This indicates a multi-head self-attention mechanism based on a shift window. This represents a multilayer perceptron.

[0105] In one embodiment, the error analysis module 504 is specifically used to parse the preliminary reconstructed raster data to obtain several reconstructed values ​​of several pixels in the preliminary reconstructed raster data. Parse a multidimensional raster data sequence to obtain several original values ​​of several pixels in the multidimensional raster data sequence; By comparing several reconstructed values ​​with several original values, several pixel error values ​​are obtained. The formula for calculating the pixel error value is as follows:

[0106] in, Representing coordinates Pixel error value at that location This represents the original value of the original multidimensional raster data at this point. This represents the reconstructed value of the raster data at this point; a pixel error distribution map is constructed based on several pixel error values.

[0107] In one embodiment, the secondary compression module 505 is specifically used to receive a preset error tolerance threshold, randomly determine any pixel in the pixel error distribution map as the target pixel; if the target pixel error value of the target pixel exceeds the error tolerance threshold, then the target pixel is determined to be an abnormal pixel, and the pixel coordinate information of the target pixel is recorded; the numerical correction amount of the target pixel is obtained based on the reconstructed value and the original value of the target pixel; the numerical correction amount and the pixel coordinate information are encapsulated to obtain the abnormal feature vector of the target pixel; all pixels in the pixel error distribution map are analyzed one by one to obtain several abnormal feature vectors, and the several abnormal feature vectors are arranged to form abnormal pixel information.

[0108] In one embodiment, the secondary compression module 505 is specifically used to statistically analyze the probability distribution of discrete coordinate values ​​corresponding to several pixel coordinate information in the abnormal pixel information, construct a Huffman tree based on the probability distribution, and calculate the average code length of the discrete coordinate values. The formula for calculating the average code length is as follows:

[0109] in, The average code length of the discrete coordinate values. The size of the set of discrete coordinate values. For the first The probability of each discrete coordinate value occurring. The length of the binary code corresponding to the discrete coordinate value is given; based on several discrete coordinate values ​​and several average code lengths, several pixel coordinate information is encoded in a Huffman tree using variable-length binary encoding to generate an auxiliary error correction bitstream.

[0110] This application also discloses a computer device.

[0111] Specifically, the computer device includes a memory and a processor, and the memory stores a computer program that can be loaded by the processor and executed as described above for a multidimensional raster data compression method.

[0112] This application also discloses a computer-readable storage medium.

[0113] Specifically, the computer-readable storage medium stores a computer program that can be loaded by a processor and executed as described above in a multidimensional raster data compression method. The computer-readable storage medium includes, for example, various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0114] This specific embodiment is merely an explanation of the present invention and is not intended to limit the invention. After reading this specification, those skilled in the art can make modifications to this embodiment without contributing any inventive step, but such modifications are protected by patent law as long as they are within the scope of the claims of the present invention.

Claims

1. A method for compressing multidimensional raster data, characterized in that, The method is based on the Transformer super-resolution network, and the method includes: Receive a multidimensional raster data sequence to be compressed, and perform downsampling preprocessing on the multidimensional raster data sequence to obtain a low-resolution image sequence; The low-resolution image sequence is encoded and compressed to obtain the basic video bitstream; A lightweight super-resolution reconstruction model is constructed based on the Transformer super-resolution network. After decoding the basic video bitstream, the lightweight super-resolution reconstruction model is used to perform super-resolution reconstruction to obtain preliminary reconstructed raster data of the original resolution. By comparing the preliminary reconstructed raster data with the multidimensional raster data sequence, a pixel error distribution map is obtained; Abnormal pixel information is extracted from the pixel error distribution map according to a preset error tolerance threshold, and the abnormal pixel information is compressed a second time to obtain an auxiliary error correction bitstream. The base video bitstream and the auxiliary error correction bitstream are encapsulated to obtain the final compressed data packet.

2. The method according to claim 1, characterized in that, The downsampling preprocessing of the multidimensional raster data sequence to obtain a low-resolution image sequence includes: The multidimensional raster data sequence is denoised to obtain a first multidimensional raster data sequence; The resolution of the first multidimensional raster data sequence is reduced by using a bicubic interpolation algorithm to obtain a low-resolution image sequence.

3. The method according to claim 1, characterized in that, The lightweight super-resolution reconstruction model built based on the Transformer super-resolution network, after decoding the basic video bitstream, is used to perform super-resolution reconstruction to obtain preliminary reconstructed raster data at the original resolution, including: A lightweight super-resolution reconstruction model is constructed based on the Transformer super-resolution network. The lightweight super-resolution reconstruction model includes a shallow feature extraction module, a deep feature modeling module, and a reconstruction module. The deep feature modeling module includes several lightweight residual deep feature groups. Decoding the base video bitstream yields a reconstructed low-resolution image sequence; The shallow feature extraction module is used to extract shallow features from the low-resolution image sequence to obtain shallow features; The shallow features are sequentially input into several lightweight residual deep feature groups, and deep features are extracted from the several lightweight residual deep feature groups to obtain deep features. The deep features are then fed into the reconstruction module after being connected via global residuals to obtain preliminary reconstructed raster data at the original resolution.

4. The method according to claim 1, characterized in that, The step of sequentially inputting the shallow features into several lightweight residual deep feature groups, and extracting deep features from these lightweight residual deep feature groups to obtain deep features includes: The shallow features are sequentially input into several lightweight residual deep feature groups, and deep features are extracted from these groups. The calculation formula for the deep features is as follows: in, For input features, The deep features are output. Presentation layer normalization operation, This indicates a multi-head self-attention mechanism based on a shift window. This represents a multilayer perceptron.

5. The method according to claim 1, characterized in that, The step of comparing the initially reconstructed raster data with the multidimensional raster data sequence to obtain the pixel error distribution map includes: The preliminary reconstructed raster data is parsed to obtain several reconstructed values ​​for several pixels in the preliminary reconstructed raster data; The multidimensional raster data sequence is parsed to obtain several original values ​​of several pixels in the multidimensional raster data sequence; By comparing several reconstructed values ​​and several original values, several pixel error values ​​are obtained. The formula for calculating the pixel error value is as follows: in, Representing coordinates Pixel error value at that location This represents the original value of the original multidimensional raster data at this point. This indicates the reconstructed value of the raster data at this point in the initial reconstruction. A pixel error distribution map is constructed based on several of the pixel error values.

6. The method according to claim 1, characterized in that, The step of extracting abnormal pixel information from the pixel error distribution map according to a preset error tolerance threshold includes: Receive a preset error tolerance threshold and randomly determine any pixel in the pixel error distribution map as the target pixel; If the target pixel error value of the target pixel exceeds the error tolerance threshold, the target pixel is determined to be an abnormal pixel, and the pixel coordinate information of the target pixel is recorded. The numerical correction amount of the target pixel is obtained based on the reconstructed value of the target pixel and the original value of the target pixel; The abnormal feature vector of the target pixel is obtained by encapsulating the numerical correction amount and the pixel coordinate information; By analyzing each pixel in the pixel error distribution map, several abnormal feature vectors are obtained, and these abnormal feature vectors are arranged to form abnormal pixel information.

7. The method according to claim 1, characterized in that, The secondary compression of the abnormal pixel information to obtain the auxiliary error correction bitstream includes: The probability distribution of discrete coordinate values ​​corresponding to several pixel coordinate information in the abnormal pixel information is statistically analyzed, and a Huffman tree is constructed based on the probability distribution. The average code length of the discrete coordinate values ​​is calculated using the following formula: in, The average code length of the discrete coordinate values. The size of the set of discrete coordinate values. For the first The probability of each discrete coordinate value occurring. The length of the binary code corresponding to this discrete coordinate value; Based on several discrete coordinate values ​​and several average code lengths, several pixel coordinate information are encoded in a Huffman tree using variable-length binary encoding to generate an auxiliary error correction bitstream.

8. A multidimensional raster data compression system, characterized in that, The system is based on the Transformer super-resolution network, and the system includes: The data receiving and processing module (501) is used to receive the multidimensional raster data sequence to be compressed, and to downsample and preprocess the multidimensional raster data sequence to obtain a low-resolution image sequence; The encoding and compression module (502) is used to encode and compress the low-resolution image sequence to obtain a basic video bitstream; The decoding and reconstruction module (503) is used to construct a lightweight super-resolution reconstruction model based on the Transformer super-resolution network, and to perform super-resolution reconstruction using the lightweight super-resolution reconstruction model after decoding the basic video bitstream, so as to obtain preliminary reconstructed raster data of the original resolution. The error analysis module (504) is used to compare the preliminary reconstructed raster data with the multidimensional raster data sequence to obtain a pixel error distribution map; The secondary compression module (505) is used to extract abnormal pixel information from the pixel error distribution map according to a preset error tolerance threshold, and to compress the abnormal pixel information to obtain an auxiliary error correction bitstream. The data integration module (506) is used to encapsulate the basic video bitstream and the auxiliary error correction bitstream to obtain the final compressed data packet.

9. A computer device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program that can be loaded by the processor and executed according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer program is stored that can be loaded by a processor and executed according to any one of claims 1 to 7.

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