Atmospheric turbulence wavefront reconstruction method based on attention-learnable activation collaborative mechanism

Abstract

The present application belongs to the field of atmospheric turbulence wavefront aberration detection, and discloses an atmospheric turbulence wavefront reconstruction method based on attention-learnable activation collaborative mechanism, aiming to solve the problems of difficulty in modeling full connection layer caused by high-order nonlinear coupling of phase, insufficient feature extraction ability of traditional convolution architecture and imbalance of Zernike coefficient reconstruction error in phase reconstruction of existing end-to-end neural network. The method includes collecting in-focus and out-of-focus images of a light spot and corresponding distortion phase to construct a training data set, constructing an attention encoder and a Kolmogorov-Arnold network, realizing high-precision mapping of high-order aberration features by a learnable activation function, optimizing network parameters by using an error weighted mean square error loss function, and finally deploying the trained neural network to realize high-speed reasoning. The method proposed in the present application provides a high-precision and high-speed scheme for atmospheric turbulence distortion wavefront aberration detection.

Description

Technical Field

[0001] This invention relates to a deep learning-based method for detecting atmospheric turbulence wavefront aberrations, specifically a method for detecting atmospheric turbulence distortion wavefronts by fusing attention mechanisms and learnable activation functions. Background Technology

[0002] Deep learning-based atmospheric wavefront aberration sensing is an important detection technique, particularly suitable for real-time aberration correction in adaptive optics systems, astronomical observations, and high-energy laser transmission. This method simultaneously acquires in-focus and out-of-focus images and the corresponding distorted wavefront phase using an optical imaging system. Data-driven mapping from intensity maps to Zernike coefficients of the distorted wavefront phase is then performed via a neural network, enabling atmospheric wavefront aberration detection. Despite significant progress, existing end-to-end neural network methods still face three major bottlenecks: failure in high-order nonlinear modeling of the phase. Since wavefront distortion caused by atmospheric turbulence is essentially a strongly nonlinear coupling process of multi-scale vortices, high-order cross-correlation exists between its Zernike coefficients. Traditional fully connected layers, limited by the finite nonlinear capacity of fixed activation functions, produce significant biases when fitting high-dimensional manifolds. Furthermore, the utilization rate of gradient information in intensity images is low. While out-of-focus images contain first-order gradient information of the wavefront phase, the local receptive field design of traditional convolutional neural networks struggles to model long-range phase gradient correlations, leading to generalization defects due to weak feature extraction capabilities. Finally, there is the problem of imbalanced Zernike coefficient reconstruction errors. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide an atmospheric turbulence wavefront reconstruction method based on the attention-learnable activation synergistic mechanism. The method can quickly and accurately solve the distorted wavefront phase caused by turbulence, can more effectively model complex turbulence, has strong high-order nonlinear modeling capabilities, high feature extraction efficiency, more balanced reconstruction error, and strong turbulence generalization performance.

[0004] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0005] A method for reconstructing atmospheric turbulence wavefronts based on an attention-learnable activation synergistic mechanism includes the following steps:

[0006] S1. High-speed synchronous acquisition of in-focus and out-of-focus images of the target and the corresponding distorted wavefront phase through an optical imaging system. The in-focus and out-of-focus intensity maps are stacked and used as input to a neural network. The Zernike coefficients of the distorted phase are used as labels for the neural network to complete the construction of the dataset.

[0007] S2. Construct a neural network architecture based on an attention mechanism encoder and a Kolmogorov-Arnold network;

[0008] S3. Train the neural network using the error-weighted root mean square loss function, backpropagate the gradient of the loss function value to update the parameters of the network model, and obtain a fully trained neural network. Finally, a high-precision, high-frame-rate atmospheric turbulence distortion aberration detection neural network is obtained.

[0009] Preferably, in step S2, the attention mechanism encoder adopts a hierarchical cascaded architecture, including a primary feature encoder composed of four levels of residual convolution stacked, an intermediate feature enhancement unit integrating a single-level residual convolution and a spatial-channel multi-head self-attention mechanism module, and a terminal feature refinement unit composed of a single-level residual convolution and a channel attention module. The progressive extraction and adaptive fusion of multi-scale features are achieved through cross-level skip connections.

[0010] Preferably, the residual convolution is implemented by combining two convolutional layers with a kernel size of 3×3, a stride of 1, and padding of 1, and a convolutional layer with a kernel size of 1 and a stride of 1, a normalization layer, a GELU-type activation function, and an average pooling layer.

[0011] Preferably, the spatial channel multi-head self-attention module consists of a spatial-channel joint coding unit, a multi-head self-attention unit, and a feature fusion unit. The spatial-channel joint coding unit generates query, key, and value vectors through 1×1 convolution. The multi-head self-attention unit flattens the features in the spatial dimension and then performs multi-head segmentation in the channel dimension. The feature fusion unit consists of layer normalization, residual connection, two 3×3 depthwise separable convolutions, and the GELU activation function.

[0012] Preferably, the channel attention module consists of a global mean pooling layer, two fully connected layers, and a sigmoid activation function.

[0013] Preferably, in step S2, the Kolmogorov-Arnold network is based on the Kolmogorov-Arnold representation theorem and constructs a dynamic adaptive nonlinear mapping through learnable spline basis functions, which can dynamically adjust the shape of the activation function according to the input features.

[0014] Preferably, in step S3, the error-weighted root mean square loss function is constructed through a dynamic weight allocation mechanism. The statistical distribution of the error is reconstructed by the Zernike coefficients in the historical training cycle. The Zernike coefficient errors are normalized and mapped to the interval [1,10] to generate an adaptive weight matrix. After performing the Hadamard product operation between the weight matrix and the mean square error of the current round, the square root operation of the weighted tensor is performed, and finally the loss evaluation value with error balance characteristics is output.

[0015] Preferably, in step S3, the gradient value of the loss function is backpropagated multiple times to update the weights and bias parameters of the neural network, including parameter learning in the learnable activation function. When the loss function value is less than a preset stopping value, the updating of the weights and bias parameters of the neural network is stopped, and a fully trained neural network is obtained.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] 1. Existing deep learning-based wavefront detection methods employ fully connected layers and fixed activation functions (such as ReLU and Sigmoid), essentially approximating the target function through linear combination and piecewise nonlinear transformation. However, wavefront distortion caused by atmospheric turbulence exhibits strong nonlinear coupling characteristics, with high-order cross-correlation among Zernike coefficients, such as the nonlinear superposition effect of low-order defocus terms and high-order coma. Traditional fully connected layers, limited by the static characteristics of activation functions and rigid connections between neurons, cannot accurately model such complex nonlinearities. This invention introduces a Kolmogorov-Arnold network, based on the Kolmogorov-Arnold representation theorem, constructing a dynamic adaptive nonlinear mapping through learnable spline basis functions. This allows for dynamic adjustment of the activation function's shape according to input features, thereby accurately fitting the nonlinear coupling relationship between Zernike coefficients.

[0018] 2. Traditional convolutional networks extract image features through local receptive fields. However, wavefront gradient information in defocused images exhibits long-range correlations, such as the phase gradient difference between the center and edge of turbulent vortices. Furthermore, different frequency domain components, such as low-frequency defocus and high-frequency astigmatism, contribute differently to the Zernike coefficients, making it difficult for traditional methods to effectively model such cross-domain correlations. This invention achieves physically guided feature enhancement through a dual-domain attention encoder. Spatial attention dynamically perceives the core region of turbulent vortices, overcoming the limitations of local receptive fields and accurately capturing the global correlation of phase gradients. Channel attention achieves energy separation of different Zernike modes, improving the model's adaptability to changes in turbulence intensity. The physically guided feature selection mechanism suppresses random noise interference in atmospheric turbulence, enhancing stability in complex environments. The two mechanisms work together to achieve physically interpretable feature fusion, significantly improving the model's adaptability to untrained turbulence intensity and enhancing stability compared to traditional methods.

[0019] 3. Existing deep learning-based wavefront detection methods commonly use mean square error (MSE) or root mean square error (RMSE) as the loss function, leading to an imbalance in Zernike coefficient reconstruction errors. This invention proposes an error-weighted root mean square loss function. Traditional methods fail to consider the different influences of Zernike coefficients of different orders on phase reconstruction, resulting in significantly higher and unevenly distributed reconstruction errors for lower-order aberrations compared to higher-order aberrations, thus introducing systematic biases into the phase reconstruction results. This method constructs dynamic weight coefficients that are positively correlated with the magnitude of Zernike coefficient errors, enabling the neural network to adaptively enhance the optimization of larger error terms during training, thereby achieving a balance in the reconstruction errors of Zernike coefficients of different orders and effectively eliminating systematic phase biases. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the implementation of the atmospheric turbulence wavefront reconstruction method based on the attention-learnable activation collaborative mechanism of this invention.

[0021] Figure 2 This is a diagram of the neural network architecture of the attention mechanism-based encoder and the Kolmogorov-Arnold network of the present invention. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0023] See Figure 1 The atmospheric turbulence wavefront reconstruction method based on the attention-learnable activation synergistic mechanism of this invention includes the following steps:

[0024] S1. High-speed synchronous acquisition of in-focus and out-of-focus images of the target and the corresponding distorted wavefront phase through an optical imaging system. The in-focus and out-of-focus intensity maps are stacked and used as input to a neural network. The Zernike coefficients of the distorted phase are used as labels for the neural network to complete the construction of the dataset.

[0025] S2. Construct a neural network architecture based on an attention mechanism encoder and a Kolmogorov-Arnold network;

[0026] S3. Train the neural network using the error-weighted root mean square loss function, backpropagate the gradient of the loss function value to update the parameters of the network model, and obtain a fully trained neural network. Finally, a high-precision, high-frame-rate atmospheric turbulence distortion aberration detection neural network is obtained.

[0027] See Figure 2This paper presents an atmospheric turbulence wavefront reconstruction method based on an attention-learnable activation collaborative mechanism. Its neural network structure is composed of an attention mechanism encoder and a Kolmogorov-Arnold network architecture. The attention mechanism encoder adopts a hierarchical cascaded architecture, including a primary feature encoder consisting of four stacked residual convolutions, an intermediate feature enhancement unit integrating single-level residual convolutions and spatial-channel multi-head self-attention modules, and a terminal feature refinement unit composed of single-level residual convolutions and channel attention modules. Progressive extraction and adaptive fusion of multi-scale features are achieved through cross-level skip connections.

[0028] See Figure 2 The atmospheric turbulent wavefront reconstruction method based on the attention-learnable activation collaborative mechanism is implemented by combining the residual convolution with two convolutional layers of size 3×3, stride 1, padding 1, and one convolutional layer of size 1, stride 1, normalization layer, GELU type activation function, and mean pooling layer.

[0029] See Figure 2 The spatial-channel multi-head self-attention module consists of a spatial-channel joint encoding unit, a multi-head self-attention branch, and a feature fusion unit. The spatial-channel joint encoding unit generates query, key, and value vectors through 1×1 convolution. The multi-head self-attention flattens the features in the spatial dimension and then performs multi-head segmentation in the channel dimension. The feature fusion unit consists of layer normalization, residual connections, two 3×3 depthwise separable convolutions, and a GELU activation function.

[0030] See Figure 2 The channel attention module consists of a global mean pooling layer, two fully connected layers, and a sigmoid activation function.

[0031] See Figure 2 The Kolmogorov-Arnold network is based on the Kolmogorov-Arnold representation theorem. It constructs a dynamic adaptive nonlinear mapping through learnable spline basis functions, which can dynamically adjust the shape of the activation function according to the input features.

[0032] The above are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above content. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for reconstructing atmospheric turbulent wavefronts based on an attention-learnable activation collaborative mechanism, characterized in that, Includes the following steps: S1. High-speed synchronous acquisition of in-focus and out-of-focus images of the target and the corresponding distorted wavefront phase through an optical imaging system. The in-focus and out-of-focus intensity maps are stacked and used as input to a neural network. The Zernike coefficients of the distorted phase are used as labels for the neural network to complete the construction of the dataset. S2. Construct a neural network architecture based on an attention mechanism encoder and a Kolmogorov-Arnold network; the attention mechanism encoder adopts a hierarchical cascaded architecture, including a primary feature encoder composed of four stacked residual convolutions, an intermediate feature enhancement unit integrating single-level residual convolutions and spatial-channel multi-head self-attention modules, and a terminal feature refinement unit composed of single-level residual convolutions and channel attention modules. Progressive extraction and adaptive fusion of multi-scale features are achieved through cross-level skip connections; wherein... The residual convolution is implemented by combining two convolutional layers with a kernel size of 3×3, a stride of 1, and padding of 1, a set of convolutional layers with a kernel size of 1 and a stride of 1, a normalization layer, a GELU-type activation function, and an average pooling layer. The spatial-channel multi-head self-attention module consists of a spatial-channel joint coding unit, a multi-head self-attention branch, and a feature fusion unit. The spatial-channel joint coding unit generates query, key, and value vectors through 1×1 convolution. The multi-head self-attention flattens the features in the spatial dimension and then performs multi-head segmentation in the channel dimension. The feature fusion unit consists of layer normalization, residual connection, two 3×3 depthwise separable convolutions, and the GELU activation function. The channel attention module consists of a global mean pooling layer, two fully connected layers, and a sigmoid activation function; Kolmogorov-Arnold Network is based on the Kolmogorov-Arnold representation theorem. It constructs a dynamic adaptive nonlinear mapping through learnable spline basis functions, which can dynamically adjust the shape of the activation function according to the input features. S3. Train the neural network using the error-weighted root mean square loss function, and backpropagate the gradient of the loss function value to update the parameters of the network model, thus obtaining a fully trained atmospheric turbulence distortion aberration detection neural network. The error-weighted root mean square loss function is constructed through a dynamic weight allocation mechanism. By normalizing and mapping each Zernike coefficient error to the [1,10] interval through the statistical distribution of the Zernike coefficient reconstruction error in the historical training cycle, an adaptive weight matrix is ​​generated. After performing the Hadamard product operation between the weight matrix and the mean square error of the current round, the square root operation of the weighted tensor is performed, and finally, a loss evaluation value with error balance characteristics is output.

2. The atmospheric turbulence wavefront reconstruction method based on attention-learnable activation synergy mechanism according to claim 1, characterized in that, In step S3, the gradient value of the loss function is backpropagated multiple times to update the weights and bias parameters of the neural network, including parameter learning in the learnable activation function. When the loss function value is less than a preset stopping value, the updating of the weights and bias parameters of the neural network is stopped, and a fully trained neural network is obtained.

Images