A signal reconstruction method and system based on implicit neural representation

Abstract

The disclosure provides a signal reconstruction method and system based on implicit neural representation, relating to the technical field of signal reconstruction, comprising: establishing a series of basic metric grids with different distance metrics for the multimedia data to be processed, constructing different feature spaces through multiple distance metrics, and establishing feature grids in these spaces to store features related to different order derivatives; obtaining the features of the signal at different orders through the coordinate index related feature grid of the signal to be reconstructed; using a high-order term extrapolation decoder to fuse features of different orders in each layer, gradually refining the reconstruction result, and converting the reconstructed features into target signal values through the output layer; the application uses multiple basic metric grids to fit any nonlinearity of the target signal in the feature space, uses hash mapping to store different metric grids respectively to improve the compactness of the model, and improves the accuracy, adaptability and stability of the implicit neural representation method.

Description

Technical Field

[0001] This disclosure relates to the field of signal reconstruction technology, specifically to a signal reconstruction method and system based on implicit neural representation. Background Technology

[0002] Driven by the digital age, technologies such as augmented reality (AR), virtual reality (VR), and 3D reconstruction are playing an increasingly important role in scientific research and practical production and daily life. These technologies generate a large amount of multimodal data every day, including images, videos, and 3D models. However, most current signal characterization methods focus on a specific data format, which leads to the need for different technical solutions for downstream tasks such as signal transmission and compression.

[0003] With the rapid development of deep learning technology, many researchers have applied implicit neural representations (INRs) to computer vision and graphics. As a unified signal representation method, implicit neural representation trains a dedicated neural network for each target signal. Utilizing the flexibility of neural network inputs and outputs, it can adapt to different types of signals simply by modifying the supervision information during training. In particular, it can effectively process three-dimensional data, facilitating the efficient storage and processing of signals of different modalities. The expressive power of implicit neural representations mainly depends on three aspects: the ability to fit complex signals, the compactness of the neural network, and the time required to fit the target signal. This method has a simple structure and a small number of parameters, but it is difficult to fit complex or large-scale signals, and the training time is relatively long, which limits its practical application.

[0004] In recent years, implicit neural representation methods (also known as hybrid representations) based on explicit structures such as voxel grids have been extensively studied. These methods use a set of feature vectors to represent local regions of a signal and use interpolation as an indexing rule to calculate the features of a query point by weighting the local features. A lightweight decoder then converts these features into the target signal value. These methods significantly accelerate fitting speed and accuracy by storing local features of the signal, and can adjust the size of the feature grid according to the complexity of the signal, thus achieving efficient reconstruction of large-scale signals. However, explicitly storing features reduces the compactness of the neural representation, and the indexing rule using simple linear interpolation also limits model performance. When the signal is more complex, denser local feature representation is required, further exacerbating parameter inefficiency. Since the complexity of the signal varies in different regions, using the same number of features to fit local signals at all locations leads to significant redundancy. Existing methods construct data structures for specific signals during training through heuristic strategies such as pruning and merging, or introduce sparsity constraints by simplifying the network structure to reduce the number of stored features, but these methods cannot improve the fitting ability for complex signals.

[0005] The shortcomings of the aforementioned implicit neural representation methods in terms of accuracy, adaptability, and stability can be summarized as follows:

[0006] 1) Implicit neural representations based on feature grids use simple line interpolation, resulting in poor reconstruction performance;

[0007] 2) The feature grid storage is highly redundant and the parameters are inefficient;

[0008] 3) The decoder has a simple structure but weak nonlinear fitting ability. Summary of the Invention

[0009] To address the aforementioned issues, this disclosure proposes a signal reconstruction method and system based on implicit neural representation. It uses multiple basic metric grids to fit arbitrary nonlinearities of the target signal in the feature space, utilizes hash mapping to store different metric grids to improve model compactness, and gradually refines nonlinear features and converts them into the target signal through a high-order term extrapolation decoder, thereby improving the accuracy, adaptability, and stability of the implicit neural representation method.

[0010] According to some embodiments, the present disclosure adopts the following technical solutions:

[0011] A signal reconstruction method based on implicit neural representation includes:

[0012] Drawing on Taylor expansion, a series of basic metric grids with different distance measures are established for the multimedia data to be processed. Different feature spaces are constructed through multiple distance measures, and feature grids are built in these spaces to store features related to different derivatives.

[0013] By indexing the feature grid related to the coordinates of the signal to be reconstructed, the characteristics of the signal at different orders can be obtained;

[0014] By using a higher-order term extrapolation decoder, features of different orders are fused in each layer to gradually refine the reconstruction results, and the reconstructed features are converted into target signal values ​​through the output layer.

[0015] According to some embodiments, the present disclosure adopts the following technical solutions:

[0016] A signal reconstruction system based on implicit neural representation, comprising:

[0017] The grid construction module is configured to: draw on Taylor expansion to establish a series of basic metric grids with different distance measures for the multimedia data to be processed, construct different feature spaces through multiple distance measures, and build feature grids in these spaces to store features related to different derivatives;

[0018] The feature indexing module is configured to: index the relevant feature grid by the coordinates of the signal to be reconstructed, thereby obtaining the features of the signal at different orders;

[0019] The signal decoding module is configured to: use a higher-order term extrapolation decoder to fuse features of different orders in each layer, gradually refine the reconstruction results, and convert the reconstructed features into target signal values ​​through the output layer.

[0020] According to some embodiments, the present disclosure adopts the following technical solutions:

[0021] A computer program product includes a computer program that, when executed by a processor, implements the signal reconstruction method based on implicit neural representation.

[0022] According to some embodiments, the present disclosure adopts the following technical solutions:

[0023] A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the signal reconstruction method based on implicit neural representation.

[0024] According to some embodiments, the present disclosure adopts the following technical solutions:

[0025] An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform a signal reconstruction method based on implicit neural representation.

[0026] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0027] This invention uses multiple basic metric grids to fit arbitrary nonlinearities of the target signal in the feature space. It utilizes hash mapping to store different metric grids to improve model compactness. The features indexed in the basic metric grids are used as inputs to the higher-order term extrapolation decoder. At each layer of the decoder, the features of different metric grids are multiplied with the decoder features through Hadamard product to predict higher-order terms. The nonlinear features are gradually refined and converted into the target signal, which improves the reconstruction quality. It has a more obvious advantage, especially for signals with larger scale and more complex details. It significantly reduces erroneous holes and spikes while maintaining model compactness. Attached Figure Description

[0028] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0029] Figure 1 This is an overall framework diagram of Example 1.

[0030] Figure 2 This is a structural diagram of the high-order term extrapolation decoder in Example 1.

[0031] Figure 3 This is a comparison chart of the 2D image fitting results for Example 1.

[0032] Figure 4 This is a comparison chart of the 2D image fitting results error in Example 1.

[0033] Figure 5 This is a comparison chart of the fitting results of the three-dimensional model in Example 1.

[0034] Figure 6 This is a comparison chart of the 5D neural radiation field reconstruction results in Example 1. Detailed Implementation

[0035] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0036] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0037] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0038] Terminology Explanation:

[0039]

[0040]

[0041] Example 1

[0042] One embodiment of this disclosure provides a signal reconstruction method based on implicit neural representation, including:

[0043] Step S1: Using Taylor expansion, establish a series of basic metric grids with different distance measures for the multimedia data to be processed. Construct different feature spaces through multiple distance measures, and establish feature grids in these spaces to store features related to different derivatives.

[0044] Step S2: By indexing the relevant feature grid using the coordinates of the signal to be reconstructed, the features of the signal at different orders can be obtained;

[0045] Step S3: Using a higher-order term extrapolation decoder, features of different orders are fused in each layer to gradually refine the reconstruction results, and the reconstructed features are converted into target signal values ​​through the output layer.

[0046] As one embodiment, this disclosure provides a signal reconstruction method based on implicit neural representation, such as... Figure 1 As shown, firstly, a basic metric grid is established by drawing inspiration from Taylor expansion. Different nonlinear spaces are constructed using various nonlinear distance metrics to approximate different higher-order terms in the Taylor expansion, and feature grids are generated in these spaces. The coordinates x of the input signal to be reconstructed are used to index these feature grids, thereby obtaining a nonlinear approximation of the signal in the latent space. Secondly, based on the sparsity characteristics of different higher-order terms, hash maps of different lengths are designed for each feature grid to achieve efficient storage and maintain the compactness of the model. Finally, in the decoding stage, the features indexed in each metric grid are summed as the initial input. Features of different orders are fused in each layer to gradually refine the reconstruction result. The reconstructed features are then converted into target signal values ​​through the output layer. The specific implementation process is described in detail below.

[0047] First, let me briefly introduce the theoretical knowledge used:

[0048] Given a set of T observations of a target signal. Implicit neural representation is defined as a modeling signal coordinate x to the corresponding signal value Neural network mapping:

[0049]

[0050] The original implicit neural representation method directly fits the signal using a fully connected neural network, taking the signal's coordinates as input and performing end-to-end supervised training with the signal values, as expressed by the formula:

[0051]

[0052] in, W represents the output feature of the l-th layer. l and b l ψ(·) is the learnable parameter of this layer, ψ(·) is the activation function, and L is the total number of network layers.

[0053] The grid-based implicit neural representation uses a set of feature vectors to represent local regions of the signal and interpolation as the indexing rule. It calculates the features of a query point by weighting the local features and then converts these features into the target signal value using a lightweight decoder. This can be expressed by the following formula:

[0054]

[0055] Wherein, the feature grid is represented as Discrete coordinates x defined in the input domain i Above, g(·) is a distance-related indexing function, and the commonly used distance metric is linear distance |xx. i |, decoder f d It is usually a simple, fully connected network.

[0056] Taylor series expansion is a formula that uses information about a function at a point to describe the values ​​of that function in its vicinity. Its initial purpose was to approximate the function's behavior around a point using a polynomial. Let n be a positive integer. If a function f defined on an interval containing a is differentiable to the order n+1 at point a, then for any x on this interval, we have:

[0057]

[0058] The polynomial here is called the Taylor expansion of the function at a, and the remainder R n (x) is the remainder term of Taylor's formula, which is (xa). n The higher-order infinitesimals.

[0059] Based on the above theoretical knowledge, the following will discuss... Figure 1 The three stages are explained below:

[0060] I. Constructing the basic metric grid:

[0061] In grid-based implicit neural representations, the grid Z can be viewed as a discrete feature representation of a continuous signal in the feature space, and a continuous linear approximation can be obtained through an index function. Existing methods use linear interpolation as the indexing rule, but the target signal often exhibits complex nonlinear characteristics, corresponding to a complex nonlinear feature space. Therefore, this embodiment proposes that any point of a continuous function can be approximated by a Taylor expansion of polynomials containing terms of different orders at its neighboring points, using a series of basic metric grids to fit the complex nonlinear representation of the signal in the feature space.

[0062] First, according to the Taylor expansion, the nonlinear higher-order terms have the following form:

[0063]

[0064] Where x and x i Z represents the coordinates of the current query point (i.e., the coordinates of the signal to be reconstructed) and the vertex coordinates of the stored features in the grid, respectively. (n) (x i ) indicates that the feature is at vertex x iThe nth derivative at (xx) i ) n This indicates that a nonlinear distance metric based on a polynomial is used as a basis function.

[0065] Then, based on the above formula for nonlinear higher-order terms, a series of basic metric grids are established. Different nonlinear distance metrics are specified to approximate polynomials of different orders. Feature grids are established in these metric spaces to store features related to derivatives of different orders.

[0066] Therefore, a series of basic metric grids with different nonlinear metrics are constructed as follows:

[0067]

[0068] in, This indicates that the definition is in the metric d. p For the feature grid below, in order to maintain consistency with Taylor expansion, the exponential form of the p-norm can be used as a metric of different orders.

[0069] For query point x, this embodiment indexes all basic metric grids according to the defined different metrics:

[0070]

[0071] In the optimization process of implicit neural representation, the indexing process designed in this embodiment can learn different orders of derivatives of the ideal features of the signal through a basic metric grid, and generate higher-order terms in the Taylor expansion through metric-based indexing.

[0072] As a special case, the features indexed in the first basic metric grid... It provides a linear approximation of latent spatial features, consistent with existing grid-based neural representation methods; while other basic metrics index features in the grid. This represents the characteristics induced by higher-order derivatives, providing nonlinear terms.

[0073] By establishing a series of basic metric grids, it is possible to fit any nonlinearity exhibited by complex signals in the feature space, thereby achieving accurate fitting of complex signals. In addition to using the p-norm as a nonlinear metric in accordance with the Taylor expansion, different basic metric grids can also be defined, because these metrics can be further represented using Taylor expansion, thereby achieving more complex nonlinear fitting.

[0074] II. Compact Representation Based on Hash Maps:

[0075] Compared to the general method, for each vertex coordinate x in the mesh iThis requires storing multiple features from different basic metric grids, representing linear approximations and higher-order terms of the signal features. Using a hash table to store the feature grid is a common compact representation, essentially leveraging the sparsity of the stored features to store features in a hash table with a much smaller number of features than the feature grid itself. However, simply adding the number of basic metric grids as an additional dimension to construct a hash map not only increases the probability of hash collisions in space but also causes collisions between different basic metric grids. Since different basic metric grids contain features of different orders, these hash collisions can significantly impact fitting accuracy. Therefore, this embodiment prevents such collisions by hashing the basic metric grids separately.

[0076] Because different fundamental metric grids store information about derivatives of different orders, the sparsity of the grids varies, exhibiting a characteristic where sparsity increases with the order of the derivative. In the smooth regions of the signal, higher-order derivatives are all 0, making... Linear approximation of sparsity ratio characteristics Much larger; therefore, this embodiment further encourages feature fusion in higher-order terms by setting a shorter hash table length for the higher-order metric grid, and the designed hash map can be represented as:

[0077]

[0078] in, This represents the bitwise XOR operation, π. j t is the specified large prime number, and t is the set hash table length.

[0079] By using the basic metric grid compression representation based on hash coding as described above, the model compactness is improved. Therefore, the number of grid parameters is similar to that of general methods. However, due to the use of nonlinear metrics to index features from different grids, this example obtains a more accurate nonlinear representation of the target signal in the latent space.

[0080] III. Design of a higher-order term extrapolation decoder:

[0081] Using hash mapping effectively reduces redundancy in the basic metric grid, but to maintain the method's compactness and fitting speed, three basic metric grids (including a linear metric) are used to balance representation accuracy and efficiency. To further reduce approximation errors caused by the limited number of grids, this embodiment further develops a higher-order term extrapolation decoder, which progressively predicts higher-order terms based on the linear approximations and lower-order terms stored in the grids, such as... Figure 2 As shown:

[0082] First, the different basic metric features indexed by the x-coordinate of the signal to be reconstructed. Perform an addition operation and use it as the decoder input:

[0083]

[0084] h0 can be seen as an initial approximation of the nonlinear characteristic, obtained from the basic metric grid.

[0085] In each layer of the decoder, the features first pass through a linear layer and an activation function. Then, the linear approximation features and relatively low-order terms stored in different metric grids are input into the modulation layer. The outputs of the linear layers are then processed by activation functions and aggregated using a Hadamard product to generate higher-order terms. Taking the l-th layer of the decoder as an example, this process is as follows:

[0086]

[0087]

[0088] in, ω represents the approximate value of the gradually refined nonlinear features during the decoding process. l (·) and γ l (·) represent the decoder backbone layer and modulation layers with different order features, respectively. ω and σ γ These are the activation functions for the backbone layer and the modulation layer. In this embodiment, sin and sin are used respectively. 2 .

[0089] By simplifying the activation function, each layer of the decoder multiplies the current nonlinear feature with features of different orders through a Hadamard product, effectively increasing the highest order of the predicted nonlinear feature. After an M-layer decoder, the theoretically achievable highest order of the nonlinear approximation feature is: Finally, the refined nonlinear feature h M Transformed to the signal domain via a linear layer:

[0090]

[0091] Among them, W o and b o Represents the learnable parameters of a linear layer. This represents the predicted signal value.

[0092] The effectiveness of this embodiment was verified through experiments. In the experimental setup, the algorithm model of this embodiment was deployed on the PyTorch platform, and training and testing were completed on an NVIDIA GeForce RTX 3090 GPU, enabling end-to-end training of the network. The number of basic metric grids was set to 3, and [x...] was used... 2 ,x 3[sin(·),arcsin(·)], [sin(·),cos(·)] are used as nonlinear metrics for testing. The higher-order term extrapolation decoder consists of five layers, with a hidden layer width of 64, and the modulation layer inputs are... The initial learning rate is 1e-3, and a cosine annealing learning rate decay strategy is used. Different loss functions are used for different types of signals, including mean-square error (MSE) and mean absolute percentage error (MAPE).

[0093] This embodiment was tested on various implicit neural representation tasks, including 2D image fitting, 3D symbolic distance function fitting, and 5D neural radiation field reconstruction (3D scene reconstruction). The specific implementation of different tasks will be described below:

[0094] For 2D image signal fitting, the Kodak dataset was first used for testing. The number of model parameters was controlled to approximately 207k by adjusting the hash table length T and the resolution of the basic metric grid. The model was trained for 20,000 steps, and PSNR and SSIM were used to evaluate the quality of the reconstructed images. For 3D symbolic distance function signals, this embodiment used the Stanford 3D Scan Repository and a complex "engine" 3D model for testing. The number of parameters was set to 905K, and the model was trained for 20,000 steps. Intersection over Union (IoU), Normal Angular Error (NAE), and Chamfer Distance (CD) were used as evaluation metrics for comprehensive comparison. For 5D neural radiation field reconstruction (3D scene signals), the Blender dataset was used for testing. The model was first configured based on NerfAcc parameters to maintain comparability, trained for 30,000 steps, and PSNR, SSIM, and LPIPS (VGG) were used to evaluate the quality of the new perspective images of the 3D scene.

[0095] Table 1 compares the results with existing methods on the 2D image signal fitting task.

[0096]

[0097]

[0098] The experimental results are compared and analyzed below. Table 1 shows the 2D image signal fitting test results. "↑" and "↓" indicate that lower and higher indices, respectively, indicate better performance. It can be seen that compared to the original method, this embodiment improves the quality of the reconstructed image while maintaining model compactness. Furthermore, in tests with different parameter values, the method proposed in this embodiment consistently achieved the highest reconstruction quality. A comparison of 2D image fitting results is provided below. Figure 3 As shown, this embodiment achieves more accurate reconstruction in image detail areas. Secondly, this embodiment demonstrates scalability by using a larger-scale image testing method. The error graphs of this embodiment and the original method are shown below. Figure 4 As shown, it can be seen that it has a more obvious advantage on signals with larger scale and more complex details.

[0099] Table 2 compares the results with existing methods on the 3D symbolic distance function fitting task.

[0100]

[0101] The test results of the 3D symbolic distance function signal are shown in Table 2. The results show that the normal vector angle error on the Stanford 3D scanning repository in this embodiment is reduced by an average of 9.6% compared to the original method, and by 3.4% compared to the current best method, while maintaining optimal performance in other metrics; the fitting results of the "engine" 3D model are compared to... Figure 5 As shown, this embodiment produces more complete reconstruction results in complex areas, with a significant reduction in erroneous holes and spikes.

[0102] Table 3 compares the results with existing methods on the 5D neural radiation field reconstruction task.

[0103]

[0104] The test results of 5D neural radiation field reconstruction (3D scene signal) are shown in Table 3. In this embodiment, the reconstruction results on 8 scenes in the Blender dataset show improvements over the original method in all evaluation metrics, while maintaining a compact model parameter set. A comparison of the 5D neural radiation field reconstruction results is shown below. Figure 6 As shown, the advantages of this method are more obvious in the detailed areas of the scene.

[0105] In summary, this embodiment addresses a hybrid representation method based on feature grids in implicit neural representations. It uses multiple basic metric grids to fit arbitrary nonlinearities of the target signal in the feature space, and utilizes hash mapping to store different metric grids to improve model compactness. Features indexed in the basic metric grids are used as input to the higher-order term extrapolation decoder. At each layer of the decoder, the features of different metric grids are multiplied by the decoder features through a Hadamard product to predict higher-order terms, progressively refining the nonlinear features and converting them into the target signal. Experiments on various signal fitting tasks, including 2D images, 3D symbolic distance functions, and 3D scenes (5D neural radiation fields), demonstrate that this embodiment improves both fitting accuracy and model compactness compared to existing methods.

[0106] Example 2

[0107] One embodiment of this disclosure provides a signal reconstruction system based on implicit neural representation, comprising:

[0108] The grid construction module is configured to: draw on Taylor expansion to establish a series of basic metric grids with different distance measures for the multimedia data to be processed, construct different feature spaces through multiple distance measures, and build feature grids in these spaces to store features related to different derivatives;

[0109] The feature indexing module is configured to: index the relevant feature grid by the coordinates of the signal to be reconstructed, thereby obtaining the features of the signal at different orders;

[0110] The signal decoding module is configured to: use a higher-order term extrapolation decoder to fuse features of different orders in each layer, gradually refine the reconstruction results, and convert the reconstructed features into target signal values ​​through the output layer.

[0111] Example 3

[0112] One embodiment of this disclosure provides a computer program product, including a computer program that, when executed by a processor, implements the signal reconstruction method based on implicit neural representation.

[0113] Example 4

[0114] One embodiment of this disclosure provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the signal reconstruction method based on implicit neural representation.

[0115] Example 5

[0116] One embodiment of this disclosure provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to perform a signal reconstruction method based on implicit neural representation.

[0117] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0118] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0119] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A signal reconstruction method based on implicit neural representations, characterized in that, Comprising: According to the Taylor expansion, a series of basic metric grids with different distance metrics are established for the multimedia data to be processed, different feature spaces are constructed by multiple distance metrics, and feature grids are established in these spaces to store features related to different order derivatives; By indexing the feature grids related to the coordinates of the signal to be reconstructed, the features of the signal at different orders are obtained; Using a high-order term extrapolation decoder, the features at different orders are fused in each layer to gradually refine the reconstruction result, and the reconstructed features are converted into target signal values through the output layer; Wherein, the series of basic metric grids with different distance metrics are represented by the formula: wherein, represents a basic metric grid defined in a metric space, and respectively represent the coordinates of a point in the multimedia data and the coordinates of a vertex storing a feature in the grid. The series of basic metric grids with different distance metrics are: The first fundamental metric grid provides a linear approximation of the feature space, while the other fundamental metric grid is a non-linear approximation constructed from a Taylor expansion.

2. The method of claim 1, wherein the implicit neural representation is based on a neural network. The nonlinear approximation constructed according to the Taylor expansion is represented by nonlinear high-order terms: wherein, and denote the coordinates of a point in the multimedia data and the coordinates of a vertex storing a feature in the grid, denote the derivative of the feature at the vertex , denote the non-linear distance metric based on a polynomial as a basis function.

3. The method of claim 1, wherein Also comprising: According to the sparsity characteristics of different high-order terms, different length hash mappings are designed for each feature grid.

4. The method of claim 1, wherein the implicit neural representation is based on a neural network. In each layer of the high-order term extrapolation decoder, the features first pass through a linear layer and an activation function, and then input linear modulation layers with linear approximations and relatively low-order terms stored in the basic metric grids, and the output is aggregated with the decoder output through Hadamard product to generate high-order terms.

5. A signal reconstruction system based on implicit neural representations, characterized in that, Adopting the signal reconstruction method according to any one of claims 1-4, comprising: The grid construction module is configured to: according to the Taylor expansion, a series of basic metric grids with different distance metrics are established for the multimedia data to be processed, different feature spaces are constructed by multiple distance metrics, and feature grids are established in these spaces to store features related to different order derivatives; The feature indexing module is configured to: by indexing the feature grids related to the coordinates of the signal to be reconstructed, the features of the signal at different orders are obtained; The signal decoding module is configured to: using a high-order term extrapolation decoder, the features at different orders are fused in each layer to gradually refine the reconstruction result, and the reconstructed features are converted into target signal values through the output layer.

6. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the signal reconstruction method based on implicit neural representation according to any one of claims 1-4.

7. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium is used to store computer instructions, which are executed by the processor to realize the signal reconstruction method based on implicit neural representation according to any one of claims 1-4.

8. An electronic device, comprising: Comprising: A processor, a memory and a computer program; wherein the processor is connected with the memory, and the computer program is stored in the memory, when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the signal reconstruction method based on implicit neural representation according to any one of claims 1-4.

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