Image denoising method and system based on differential equation and deep learning network

Abstract

The invention discloses an image denoising method and system based on a differential equation and a deep learning network. The method comprises the following steps: inputting a noise image subjected to image preprocessing into a differential equation NODE model and an improved deep learning network UNet; extracting multi-level features of the noise image layer by layer through a multi-scale channel feature fusion module of an improved UNet network; attention is increased for shallow information in the network through an attention mechanism module; and carrying out continuous time dynamic modeling by using a NODE model, taking the improved UNet network as a neural network vector field in the NODE model, and simulating a continuous time evolution process through an ODE solver to obtain a clear image. Through the fusion of ODE modeling and the deep learning network, the dependence on large-scale annotation data is reduced, parameters are evolved and optimized by using continuous time characteristics, the generalization ability of the model to complex noise is improved, and a good denoising effect can be obtained under the condition of few sample training.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to an image denoising method, computing device, and storable medium based on differential equations and deep learning networks. Background Art

[0002] Image denoising is generally regarded as a key task in the field of computer vision and image processing, and is widely used in scenarios such as medical image analysis, remote sensing image processing, industrial inspection, and autonomous driving.

[0003] Traditional image denoising methods are primarily based on partial differential equation (PDE) models (such as the PM model and the TV model), which suppress noise while preserving edges through anisotropic diffusion. However, traditional PDE methods rely on manual adjustment of gradient thresholds, which can easily misclassify noise as edges in high-noise environments. This can lead to residual noise or oversmoothing, causing staircase effects and blurred edges. Furthermore, PDE models are computationally complex, making them difficult to adapt to complex noise distributions and high-dimensional data.

[0004] In recent years, deep learning methods (such as convolutional neural networks and residual networks) have demonstrated excellent performance in denoising tasks due to their powerful feature learning capabilities. However, these methods rely on large amounts of labeled data, resulting in poor interpretability and overfitting in small sample sizes. Some deep models struggle to distinguish between detail and noise in low-noise conditions, leading to loss of high-frequency information. Neither traditional methods nor deep learning applications alone can achieve a balanced balance between noise suppression and detail preservation.

[0005] To address these issues, existing technologies attempt to combine the theoretical advantages of differential equations with the flexibility of deep learning. However, these fusion models are often limited by insufficient dynamic modeling or computational inefficiency. For example, deep networks based on discrete layer structures struggle to simulate continuous-time evolution processes, while the simple combination of traditional differential equations and shallow networks cannot fully capture multi-scale features and complex noise patterns.

[0006] Existing technologies, such as the invention patent application CN201810442970.5, rely on a static diffusion model based on a fourth-order partial differential equation. This model, without deep learning, relies on manually designed diffusion functions and mitigates the staircase effect only by adjusting the order. This model has limited adaptability to complex noise (such as non-Gaussian noise and spatially heterogeneous noise). Furthermore, it relies on extensive experimental parameter adjustments (such as the diffusion coefficient) and suffers from high simulation computational complexity (requiring MATLAB iterative solutions), making it difficult to adapt to the real-time requirements of real-world scenarios.

[0007] For example, the invention patent with application number CN202510153138.3 uses a two-stage serial architecture of traditional PDE and DnCNN (first diffusion model denoising, then CNN secondary processing). It is necessary to tune the threshold parameters and number of iterations of the PDE and the hyperparameters of the CNN separately, which makes the optimization coordination difficult and prone to falling into local optimality. In addition, DnCNN, as the second-stage processor, mainly relies on local convolution kernels to capture features and lacks multi-scale perception and global context modeling capabilities. The two-stage serial processing (PDE iteration + CNN forward pass) doubles the computational overhead and poor real-time performance.

[0008] Therefore, there is an urgent need for an image denoising method that is efficient, robust, interpretable, and adaptable to multiple noise levels to break through the performance bottleneck of existing technologies. Summary of the Invention

[0009] One of the purposes of the embodiments of the present invention is to address the shortcomings of the above-mentioned existing technologies and propose an image denoising method based on differential equations and deep learning networks. By constructing an end-to-end UNet-NODE dynamic fusion model and combining multi-scale features with the attention mechanism, the coordinated optimization of high-precision denoising and edge protection is achieved to solve the technical problems in the existing technology of insufficient detail retention in complex noise scenes, poor generalization of small sample training, and low computational efficiency, while also taking into account the balance between robustness and computational efficiency in small sample scenarios.

[0010] In order to solve the above technical problems, in a first aspect, an embodiment of the present invention provides an image denoising method based on differential equations and a deep learning network, the method comprising:

[0011] The pre-processed noisy image is input into the differential equation NODE model and the improved deep learning network UNet;

[0012] Extracting multi-level features of the noisy image layer by layer through the multi-scale channel feature fusion module of the improved deep learning network UNet, wherein the multi-level features include shallow edge texture and deep semantic information;

[0013] Increase attention to shallow information in the network through the attention mechanism module;

[0014] The NODE model is used for continuous-time dynamic modeling. The improved deep learning network UNet is used as the neural network vector field in the NODE model. The continuous-time evolution process is simulated by the ODE solver to obtain a clear image.

[0015] In a second aspect, an embodiment of the present invention further provides an image denoising system based on differential equations and deep learning networks, the system comprising a differential equation NODE model and an improved deep learning network UNet, wherein the improved deep learning network UNet comprises: an encoder, a decoder, a multi-scale channel feature fusion module, and an attention mechanism module, wherein three skip connections are formed between the encoder and the decoder by adding the multi-scale channel feature fusion module and the attention mechanism module, wherein the multi-scale channel feature fusion module is used in each skip connection, and the attention mechanism module is added to the skip connection of the lowest layer;

[0016] The multi-level features of the noisy image are extracted layer by layer through the multi-scale channel feature fusion module of the improved deep learning network UNet, wherein the multi-level features include shallow edge texture and deep semantic information, and the attention mechanism module is used to increase attention to the shallow information in the network, thereby obtaining the vector field of the improved deep learning network UNet;

[0017] The differential equation NODE model uses the improved deep learning network UNet as the neural network vector field in the NODE model, simulates the continuous time evolution process through the ODE solver, and obtains a clear image.

[0018] In a third aspect, an embodiment of the present invention further provides a computing device comprising a processor and a memory, wherein the memory is used to store a computer program, the computer program comprises program instructions, and the processor is configured to call the program instructions to execute the method as described above.

[0019] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, wherein the computer program includes program instructions, and when the program instructions are executed by a processor or a calculator, the processor executes the method as described above.

[0020] Compared with the prior art, the image denoising method and system based on differential equations and deep learning networks provided by the embodiments of the present invention have at least the following beneficial effects:

[0021] Based on the UNet network architecture and improved on the UNet network, the neural ordinary differential equation (NODE) ​​framework is integrated to build an end-to-end dynamic denoising. The image denoising process is modeled as a continuous-time dynamic system, and the evolution path is adaptively adjusted through the ODE solver, so as to combine the interpretability advantages of differential equation theory with the powerful feature extraction capabilities of deep learning. By adding a multi-scale channel feature fusion module (MSCFM) and a contrast enhancement attention mechanism module (CEA) to improve the deep learning network UNet, the edge and texture features are explicitly captured during the noise suppression process, achieving accurate denoising and detail preservation under various levels of Gaussian noise conditions; feature extraction is performed through the multi-scale channel feature fusion module, explicitly extracting local details, regional structures and global semantic features, preserving high-precision details in complex noise scenes, and combining continuous-time dynamic modeling to achieve an adaptive balance between noise suppression and edge protection.

[0022] By integrating dynamic ODE modeling with an improved deep learning network UNet structure, the model reduces reliance on large-scale annotated data and optimizes parameter efficiency using continuous-time feature evolution. This significantly improves the model's generalization ability for complex noise distributions, enabling it to achieve good denoising results even with few-sample training. Furthermore, an adaptive step-size solution strategy optimizes computational efficiency, achieving a balance between training time and denoising accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The preferred embodiments will be described below in a clear and understandable manner with reference to the accompanying drawings to further illustrate the above-mentioned characteristics, technical features, advantages and implementation methods of the present invention.

[0024] Figure 1 A schematic diagram of the UNet network structure in an image denoising system based on differential equations and deep learning networks according to an embodiment of the present invention;

[0025] Figure 2 This is a schematic diagram of the combination of differential equations and deep learning networks in an image denoising system based on differential equations and deep learning networks according to an embodiment of the present invention;

[0026] Figure 3 This is a schematic diagram of the structure of a multi-scale channel feature fusion module in a UNet network in an image denoising system based on differential equations and deep learning networks according to an embodiment of the present invention;

[0027] Figure 4 This is a schematic diagram of an attention mechanism module in a UNet network in an image denoising system based on differential equations and deep learning networks according to an embodiment of the present invention;

[0028] Figure 5 The figure is a schematic diagram of the structure of a computing device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the specific embodiments of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings and other embodiments can be obtained based on these drawings without inventive work.

[0030] To simplify the drawings, only the parts related to the invention are schematically shown in each figure. They do not represent the actual structure of the product. In addition, to simplify the drawings and facilitate understanding, in some figures, only one of the components with the same structure or function is schematically depicted or labeled. In the embodiments of the present invention, "one" not only means "only one" but also "more than one". The following mainly uses some specific embodiments as examples to describe in detail the implementation of the technical solution of the present invention.

[0031] like Figure 1 As shown, in order to achieve the purpose of the present invention, an embodiment of the present invention provides an image denoising system based on differential equations and deep learning networks, wherein the system includes a differential equation NODE model and an improved deep learning network UNet, wherein the improved deep learning network UNet includes: an encoder, a decoder, a multi-scale channel feature fusion module and an attention mechanism module, and three skip connections are formed between the encoder and the decoder by adding the multi-scale channel feature fusion module and the attention mechanism module, wherein the multi-scale channel feature fusion module is used in each skip connection, and the attention mechanism module is added to the skip connection of the lowest layer;

[0032] The multi-level features of the noisy image are extracted layer by layer through the multi-scale channel feature fusion module of the improved deep learning network UNet, wherein the multi-level features include shallow edge texture and deep semantic information, and the attention mechanism module is used to increase attention to the shallow information in the network, thereby obtaining the vector field of the improved deep learning network UNet;

[0033] The differential equation NODE model uses the improved deep learning network UNet as the neural network vector field in the NODE model, simulates the continuous time evolution process through the ODE solver, and obtains a clear image.

[0034] The embodiments of the present invention can be implemented through the following technical solutions:

[0035] like Figure 1 As shown, an improved deep learning network based on the UNet structure is constructed to output a vector field.

[0036] The improved deep learning network includes: an input layer, an encoder consisting of an upsampling module and several convolutional layers, a multi-scale channel feature fusion module (MSCFM), an attention mechanism (CEA), a decoder consisting of a downsampling module and several convolutional layers, and an output layer.

[0037] The improved deep learning network can effectively improve the image denoising performance, especially the restoration effect under low-noise conditions, by adding multi-scale channel feature fusion and contrast enhancement attention mechanism on the basis of the original UNet structure.

[0038] The input layer is used to receive the input noisy image (hereinafter referred to as the "noisy image"). The noisy image is a polluted image, and the task of the deep network is to remove the noise and restore the clearest possible image.

[0039] The downsampling module reduces the spatial size of the feature map by layer-by-layer downsampling (e.g., 2×2 max pooling) and extracts low-level features of the image (e.g., texture, edges, etc.). In this process, image details are gradually abstracted and encoded, laying the foundation for subsequent high-level semantic extraction.

[0040] The multi-scale channel feature fusion module (MSCFM) fuses the low-level features extracted from different levels according to channels, taking into account multi-scale semantics and detail information, thereby achieving a more comprehensive understanding of image content and facilitating detail reconstruction.

[0041] The attention mechanism module (CEA) is used to weight the image to highlight important areas (such as edges or details in the image) while suppressing irrelevant parts. Through the attention mechanism, we can focus more on recovering key information and enhance the denoising effect.

[0042] The upsampling module uses interpolation upsampling to restore the spatial size of the feature map layer by layer, and combines the jump connection of the corresponding downsampling stage to gradually reconstruct the image details, and finally outputs a feature map with the same original size.

[0043] The output layer uses a 1×1 convolution to map the last layer features back to the image channel (single channel or three channels) and generates the final denoised image through a Sigmoid activation function.

[0044] It is worth noting that the embodiment of the present invention is based on the UNet model, and improves it by adding a multi-scale channel feature fusion module and an attention mechanism module to the three skip connections of the UNet model. That is, the multi-scale channel feature fusion module is used in each skip connection. At the same time, in order to improve the performance of the network model under low-level noise, an attention mechanism is additionally added to the shallowest skip connection.

[0045] like Figure 1As shown, the skip connection (Skip Connection, also called skip layer connection, jump connection) is reflected in Figure 1 The black dotted line in the figure shows that the improved deep learning network UNet of the embodiment of the present invention uses a total of three skip connections. Simply put, convolution layer 7 comes from the upsampling of convolution layer 6 plus the skip features of convolution layer 1 (here convolution layer 1 has undergone attention mechanism and feature fusion); convolution layer 6 comes from the upsampling of convolution layer 5 plus the skip features of convolution layer 2 (here convolution layer 2 has undergone feature fusion); convolution layer 5 comes from the upsampling of convolution layer 4 plus the skip features of convolution layer 3 (convolution layer 3 has also undergone feature fusion).

[0046] Among them, such as Figure 3 As shown, the feature fusion is completed by a multi-scale channel feature fusion module, and the multi-scale channel feature fusion module specifically includes:

[0047] The upsampling unit is used to upsample the input noise image feature X before the initial convolution operation to obtain the feature X upsampled ;

[0048] Initial convolution operation unit, used to obtain the feature X after upsampling upsampled Perform a standard 3×3 initial convolution operation to extract the initial feature F1, see formula 5.1:

[0049] F1=Conv(X upsampled )(5.1);

[0050] Among them, Conv represents a 3×3 standard convolution operation, and the dimension of the output feature is

[0051] The first segmentation unit is used to segment the initial feature F1 into two parts F along the channel direction. 1,1 and F 1,2 , see formula 5.2:

[0052] F1→[F 1,1 ,F 1,2 ] (5.2);

[0053] in,

[0054] The first convolution operation unit is used to perform convolution on the segmented F 1,1 Perform convolution operation and extract mid-scale features through 5×5 hole convolution, see formula 5.3:

[0055] F2=GroupConv 5×5,dilated (F 1,1 )(5.3);

[0056] The second segmentation unit is used to segment the output features again to obtain F 2,1 and F 2,2 , see formula 5.4:

[0057] F2→[F 2,1 ,F 2,2 ] (5.4);

[0058] in,

[0059] The second convolution operation unit is used to 2,1 Further use 7×7 hole convolution to extract global features, see formula 5.5:

[0060] F3=GroupConv 7×7,dilated (F 2,1 )(5.5);

[0061] in,

[0062] The third convolution operation unit is used for F 1,2 After 1×1 convolution operation and applying GELU activation function, the processed features are as follows:

[0063] F 1,2 =Conv 1×1,GELU (F 1,2 )(5.6);

[0064] The dimension of the output feature is

[0065] Splicing unit, used to combine multi-scale features F3, F 2,2 and F 1,2 Splice along the channel direction to obtain the fused feature F agg , see formula 5.7:

[0066] [F3,F 2,2 ,F 1,2 ]→F agg (5.7);

[0067] Residual connection unit, used to combine feature F1 and aggregated feature F agg Perform residual connection to obtain the final output feature F out , see formula 5.8:

[0068] F out =F1+F agg (5.8);

[0069] The downsampling unit is used to perform downsampling operation at the output stage to restore the size of the output feature map to the original size.

[0070] The attention mechanism only works on the shallowest layer, which is reflected in the skip connection process of convolution layer 1, such as Figure 1 In the figure, the box in the lower right corner indicates that each convolutional layer performs a 3x3 convolution and then activates it with ReLU.

[0071] The skip connection can be simply expressed by the formula:

[0072] Conv5=Fuse(Up(Conv4),Skip(Conv3+MSCFM));

[0073] Conv6=Fuse(Up(Conv5),Skip(Conv2+MSCFM));

[0074] Conv7=Fuse(Up(Conv6),Skip(Conv1+CEA+MSCFM));

[0075] like Figure 4 As shown, the attention mechanism module specifically includes:

[0076] The gradient calculation unit is used to calculate the gradient of the input features in the X and Y directions respectively, see formula 5.9:

[0077] G x =X*K x ,G y =X*K y (5.9);

[0078] Among them, K x and K y They are the convolution kernels used to calculate horizontal and vertical gradients respectively, * indicates the convolution operation;

[0079] The synthesis unit is used to synthesize the gradient amplitudes in two directions, see formula 5.10:

[0080] D=|G x |+|G y | (5.10);

[0081] The normalization unit is used to normalize the synthesized gradient amplitude, see formula 5.11:

[0082]

[0083] Among them, ε is a very small constant, and C represents the normalized contrast map;

[0084] The activation unit is used to input the normalized contrast map C into a 3×3 convolutional layer and obtain the spatial attention map through the Sigmoid activation function, see formula 5.12:

[0085] A=σ(Conv 3×3 (C))(5.12);

[0086] Among them, σ(·) is the Sigmoid activation function, Represents the generated attention map;

[0087] The image enhancement unit is used to multiply the attention map A by the input feature X element by element to obtain the enhanced output feature, see formula 5.13:

[0088] X out =X⊙A(5.13);

[0089] where ⊙ represents element-wise multiplication.

[0090] In addition, the embodiment of the present invention also introduces a NODE model with controllable time step composed of TorchDyn ODE solver, such as Figure 2 As shown, the UNet-NODE part is the vector field, which is the above Figure 1 The complete model of the deep learning network UNet in .

[0091] The improved deep learning network is based on the UNet structure, which is regarded as a vector field in NODE and is passed into the solver for denoising.

[0092] The TorchDyn ODE solver receives the following inputs:

[0093] 1. UNet vector field; 2. Noisy image; 3. Specified time step; 4. Other acceptable parameters. Output: denoised image.

[0094] The entire process from the noisy image at t = 0 to the denoised image at t = 10 is based on NODE. The vector field called inside NODE is the deep learning network part UNet.

[0095] In the NODE framework, UNet is regarded as a continuous "vector field" f θ(x, t) takes as input the current noisy image x and a "virtual time" t, with θ being a time-varying parameter, and outputs the instantaneous rate of change of each pixel, dx / dt. This vector field is then numerically integrated using the ODE solver provided by TorchDyn, gradually removing the noise at a "continuous depth" to ultimately obtain a clear image. In other words, the improved deep learning network UNet defines the direction of image evolution, while the ODE solver smoothly and differentiably evolves the state along this direction. Together, they form the end-to-end trainable continuous network in NODE.

[0096] In this embodiment, the NODE model time step is set to 10, indicating that the model discretizes the ODE at 10 equally spaced time points, thereby gradually solving the system's state changes. Within each time step, the ODE solver optimizes the network parameters through backpropagation to obtain the final image reconstruction result.

[0097] The entire back-propagation process also solves an adjoint differential equation and integrates backward in time to calculate all gradients at once, avoiding the layer-by-layer calculation mode of traditional back-propagation.

[0098] In an embodiment of the present invention, a method for image denoising based on differential equations and deep networks is also provided, the method comprising:

[0099] The pre-processed noisy image is input into the differential equation NODE model and the improved deep learning network UNet;

[0100] Extracting multi-level features of the noisy image layer by layer through the multi-scale channel feature fusion module of the improved deep learning network UNet, wherein the multi-level features include shallow edge texture and deep semantic information;

[0101] Increase attention to shallow information in the network through the attention mechanism module;

[0102] The NODE model is used for continuous-time dynamic modeling. The improved deep learning network UNet is used as the neural network vector field in the NODE model. The continuous-time evolution process is simulated by the ODE solver to obtain a clear image.

[0103] The specific implementation steps of the above-mentioned image denoising method based on differential equations and deep networks are as follows:

[0104] First, the noise image is input and preprocessed, that is, the noise image to be processed is input into the deep learning network based on differential equations and improvements, and standardized preprocessing (such as data enhancement and size adjustment) is performed to ensure that the input format is adapted to the network structure.

[0105] Then, UNet is used for multi-scale feature extraction. That is, the multi-level features of the image are extracted layer by layer through the multi-scale channel feature fusion module, including shallow edge texture and deep semantic information. Among them, the multi-scale channel feature fusion module adds or cascades the channel weight vectors of different scales and levels, so that the network has information from multiple receptive fields at the same time. While retaining shallow details (high-frequency information), it also takes into account deep semantics (low-frequency information), improving the network's detection and segmentation capabilities for targets of multiple scales. The contrast enhancement attention mechanism module increases attention to shallow information in the network, allowing the model to focus more on shallow texture features, improving the model's denoising ability and robustness.

[0106] Again, continuous time dynamic modeling is performed through the NODE model. Figure 1 The improved deep learning network UNet model in the paper is used as the neural network vector field in NODE. The continuous time evolution process is simulated through the ODE solver (such as TorchDyn). It relies on the dynamic update in the UNet model to adaptively adjust the dynamic balance between noise suppression and detail preservation.

[0107] Then, the embodiment of the present invention also performs a hybrid loss function calculation, that is, using the mean square error (MSE) and the regularization term hybrid loss function to evaluate the pixel-level difference and structural similarity between the denoised image and the true clean image, and optimizes the model parameters based on the solver back propagation.

[0108] Preferably, the embodiment of the present invention further performs denoising result output and visualization to output a denoised high-definition image, providing an intuitive basis for algorithm tuning and effect verification.

[0109] Here, we first introduce the principle of neural differential equations in an embodiment of the present invention:

[0110] Image denoising aims to restore the original image x from the noisy image y. Its mathematical model can be expressed as:

[0111] y=x+ε;

[0112] where ε is the additive noise.

[0113] In the NODE framework, the image denoising process is implemented through dynamic modeling. The specific steps are as follows:

[0114] First, the noise image y is used as the initial input, and the initial value of the hidden state is set to: h(0) = y;

[0115] Next, dynamic evolution modeling uses a neural network to learn the vector field f(h(t),θ(t)), which describes the evolution of features over time t and gradually attenuates noise. Its differential equation is expressed as follows: f represents the UNet neural network vector field, which has two internal parameters: one is the image-related function h at time t, and the other θ represents the time-dependent internal parameters of the neural network. h(t) represents the image, which changes over time.

[0116]

[0117] Among them, f(·) is a nonlinear transformation implemented by a multi-layer convolutional neural network, and θ(t) is a time-varying parameter.

[0118] Next, through ODE solution and feature evolution, the TorchDyn solver is used to numerically integrate the ordinary differential equation from the initial time t = 0 to the end time t = T, and the final feature representation is obtained:

[0119]

[0120] The above formula shows the working principle of NODE: output image h(T) = initial noise image h(0) + integral of a specified time step. The integral here is solved by ODE solver, which contains Figure 1 UNet vector field in ;

[0121] Integration is the process of "removing noise step by step" - the network passes through UNet at each time t, that is Figure 1 The vector field in is used to calculate the current rate of change dh / dt, and these small changes are then numerically accumulated by the ODE solver.

[0122] Finally, the denoised image is output, and the hidden state h(T) at the end of the evolution is output as the denoising result, that is: xdenoised = h(T);

[0123] Through continuous time dynamic evolution, NODE gradually suppresses noise and restores image details. The specific evolution process is as follows:

[0124] 1. Input the image (noise image) as the initial state h(0) and set the neural network vector field f.

[0125] 2. Use the TorchDyn solver to integrate over the time interval [0, T] to obtain h(T), and construct a time step sequence based on the number of time steps;

[0126] in

[0127] Use the solver to integrate the initial value to obtain the state corresponding to each time point.

[0128] The entire solution process is to approximate the integral:

[0129]

[0130] The solver in TorchDyn can use adaptive step size to control the error.

[0131] The adaptive step-size solver is based on the Runge-Kutta (RK) method, specifically the Dormand-Prince5(4) (abbreviated as dopri5). This method dynamically adjusts the step size by estimating the local truncation error, thereby improving computational efficiency while ensuring numerical stability. Essentially, it continuously evaluates the function f to accumulate integrals. The model update process uses the adjoint method provided by TorchDyn to reversely solve the gradient and update the network parameters.

[0132] 3. Return the final state: After the solver calculates the states of all time points, the code takes the last state h(T) as the output, which is the denoised image.

[0133] In image denoising tasks, noise can be distributed across different scales and regions of the image, encompassing both local details and global textures. Efficiently extracting and fusing multi-scale features is crucial for improving denoising performance. To this end, embodiments of the present invention incorporate a multi-scale channel feature fusion module to enhance the model's ability to model multi-scale information while improving the accuracy of feature representation while maintaining computational efficiency.

[0134] The multi-scale channel feature fusion module realizes the coordination between local details and global structure of the image through multi-branch convolution and channel feature fusion mechanism. Its feature extraction model is as follows: Figure 3 shown.

[0135] Feature extraction involves extracting information at different levels from an image through the multi-layer architecture of an improved deep learning network, UNet. Specifically, UNet's structure includes multiple encoding and decoding steps. During encoding, the network gradually compresses the image size to extract low-level features (such as edges, textures, and other details). During decoding, the network gradually restores the image size and, combined with the features extracted by the encoding layers, helps recover more complex details and structures within the image. This multi-layered architecture enables the network to capture information at different scales and depths within the image, thereby better preserving detail and suppressing noise.

[0136] The multi-layer architecture and encoder-decoder here are for Figure 1Convolution 1, convolution 2, convolution 3 and convolution 4 constitute the encoder part (Encoder) of the entire model. These four blocks can be regarded as encoding layers; convolution 5, convolution 6 and convolution 7 constitute the decoder part (Decoder) of the model. These three layers can be regarded as decoding layers. The multi-scale channel feature fusion module and the attention mechanism module act in the skip connection.

[0137] The core idea of ​​MSCFM (Multi-scale Channel Feature Fusion Module) is to use convolutions with different receptive fields (such as 3×3, 5×5 and 7×7 convolutions) to capture local and global multi-scale features in the image, and to achieve the fusion of multi-scale information through channel splitting and feature aggregation.

[0138] Traditional multi-scale methods typically directly stack convolution operations of different sizes, which can easily lead to a rapid increase in computational complexity and parameter count. In contrast, MSCFM effectively reduces computational costs by splitting feature channels (Channel Splitting) and grouping convolutions (Grouped Convolution), while retaining the advantages of multi-scale feature extraction.

[0139] The specific structure of MSCFM is as follows Figure 3 As shown, the input features Go through the following processing steps:

[0140] 1. Upsampling operation:

[0141] Before the initial convolution, the input feature X is first upsampled to reduce the size of the feature map from Expand to This ensures that subsequent operations (especially 7×7 dilated convolution) can avoid size mismatch issues.

[0142] 2. Initial convolution operation:

[0143] For the upsampled input feature X upsampled Perform a standard 3×3 convolution operation to extract the initial feature F1, see formula (5.1):

[0144] F1=Conv(X upsampled )(5.1);

[0145] Among them, Conv represents a 3×3 standard convolution operation, and the output feature dimension is

[0146] 3. Feature channel segmentation:

[0147] Split the initial feature F1 into two parts F1,1 and F1,2 along the channel direction, see formula (5.2):

[0148] F1→[F1,1 ,F 1,2 ] (5.2);

[0149] in,

[0150] 4. Multi-scale convolution processing:

[0151] The segmented F1,1 is convolved with a larger receptive field. First, the mid-scale features are extracted through a 5×5 dilated convolution, as shown in Equation (5.3):

[0152] F2=GroupConv 5×5,dilated (F 1,1 )(5.3);

[0153] The output features are split again to obtain F2,1 and F2,2, as shown in formula (5.4):

[0154] F2→[F 2,1 ,F 2,2 ] (5.4);

[0155] in,

[0156] Then, 7×7 dilated convolution is further used to extract global features with a larger receptive field for F2,1, as shown in formula (5.5):

[0157] F3=GroupConv 7×7,dilated (F 2,1 )(5.5);

[0158] in,

[0159] 5. Channel processing and activation:

[0160] At this stage, F1,2 undergoes a 1×1 convolution operation and applies the GELU activation function. The processed features are as follows:

[0161] F 1,2 =Conv 1×1,GELU (F 1,2 )(5.6);

[0162] The output feature dimension is

[0163] 6. Feature Aggregation

[0164] Finally, the multi-scale features F3, F2,2 and F1,2 are spliced ​​along the channel direction to obtain the fused feature F agg , see formula (5.7):

[0165] [F3,F2,2 ,F 1,2 ]→F agg (5.7);

[0166] 7. Residual connection processing:

[0167] The early feature F1 and the aggregated feature Fagg are connected by residual connection to obtain the final output feature Fout, as shown in formula (5.8): The concat operation performed here directly concatenates the two features directly in the channel dimension. In fact, the two feature dimensions and the number of channels here are the same. Assuming the number of channels is 64, in pytorch, concat is first used, that is, the number of channels becomes 64+64, and then a 1x1 convolution is performed to reduce the number of channels back to 64. This process can be directly described by residual connection without expansion. The formula can be changed to F out =concat(F1,F agg )

[0168] F out =F1+F agg (5.8);

[0169] Among them, the residual connection ensures the direct transmission of input features and promotes the effective propagation of gradients.

[0170] 8. Downsampling operation:

[0171] Finally, a downsampling operation is performed at the output stage to restore the size of the output feature map to its original size. This operation ensures that the height and width of the feature map remain unchanged, and only the number of channels changes. Output feature X downsampled The size is

[0172] The multi-scale channel feature fusion module (MSCFM) has the following characteristics and advantages:

[0173] On the one hand, multi-scale feature extraction is achieved. That is, by combining 3×3, 5×5 and 7×7 convolution operations, MSCFM can effectively capture local, regional and global receptive field information, thereby improving the ability to model noise of different scales.

[0174] Secondly, by splitting channels and adopting group convolution, MSCFM significantly reduces the amount of computation and parameters, while maintaining the effect of multi-scale feature extraction, making the calculation more efficient.

[0175] Thirdly, MSCFM fully integrates information of different scales through feature fusion and residual connection, retains the original information of input features through residual connection, and further enhances the stability and convergence speed of the model.

[0176] In addition, the MSCFM module, as the core component in the dynamic evolution of UNet-NODE, provides strong support for denoising tasks in terms of multi-scale modeling and feature expression.

[0177] like Figure 1 As shown in the figure, in image denoising tasks, the difference between noise and real image details under low-noise conditions is very small, and noise signals in shallow features are often difficult to distinguish. To effectively extract shallow information under low noise levels, the embodiment of the present invention introduces a low-level contrast enhancement attention mechanism module (CEA module), which aims to dynamically enhance the response of key areas such as edges and textures in the image while suppressing redundant information, thereby improving denoising performance.

[0178] like Figure 4 As shown in Figure 1, the gradient magnitude of the image in the X and Y directions is calculated through the low-level contrast enhancement attention mechanism module to enhance the response of the low-contrast area, thereby highlighting the important edge and detail information in the image.

[0179] Then, after normalization, a 3×3 convolution and Sigmoid activation function are used to generate an attention map, which is weightedly fused with the input image to obtain the enhanced feature map.

[0180] like Figure 4 As shown, the CEA module mainly includes the following steps:

[0181] 1. Gradient calculation and amplitude synthesis:

[0182] For input features Calculate the gradient in the X and Y directions respectively to capture the local change information of the image, see formula (5.9):

[0183] G x =X*K x ,G y =X*K y (5.9);

[0184] where K x and K y are the convolution kernels used to calculate the horizontal and vertical gradients, respectively. * indicates the convolution operation. Then the gradient amplitudes in the two directions are synthesized, as shown in Equation (5.10):

[0185] D=|G x |+|G y | (5.10);

[0186] 2. Amplitude normalization:

[0187] In order to eliminate the scale difference of the amplitude, the synthesized gradient amplitude is normalized, see formula (5.11):

[0188]

[0189] Where ε is a very small constant used to prevent division by zero, and C represents the normalized contrast map.

[0190] 3. Generate attention map:

[0191] The normalized contrast map C is input into a 3×3 convolutional layer, and the spatial attention map is obtained by the Sigmoid activation function, as shown in formula (5.12):

[0192] A=σ(Conv 3×3 (C))(5.12);

[0193] Where σ(·) is the Sigmoid activation function, Represents the generated attention map, whose value reflects the importance of each position in the image.

[0194] 4. Feature weighting:

[0195] Finally, the attention map A is multiplied element-by-element by the input feature X to achieve dynamic weighting of the key area and obtain the enhanced output feature, as shown in formula (5.13):

[0196] X out =X⊙A(5.13);

[0197] where ⊙ denotes element-wise multiplication.

[0198] Through this process, the CEA module focuses on extracting shallow information at low noise levels, enhancing the response of key image regions such as edges and textures, thereby effectively improving denoising performance. The module's dynamic feature weighting mechanism effectively suppresses redundant information while preserving details, providing more refined input for subsequent deep feature extraction.

[0199] Furthermore, the embodiment of the present invention also combines pixel-level reconstruction loss and regularization terms to improve the denoising effect while avoiding overfitting.

[0200] First, the core goal of the denoising task is to make the model output image x and the real noise-free image x GT As close as possible. To this end, the mean square error loss (MSE) is used as the basic pixel-level loss, which is defined as formula (5.14):

[0201]

[0202] Where N represents the total number of pixels in the image. MSE loss can effectively measure the reconstruction error between the denoising result and the true image.

[0203] In order to enhance the generalization ability of the model, regularization terms are used to prevent overfitting and improve the robustness of denoising. Regularization terms include weight regularization and gradient regularization, which are defined as Equation (5.15) and Equation (5.16) respectively:

[0204]

[0205] Where θ is all the parameters of the model.

[0206]

[0207] Among them, x i,j Represents the pixel value at position (i, j) in the denoised image.

[0208] Combining the above two losses, the total loss function of the denoising model is formula (5.17):

[0209] L total =λ1L MSE +λ2L reg +λ3L grad (5.17);

[0210] Among them, λ1, λ2, and λ3 are weight hyperparameters used to adjust the importance of different loss terms.

[0211] Through the above loss function, the embodiment of the present invention can avoid overfitting while ensuring the denoising effect and improve the restoration effect of image details.

[0212] In order to verify the effect of the above-mentioned model in the embodiment of the present invention in image denoising, the inventors selected multiple classic data sets to construct a mixed data set during the verification stage, covering diverse content such as high-resolution images, natural scenes, and urban scenes. Specifically, it includes the DIV2K data set, the BSD500 data set, and the Urban100 data set. The mixed data set is designed to simulate noise distribution and image diversity that are closer to real scenes, so as to verify the generalization ability of the model in different scenes and resolutions. The images in the above three data sets are randomly combined to construct a diverse training and test data set to ensure the coverage and representativeness of the experimental data.

[0213] In order to further improve the generalization ability of the model and enhance the diversity of training data, this experiment introduced a variety of data enhancement strategies in data preprocessing and reasonably divided the mixed data set to ensure the scientificity and fairness of training and testing.

[0214] Data augmentation is an important means of improving the robustness and performance of deep learning models. In this experiment, to simulate noise distribution and image transformations in different scenarios, high-resolution images were first randomly cropped into fixed-size sub-images for training. The specific crop size was 64x64, balancing computational overhead with the preservation of high-resolution information. The training images were then randomly rotated 90°, 180°, and 270°, as well as horizontally flipped, to increase data diversity. The brightness and contrast of the images were randomly adjusted to simulate lighting variations found in real environments.

[0215] To scientifically evaluate model performance, this experiment randomly selected 80% of the images in the mixed dataset as the training set for learning model parameters. 10% of the images were selected as the validation set for hyperparameter tuning and model selection. The remaining 10% of the images were retained as the test set to evaluate the final model performance. The grayscale image performance was tested on the Set12 dataset, using PSNR as the image quality metric.

[0216] Table 5.3 shows the average PSNR (dB) results of the Gaussian grayscale image denoising method on the Set68 dataset under various noise levels; Table 5.4 shows the average SSIM results of the Gaussian grayscale image denoising method on the Set68 dataset under various noise levels.

[0217] Table 5.3

[0218]

[0219] Table 5.4

[0220]

[0221] The Adam optimizer was used, with a learning rate of 1×10-4, a batch size of 32, and a maximum number of training rounds of 50. Each image was split into 300 random blocks of a fixed size for training. The pt weight file of each round was saved during the training process. All experiments were uploaded to the parallel Training is performed on a supercomputing cloud server cluster. For the UNet-NODE model with the above parameters, when the time step is set to N = 10, using CUDA accelerated computing, one training session takes about 60 hours.

[0222] It's worth noting that if the dataset is complex and the images contain a lot of information, the time step can be increased appropriately to achieve better denoising results. However, increasing the time step will linearly increase the model training time. In general, setting N = 10 achieves a good balance between training accuracy and efficiency. The specific setting can be adjusted according to actual conditions.

[0223] In a third aspect, an embodiment of the present invention further provides a computing device, which includes a processor and a memory, the memory being used to store a computer program, the computer program including program instructions, and the processor or calculator being configured to call the program instructions to execute the method as described above.

[0224] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, wherein the computer program includes program instructions, and when the program instructions are executed by a processor or a calculator, the processor or the calculator executes the method as described above.

[0225] like Figure 5 As shown, an embodiment of the present application provides a computing device, which includes a processor or a calculator (not shown) 1001 and a memory 1002. The processor or calculator 1001 and the memory 1002 can be interconnected via a communication bus 1003. The communication bus 1003 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The communication bus 1003 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, the memory 1002 is used to store a computer program, which includes program instructions. The processor 1001 is configured to call the program instructions, and the above program includes a method for executing some or all of the steps in the aforementioned method.

[0226] The processor 1001 may be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits for controlling the execution of the above program.

[0227] The memory 1002 may be a read-only memory (ROM) or other type of static storage device that can store static information and instructions, a random access memory (RAM) or other type of dynamic storage device that can store information and instructions, or an electrically erasable programmable read-only memory (EEPROM), a compact disc (CD-ROM) or other optical disc storage, an optical disc storage (including a compact disc, laser disc, optical disc, digital versatile disc, Blu-ray disc, etc.), a magnetic disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory may exist independently and be connected to the processor via a bus. The memory may also be integrated with the processor.

[0228] The computing device 1000 may further include a communication module 1004 and a display 1005. The communication module 1004 may be connected to the optical tracking device for communication. The communication module 1004 may be a wireless communication module (eg, a WiFi module, a Bluetooth module, etc.) or a wired communication module.

[0229] In addition, the computing device 1000 may also include common components such as a communication interface (eg, a USB interface, a microphone interface, etc.), an antenna, etc., which will not be described in detail here.

[0230] It should be noted that for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that this application is not limited by the order of the actions described, because according to this application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by this application.

[0231] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0232] In the several embodiments provided in this application, it should be understood that the disclosed devices can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, and the indirect coupling or communication connection of devices or units can be electrical or other forms.

[0233] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0234] In addition, the functional units in the various embodiments of the application may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software program modules.

[0235] If the integrated unit is implemented in the form of a software program module and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a memory, including a number of instructions for enabling a computer device (which can be a personal computer, server or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned memory includes: U disk, read-only memory (ROM), random access memory (RAM), mobile hard disk, magnetic disk or optical disk, etc., various media that can store program code.

[0236] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable memory, which may include: a flash drive, a read-only memory, a random access memory, a magnetic disk or an optical disk, etc.

[0237] The above is a detailed introduction to the embodiments of the present application. Specific examples are used in the embodiments of the present invention to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method of the present application and its core idea. At the same time, for those skilled in the art, according to the ideas of the present application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present application.

[0238] It should be noted that the above embodiments can be freely combined as needed. The above are only preferred embodiments of the present invention. It should be pointed out that those skilled in the art can make several improvements and modifications without departing from the principles of the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An image denoising method based on differential equations and deep learning networks, characterized in that: The method comprises: The pre-processed noisy image is input into the differential equation NODE model and the improved deep learning network UNet; By improving the multi-scale channel feature fusion module of UNet, multi-level features of the noisy image are extracted layer by layer. The multi-level features include shallow edge texture and deep semantic information. Increase attention to shallow information in the network through the attention mechanism module; The NODE model is used for continuous-time dynamic modeling. The improved deep learning network UNet is used as the neural network vector field in the NODE model. The continuous-time evolution process is simulated by the ODE solver to obtain a clear image.

2. The image denoising method based on differential equations and deep learning networks according to claim 1, wherein: The improved deep learning network UNet includes an encoder, a decoder, a multi-scale channel feature fusion module and an attention mechanism module. Three skip connections are formed between the encoder and the decoder by adding the multi-scale channel feature fusion module and the attention mechanism module. The multi-scale channel feature fusion module is used in each skip connection, and the attention mechanism module is added to the skip connection to the lowest layer.

3. The image denoising method based on differential equations and deep learning networks according to claim 2, wherein: The multi-level features of the noise image are extracted layer by layer by improving the multi-scale channel feature fusion module of UNet. Specifically, Before the initial convolution operation, the input noise image feature X is upsampled to obtain the feature X upsampled ; The feature X obtained after upsampling upsampled Perform a standard 3×3 initial convolution operation to extract the initial feature F1, see formula 5.1: F1=Conv(X upsampled ) (5.1); Among them, Conv represents a 3×3 standard convolution operation, and the dimension of the output feature is Split the initial feature F1 into two parts along the channel direction 1,1 and F 1,2 , see formula 5.2: F1→[F 1,1 ,F 1,2 ] (5.2); in, After the segmentation, F 1,1 Perform convolution operation and extract mid-scale features through 5×5 hole convolution, see formula 5.3: F2=GroupConv 5×5,dilated (F 1,1 ) (5.3); The output features are segmented again to obtain F 2,1 and F 2,2 , see formula 5.4: F2→[F 2,1 ,F 2,2 ] (5.4); in, F 2,1 Further use 7×7 hole convolution to extract global features, see formula 5.5: F3=GroupConv 7×7,dilated (F 2,1 ) (5.5); in, F 1,2 After 1×1 convolution operation and applying GELU activation function, the processed features are as follows: F 1,2 =Conv 1×1,GELU (F 1,2 ) (5.6); The dimension of the output feature is The multi-scale features F3, F 2,2 and F 1,2 Splice along the channel direction to obtain the fused feature F agg , see formula 5.7: <h2 style=";text-align:left;direction:ltr">[F3,F<h2 style=";text-align:left;direction:ltr"> 2,2 <h2 style=";text-align:left;direction:ltr"> ,F<h2 style=";text-align:left;direction:ltr"> 1,2 <h2 style=";text-align:left;direction:ltr"> ]→F<h2 style=";text-align:left;direction:ltr"> agg <h2 style=";text-align:left;direction:ltr"> (5.7); For feature F1 and aggregated feature F agg Perform residual connection to obtain the final output feature F out , see formula 5.8: F out =F1+F agg (5.8); A downsampling operation is performed at the output stage to restore the size of the output feature map to its original size.

4. The image denoising method based on differential equations and deep learning networks according to claim 1, wherein: The attention mechanism module increases attention to shallow information in the network specifically including: Calculate the gradient of the input feature in the X and Y directions respectively, see formula 5.9: G x =X*K x ,G y =X*K y (5.9); Among them, K x and K y They are the convolution kernels used to calculate horizontal and vertical gradients respectively, * indicates the convolution operation; Then the gradient amplitudes in the two directions are synthesized, see formula 5.10: D=|G x |+|G y | (5.10); The synthesized gradient amplitude is normalized, see formula 5.11: Among them, ε is a very small constant, and C represents the normalized contrast map; The normalized contrast map C is input into a 3×3 convolutional layer and the spatial attention map is obtained by the Sigmoid activation function, see formula 5.12: A=σ(Conv 3×3 (C))(5.12); Among them, σ(·) is the Sigmoid activation function, Represents the generated attention map; Multiply the attention map A by the input feature X element by element to obtain the enhanced output feature, see formula 5.13: X out =X⊙A(5.13); where ⊙ represents element-wise multiplication.

5. The image denoising method based on differential equations and deep learning networks according to claim 1, wherein: The NODE model is used for continuous-time dynamic modeling. The improved deep learning network UNet is used as the neural network vector field in the NODE model. The continuous-time evolution process is simulated through the ODE solver to obtain a clear image. Specifically, the following are included: The improved deep learning network UNet is a continuous "vector field" f θ (x, t), which inputs the current noisy image x and virtual time t, θ is a time-varying parameter, and outputs the instantaneous change rate dx / dt of each pixel; By numerically integrating the vector field with the help of the TorchDyn solver, the noise can be removed step by step at "continuous depth" to ultimately obtain a clear image.

6. An image denoising system based on differential equations and deep learning networks, characterized in that: The system includes a differential equation NODE model and an improved deep learning network UNet, wherein the improved deep learning network UNet includes: an encoder, a decoder, a multi-scale channel feature fusion module and an attention mechanism module, and three skip connections are formed between the encoder and the decoder by adding the multi-scale channel feature fusion module and the attention mechanism module, wherein the multi-scale channel feature fusion module is used in each skip connection, and the attention mechanism module is added to the skip connection of the lowest layer; The multi-level features of the noisy image are extracted layer by layer through the multi-scale channel feature fusion module of the improved deep learning network UNet, wherein the multi-level features include shallow edge texture and deep semantic information, and the attention mechanism module increases attention to the shallow information in the network, thereby obtaining a vector field of the improved deep learning network UNet; The differential equation NODE model uses the improved deep learning network UNet as the neural network vector field in the NODE model, simulates the continuous time evolution process through the ODE solver, and obtains a clear image.

7. The image denoising system based on differential equations and deep learning networks according to claim 6, wherein: The multi-scale channel feature fusion module specifically includes: The upsampling unit is used to upsample the input noise image feature X before the initial convolution operation to obtain the feature X upsampled ; Initial convolution operation unit, used to obtain the feature X after upsampling upsampled Perform a standard 3×3 initial convolution operation to extract the initial feature F1, see formula 5.1: F1=Conv(X upsampled )(5.1); Among them, Conv represents a 3×3 standard convolution operation, and the dimension of the output feature is The first segmentation unit is used to segment the initial feature F1 into two parts F along the channel direction. 1,1 and F 1,2 , see formula 5.2: F1→[F 1,1 ,F 1,2 ] (5.2); in, The first convolution operation unit is used to perform convolution on the segmented F 1,1 Perform convolution operation and extract mid-scale features through 5×5 hole convolution, see formula 5.3: F2=GroupConv 5×5,dilated (F 1,1 )(5.3); The second segmentation unit is used to segment the output features again to obtain F 2,1 and F 2,2 , see formula 5.4: F2→[F 2,1 ,F 2,2 ] (5.4); in, The second convolution operation unit is used to 2,1 Further use 7×7 hole convolution to extract global features, see formula 5.5: F3=GroupConv 7×7,dilated (F 2,1 )(5.5); in, The third convolution operation unit is used for F 1,2 After 1×1 convolution operation and applying GELU activation function, the processed features are as follows: F 1,2 =Conv 1×1,GELU (F 1,2 )(5.6); The dimension of the output feature is Splicing unit, used to combine multi-scale features F3, F 2,2 and F 1,2 Splice along the channel direction to obtain the fused feature F agg , see formula 5.7: <h2 style=";text-align:left;direction:ltr">[F3,F<h2 style=";text-align:left;direction:ltr"> 2,2 <h2 style=";text-align:left;direction:ltr"> ,F<h2 style=";text-align:left;direction:ltr"> 1,2 <h2 style=";text-align:left;direction:ltr"> ]→F<h2 style=";text-align:left;direction:ltr"> agg <h2 style=";text-align:left;direction:ltr"> (5.7); Residual connection unit, used to combine feature F1 and aggregated feature F agg Perform residual connection to obtain the final output feature F out , see formula 5.8: F out =F1+F agg (5.8); The downsampling unit is used to perform downsampling operation at the output stage to restore the size of the output feature map to the original size.

8. The image denoising system based on differential equations and deep learning networks according to claim 6, wherein: The attention mechanism module specifically includes: The gradient calculation unit is used to calculate the gradient of the input features in the X and Y directions respectively, see formula 5.9: G x =X*K x ,G y =X*K y (5.9); Among them, K x and K y They are the convolution kernels used to calculate horizontal and vertical gradients respectively, * indicates the convolution operation; The synthesis unit is used to synthesize the gradient amplitudes in two directions, see formula 5.10: D=|G x |+|G y | (5.10); The normalization unit is used to normalize the synthesized gradient amplitude, see formula 5.11: Among them, ε is a very small constant, and C represents the normalized contrast map; The activation unit is used to input the normalized contrast map C into a 3×3 convolutional layer and obtain the spatial attention map through the Sigmoid activation function, see formula 5.12: A=σ(Conv 3×3 (C))(5.12); Among them, σ(·) is the Sigmoid activation function, Represents the generated attention map; The image enhancement unit is used to multiply the attention map A by the input feature X element by element to obtain the enhanced output feature, see formula 5.13: X out =X⊙A(5.13); where ⊙ represents element-wise multiplication.

9. A computing device, characterized in that The computing device includes a processor and a memory, the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions to execute the method according to any one of claims 1 to 5.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, wherein the computer program includes program instructions. When the program instructions are executed by a processor, the processor or the computer executes the method according to any one of claims 1 to 5.

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