Frequency spectrum map reconstruction method based on residual self-encoder under sparse data condition

Abstract

The invention discloses a spectrum map reconstruction method based on a residual auto-encoder under a sparse data condition. The method comprises the following steps: acquiring size information, measurement node information, measurement frequency and radiation source information of a monitoring area; dividing a monitoring area into grids with fixed sizes, mapping the spectrum intensity information of the measurement points to the closest grid points, and constructing a monitoring area matrix; modeling frequency spectrum intensity at different grid points, and calculating path loss according to an improved close-range free space reference distance path loss model to obtain a sparse frequency spectrum map in a plane form; carrying out data enhancement to obtain a training set and carrying out global normalization on data of the training set; performing expansion to obtain multi-channel data, and constructing various loss functions to obtain a total loss function; and constructing a residual self-encoder network based on a spectrum coupling attention module, carrying out network training, and carrying out sparse spectrum map reconstruction. According to the method, the high-precision spectrum map of the target area can be accurately reconstructed under the sparse data condition.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and machine learning technology, specifically relating to a spectrum map reconstruction method based on residual autoencoders under sparse data conditions. Background Technology

[0002] With the rapid development of cognitive radio and information technology, the number of smart terminals and their various services in wireless communication networks has increased dramatically, leading to a pressing need to address the shortage of spectrum resources. Electromagnetic spectrum situation maps (or spectrum maps for short) can visualize electromagnetic spectrum resources, such as radiation source locations and bandwidth utilization, on a geographic map. They characterize the real-time spectrum situation within a target area from multiple dimensions, including geographic location, frequency, time, and energy, and have become an important tool for managing and utilizing spectrum resources.

[0003] Spectrum maps can be obtained by monitoring and sampling within a target area using spectrum monitoring devices such as drones and low-orbit satellites. However, in practical applications, due to complex urban terrain, building obstruction, noise interference, and other factors, it is usually impossible to obtain a complete spectrum map based on the sparse spectrum data collected by monitoring devices. Therefore, it is necessary to study methods for reconstructing efficient spectrum maps.

[0004] Traditional model-driven reconstruction methods rely primarily on accurate propagation models and radiation source information; however, propagation models struggle to accurately reflect reality in irregular or complex environments, and obtaining sufficient radiation source information through sparse data is also difficult. Data-driven reconstruction methods learn complex spectral distribution characteristics from historical data using machine learning or deep learning methods, but their performance largely depends on the quantity and quality of the data, and they generally lack awareness of global frequency information. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a spectrum map reconstruction method based on residual autoencoders under sparse data conditions. The method employs a multi-channel input residual autoencoder and adds a spectrum coupling attention module to the network, thereby enabling accurate reconstruction of a high-precision spectrum map of the target region under sparse data conditions.

[0006] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0007] A spectrum map reconstruction method based on residual autoencoders under sparse data conditions includes:

[0008] Step 1: Obtain the size information, measurement node information, measurement frequency, and radiation source information of the monitoring area;

[0009] Step 2: Based on the size information and measurement node information of the monitoring area, the monitoring area is divided into grids of fixed size and the spectral intensity information of the measurement points is mapped to the grid points closest to them, thereby constructing a monitoring area matrix containing sparse spectral intensity information;

[0010] Step 3: Based on the monitoring area matrix and measurement frequency and radiation source information, model the spectral intensity at different grid points, perform frequency shifting under narrowband conditions, calculate the path loss from each grid point to the receiving antenna according to the improved near-range free space reference distance path loss model, and obtain a sparse spectrum map in planar form.

[0011] Step 4: Perform noise injection data augmentation on the sparse spectrum map, obtain a training set based on the augmented sparse spectrum intensity data, and perform global normalization on the training set data;

[0012] Step 5: Expand the normalized training data into multi-channel data including spectrum signal strength channel, mask channel, building channel and source channel, and construct the loss function combining the mask channel and spectrum signal strength channel, the loss function of the building channel and the loss function of the source channel, and then obtain the total loss function;

[0013] Step 6: Construct a residual autoencoder network based on the spectrum-coupled attention module and train the network using the multi-channel data and the total loss function. Then, use the trained network to reconstruct the sparse spectrum map.

[0014] To optimize the above technical solution, the specific measures also include:

[0015] Step 2 above specifically includes:

[0016] Based on the size information of the monitoring area, the monitoring area is divided according to the set grid resolution. Divide the grid into a fixed-size grid and calculate the coordinates of each grid point. Then, the distance between each measurement point and each grid point is calculated;

[0017] The spectral intensity information of each measurement point is mapped to the grid point closest to that measurement point to obtain the spectral intensity information of the corresponding grid point. This allows for the construction of a monitoring area matrix containing sparse spectral intensity information.

[0018] (2)

[0019] in This represents the set of grid points that map the measurement points.

[0020] Step 3 above models the spectral intensity at different grid points as follows:

[0021] (3)

[0022] in, For the first The emission intensity of each radiation source; For grid points At frequency The frequency response at that point, For grid points Noise at that location This refers to the number of radiation sources.

[0023] The frequency offset mentioned in step 3 above is: for the measured frequency Offset using the following formula:

[0024] (4)

[0025] in It is the center frequency. It refers to the signal bandwidth.

[0026] The improved near-range free-space reference distance path loss model described in step 3 above is as follows:

[0027] (5)

[0028] in, and These are parameters related to the environment; This represents the distance between the grid points and the receiving antenna; The receiver height; It is the center frequency; For shadow fading that follows a zero-mean Gaussian distribution.

[0029] Step 4 above describes data augmentation of the sparse spectral map, specifically as follows:

[0030] Gaussian noise and speckle noise were randomly injected into each missing spectral map sample, with the noise specifically added at the corresponding grid points:

[0031] (6)

[0032] (7)

[0033] in, This is the original sparse spectral intensity data. For the enhanced sparse spectral intensity data, With a mean of 0 and a standard deviation of Gaussian distribution, Set values ​​for users, This is speckle noise. To conform to a mean of 0 and a standard deviation of The random noise matrix with a Gaussian distribution.

[0034] Step 4 above describes the global normalization of the training set data, which is specifically as follows:

[0035] (8)

[0036] in, , For grid points before and after global normalization In frequency The sparse spectral intensity below; It is the global minimum value set by the user; It is the global maximum value obtained by traversing the sparse spectral data of the training set.

[0037] The loss function for combining the mask channel and the spectral signal strength channel in step 5 above is:

[0038] (10)

[0039] in, This represents the number of missing grid points. Grid points predicted by the residual autoencoder network In frequency The spectral signal strength value below, The spectral signal strength values ​​in the normalized spectral map; The masking channel is a mask matrix used to distinguish between grid points and missing grid points obtained from the normalized spectrum map; The square of the Frobenius norm; For the set of missing grid points;

[0040] The loss function for the building passageway is:

[0041] (11)

[0042] in This represents the number of grid points corresponding to the building boundary. The set of boundary points of the building. These are boundary values;

[0043] The loss function of the source channel is:

[0044] (12)

[0045] in This represents the number of grid points corresponding to the radiation source. Given the spectral signal strength of a known source, This is the set of grid points associated with the radiation source.

[0046] The residual autoencoder network constructed in step 6 above includes an encoder, a decoder, local skip connections, global skip connections, and a spectral-coupled attention module;

[0047] The encoder includes three stacked residual convolutional blocks, each containing three convolutional layers. The input of the first convolutional layer and the output of the third convolutional layer are added together through local skip connections to learn residual features. An average pooling layer is provided at the end of each residual convolutional block.

[0048] The decoder includes three stacked transposed residual convolutional blocks, each containing three transposed convolutional layers. The input of the first transposed convolutional layer and the output of the third transposed convolutional layer are added through a local skip connection. A bilinear interpolation upsampling layer is provided at the end of the transposed residual convolutional block.

[0049] The encoder and decoder contain three global skip connections that bypass the intermediate layer, connecting the corresponding residual convolutional block and the transposed residual convolutional block;

[0050] The spectrum-coupled attention module is built in the latent variable space of the encoder and decoder and is used to extract frequency features;

[0051] The operation of the spectrum-coupled attention module is as follows:

[0052] The features obtained from the encoder output are used as input features. Input features are transformed using Fast Fourier Transform. Transforming from the spatial domain to the frequency domain yields the frequency components in the frequency domain. ;

[0053] An attention-weighted mechanism is introduced, along with a learnable weighting matrix. Different attention weights are applied to each frequency component in the frequency domain to obtain the weighted frequency domain features. :

[0054] (16)

[0055] in For Hadama accumulation, It is a weighted matrix;

[0056] The weighted frequency domain features are obtained through inverse Fourier transform. Transform back to the spatial domain and output the reconstructed spatial domain features. ;

[0057] Using residual connections to integrate input features With reconstructed spatial domain features The features are added together to obtain the final output feature map. And input it into the decoder to reconstruct the spectrum map.

[0058] The forward propagation process of the residual autoencoder network described above is as follows:

[0059] (19)

[0060] in For the first Layer features, For convolutional layer or transposed convolutional layer weights, For bias, For activation function, The normalized sparse spectral intensity data, Input features to the input layer.

[0061] The present invention has the following beneficial effects:

[0062] This invention incorporates frequency components when modeling spectral signal strength and considers the impact of receiver height on the path loss model. When there are few sparse data samples, noise injection is used to increase the number of samples, and the model input is modified to include multi-channel data containing spectral signal strength channels, mask channels, building channels, and source channels, which increases the available features during model training and thus improves the model reconstruction accuracy.

[0063] This invention uses a residual autoencoder network model containing local and global skip connections to reconstruct sparse spectral maps, improving the model's feature transfer and extraction capabilities. It also constructs a spectral coupled attention module to force the model to extract frequency components that are helpful for the reconstruction task, and uses a weighted attention mechanism to dynamically adjust the importance of frequency components, helping the model to better recover map details. Attached Figure Description

[0064] Figure 1 The flowchart of the spectrum map reconstruction method based on residual autoencoder under sparse data conditions of the present invention is as follows;

[0065] Figure 2 This is a schematic diagram of the multi-channel input residual autoencoder used in this invention;

[0066] Figure 3 This is a complete real spectrum map used for comparison in this invention;

[0067] Figure 4 The monitoring sparse spectrum data used for reconstruction in this invention;

[0068] Figure 5This is a spectrum map reconstructed from the residual autoencoder model of the present invention. Detailed Implementation

[0069] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0070] This invention presents a spectral map reconstruction method based on a residual autoencoder under sparse data conditions. Specifically addressing the scenario of sparse electromagnetic spectrum intensity data, it proposes a multi-channel input residual autoencoder. This autoencoder integrates multi-channel features such as building information, radiation source locations, and path loss into its input. Furthermore, it deeply integrates a spectrum-coupled attention module into the network, enabling efficient spectral map reconstruction even with scarce data. Figure 1 As shown, the method includes the following steps:

[0071] Step 1: Obtain the size information, measurement node information, measurement frequency, and radiation source information of the monitoring area;

[0072] In the embodiment, the monitoring area is determined. Record its length and width Number of measurement nodes , frequency measurement Number of radiation sources The location, as well as the measurement location information and spectral intensity information of each node.

[0073] Step 2: Based on the size information and measurement node information of the monitoring area, the monitoring area is divided into grids of fixed size and the spectral intensity information of the measurement points is mapped to the grid points closest to them, thereby constructing a monitoring area matrix containing sparse spectral intensity information;

[0074] In the embodiment, the monitoring area The data is divided into a fixed-size grid, thus representing it as a matrix. The grid resolution is set to... Grid points The grid points are evenly distributed along the x and y axes. The number of grid points along the x-axis is... In the y-axis direction, the number of grid points is Grid points The coordinates are

[0075] (1)

[0076] in and ,express Number of grid cells.

[0077] The monitoring area has Measurement points ,correspond Individual spectral intensity information Calculate the measurement points With grid points Euclidean distance The nearest grid point is located and set as the new measurement point. Based on user-defined parameters, spectral intensity information is collected at the corresponding locations within the monitoring area. The monitoring area is in matrix form.

[0078] (2)

[0079] in This represents the set of grid points that map the measurement points, i.e., the set of sampled grid points (grid points assigned to the measurement point data). A subset of.

[0080] Step 3: Based on the monitoring area matrix and measurement frequency and radiation source information, model the spectral intensity at different grid points, perform frequency shifting under narrowband conditions, calculate the path loss from each grid point to the receiving antenna according to the improved near-range free space reference distance path loss model, and obtain a sparse spectrum map in planar form.

[0081] In the embodiment, the monitoring area is obtained. The sparse data within the data is processed, and the coordinates of all grid points in the sparse data, along with the spectral intensity information at those points, are obtained. The spectral intensity information is then modeled. The specific implementation steps are as follows:

[0082] Different grid points The spectral intensity at that point can be expressed as

[0083] (3)

[0084] in, For the first The emission intensity of each radiation source; For grid points The frequency response at that point, here we use (The square of the frequency response amplitude) represents the channel gain; For grid points Noise level.

[0085] The radiation source in this method is in a stationary state, therefore and It remains constant for each measurement. It is decomposed into path loss, shadowing fading, and multipath effects, but due to the consideration of narrowband scenarios, the frequency-selective fading caused by multipath effects is ignored. For frequency... Under normal circumstances, the center frequency is used as a reference, and the frequency is written as an offset according to equation (4).

[0086] (4)

[0087] in It is the center / carrier frequency. It is the signal bandwidth. However, in the case of narrowband, it can be approximated as... This is also known as the flat fading hypothesis.

[0088] For path loss and shadow fading, this method employs an improved close-in (CI) free-space reference range path loss model. Compared to the ordinary CI model, this method considers the receiver height. The impact on the path loss exponent is considered while maintaining the physical basis of the CI model. Specifically,

[0089] (5)

[0090] in and These are environment-related parameters, and they can vary greatly in different scenarios; The distance between the grid points and the receiving antenna is expressed in meters (m). It is the center frequency measured in gigahertz (GHz); For shadow fading that follows a zero-mean Gaussian distribution.

[0091] Through the second and third steps above, the sparse spectral intensity data is transformed into a planar sparse spectral map.

[0092] Step 4: Perform noise injection data augmentation on the sparse spectrum map, obtain a training set based on the augmented sparse spectrum intensity data, and perform global normalization on the training set data;

[0093] In this embodiment, data augmentation and preprocessing are performed on the sparse spectral map. The specific implementation steps are as follows:

[0094] First, a noise injection method is used to process the sparse spectral intensity data. Data augmentation was performed by randomly injecting Gaussian noise and speckle noise into each of the obtained missing spectral map samples. The noise was added at the corresponding grid points.

[0095] (6)

[0096] (7)

[0097] The Gaussian noise has zero mean and standard deviation. , The value is set by the user, but please note... Values ​​that are too large can damage the signal structure. Gaussian noise is used to simulate thermal noise and sensor noise in the environment; speckle noise is multiplicative noise, and its standard deviation ranges from [value missing]. It is used to simulate the errors caused by signal propagation and antenna jitter.

[0098] After obtaining the enhanced sparse samples, the user divides all sparse spectral map samples into training, validation, and test sets according to a set ratio. Then, the training set data is globally normalized according to equation (8).

[0099] (8)

[0100] in It is the global minimum value in sparse spectral data, which is set by the user; It is the global maximum value obtained by traversing the sparse spectral data. (This refers to the original monitoring data matrix.) For each grid point containing data, global normalization is performed and the value is replaced.

[0101] Step 5: Expand the normalized training data into multi-channel data including spectrum signal strength channel, mask channel, building channel and source channel, and construct the loss function combining the mask channel and spectrum signal strength channel, the loss function of the building channel and the loss function of the source channel, and then obtain the total loss function;

[0102] In this embodiment, the preprocessed sparse spectral data is expanded into multi-channel data, and the loss function is modified accordingly. The specific steps are as follows:

[0103] Modify the training set input to multi-channel data that includes spectrum signal strength channel, mask channel, building channel, and source channel.

[0104] The mask channel is used to distinguish between grid points and missing grid points obtained from the sparse spectrum map. A mask matrix is ​​set as shown in equation (9).

[0105] (9)

[0106] Among the grid points When the mask value is 1, it means that data has been detected at the grid point; when the mask value is 0, it means that the grid point is missing data.

[0107] The following loss function is defined by combining the mask channel with the spectral signal intensity channel.

[0108] (10)

[0109] in This represents the number of missing grid points. The signal strength value predicted by the residual autoencoder model used in this method is [value]. The normalized spectral signal intensity values ​​from the original map. For the entire monitoring area Subtract the set of sampling grid points That is, the set of missing grid points.

[0110] Building access identification uses building boundaries in a sparse spectral map, and the following loss function is defined based on the Dirichlet boundary conditions.

[0111] (11)

[0112] in This represents the number of grid points corresponding to the building boundary. The set of boundary points of the building. These are the defined boundary values.

[0113] The source channel forces the model output to match the source intensity at a known source location, and the loss function is defined as follows:

[0114] (12)

[0115] in This represents the number of grid points corresponding to the radiation source. Given the spectral signal strength of a known source, This is the set of grid points associated with the radiation source.

[0116] Finally, weight all losses are calculated.

[0117] (13)

[0118] in , , These are weighting parameters used to weigh the contribution of each loss.

[0119] Step 6: Construct a residual autoencoder network based on the spectrum-coupled attention module and train the network using the multi-channel data and the total loss function. Then, use the trained network to reconstruct the sparse spectrum map.

[0120] In this embodiment, a residual autoencoder network is constructed, a spectral coupling attention module is fused into the network, and the residual autoencoder network is trained. Then, a sparse spectral map is input into the network to complete the sparse spectral map reconstruction. The specific steps are as follows:

[0121] The residual autoencoder network constructed by this method consists of four parts: encoder, decoder, skip connections, and spectral-coupled attention module. The specific model is as follows: Figure 2 As shown.

[0122] The encoder consists of three stacked residual convolutional blocks, each containing three convolutional layers activated by the LeakyReLU activation function. Skip connections sum the input of the first convolutional layer to the output of the third convolutional layer to learn residual features. An average pooling layer is used at the end of the residual convolutional block to reduce the dimensionality of these features. The decoder structure is symmetrical to the encoder, but the convolutional layers are replaced with transposed convolutional layers, and the average pooling layers are replaced with bilinear interpolation upsampling layers. It also contains the same skip connections. Three global skip connections, bypassing intermediate layers, connect the encoder and decoder to the corresponding residual convolutional blocks.

[0123] Within the latent variable space of the encoder and decoder, this method constructs a spectral-coupled attention module that focuses on different frequency components in the frequency domain. Assume the features output from the encoder of the network are...

[0124] (14)

[0125] in For batch size, For the number of channels, and For the height and width of the space.

[0126] The input features are transformed from the spatial domain to the frequency domain using the Fast Fourier Transform.

[0127] (15)

[0128] in The Fourier transform yields the characteristics in the frequency domain.

[0129] Subsequently, an attention weighting mechanism is introduced, which includes a learnable weighting matrix. Different attention weights are applied to each frequency component in the frequency domain.

[0130] (16)

[0131] in Hadamard product, weighted matrix The importance of dynamically adjusting frequency components is emphasized in order to highlight frequency components that are helpful for model reconstruction tasks.

[0132] The weighted frequency domain features are then transformed back to the spatial domain using an inverse Fourier transform.

[0133] (17)

[0134] in The inverse Fourier transform outputs the reconstructed spatial domain features.

[0135] To preserve the original features and prevent information loss due to frequency domain filtering, residual connections are used to integrate the input features. Weighted output Add them together:

[0136] (18)

[0137] in The final output feature map is then input into the decoder.

[0138] The forward propagation process of the residual autoencoder network is shown in equation (19).

[0139] (19)

[0140] in For the first Layer features, For convolutional layer / transposed convolutional layer weights, For bias, This is the normalized sparse spectral intensity data.

[0141] The network then calculates the error based on the loss function constructed in step 5, and backpropagates it to each layer to update the network weights and biases for training. The sparse spectrum map is then input into the trained and converged network to predict the spectral intensity information of all grid points, completing the sparse spectrum map reconstruction.

[0142] This embodiment assumes that there are 4 radiation sources in the monitoring area, corresponding to the locations... Transmission frequency Transmission power The specific parameters are shown in Table 1.

[0143] Table 1 Radiation source configuration parameters

[0144]

[0145] Step 1: Set the monitoring area length and width , frequency measurement .

[0146] Step 2: Divide the monitoring area into A grid of size 5625 was used to monitor the area. Spectral intensity data was collected from the monitoring area at a sampling rate of 5%. The collected spectral data was recorded as follows: ,like Figure 4 As shown. The complete real-world spectrum map used for comparison is as follows. Figure 3 As shown.

[0147] Step 3: Calculate the received spectral intensity using formulas (3) to (5). The signal bandwidth is 5MHz, which meets the narrowband condition. Therefore, the frequency-selective fading caused by multipath effects can be ignored, while the flat fading assumption is also satisfied.

[0148] This embodiment sets the receiver height. Distance between grid points and receiving antenna This can be obtained from sparse data; this embodiment considers urban areas with plain terrain, and focuses on environmentally related parameters in the path loss index. and and the standard deviation in shadow fading In line-of-sight (LOS) propagation, set to In non-line-of-sight (NLOS) propagation, the three parameters are set as follows for reflection: In the case of diffraction ; Calculate the path loss from each grid point to the receiving antenna according to formula (5), which is related to the channel gain. Inversely proportional; then the received spectral intensity of each grid point is calculated according to formula (3). This transforms sparse spectral data into a grid-based sparse spectral map.

[0149] Step 4: Data augmentation by injecting noise into the sparse spectral data samples using equations (6) and (7). Assume that this implementation scheme pre-obtains 2500 sparse spectral map samples, and increases the number of sparse map samples to 5000 by randomly adding Gaussian noise and speckle noise. After obtaining the augmented samples, the user divides the data into training, validation, and test sets according to a ratio of 70%, 15%, and 15%, respectively.

[0150] The training set data is globally normalized according to equation (8), and the global maximum value is calculated by traversing through all sparse samples of the training set. Set the global minimum value to The spectral intensity value of the grid point where the building is located is also set to Therefore, after normalization, the grid points where the buildings are located... For grid points with missing data, their normalized values ​​remain the same. However, by using the mask matrix (9), the model is trained to focus on missing data grid points rather than the grid points where buildings are located.

[0151] After normalizing the training set, use its parameters. , The same normalization steps are performed on the validation set and the test set to avoid the risk of data leakage caused by global normalization.

[0152] Step 5: Modify the training data input to the model to multi-channel data including spectrum signal strength channel, mask channel, building channel and source channel, and set the corresponding loss functions for them using equations (9), (10), (11) and (12). Finally, weight all loss functions using equation (13).

[0153] Step 6: Build as follows Figure 2 The residual autoencoder network model shown inputs sparse spectral map samples into the model. Through the encoder and skip connection module, the high-dimensional map is compressed into low-dimensional features as shown in equation (14). Input low-dimensional features into the latent variable space. A spectrum-coupled attention module is constructed using equations (15), (16), (17), and (18) to build weighted features. Finally, the output with the same dimension as the input is obtained through upsampling and transposed convolution in the decoder. The entire process is propagated forward using equation (19), and the loss function (13) is minimized through backpropagation and gradient descent, thereby enabling the network to converge and improving the accuracy of the reconstructed spectrum map. The final reconstructed spectrum map is as follows: Figure 5 As shown.

[0154] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A spectral map reconstruction method based on residual autoencoders under sparse data conditions, characterized in that, include: Step 1: Obtain the size information, measurement node information, measurement frequency, and radiation source information of the monitoring area; Step 2: Based on the size information and measurement node information of the monitoring area, the monitoring area is divided into grids of fixed size and the spectral intensity information of the measurement points is mapped to the grid points closest to them, thereby constructing a monitoring area matrix containing sparse spectral intensity information; Step 3: Based on the monitoring area matrix and measurement frequency and radiation source information, model the spectral intensity at different grid points, perform frequency shifting under narrowband conditions, calculate the path loss from each grid point to the receiving antenna according to the improved near-range free space reference distance path loss model, and obtain a sparse spectrum map in planar form. Step 4: Perform noise injection data augmentation on the sparse spectrum map, obtain a training set based on the augmented sparse spectrum intensity data, and perform global normalization on the training set data; Step 5: Expand the normalized training data into multi-channel data including spectrum signal strength channel, mask channel, building channel and source channel, and construct the loss function combining the mask channel and spectrum signal strength channel, the loss function of the building channel and the loss function of the source channel, and then obtain the total loss function; Step 6: Construct a residual autoencoder network based on the spectrum-coupled attention module and train the network using the multi-channel data and the total loss function. Then, use the trained network to reconstruct the sparse spectrum map.

2. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, Step 2 specifically includes: Based on the size information of the monitoring area, the monitoring area is divided according to the set grid resolution. Divide the grid into a fixed-size grid and calculate the coordinates of each grid point. Then, the distance between each measurement point and each grid point is calculated; The spectral intensity information of each measurement point is mapped to the grid point closest to that measurement point to obtain the spectral intensity information of the corresponding grid point. This allows for the construction of a monitoring area matrix containing sparse spectral intensity information. （2）； in This represents the set of grid points that map the measurement points.

3. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, Step 3, which models the spectral intensity at different grid points, is as follows: （3）； in, For the first The emission intensity of each radiation source; For grid points At frequency The frequency response at that point, For grid points Noise at that location This represents the number of radiation sources.

4. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, The frequency offset mentioned in step 3 is: for the measured frequency Offset using the following formula: （4）； in It is the center frequency. It refers to the signal bandwidth.

5. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, The improved near-range free-space reference distance path loss model described in step 3 is as follows: （5）； in, and These are parameters related to the environment; This represents the distance between the grid points and the receiving antenna. The receiver height; It is the center frequency; For shadow fading that follows a zero-mean Gaussian distribution.

6. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, Step 4 involves data augmentation of the sparse spectral map, specifically as follows: Gaussian noise and speckle noise were randomly injected into each missing spectral map sample, with the noise specifically added at the corresponding grid points: （6）； （7）； in, This is the original sparse spectral intensity data. For the enhanced sparse spectral intensity data, With a mean of 0 and a standard deviation of Gaussian distribution, Set values ​​for users, This is speckle noise. To conform to a mean of 0 and a standard deviation of The random noise matrix with a Gaussian distribution.

7. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, Step 4 involves globally normalizing the training set data, as detailed below: （8）； in, , For grid points before and after global normalization In frequency The sparse spectral intensity below; It is the global minimum value set by the user; It is the global maximum value obtained by traversing the sparse spectral data of the training set.

8. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, The loss function for combining the mask channel and the spectral signal strength channel in step 5 is: (10); in, This represents the number of missing grid points. Grid points predicted by the residual autoencoder network In frequency The spectral signal strength value below, The spectral signal strength values ​​in the normalized spectral map; The masking channel is a mask matrix used to distinguish between grid points and missing grid points obtained from the normalized spectrum map; The square of the Frobenius norm; For the set of missing grid points; The loss function for the building passageway is: （11）； in This represents the number of grid points corresponding to the building boundary. The set of boundary points of the building. These are boundary values; The loss function of the source channel is: （12）； in This represents the number of grid points corresponding to the radiation source. Given the spectral signal strength of a known source, This is the set of grid points associated with the radiation source.

9. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, The residual autoencoder network constructed in step 6 includes an encoder, a decoder, local skip connections, global skip connections, and a spectral-coupled attention module; The encoder includes three stacked residual convolutional blocks, each containing three convolutional layers. The input of the first convolutional layer and the output of the third convolutional layer are added together through local skip connections to learn residual features. An average pooling layer is provided at the end of each residual convolutional block. The decoder includes three stacked transposed residual convolutional blocks, each containing three transposed convolutional layers. The input of the first transposed convolutional layer and the output of the third transposed convolutional layer are added through a local skip connection. A bilinear interpolation upsampling layer is provided at the end of the transposed residual convolutional block. The encoder and decoder contain three global skip connections that bypass the intermediate layer, connecting the corresponding residual convolutional block and the transposed residual convolutional block; The spectrum-coupled attention module is built in the latent variable space of the encoder and decoder and is used to extract frequency features; The operation of the spectrum-coupled attention module is as follows: The features obtained from the encoder output are used as input features. Input features are transformed using Fast Fourier Transform. Transforming from the spatial domain to the frequency domain yields the frequency components in the frequency domain. ; An attention-weighted mechanism is introduced, along with a learnable weighting matrix. Different attention weights are applied to each frequency component in the frequency domain to obtain the weighted frequency domain features. : （16）； in For Hadama accumulation, It is a weighted matrix; The weighted frequency domain features are obtained through inverse Fourier transform. Transform back to the spatial domain and output the reconstructed spatial domain features. ; Using residual connections to integrate input features With reconstructed spatial domain features The features are added together to obtain the final output feature map. And input it into the decoder to reconstruct the spectrum map.

10. The spectral map reconstruction method based on residual autoencoder under sparse data conditions according to claim 1, characterized in that, The forward propagation process of the residual autoencoder network is as follows: （19）； in For the first Layer features, For the weights of convolutional layers or transposed convolutional layers, For bias, For activation function, The normalized sparse spectral intensity data, Input features to the input layer.

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