Seismic data five-dimensional fast interpolation method based on convolutional neural network
Through a low-dimensional network and progressive self-enhancement training strategy, combined with mask self-supervision and sliding window strategies, the problems of high training cost and poor generalization in 5D reconstruction of seismic data are solved, and efficient and accurate 5D seismic data interpolation is achieved.
Patent Information
- Application Number
- CN202510874745.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-27
- Publication Date
- 2025-10-17
AI Technical Summary
Existing deep learning-based 5D reconstruction methods for seismic data have problems such as high training cost and poor generalization, making it difficult to meet the requirements of high-precision and high-efficiency processing of seismic big data.
A low-dimensional network is used to construct a 5D reconstruction module, and the low-dimensional sub-network is trained through a progressive self-enhancement training strategy. Combined with the mask self-supervision strategy and the overlapping sliding window strategy, efficient 5D seismic data interpolation is achieved.
It significantly reduces computing resource requirements, improves interpolation accuracy and efficiency, and achieves high-precision 5D seismic data reconstruction with higher accuracy and lower computational cost compared to traditional methods.
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Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of seismic signal processing, and particularly relates to a five-dimensional fast interpolation method for seismic data based on a convolutional neural network. BACKGROUND
[0002] Due to the limitation of physical conditions and the consideration of economic conditions, the collected seismic data usually has missing data, and the missing seismic data will affect the subsequent migration imaging, inversion and interpretation. Therefore, the interpolation reconstruction of the missing seismic data is an important step in seismic signal processing. Current exploration technology is mostly three-dimensional exploration, and the data collected by three-dimensional seismic exploration has five dimensions (source horizontal and vertical coordinates, receiver horizontal and vertical coordinates, and time dimension). Direct 5D reconstruction of the data can fully utilize the correlation characteristics of different azimuths and offsets in high-dimensional seismic data, consider more spatial information characteristics, and more accurately predict the amplitude and phase changes of the missing traces.
[0003] At present, the 5D reconstruction method of seismic data is mainly the traditional method, including the anti-leakage Fourier transform interpolation method (ALFT), the minimum weighted norm reconstruction, the prediction filter method, the matrix and tensor reduction, the dictionary learning method and the like. With the gradual change of oil and gas exploration targets to deep water, deep layer, complex structure and complex lithology reservoir, the complexity and acquisition scale of data are increasing, the traditional method depends on the model prior assumption, and the parameters need to be manually adjusted for each data to be reconstructed, which cannot well meet the processing requirements of high precision and high efficiency of seismic big data. Therefore, it is necessary to develop an intelligent reconstruction method.
[0004] In recent years, the deep learning method has caused extensive research in the field of 2D and 3D reconstruction of seismic data, and has achieved remarkable results, but still faces challenges in 5D interpolation. The main reasons include two points: on the one hand, the high-dimensional characteristics make the 5D data volume increase sharply, and the deep learning method faces the difficulty of training storage; on the other hand, the commonly used deep learning code platform only provides one-dimensional to three-dimensional convolution operators, which makes it difficult for the commonly used convolutional neural network (CNN) to be directly extended to five dimensions.
[0005] Currently, deep learning-based 5D reconstruction of seismic data is still in its exploratory stages. Existing research falls into three main categories. One approach rearranges 5D data blocks into one-dimensional vectors and then uses a multilayer perceptron (MLP) for reconstruction. Due to computational resource constraints, this approach is typically limited to very small data blocks and uses a small number of MLP neurons and layers. Another approach is based on neural tensor radiation fields. This approach uses an MLP to establish a mapping from spatial coordinates to radiation field data to simulate the forward modeling process. However, the network models trained by this approach lack generalization ability and require repeated training for different data blocks, significantly increasing computational costs and reducing the practicality of the method. Fang et al. designed a novel 5D convolutional neural network (CCNet-5D) by constructing a cascade of 3D2D convolutional layers, introducing CNNs for 5D reconstruction of seismic data for the first time. However, due to computational resource constraints, this approach can only process small-scale data blocks as basic units. Furthermore, the network architecture used in this study is relatively simple (comprising only 4–6 stacked convolutional layers), and the training process is computationally expensive and inefficient. Therefore, developing an efficient and scalable deep learning 5D reconstruction method for seismic data is an urgent problem to be solved. Summary of the Invention
[0006] The purpose of the present invention is to provide a five-dimensional fast interpolation method for seismic data based on convolutional neural networks in order to solve the problems of high training cost and poor generalization of existing deep learning-based seismic data 5D reconstruction methods.
[0007] The above-mentioned purpose of this application is achieved through the following technical solutions: S1: Use low-dimensional networks to build a 5D reconstruction module; obtain original seismic data with missing traces; S2: Using seismic data and a progressive self-enhancement training strategy, the low-dimensional sub-network in the 5D reconstruction module is self-enhanced. S3: Obtain the seismic data of the work area to be reconstructed; use the trained 5D reconstruction module to interpolate and reconstruct the seismic data of the work area.
[0008] Optionally, step S1 includes: S11: The original seismic data with missing traces is , the five dimensions of seismic data are expressed as ; Constructor dimension collection ,in for A subset of , The number of elements contained , and all The union of the five dimensions is covered, i.e. ; S12: The 5D reconstruction module includes low-dimensional sub-networks, denoted as , the low-dimensional sub-networks are along the sub-dimensions to reconstruct the seismic data; The output of the low-dimensional sub-network is the updated guide data; The input of the low-dimensional sub-network is the dual-channel data, two channels are the original seismic data containing missing traces and the updated guide data of the previous low-dimensional sub-network .
[0009] Optionally, step S2 includes: S21: set the self-enhancement round number to ; S22: construct the guide data and the guide training data set , the initial values are set to 0, denoted as and ; S23: for the self-enhancement training of the th round, the steps are: train the low-dimensional sub-network , update and to and ; train the low-dimensional sub-network , update and to and ; train sequentially until all the low-dimensional sub-networks are trained and the updated and are obtained, completing one round of self-enhancement; record and as and ; S24: take the th round of self-enhancement training and as the initial values; based on and , repeat step S23 to perform the +1th round of training until the total rounds of self-enhancement training are completed, obtaining the trained low-dimensional sub-networks, denoted as .
[0010] Optionally, step S23 comprises: training the low-dimensional subnetwork using a mask self-supervised strategy; constructing a self-supervised training data pair from the original seismic data containing missing traces, by: extracting a data block along the dimension from , and normalizing it, denoted as , and denoting the sampling operator corresponding to each data block as ; for each data block, generating a new mask operator, denoted as ; constructing a self-supervised training data pair, with the input being and the label being , wherein represents the Hadamard product.
[0011] Optionally, step S23 further comprises: the input of the low-dimensional subnetwork is two-channel data , wherein is the data block extracted from , the extraction position corresponding to , and are stacked along the channel direction to form the input of the two-channel low-dimensional subnetwork.
[0012] Optionally, step S23 further comprises: the training of the low-dimensional subnetwork is completed by optimizing an algorithm to minimize a self-supervised loss function, and the self-supervised loss function is calculated as follows:
[0013] wherein represents the square of the Frobenius norm.
[0014] Optionally, step S23 further comprises: updating using the trained low-dimensional subnetwork to obtain ; using an overlapping sliding window strategy to extract data blocks and from and , wherein is the number of data blocks obtained by the sliding window strategy, and All are normalized data; Will and Stack along the channel dimension to construct a two-channel input data block and input it into the trained network Output ; Will and Stacked along the channel dimension and fed back into the network , the output is recorded as ; Reorganize according to sliding window position , and denormalize to get .
[0015] Optionally, step S23 further includes: use renew get ,as follows: from Middle Edge Dimension randomly selects some sub-data pairs Update, that is, randomly select ,make
[0016] The subscript Indicates along The intercepted sub-data, express exist The number of data points in the complement set.
[0017] Optionally, step S3 includes: S31: Set the number of iterations of the 5D reconstruction module to ; S32: Constructing guidance data , its initial value is set to 0, recorded as ; S33: For Round iteration, the steps are: using the trained low-dimensional sub-network renew for ; Using the trained low-dimensional sub-network renew for ; Continue in sequence until you get ; polymerization , the output is recorded as ; The aggregation method is:
[0018] wherein, and respectively represent and the first seismic trace, is a weight parameter, controlled by the local sampling rate of the larger the larger; S34: repeat step S33 until all iterations are completed, obtaining the interpolation result , is the output of the th iteration, indicates the sampling operator corresponding to the original data .
[0019] An electronic device includes a processor, a memory, a user interface, and a network interface, the memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform a five-dimensional fast interpolation method for seismic data based on a convolutional neural network.
[0020] The technical scheme provided by the present application has the beneficial effects that: 1. The trained coupled 3D and 2D network separated on low-dimensional data has a training length as long as that of a general 3D-CNN and 2D-CNN network, greatly reducing the demand of the 5D reconstruction method for computing resources. The interpolation accuracy of the present application is better than that of the 3D-Unet method reconstructed along three sub-dimensions, and the present application is a high-precision, high-efficiency, and intelligent interpolation method.
[0021] 2. The present application is a new five-dimensional interpolation method for seismic data based on a convolutional neural network. Compared with the existing three-dimensional convolutional neural network-based seismic data interpolation method, the present application can extract five-dimensional features of data at the same time, and has higher accuracy. Compared with the CCNet-5D method, the present application can separately train 3D and 2D networks, thereby increasing the data scale in the network information flow, constructing a more complex network structure, and reducing the training length. BRIEF DESCRIPTION OF DRAWINGS
[0022] The present application will be further described below in conjunction with the drawings and examples, and the drawings are as follows: Figure 1 is a step diagram in the embodiment of the present application; Figure 2is a 3D network and a 2D network structure diagram in the embodiments of the present application; Figure 3 is a progressive self-enhancement training framework diagram in the embodiments of the present application; Figure 4 is a reconstruction flowchart of work area seismic data in the embodiments of the present application; Figure 5 is a simulation data display diagram in the embodiments of the present application; Figure 6 is a simulation data interpolation result diagram in the embodiments of the present application; Figure 7 is an electronic device structure schematic diagram in the embodiments of the present application. DETAILED DESCRIPTION
[0023] In order to have a clearer understanding of the technical features, objectives and effects of the present application, the specific embodiments of the present application will be described in detail with reference to the drawings.
[0024] The embodiments of the present application provide a five-dimensional fast interpolation method for seismic data based on a convolutional neural network.
[0025] Please refer to Figure 1 , Figure 1 is a step diagram of a five-dimensional fast interpolation method for seismic data based on a convolutional neural network in the embodiments of the present application, comprising: S1: constructing a 5D reconstruction module by using a low-dimensional network; obtaining original seismic data containing missing traces; S2: performing self-enhancement training on the low-dimensional sub-network in the 5D reconstruction module by using the seismic data and combining a progressive self-enhancement training strategy; S3: obtaining work area seismic data to be reconstructed, and using the trained 5D reconstruction module to perform interpolation reconstruction on the work area seismic data.
[0026] Figure 1 The work area data in the above formula is the work area seismic data.
[0027] Step S1 comprises: S11: denoting the original seismic data containing missing traces as , and the five dimensions of the seismic data are denoted as ; In a specific implementation of the present application, the seismic data can be arranged into a five-dimensional data body in multiple domains, including: shot-receiver domain (source horizontal and vertical coordinates, receiver point horizontal and vertical coordinates, and time dimension), common midpoint domain (center point horizontal and vertical coordinates, offset horizontal and vertical coordinates, and time, or center point horizontal and vertical coordinates, offset, azimuth, and time), OVT domain (center point horizontal and vertical coordinates, offset, azimuth, and time), etc.
[0028] Constructing a sub-dimension set ,in for A subset of , The number of elements contained , and all The union of covers all 5 dimensions, that is, ; S12: The 5D reconstruction module includes A low-dimensional subnetwork, represented as , the low-dimensional subnetwork along the sub-dimension Reconstruction of seismic data; Low-dimensional subnetwork The output of is the updated guidance data; Low-dimensional subnetwork The input is dual-channel data, the two channels are the original seismic data with missing traces and the upper layer low-dimensional sub-network Updated boot data.
[0029] As an example, when , , When , the 5D reconstruction module consists of a 3D convolutional network and a 2D convolutional network. Figure 2 As shown, Select the classic 3D-Unet network ( Figure 2 a) In the figure, the cube represents the feature map, the number below the feature map indicates the number of channels, and the arrows indicate different types of operations. The network as a whole is an encoding and decoding structure, including three layers of downsampling and three layers of upsampling. Downsampling uses a maximum pooling operation with a stride of 2, and upsampling uses nearest neighbor interpolation; Select 2D residual network ( Figure 2 b) It contains 4 residual modules. In addition to the input and output, the number of feature channels is 64. The two networks are respectively and express.
[0030] Step S2 includes: S21: Set the number of self-enhancement rounds to ; S22: Constructing boot data and bootstrap training dataset , whose initial value is set to 0, respectively and ; S23: For The steps of self-reinforcement training are: Training low-dimensional sub-network ,renew and For and ; training low-dimensional sub-networks , updating and for and ; training in turn until all low-dimensional sub-networks are trained and updated and , completing a round of self-enhancement; and and are recorded as and ; S24: taking and trained in the round of self-enhancement as initial values; based on and , repeating step S23 to train for the +1 round until completing all rounds of self-enhancement training, obtaining trained low-dimensional sub-networks, recorded as .
[0031] As an embodiment, as shown in FIG. 2, in the Figure 3 round of self-enhancement, in turn, train and and update and . Taking for example, first, from the original missing data , intercept 2D data blocks in the direction as training data sets, for each data block, normalize it to [-1, 1] by dividing the maximum value of the absolute value of all signal points, and record the normalized training data set as . Each data block corresponds to an original sampling operator, recorded as . Then, for each data block, randomly generate a new mask operator, recorded as ; and use the mask operator to construct a self-supervised training data pair, the input is , and the label is , , , where represents Hadamard product. Finally, intercept the data set corresponding to from , and record the normalized data set as , and and stacked as input, labels, by minimizing the following loss function:
[0032] After training, based on the trained , the and are updated by two-step reconstruction method. First, data blocks and are intercepted from and respectively using overlapping sliding window strategy, where is the number of data blocks obtained by sliding window strategy, and are normalized data; then, and are stacked along the channel dimension to construct two-channel input data blocks, which are input into the trained network to obtain the output ; next, and are stacked along the channel dimension and input into the network again to obtain the output denoted as ; according to the sliding window position, is reorganized and de-normalized to obtain . Using to update obtains . From , a part of sub-data pairs are randomly selected along the dimension to update to obtain . The training of is similar to that of . Since is the last network in the 5D reconstruction module, it is denoted as .
[0033] Step S23 includes: training the low-dimensional sub-network using a mask self-supervised strategy; constructing a self-supervised training data pair from the original seismic data with missing traces , as follows: intercepting data blocks along the dimension from , and normalizing them, denoted as , and denoting the sampling operator corresponding to each data block as ; For each data block, a new mask operator is generated, denoted as ; The self-supervised training data pair is constructed, the input is , and the label is , , where represents the Hadamard product.
[0034] Step S23 further includes: The input of the low-dimensional subnetwork is two-channel data , where is the data block intercepted in , and the interception position corresponds to , and are stacked along the channel direction to form the input of the two-channel low-dimensional subnetwork.
[0035] Step S23 further includes: The training of the low-dimensional subnetwork is completed by optimizing the algorithm to minimize the self-supervised loss function, and the self-supervised loss function is calculated as follows:
[0036] , where represents the square of the Frobenius norm.
[0037] Step S23 further includes: The trained low-dimensional subnetwork is used to update to obtain ; The data blocks and are intercepted from and using the overlapping sliding window strategy, where is the number of data blocks obtained by the sliding window strategy, and are normalized data; The and are stacked along the channel dimension to construct a two-channel input data block, which is input into the trained network to obtain the output ; The and are stacked along the channel dimension and input into the network again to obtain the output, denoted as ; Reorganize according to the sliding window position , and get the inverse normalization .
[0038] Step S23 also includes: Update to get , as follows: From , along dimensional random selection of part of the data pairs Update, that is, randomly selected , let
[0039] Where the subscript indicates the sub-data along , and indicates The number of data points in the complement of .
[0040] As an embodiment, the signal-to-noise ratio (SNR) of the sampled seismic trace in and is used to evaluate the performance of the network after the first round of training. The SNR calculation formula is as follows:
[0041] Where, is the sampling operator corresponding to .
[0042] Step S3 includes: S31: Set the number of iterations of the 5D reconstruction module to ; S32: Construct the guide data , whose initial value is set to 0, denoted as ; S33: For the first iteration, the steps are: update to using the trained low-dimensional sub-network ; update to using the trained low-dimensional sub-network ; and the like, until is obtained. Aggregate to obtain the output, denoted as ; The aggregation method is:
[0043] in, and Respectively and of The first earthquake track, is the weight parameter, The local sampling rate control, , The bigger the The bigger; S34: Repeat step S33 until all Iterations, get the interpolation result , For the The output of the iteration, Represents the original data The corresponding sampling operator.
[0044] As an embodiment, simulation data is used to verify the interpolation effect of the present invention. The data is the SEG open source C3 narrow azimuth data, which contains 51 routes, 96 guns per route, 8 cables, 68 receivers per cable, and 625 time sampling points per receiver. The two abnormal route data and the first 27 gun sets with low coverage in each route are removed, and the data are arranged in the order of time, gun-y, detector-y, gun-x, and detector-x into a 5D data volume with a size of 625×69×68×49×8. The first three dimensions correspond to the present invention. , the last two dimensions correspond to 90% of the seismic traces were artificially removed randomly to construct 90% missing data. Figure 5 A common shot point gather is shown, with the shot point coordinates being (20, 20). Figure 5 a is the complete data, Figure 5 b represents 90% missing data.
[0045] As an embodiment, the present invention is used to reconstruct 90% of missing data. is 8, is 6. Randomly intercept data training samples from 5D data, and Conduct training, and in each round of self-enhancement, and Train for 10 rounds in sequence. The number of training samples is 10000, the data block size is 48×48×48, and the batch size is set to 20. The number of training samples is 100,000, the data block size is 49×8, and the batch size is set to 20. Mask operator and The missing rate is set to 60%, the learning rate is set to 0.0001, and the network parameters are trained by the Adam gradient descent method. The trained 3D and 2D networks are recorded as and .
[0046] As an example, during the testing phase, Figure 4 The process reconstructs the 5D data. Dimension, based on The network is reconstructed using an overlapping sliding window strategy with a sliding window size of 48×48×48, a step size of 24, and the average of the overlapping parts. Dimension, direct use The 2D slices of size 49×8 were reconstructed. Comparing the reconstruction results of the present invention with those of 3D-Unet, in terms of SNR, the SNR of the 3D-Unet result was 3.72dB, while the SNR of the present invention result was 8.84dB, which was 5.12dB higher than that of 3D-Unet. Figure 6 The common shot gather with shot coordinates (20, 20) and detector-x coordinate 2 was intercepted to compare the reconstruction effects of the present invention and 3D-Unet. Figure 6 (a)-(d) show the complete data, 90% missing data, 3D-Unet reconstruction, and the reconstruction of the present invention, respectively. As can be seen from the figures, in areas with continuous missing data, the reconstruction of the present invention has a clearer event structure and better signal protection, demonstrating that the present invention is a very effective five-dimensional interpolation method.
[0047] This application also discloses an electronic device. Figure 7 , Figure 7 Schematic diagram of the structure of an electronic device disclosed in an embodiment of the present application. The electronic device 500 may include: at least one processor 501, at least one network interface 504, a user interface 503, a memory 505, and at least one communication bus 502.
[0048] The communication bus 502 is used to implement the connection and communication between these components.
[0049] The user interface 503 may include a display screen, and the optional user interface 503 may also include a standard wired interface or a wireless interface.
[0050] The network interface 504 may optionally include a standard wired interface or a wireless interface (such as a WI-FI interface).
[0051] The above merely specific examples of the present disclosure, and cannot limit the scope of the present disclosure. That is, any equivalent changes and modifications made in accordance with the teachings of the present disclosure are still within the scope of the present disclosure.
[0052] This application is intended to cover any variations, uses, or adaptations of the present disclosure following, in general, the principles of the present disclosure and including such departures from the present disclosure that come within known or customary practice in the art to which the present disclosure pertains. The specification and drawings should be regarded as illustrative only, and the scope and spirit of the present disclosure are defined by the claims.
Claims
1. A five-dimensional fast interpolation method for seismic data based on convolutional neural network, characterized in that: The method comprises the following steps: S1: Use low-dimensional networks to build a 5D reconstruction module; obtain original seismic data with missing traces; S2: Using seismic data and a progressive self-enhancement training strategy, the low-dimensional sub-network in the 5D reconstruction module is self-enhanced. S3: Obtain the seismic data of the work area to be reconstructed; use the trained 5D reconstruction module to interpolate and reconstruct the seismic data of the work area.
2. The five-dimensional fast interpolation method for seismic data based on convolutional neural network according to claim 1, characterized in that: Step S1 includes: S11: The original seismic data with missing traces is , the five dimensions of seismic data are expressed as ; Constructor dimension collection ,in for A subset of , The number of elements contained , and all The union of covers all 5 dimensions, that is ; S12: The 5D reconstruction module includes A low-dimensional subnetwork, represented as , the low-dimensional subnetwork along the sub-dimension Reconstruction of seismic data; Low-dimensional subnetwork The output of is the updated guidance data; Low-dimensional subnetwork The input is dual-channel data, the two channels are the original seismic data with missing traces and the upper layer low-dimensional sub-network Updated boot data.
3. The five-dimensional fast interpolation method for seismic data based on convolutional neural network according to claim 2, characterized in that: Step S2 includes: S21: Set the number of self-enhancement rounds to ; S22: Constructing boot data and bootstrap training dataset , whose initial value is set to 0, respectively and ; S23: For The steps of self-reinforcement training are: Training low-dimensional sub-network ,renew and for and ; Training low-dimensional sub-network ,renew and for and ; The training continues until all low-dimensional sub-networks have completed training and obtained updated and , complete a round of self-enhancement; and Recorded as and ; S24: After rounds of self-enhancement training and As initial value; based on and Repeat step S23 to perform the +1 round of training until all are completed After a round of self-enhancement training, a trained low-dimensional sub-network is obtained, which is recorded as .
4. The five-dimensional fast interpolation method for seismic data based on convolutional neural network according to claim 3, characterized in that: Step S23 includes: A masked self-supervision strategy is used to train low-dimensional sub-networks Conduct training; From the original seismic data with missing traces Construct self-supervised training data pairs in the following way: Middle Edge Dimension truncation Data blocks, and normalized, recorded as , and the sampling operator corresponding to each data block is ; For each data block, a new mask operator is generated, denoted as ; Construct self-supervised training data pairs, the input is , tagged , ,in represents the Hadamard product.
5. The five-dimensional fast interpolation method for seismic data based on convolutional neural network according to claim 4, characterized in that: Step S23 further includes: Low-dimensional subnetwork The input is two-channel data ,in for The data block intercepted in correspond, and The input of the low-dimensional sub-network with two channels is stacked along the channel direction.
6. The five-dimensional fast interpolation method for seismic data based on convolutional neural network according to claim 5, characterized in that: Step S23 further includes: Low-dimensional subnetwork The training of is completed by minimizing the self-supervised loss function through the optimization algorithm. The self-supervised loss function is calculated as follows: in, represents the square of the Frobenius norm.
7. The five-dimensional fast interpolation method for seismic data based on convolutional neural network according to claim 6, characterized in that: Step S23 further includes: Using the trained low-dimensional sub-network right Update to get ; Using overlapping sliding window strategy from and Intercept data blocks and ,in The number of data blocks obtained for the sliding window strategy, and All are normalized data; Will and Stack along the channel dimension to construct a two-channel input data block and input it into the trained network Output ; Will and Stacked along the channel dimension and fed back into the network , the output is recorded as ; Reorganize according to sliding window position , and denormalize to get .
8. The five-dimensional fast interpolation method for seismic data based on convolutional neural network according to claim 7, characterized in that: Step S23 further includes: use renew get ,as follows: from Middle Edge Dimension randomly selects some sub-data pairs Update, that is, randomly select ,make The subscript Indicates along The intercepted sub-data, express exist The number of data points in the complement set.
9. The five-dimensional fast interpolation method for seismic data based on convolutional neural network according to claim 1, characterized in that: Step S3 includes: S31: Set the number of iterations of the 5D reconstruction module to ; S32: Constructing guidance data , its initial value is set to 0, recorded as ; S33: For Round iteration, the steps are: using the trained low-dimensional sub-network renew for ; Using the trained low-dimensional sub-network renew for ; Continue in sequence until you get ; polymerization , the output is recorded as ; The aggregation method is: in, and Respectively and of The first earthquake track, is the weight parameter, The local sampling rate control, The bigger the The bigger; S34: Repeat step S33 until all Iterations, get the interpolation result , For the The output of the iteration, Represents the original data The corresponding sampling operator.
10. An electronic device, characterized in that: It includes a processor, a memory, a user interface and a network interface, the memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory so that the electronic device executes the method according to any one of claims 1 to 9.