A Deep Learning-Based Fast Imaging Method for Integrated Aperture Radio Arrays

Abstract

This invention belongs to the field of synthetic aperture radio array imaging detection, and relates to a rapid imaging method for synthetic aperture radio arrays based on deep learning. The method includes: processing observation data based on optimized parameter combinations and matrix mapping to generate a brightness temperature image training set with frequency domain correlation and high image quality; constructing an imaging neural network model composed of a pre-imaging network and an image restoration network to achieve a high-dimensional nonlinear mapping between the visibility function, the projected baseline, and the brightness temperature image; and achieving rapid, high-quality imaging of the observation data through preprocessing, data preprocessing, and real-time imaging operations. This invention is based on observation data from the Meridian Project's circular array solar radio imaging telescope, constructing a solar brightness temperature image dataset consistent with the actual observation scenario; designing an imaging neural network model adapted to different solar brightness temperature characteristics and projected baselines; and significantly improving the imaging speed of synthetic aperture radio telescopes while achieving high-quality imaging.

Description

Technical Field

[0001] This invention relates to the field of integrated aperture radio array imaging detection, and in particular to a deep learning-based rapid imaging method for integrated aperture radio arrays, used for high-quality and rapid imaging of radio interferometric data. Background Technology

[0002] Aperture Synthetic Radio Telescopes (ASTs), widely used astronomical instruments in radio astronomy, provide astronomers with crucial tools for exploring the mysteries of the universe thanks to their large field of view and high-resolution radio imaging. The Circular Array Solar Radio Imaging Telescope (DART) of the Meridian Project Phase II is a key facility in this field. It deploys 313 antenna elements on a 1km diameter ring to conduct coordinated observations of the same celestial region. Based on interferometry, it obtains the visibility function of the observed area and further reconstructs the brightness and temperature distribution image of the observed region using inversion algorithms.

[0003] Commonly used high-performance interferometric imaging techniques mainly include the CLEAN method, the G-matrix method, and compressed sensing. The CLEAN method, a classic radio astronomy imaging algorithm, constructs radio images of celestial objects step-by-step through iterative cleaning. The imaging quality of this method is closely related to the iteration step size, and the imaging speed is limited by the number of iterations and the meshing process, making it difficult to meet the requirements for real-time imaging of dynamic celestial objects such as the Sun. The G-matrix method establishes a linear relationship between the visibility function and the brightness temperature image, reconstructing the brightness temperature image using a generalized inverse matrix. In practical applications, due to the large data scale and baseline projection changes, the time cost of solving each generalized inverse matrix is ​​enormous, making it impossible to complete high-quality imaging in a short time. Compressed sensing methods utilize the sparsity of the visibility function and attempt to reconstruct images from a small amount of visibility function sampling data through advanced optimization algorithms. However, it also faces problems such as high computational complexity and limited imaging accuracy, making it difficult to achieve fast imaging while ensuring image quality.

[0004] With the development of neural network technology, its application in image processing has gradually attracted attention, providing new imaging ideas and methods for radio astronomy. However, most existing neural network imaging methods are geared towards visible light and infrared images. These methods often cannot be directly applied to radio telescope observation data due to differences in data characteristics and imaging requirements. The few deep learning imaging methods designed for synthetic aperture microwave radiometers are also mostly limited to fixed baseline projection, lacking effective methods for directly imaging visibility function sampling data under different projection baselines. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a rapid imaging method for integrated aperture telescopes based on deep learning, which accelerates the imaging speed of radio interferometric observation data while meeting high imaging quality requirements.

[0006] In view of this, the present invention proposes a rapid imaging method for integrated aperture radio arrays based on deep learning, comprising:

[0007] Based on optimized parameter combinations, multiple sets of real observation data are inverted and reconstructed, and the real observation data are matrix-mapped to recover spatial distribution information, generating a brightness temperature image training set with frequency domain correlation and high image quality. The imaging neural network model is then trained to obtain a trained imaging neural network model. The observation data includes: visibility function sampling data and projection baseline data.

[0008] The system receives real-time observation data, establishes an index mapping through one-time preprocessing, obtains a two-dimensional matrix result after preprocessing the real-time observation data, inputs it into a trained imaging neural network, and obtains a brightness temperature image, thereby achieving high-quality and rapid imaging of the integrated aperture radio array.

[0009] The imaging neural network includes a pre-imaging network and an image restoration network. The pre-imaging network integrates two-dimensional matrix-based visibility function sampling data and projection baseline data to achieve feature compression and coarse imaging. The image restoration network is based on an improved U-Net architecture and introduces an image pyramid and a self-attention mechanism to enhance multi-scale feature representation and achieve detailed reconstruction of the coarse imaging results.

[0010] Preferably, the process of generating the brightness temperature image training set includes:

[0011] Data Division: Based on the antenna elevation angle, the real solar radio observation data are divided into high elevation angle data and low elevation angle data. The data at noon corresponds to the high elevation angle data, and the projected baseline is approximately circular. The data in the morning and afternoon correspond to the low elevation angle data, and the projected baseline is a slender ellipse.

[0012] Brightness temperature image inversion and reconstruction under multi-parameter constraints: Based on the projected baseline data, frequency domain resampling and regularized grid mapping are performed on the visibility function sampling data to obtain regularized visibility data; multi-group imaging experiments are conducted under different pixel scales and maximum iteration depth parameters, and the peak signal-to-noise ratio of the image is used as the imaging quality index to determine the optimal parameter combination; using the determined optimal parameter combination, the regularized visibility data is subjected to inverse fast Fourier transform and iterative deconvolution based on the CLEAN algorithm to obtain the cleaned brightness temperature image;

[0013] Matrix mapping: Based on the length and orientation angle of the projection baseline data, the visibility function sampling data and the projection baseline data are matrixed into a two-dimensional matrix to restore the spatial distribution information;

[0014] Training sample construction: The cleaned brightness temperature image is paired with the corresponding two-dimensional matrixed visibility function sampling data and projection baseline data to generate a brightness temperature image training set.

[0015] Preferably, the pre-imaging network includes: a visibility-baseline feature fusion module, a feature extraction module, and a coarse imaging module; wherein,

[0016] The input to the visibility-baseline feature fusion module is two-dimensional matrix-based visibility function sampling data. With projection baseline data The output is a feature fusion map. ;

[0017] The input to the feature extraction module is the feature fusion map. The output is multiple feature maps;

[0018] The input to the coarse imaging module is multiple feature maps output by the feature extraction module, and the output is the coarse imaging result. .

[0019] Preferably, the processing procedure of the visibility-baseline feature fusion module includes: two-dimensional matrix-based visibility function sampling data. With projection baseline data After passing through multiple linear layers with progressively increasing feature dimensions, the data is then processed by a Gaussian error linear function to achieve nonlinear representation of high-dimensional features. Next, it passes through multiple dimensionality-reducing linear layers and another Gaussian error linear function, and is then residually connected to the input data to mitigate gradient vanishing, resulting in a feature fusion map. ;

[0020] The processing steps of the feature extraction module include: feature fusion map After dimension adjustment, multiple convolutional modules are input; each convolutional module includes a two-dimensional convolutional layer, a Gaussian error linear function, and a max pooling layer. The number of channels in the two-dimensional convolutional layer increases with the layer to enhance the feature representation capability, and finally outputs a set of multi-scale feature maps.

[0021] The coarse imaging module's processing steps include: adjusting the shape of the multi-scale feature maps output by the feature extraction module, then inputting them into a linear layer and a Gaussian error linear function to obtain the corresponding multi-scale image domain features; weighted fusion of image domain features at adjacent scales, and inputting them into a cascaded structure composed of a two-dimensional convolutional layer and a Gaussian error linear function to extract multi-scale related information and generate fused features; further adding the fused features to the low-scale image domain features, and outputting the coarse imaging result via the cascaded structure composed of a two-dimensional convolutional layer and a Gaussian error linear function. .

[0022] Preferably, the image restoration network includes an encoder and a decoder, wherein,

[0023] The encoder is used to process the input coarse imaging result. Perform multi-layer convolutional feature extraction and hierarchical feature compression to output a multi-scale feature set;

[0024] The decoder is used to reconstruct and progressively fuse the multi-scale feature set output by the encoder to recover spatial details and brightness temperature structure information, and output the final imaging result. .

[0025] Preferably, the encoder includes at least three downsampling layers, each downsampling layer including a convolutional module, a self-attention module, an image pyramid module, and a pooling layer;

[0026] The convolution module includes a two-dimensional convolutional layer and a linear rectified function with leakage;

[0027] The self-attention module includes a two-dimensional convolutional layer and a matrix multiplication operation;

[0028] The image pyramid module includes multiple parallel adaptive pooling layers, two-dimensional convolutional layers, batch normalization layers, a linear rectified function with leakage, and a bilinear interpolation function. The parallel outputs are weighted and fused, and then subjected to a sigmoid operation to output a weighted value.

[0029] Preferably, the decoder includes the same number of upsampling layers as the encoder's downsampling layers. Each upsampling layer includes: multiple convolutional modules, a self-attention module, and a bilinear interpolation upsampling operation connected in sequence. The output of each upsampling layer is added to the feature vector from the encoder as the input to the next upsampling layer; wherein,

[0030] The convolution module includes a two-dimensional convolutional layer and a linear rectified function with leakage;

[0031] The self-attention module includes a two-dimensional convolutional layer and a matrix multiplication operation.

[0032] Preferably, the training objective of the pre-imaging network is to learn the mapping relationship from the visibility function domain to the image domain, and the loss function consists of a weighted sum of the perceptual loss function and the mean squared error loss function.

[0033] Preferably, the training objective of the image restoration network is to learn the mapping from image domain to image domain, and the mean squared error loss function is used to enable the image restoration network to effectively learn the ability to denoise or restore image details.

[0034] Preferably, the step of receiving real-time observation data, establishing an index mapping through one-time preprocessing, and obtaining a two-dimensional matrix result after preprocessing the real-time observation data includes:

[0035] Under the assumption that the array has no antenna faults, obtain the position of the projection baseline of the radio array under orthographic projection; determine the index IND0 of the projection baseline data in the corresponding two-dimensional matrix based on the length and orientation angle of the projection baseline.

[0036] The system detects the operating status of each antenna in the array and removes invalid antenna elements; it updates IND0 based on the invalid antenna elements to obtain the valid index IND1; it calculates the real-time projection baseline data based on the antenna elevation and azimuth information; and it applies the projection baseline data based on the valid index IND1. and visibility function sampling data Two-dimensional matrix transformation.

[0037] Compared with the prior art, the advantages of the present invention are:

[0038] 1. A solar brightness temperature image dataset was constructed based on observation data from the Circular Array Solar Radio Imaging Telescope, overcoming the difficulty of simulation datasets in representing the true characteristics of the observation equipment;

[0039] 2. The CLEAN algorithm based on optimized parameter combination was used to reconstruct the image. The spatial correlation between the visibility function sampling data and the projected baseline data in the frequency domain was restored based on two-dimensional matrix operation, and a high-quality training set was constructed.

[0040] 3. An imaging neural network was designed to adapt to image reconstruction under different solar brightness temperature characteristics and different projection baselines;

[0041] 4. Compared with the calculation process of interpolation, fast Fourier transform and iterative cleansing used in traditional imaging methods, the imaging method proposed in this invention achieves high-quality and fast imaging of integrated aperture radio arrays through the construction of pre-imaging network and image restoration network. It has the advantages of fast imaging speed and imaging quality close to the high-quality CLEAN algorithm.

[0042] 5. This invention can adapt to observation data under various projection baseline distributions, effectively solving the shortcomings of existing imaging methods that only target a single projection baseline and have limited imaging speed, and providing a new technical means for rapid imaging of aperture synthesis radio telescopes. Attached Figure Description

[0043] Figure 1 This is a flowchart of the deep learning-based rapid imaging method for integrated aperture radio arrays according to the present invention;

[0044] Figure 2 A flowchart of high-quality imaging using a traditional synthetic aperture radio array;

[0045] Figure 3 The PSNR of the clean image dataset in this invention varies with single pixel size and maximum number of iterations;

[0046] Figure 4 This is a schematic diagram of the projection baseline distribution, clean map, and dirty map of the dataset constructed in this invention;

[0047] Figure 5 This is a diagram of the pre-imaging network structure constructed for this invention;

[0048] Figure 6 The image restoration network structure diagram constructed for this invention;

[0049] Figure 7 This is a schematic diagram of the imaging results of the present invention. Detailed Implementation

[0050] like Figure 1 As shown, this invention proposes a rapid imaging method for integrated aperture radio arrays based on deep learning, the method comprising:

[0051] Based on the optimized parameter combination, multiple sets of real observation data are inverted and reconstructed, and the real observation data are matrix-mapped to restore spatial distribution information, generating a brightness temperature image training set with frequency domain correlation and high image quality, which is used to train the imaging neural network model.

[0052] The system receives real-time observation data, establishes an index mapping through one-time preprocessing, obtains a two-dimensional matrix result after preprocessing the real-time observation data, inputs it into a trained imaging neural network, and obtains a brightness temperature image, thereby achieving high-quality and rapid imaging of the integrated aperture radio array.

[0053] The imaging neural network consists of a pre-imaging network and an image restoration network. The pre-imaging network integrates two-dimensional matrix-based visibility function sampling data and projection baseline data to achieve feature compression and coarse imaging. The image restoration network is based on an improved U-Net architecture and introduces an image pyramid and a self-attention mechanism to enhance multi-scale feature representation and achieve detailed reconstruction of the coarse imaging results.

[0054] Specifically

[0055] 1. The steps for generating a brightness temperature image training set include:

[0056] Data Division: Based on the antenna elevation angle, the real solar radio observation data are divided into high elevation angle data and low elevation angle data. The data at noon corresponds to the high elevation angle data, and the projected baseline is approximately circular. The data in the morning and afternoon correspond to the low elevation angle data, and the projected baseline is a slender ellipse.

[0057] Brightness-temperature image generation under multi-parameter constraints: Based on the projection baseline data of the observation array, frequency domain resampling and regularized grid mapping are performed on the visibility function sampling data to obtain regularized visibility data; multi-group imaging experiments are conducted under different pixel scales and maximum iteration depth parameters, and the peak signal-to-noise ratio of the image is used as the imaging quality index to determine the optimal parameter combination; using the determined optimal parameter combination, the CLEAN computational imaging algorithm is used to perform inverse fast Fourier transform and iterative deconvolution on the regularized visibility data to obtain the cleaned brightness-temperature image;

[0058] Matrix mapping: Based on the length and orientation angle of the projection baseline data, the projection baseline data and the visibility function sampling data are matrixed into a two-dimensional matrix to restore the spatial distribution information;

[0059] Training sample construction: The cleaned brightness temperature image is paired with the corresponding two-dimensional matrixed visibility function sampling data and projection baseline data to construct a training set for neural network training.

[0060] 2. The training steps for an imaging neural network include:

[0061] The brightness temperature image training set is input into the imaging neural network, and the pre-imaging network and image restoration network are trained separately until the training requirements are met, resulting in a well-trained image reconstruction model.

[0062] The training process employs a two-stage training approach, with the loss function expressed as:

[0063]

[0064] in Represents the total loss function. and These represent the perceptual loss function and the mean squared error loss function, respectively. and The weights of the perceptual loss function and the mean squared error loss function are used to train the perceptual loss function at different stages; among them, the perceptual loss function adopts VGG perceptual loss.

[0065] In the first stage of the pre-imaging network training process, relatively large weights are set. To enable the network to converge as quickly as possible, while setting a smaller [size / size] Constrain the sign of the pre-imaging results; in the second stage of pre-imaging network training, set larger weights. This is to further improve the image quality of the pre-imaging results.

[0066] When training an image restoration network, directly using The loss function is used to train the network to minimize the difference between the reconstructed image and the target image.

[0067] 3. The steps for real-time processing of observation data include:

[0068] Pre-processing operations, data preprocessing operations, and real-time imaging operations.

[0069] The preprocessing operations include: assuming no antenna faults in the array, obtaining the projection baseline position of the radio array under orthographic projection. Based on the length and orientation angle of the projected baseline, determine its index IND0 in the corresponding two-dimensional matrix;

[0070] Data preprocessing operations include: detecting the operating status of each antenna in the array and removing invalid antenna elements; obtaining the valid index IND1 from IND0; and calculating the real-time projection baseline data based on the antenna elevation and azimuth information. The calculation process is as follows:

[0071]

[0072] in The elevation angle of the antenna. This is the azimuth angle of the antenna.

[0073] Based on the valid index IND1, the projected baseline and visibility function Two-dimensional matrix transformation.

[0074] Real-time imaging operations include: converting the two-dimensional matrix-based projection baseline... and visibility function Input a trained imaging neural network model to obtain high-quality imaging results.

[0075] 4. Imaging Neural Networks:

[0076] Includes: a pre-imaging network and an image restoration network; among which,

[0077] The pre-imaging network employs multiple linear layers and two-dimensional convolutional layers to compress data dimensions while fusing features of two-dimensional matrix-based visibility function sampling data and projection baseline data to output pre-imaging results.

[0078] The pre-imaging network includes: a visibility-baseline feature fusion module, a feature extraction module, and a coarse imaging module; the imaging process of the pre-imaging network is as follows: sampling data of the two-dimensional matrix-based visibility function. With projection baseline data Input the visibility-baseline feature fusion module to obtain the feature fusion map. The feature fusion map is processed by the feature extraction module to obtain the feature map. , and , , and The pre-imaging result is output after inputting into the coarse imaging module. .

[0079] (1) Visibility-Baseline Feature Fusion Module: This module includes three cascaded linear layers with continuously increasing feature dimensions, a Gaussian error linear function, four linear layers with continuously decreasing feature dimensions, and a Gaussian error linear function. It performs dimensionality increase and then dimensionality reduction operations on the feature dimensions of the input data and uses residual connections to add the input data after passing through a linear layer to prevent gradient vanishing. This captures the latent correlation between the visibility function and the projected baseline, resulting in a feature fusion map. .

[0080] (2) Feature extraction module: It includes five convolutional modules, each of which includes a cascaded two-dimensional convolutional layer, a Gaussian error linear function, and a max pooling layer; its processing flow is as follows: Feature fusion map After dimensionality transformation, the data is sequentially input into three convolutional modules to obtain the first feature map. , The second feature map is obtained after the fourth convolutional module. , The feature map is obtained after the fifth convolutional module. Each convolutional module includes a two-dimensional convolutional layer, a Gaussian error linear function, and a max pooling layer; the number of channels in the two-dimensional convolutional layers of the first four convolutional modules gradually increases, while the number of channels in the two-dimensional convolutional layers of the fifth convolutional module remains the same as that of the fourth convolutional module.

[0081] (3) Coarse imaging module: includes multiple linear layers, two-dimensional convolutional layers, and Gaussian error function. Its processing flow is as follows: for three feature maps , and After changing the shape, each input is a linear layer and a Gaussian error linear function to obtain the corresponding image domain features. and , and After addition, the data passes through two cascaded structures consisting of two-dimensional convolutional layers and Gaussian error linear functions to achieve the fusion of features at two different scales, outputting the fusion result of features at different scales. , and The results are summed and passed through two cascaded structures consisting of two-dimensional convolutional layers and a Gaussian error linear function to output a coarse imaging result. .

[0082] The image restoration network adopts the U-Net network architecture, and introduces a self-attention mechanism and an image pyramid module to enhance multi-scale feature extraction of feature maps and improve image restoration quality.

[0083] The U-Net architecture in image restoration networks consists of an encoder and a decoder. The encoder structure includes two-dimensional convolutional layers, a leaky linear rectified function, a self-attention module, and an image pyramid module, and adjusts the output feature map through the pyramid module. The decoder structure includes two-dimensional convolutional layers, a self-attention module, and a bilinear interpolation upsampling function, and performs residual connections with the feature map output by the encoder module to enhance the network's ability to express multi-scale features in the image.

[0084] The image pyramid module is used to adjust the feature maps output by the encoder in the U-Net architecture. It consists of three parallel pyramid downsampling modules, each of which comprises a cascaded adaptive max-pooling layer and a 2D convolutional layer; the input to the image pyramid module is the input feature map of each 2D convolutional layer in the U-Net architecture encoder. Feature map The pyramid downsampling module outputs three features at different scales. These features are then summed and input into a sigmoid activation function to output a weighted value. Finally, adjust the encoder output feature map. for .

[0085] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0086] Example

[0087] Embodiments of the present invention provide a rapid imaging method for integrated aperture radio arrays based on deep learning, which is implemented according to the above-proposed technical framework and the following steps:

[0088] Step 1: Constructing the Solar Brightness Temperature Image Training Set

[0089] Data Classification: DART solar observation data are divided into two categories based on elevation angle: high elevation data and low elevation data. Noon data corresponds to high elevation data, and its projected baseline is approximately circular. The morning and afternoon data correspond to low elevation data, and its projected baseline exhibits a slender elliptical distribution. Figure 4 The first image in each row is shown.

[0090] Brightness-temperature image generation under multi-parameter constraints: The CLEAN method is selected for brightness-temperature image generation. The CLEAN method is an iterative imaging algorithm based on the system point source response. Multiple parameters affect the cleansing result of the CLEAN algorithm. Here, a multi-scale CLEAN method is used for cleansing imaging. The flowchart of this method is as follows: Figure 2 As shown; using the recommended loop gain of 0.1, Figure 3 This demonstrates how the peak signal-to-noise ratio (PSNR) of the clean image changes with the maximum number of iterations and the single pixel size. It is assumed that an PSNR of 30 dB indicates sufficiently good image quality. In one embodiment, the maximum number of iterations is set to 20,000, and the single pixel size to 30 arcsec. In practical applications of this technique, appropriate loop gain and iteration convergence criteria should be selected based on the characteristics of the target source and the imaging device, such as whether the root mean square residual converges and the maximum number of iterations. Imaging was performed on high-elevation and low-elevation data respectively, and examples of the imaging results are shown below. Figure 4 As shown, the second image in each row is the clean image after CLEAN processing, and the third image is the dirty image. It can be seen that, compared with the dirty image, the clean image effectively suppresses the influence of side lobes.

[0091] Matrix mapping and training sample construction: projecting baseline and visibility function The image is then matrixed into a two-dimensional matrix based on the length and azimuth information of the projection baseline. The cleaned brightness temperature image is then paired with the corresponding two-dimensional matrixed visibility function sampling data and the projection baseline data. In one embodiment, the size of the two-dimensional matrix array is set to... The generated dataset includes 528 high elevation angle data points and 524 low elevation angle data points. The training and validation sets are divided into a test set and a training set in an 8:2 ratio. The training and validation sets are further divided into training and validation sets in an 8:2 ratio.

[0092] Step 2: Pre-imaging network structure design

[0093] Construct a pre-imaging network; the specific structure is as follows: Figure 5The pre-imaging network comprises a visibility-baseline feature fusion module, a feature extraction module, and a coarse imaging module. The pre-imaging network processes the following: A 3D array consisting of a visibility function and a projected baseline is input; this array passes through the visibility-baseline feature fusion module to obtain the fused feature map. ,Will After dimensionality transformation, the data is input into the feature extraction module to obtain the feature map. , and , , and The pre-imaging result is output after inputting into the coarse imaging module. .

[0094] Specifically, in one embodiment, after the input data passes through three linear layers with progressively increasing feature dimensions, its dimensions become... After passing through a Gaussian error linear function to enhance the nonlinear representation capability of the dimensionality-upgraded data, and then through four dimensionality-reduction linear layers and another Gaussian error linear function, the output dimension is... The input data is added to the input data after passing through a linear layer to alleviate the gradient vanishing problem, thereby obtaining the fused feature map. Its dimensions are This process can be represented as:

[0095]

[0096] in This represents the part consisting of a linear layer and a Gaussian error linear function, which is an operation of first increasing the dimension and then reducing the dimension. This represents the operation of using a linear layer to reduce the dimensionality of the input, combined with residual connections to alleviate gradient vanishing.

[0097] Feature map output by the fusion module After dimensional transformation, the dimension is Input the first three convolutional modules to obtain the first feature map. Feature map The second feature map is obtained after the fourth convolutional module. ,further The feature map is obtained after the last convolutional module. ,like Figure 5 As shown. It should be noted that each convolutional module consists of a two-dimensional convolutional layer, a Gaussian error linear function, and a max-pooling layer. In one embodiment, the size of each two-dimensional convolutional layer is [size missing]. Furthermore, the number of channels in the two-dimensional convolutional layers of the first four convolutional modules gradually increases, while the number of channels in the two-dimensional convolutional layers of the fifth convolutional module remains the same as that of the fourth convolutional module; finally, three feature maps are obtained from the output. , and The dimensions are respectively , and This process can be represented as:

[0098]

[0099] in This represents the feature extraction module.

[0100] , and Further input is given to the coarse imaging module, such as Figure 5 As shown: Feature map , and The shape is changed to fit subsequent image reconstruction. , and The dimensions are respectively , and Subsequently, the three feature vectors are processed through three linear layers and a Gaussian error linear function to initially transform them from the visibility baseline fusion space to the image space. After changing their shape, three image domain features are output. and In one embodiment, the dimensions are respectively , and ;further, and After addition, the data passes through two cascaded structures consisting of two-dimensional convolutional layers and Gaussian error linear functions to achieve the fusion of features at two different scales, outputting the fusion result of features at different scales. further with The results are summed and passed through two cascaded structures consisting of convolutional layers and a Gaussian error linear function to output the final coarse imaging result. Its dimensions are The coarse imaging module can be represented as:

[0101]

[0102] in This represents the coarse imaging network module.

[0103] Step 3: Image Restoration Network Structure Design

[0104] For the specific structure of the image restoration network, please refer to Figure 6The left side represents the encoder, and the right side represents the decoder. The encoder consists of four downsampling layers, each including a convolutional module, a self-attention module, an image pyramid module, and a max-pooling layer. The number of convolutional modules and the construction method of the self-attention module can be found in [reference needed]. Figure 6 The convolutional module consists of a 2D convolutional layer and a leaky linear rectified function (RCD). The self-attention module includes a convolutional layer and a matrix multiplication operation. The image pyramid module is connected in parallel with the convolutional and self-attention modules. It includes three parallel adaptive max-pooling layers, a 2D convolutional layer, a batch normalization layer, a leaky RCD, and a bilinear interpolation function. Finally, the outputs of the three parallel layers are summed and a sigmoid operation is performed to output a weighted value. The construction method of each downsampling layer can be referred to... Figure 6 Except for the input of the first downsampling layer, which is In addition, for the first ( For a downsampling layer, its input is a feature map. The output after passing through the convolutional module and the self-attention module is The output of the image pyramid module is a weighted value. ,Will Adjusted to As the output feature map of this downsampling layer ; After the max pooling layer, the output is... This is the input for the next downsampling layer. The input is the coarse imaging result. After the encoder section, four feature maps are output. , , and In one embodiment, the dimensions are respectively , , , This part can be represented as:

[0105]

[0106] in This represents the entire network structure of the encoder.

[0107] Feature map After the max pooling layer, the input to the decoder is obtained. In the decoder section, the decoder consists of four upsampling layers and one convolutional module. Each upsampling layer comprises multiple convolutional modules, a self-attention module, and bilinear interpolation upsampling operations. The output of each layer is added to the feature vector from the encoder as the input to the next upsampling layer. The structure of each convolutional module and self-attention module can be found in [reference needed]. Figure 6Taking the first upsampling layer as an example, its input is the feature map. After undergoing upsampling operations consisting of three convolutional modules, one self-attention module, and bilinear interpolation, the upsampling result of this layer is output. , With the output from the encoder The sum is then used as the input for the next upsampling module. After four upsampling modules, in one embodiment, the dimension of the output result is... Furthermore, the result is input into a convolutional module consisting of three two-dimensional convolutional layers to reduce the number of channels in the feature map to the desired number of channels in the image, and the output result is obtained. ,Will Compared with the input coarse imaging results Add them together to obtain the final output of the imaging neural network. The above process can be represented as:

[0108]

[0109] in Representing the imaging neural network, it can be seen that the image restoration network learns the residual between the coarse imaging result and the target image.

[0110] Step 4: Optimize the imaging neural network

[0111] This method trains the pre-imaging network and the image restoration network on the image separately.

[0112] During pre-imaging network training, the goal is to learn the mapping relationship from the visibility function domain to the image domain. Due to the complexity of this mapping relationship, it is difficult to achieve effective convergence using only the mean squared error loss function or the mean absolute error loss function. Here, we adopt a loss function composed of a weighted sum of the perceptual loss function and the mean squared error loss function. The mean squared error loss function is expressed as:

[0113]

[0114] in This represents the total number of pixels in the reconstructed image.

[0115] The perceptual loss function is calculated using a VGG network and can be expressed as:

[0116]

[0117] in, This represents a pre-trained network. Compared to the mean squared error loss function, the perceptual loss function considers not only pixel-level differences in the image but also high-level semantic information. The overall loss function can be expressed as:

[0118]

[0119] In the pre-imaging network training experiment, the following settings were first configured. =1, The value is set to 0.1 to quickly help the pre-trained network converge and learn rich visual features; thereafter, it will be set to... =0, Set to 1 for precise pixel-level optimization to improve image quality.

[0120] Unlike pre-imaging networks, the goal of image restoration networks during training is to learn the mapping from the image domain to the image domain, i.e., to denoise or restore details from the input image. Therefore, we can use the mean squared error loss function to enable the network to effectively learn the ability to denoise or restore image details. That is, the loss function used in the image restoration network training process is:

[0121] Step 5: Pre-processing operations

[0122] The DART visibility function stores data in a one-dimensional array, and the data in the one-dimensional array is arranged in the order of subtraction of antenna elements. The frequency domain correlation between adjacent elements is weak. In order to improve the frequency domain correlation between adjacent elements, the visibility function is rearranged into a two-dimensional matrix.

[0123] Before performing 2D matrixing, preprocessing is used to obtain the indices in the 2D matrix corresponding to each element in the 1D array. Specifically, the baseline length and orientation angle correspond to the sampling positions of the visibility function in the UV domain. Changes in the projected baseline only compress the baseline and do not affect the correlation between adjacent elements. Therefore, the 2D matrix index IND0 corresponding to the orthographic projection baseline can be used as the index IND0 for all projection cases. In one embodiment, we use the orthographic projection baseline under ideal conditions without antenna failure and set the array size of the 2D matrix to [value missing]. .

[0124] Step Six: Data Preprocessing

[0125] The operating status of each antenna in the detection array is checked, invalid antenna elements are filtered out, and the wireless antenna element index is further removed from IND0 to obtain the valid index IND1; based on the antenna elevation and azimuth information, the real-time projected baseline data is calculated. The calculation process is as follows:

[0126]

[0127] in The elevation angle of the antenna. This is the azimuth angle of the antenna;

[0128] Based on the valid index IND1, project the baseline. and visibility function Two-dimensional matrixing. In one embodiment, the size of the array for two-dimensional matrixing is set to... .

[0129] It's important to note that the visibility function is a complex number. To facilitate neural network training, the amplitude and phase need to be separated. Therefore, the final input to the neural network is a three-dimensional array with dimensions of... .

[0130] Step 7: Real-time Imaging Operation

[0131] To evaluate the imaging speed and quality of the network, we conducted experiments based on the PyTorch deep learning framework. Imaging times were recorded using both CPU and GPU. The CPU platform was an Intel Xeon Platinum 8358 processor (Operating system: Red Hat Enterprise Linux 4.8.5-36), and the GPU platform was an RTX 3070 (Operating system: Windows 10). The results showed that the imaging time using our method was 0.622s (CPU) and 0.030s (GPU). Compared to the ground truth, the structural similarity of the imaging results using our method on the high elevation angle dataset was 0.946, with a mean squared error of 0.000567, while the structural similarity on the low elevation angle dataset was 0.895, with a mean squared error of 0.000649. It should be noted that all the above statistics were obtained with a batch size of 1. In fact, the PyTorch framework supports multiple batches of input simultaneously, thus giving our method a speed advantage.

[0132] Figure 7 The image shows some of the imaging results. The first row shows the imaging results using our proposed fast imaging method, the second row shows the ground truth image (the imaging results using the CLEAN method), and the third row shows the residual image obtained by subtracting the ground truth image from the imaging results of our method.

[0133] The advantages of this invention are: a solar brightness temperature image dataset was constructed based on real observation data from the Circular Array Solar Radio Imaging Telescope, which is consistent with the actual observation scenario; an imaging neural network adapted to different solar brightness temperature characteristics and different projection baselines was designed; and the proposed deep learning-based imaging method can significantly improve the imaging speed of the Aperture Synthetic Radio Telescope while achieving high-quality imaging.

[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A deep learning-based fast imaging method for a synthetic aperture radio array, comprising: inverse reconstruction of multiple sets of real observation data based on an optimal parameter combination, and matrix mapping of the real observation data to recover spatial distribution information, to generate a brightness temperature image training set with frequency domain correlation and high image quality, training of an imaging neural network model, and obtaining of a trained imaging neural network model; the observation data including visibility function sampling data and projected baseline data; receiving real-time observation data, establishing an index mapping through one-time pre-processing, obtaining a two-dimensional matrix result after pre-processing of the real-time observation data, inputting the trained imaging neural network, and obtaining a brightness temperature image, so as to realize high-quality fast imaging of the synthetic aperture radio array; the imaging neural network including a pre-imaging network and an image restoration network, wherein the pre-imaging network fuses the two-dimensional matrix visibility function sampling data and the projected baseline data, to realize feature compression and coarse imaging; and the image restoration network is based on an improved U-Net architecture, and introduces an image pyramid and a self-attention mechanism to enhance multi-scale feature expression, to realize detail reconstruction of a coarse imaging result.

2. The deep learning based integrated aperture radio array fast imaging method according to claim 1, characterized in that, the generation process of the brightness temperature image training set including: data division: dividing real solar radio observation data into high-elevation data and low-elevation data according to the elevation of an antenna, wherein noon period data corresponds to the high-elevation data, and the projected baseline is approximately circularly distributed; and morning and afternoon period data corresponds to the low-elevation data, and the projected baseline is elongated and elliptically distributed; brightness temperature image inverse reconstruction under multiple parameter constraints: based on the projected baseline data, performing frequency domain resampling and regular grid mapping on the visibility function sampling data to obtain regular visibility data; performing multiple imaging experiments under different pixel scales and maximum iteration depth parameters, and determining an optimal parameter combination by taking an image peak signal-to-noise ratio as an imaging quality index; and performing inverse fast Fourier transform and iterative deconvolution on the regular visibility data based on the CLEAN algorithm by using the determined optimal parameter combination, to obtain a cleaned brightness temperature image; matrix mapping: two-dimensional matrixing the visibility function sampling data and the projected baseline data according to the length and direction angle of the projected baseline data, to recover spatial distribution information; training sample construction: pairing the cleaned brightness temperature image with the corresponding two-dimensional matrix visibility function sampling data and projected baseline data, to generate the brightness temperature image training set.

3. The deep learning based integrated aperture radio array fast imaging method according to claim 1, characterized in that, the pre-imaging network including a visibility-baseline feature fusion module, a feature extraction module, and a coarse imaging module; wherein The input of the visibility-baseline feature fusion module is two-dimensional matrixed visibility function sample data with projected baseline data , and the output is a feature fusion map ; The input of the feature extraction module is a feature fusion graph , and the output is multiple feature maps The input of the coarse imaging module is a plurality of feature maps output by the feature extraction module, and the output is a coarse imaging result .

4. The deep learning-based fast imaging method for a synthetic aperture radio array according to claim 3, characterized in that, The processing procedure of the visibility-base feature fusion module includes: two-dimensional matrixing visibility function sampling data With the projection base data After sequentially passing through multiple linear layers with increasing feature dimensions, and then passing through a Gaussian error linear function, the nonlinear representation ability of high-dimensional features is realized; then, after passing through multiple linear layers with reduced dimensions and a Gaussian error linear function, residual connection is performed with the input data to relieve gradient disappearance, and a feature fusion graph is obtained ; The processing procedure of the feature extraction module comprises a feature fusion graph After the dimension adjustment, a plurality of convolution modules are input; each of the convolution modules comprises a two-dimensional convolution layer, a Gaussian error linear function and a maximum pooling layer, the number of channels of the two-dimensional convolution layer increases with the level to enhance the feature expression capability, and a multi-scale feature map set is finally output. The processing procedure of the coarse imaging module comprises: after shape adjustment is performed on the multi-scale feature maps output by the feature extraction module, the multi-scale feature maps are respectively input into a linear layer and a Gaussian error linear function to obtain corresponding multi-scale image domain features; image domain features of adjacent scales are weighted and fused, and are input into a cascade structure composed of a two-dimensional convolution layer and a Gaussian error linear function to extract multi-scale related information and generate fused features; the fused features and low-scale image domain features are further added, and are output via a cascade structure composed of a two-dimensional convolution layer and a Gaussian error linear function .

5. The deep learning-based fast imaging method for a synthetic aperture radio array according to claim 1, characterized in that, the image restoration network including an encoder and a decoder, wherein The encoder is used for performing multi-layer convolution feature extraction and hierarchical feature compression on the input coarse imaging result to output a multi-scale feature set; The decoder is used to reconstruct and gradually fuse the multi-scale feature set output by the encoder to recover spatial details and brightness temperature structure information, and output the final imaging result .

6. The deep learning-based fast imaging method for a synthetic aperture radio array according to claim 5, characterized in that, the encoder including no less than three down-sampling layers, and each down-sampling layer including a convolution module, a self-attention module, an image pyramid module, and a pooling layer. The convolution module comprises a two-dimensional convolution layer and a leaky linear rectifier function. The self-attention module comprises a two-dimensional convolution layer and a matrix multiplication operation. The image pyramid module comprises a plurality of parallel adaptive pooling layers, two-dimensional convolution layers, batch normalization layers, leaky linear rectifier functions and bilinear interpolation functions, the outputs of the parallel layers are fused after weighting, and then a sigmoid operation is performed, and the weighted values are output.

7. The deep learning-based synthetic aperture radio array fast imaging method according to claim 6, characterized in that, The decoder comprises a same number of up-sampling layers as the number of down-sampling layers of the encoder, each up-sampling layer comprises a plurality of convolution modules, a self-attention module and a bilinear interpolation up-sampling operation connected in sequence, the output of each up-sampling layer is added to the feature vector from the encoder as the input of the next up-sampling layer; wherein, The convolution module comprises a two-dimensional convolution layer and a leaky linear rectifier function. The self-attention module comprises a two-dimensional convolution layer and a matrix multiplication operation.

8. The deep learning based integrated aperture radio array fast imaging method according to claim 1, characterized in that, The training target of the pre-imaging network is to learn the mapping relationship from the visibility function domain to the image domain, and the loss function is composed of the weighted sum of the perceptual loss function and the mean square error loss function.

9. The deep learning based integrated aperture radio array fast imaging method according to claim 1, characterized in that, The training target of the image restoration network is to learn the mapping from the image domain to the image domain, and the mean square error loss function is used to enable the image restoration network to effectively learn the ability to denoise or restore image details.

10. The deep learning based integrated aperture radio array fast imaging method according to claim 1, characterized in that, The receiving real-time observation data, the index mapping is established through one-time pre-processing, and the two-dimensional matrix result is obtained after the real-time observation data is pre-processed, comprising: Under the condition of assuming that the array has no antenna failure, the projection baseline position of the radio array under the orthographic projection is obtained; according to the length and direction angle of the projection baseline, the index IND0 of the projection baseline data in the corresponding two-dimensional matrix is determined; Detect the working state of each antenna in the array, and eliminate invalid antenna units; update IND0 according to the invalid antenna units, and obtain valid index IND1; calculate real-time projection baseline data according to the antenna elevation and azimuth angle information; update the projection baseline data according to the valid index IND1 and the visibility function sampling data Two-dimensional matrix.

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