Rydberg microwave sensor denoising method and system based on self-supervised learning

Abstract

The invention provides a Rydberg microwave sensor denoising method and system based on self-supervised learning. The method comprises the following steps: step 1, acquiring multiple groups of independent noisy measurement data of the same microwave signal through a Rydberg atom microwave sensing system; 2, preprocessing the multiple groups of independent noisy measurement data, and dividing to obtain a training set, a label set and a test set; step 3, constructing a deep learning model based on the Transform, and training the deep learning model based on the Transform to obtain an optimized de-noising model; and step 4, inputting a to-be-processed Rydberg microwave sensor noisy signal into the optimized de-noising model to obtain a de-noised clean signal. According to the method, the model can be trained only by using two groups of independent noise measurement data which are from the same signal source and have the same statistical distribution, the denoising effect of single measurement is realized, and both the denoising precision and the time resolution are considered.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and system for denoising Rydberg microwave sensors based on self-supervised learning. Background Technology

[0002] Rydberg atomic microwave sensors have significant application prospects in communications, radar, and precision measurement due to their ultra-high sensitivity, wide frequency response, and traceable SI calibration capabilities. However, when deployed in open environments, they are susceptible to non-stationary noise such as environmental electromagnetic interference, interatomic interaction noise, and thermal noise, leading to signal submersion and a severe decrease in signal-to-noise ratio.

[0003] Traditional denoising methods have significant limitations: while the multiple measurement averaging method can suppress random noise, it requires a large number of repeated measurements, sacrificing time resolution and making it unsuitable for dynamic time-varying signal scenarios; wavelet transform and Kalman filtering methods rely on noise stationarity or accurate state-space models, and their performance degrades significantly in the non-stationary noise environments actually encountered by Rydberg sensors.

[0004] In recent years, deep learning has emerged as an alternative for adaptive denoising. Models such as Recurrent Neural Networks (RNNs), Long Short-Term Memory Networks (LSTMs), and one-dimensional convolutional neural networks utilize time dependencies to separate signal from noise (e.g., in speech processing). Transformers, through their self-attention mechanism, strike a balance between noise suppression and signal detail preservation, achieving adaptive denoising by learning the features of both signal and noise. However, standard deep learning architectures (such as autoencoders) require paired noisy-clean signal datasets for supervised learning, while the clean signals from a single measurement of a Rydberg sensor are unavailable experimentally. Furthermore, the idealized clean data constructed in theory deviates from actual experimental conditions, easily leading to model overfitting.

[0005] Therefore, existing technologies lack a solution for efficient and high-fidelity noise reduction of single measurement signals from Rydberg sensors without relying on clean reference signals, which limits the application of such sensors in real-time and dynamic scenarios. Summary of the Invention

[0006] The purpose of this invention is to provide a self-supervised learning-based denoising method and system for Rydberg microwave sensors that can achieve high-fidelity denoising in a single measurement without the need for a clean reference signal, based on a self-supervised deep learning framework.

[0007] The objective of this invention can be achieved through the following technical measures: a Rydberg microwave sensor denoising method based on self-supervised learning, which includes:

[0008] Step 1: Acquire multiple sets of independent, noisy measurement data of the same microwave signal using the Rydberg atomic microwave sensing system;

[0009] Step 2: Preprocess multiple sets of independent noisy measurement data to obtain training set, label set and test set;

[0010] Step 3: Construct a Transformer-based deep learning model, train the Transformer-based deep learning model, and obtain the optimized denoising model.

[0011] Step 4: Input the noisy signal from the Rydberg microwave sensor to be processed into the optimized denoising model to obtain the denoised clean signal.

[0012] The objective of this invention can also be achieved through the following technical measures:

[0013] In step 1, the Rydberg atom microwave sensing system includes a cesium atom glass bulb, a probe light module, a coupling light module, an electrode module, a balanced detection module, an attenuation adjustment module, and a signal acquisition module. The probe light module generates a probe light, and the coupling light module generates a coupling light. The probe light and the coupling light work together to excite the cesium atoms in the cesium atom glass bulb to the Rydberg state. The electrode module applies the microwave signal to be measured and the local oscillator signal, generating an intermediate frequency (IF) signal through the atomic heterodyne effect. The IF signal includes a time-domain signal and a frequency-domain signal. The attenuation adjustment module applies different intensities of attenuation to the generated IF signal to simulate various noise scenarios and acquire noisy measurement data with different noise intensities. The balanced detection module performs balance detection on the probe light, and the signal acquisition module simultaneously acquires the time-domain signal and the frequency-domain signal to obtain multiple sets of independent noisy measurement data containing both time-domain and frequency-domain signals.

[0014] In step 2, the preprocessing of multiple sets of independent noisy measurement data includes standardization, and the standardization formula is:

[0015] Where x is the original noisy data, μ is the data mean, σ is the data standard deviation, and x′ is the standardized data.

[0016] In step 2, a first set of noisy data is selected from the preprocessed multiple sets of independent noisy measurement data as the training input, i.e., the training set, and a second set of noisy data is selected as the training label, i.e., the label set. The signal components in the first set of noisy data and the second set of noisy data are the same or highly correlated, and the noise components are independently and identically distributed. The test set is noisy measurement data independent of the training data.

[0017] In step 3, the Transformer-based deep learning model is constructed. The training set is used as input and the label set is used as the supervision target for training. The model parameters are optimized by minimizing the loss function until the training converges, and the optimized denoising model is obtained.

[0018] In step 3, the structure of the Transformer-based deep learning model includes: an input layer, a fully connected projection layer, a sinusoidal coding layer, a stacked encoder block, and an output layer; the stacked encoder block includes a multi-head self-attention mechanism, a feedforward neural network with GELU activation function, residual connections, and a dropout layer.

[0019] In step 3, the Transformer-based deep learning model uses the mean squared error function to minimize the loss function during model training. Training continues until it is verified that the loss no longer decreases significantly for 10 consecutive epochs, thus obtaining the optimal model parameters θ. * .

[0020] In step 3, the optimizer for the Transformer-based deep learning model is the Adam optimizer, with a first-order momentum decay coefficient β1 = 0.9, a second-order momentum decay coefficient β2 = 0.999, and a stability parameter ε = 10. -7 The learning rate is 1.0 × 10⁻⁶. -5 .

[0021] The method further includes, after step 4, performing a performance evaluation, comparing the obtained denoised clean signal with the average result of a large number of measurement data under the same signal conditions, and using the mean square error as a quantitative evaluation index.

[0022] The objective of this invention can also be achieved through the following technical measures: a Rydberg microwave sensor denoising system based on self-supervised learning, comprising:

[0023] The data acquisition module acquires multiple sets of independent, noisy measurement data of the same microwave signal through the Rydberg atomic microwave sensing system;

[0024] The preprocessing module preprocesses multiple sets of independent noisy measurement data;

[0025] The data preparation module divides the preprocessed multiple sets of independent noisy measurement data into training set, label set and test set;

[0026] The model training module constructs a Transformer-based deep learning model, trains the Transformer-based deep learning model, and obtains an optimized denoising model.

[0027] The denoising module inputs the noisy signal from the Rydberg microwave sensor to be processed into the optimized denoising model to obtain a clean signal after denoising.

[0028] The self-supervised learning-based Rydberg microwave sensor denoising method and system of this invention does not require a clean reference signal. It trains the model using only two sets of independent noise measurement data from the same signal source with the same statistical distribution, achieving denoising performance in a single measurement while balancing denoising accuracy and temporal resolution. Compared with existing technologies, this invention has the following technical advantages:

[0029] No clean reference signal required: It innovatively adopts a self-supervised learning paradigm and uses two sets of independent noisy measurement data for training, which completely solves the bottleneck problem of obtaining a clean reference signal for a single measurement in fields such as Rydberg quantum sensing.

[0030] High precision and high efficiency: The denoising accuracy of the trained model for a single measurement signal can reach the level of the average of tens of thousands of measurements, while reducing the signal processing time by more than three orders of magnitude, achieving a balance between high precision and high temporal resolution.

[0031] Strong generalization and adaptability: The model learns the statistical characteristics of signals and noise autonomously from the data, without relying on a pre-set noise model, and has stronger adaptability and robustness to non-stationary noise in open environments.

[0032] Flexible and Optimizable Architecture: By comparing models of different complexities such as Transformer and U-Net, the trade-off between model performance and complexity is clarified, providing clear guidance for selecting or optimizing model architectures for different application scenarios (such as embedded devices).

[0033] Promoting practical application: This invention directly addresses the core noise problem in the practical application of Rydberg sensors, providing a practical solution that significantly improves the feasibility of such sensors in applications such as real-time, dynamic microwave electric field detection and communication. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the self-supervised denoising framework and the experimental system principle diagram provided in the embodiments of the present invention;

[0035] Figure 2 This is a comparison chart of the denoising effect of the frequency domain signal under different signal attenuation indices and the average result of 10,000 tests in an embodiment of the present invention.

[0036] Figure 3 This is a graph showing the variation of the model's denoising performance (measured by MSE) with the size of the training dataset in this embodiment of the invention.

[0037] Figure 4This is a comparison chart of the denoising effects of the embodiments of the present invention and traditional methods (wavelet transform, Kalman filtering) on ​​time-domain signals;

[0038] Figure 5 This is a comparison chart of the denoising performance of different deep learning architectures (Transformer and U-Net) under the same self-supervised framework in the embodiments of the present invention;

[0039] Figure 6 This is a schematic diagram of the Transformer model structure used in an embodiment of the present invention;

[0040] Figure 7 This is a schematic diagram of the U-Net model structure used in the comparative embodiments of the present invention;

[0041] Figure 8 This is a flowchart of a specific embodiment of the self-supervised learning-based Rydberg microwave sensor noise reduction method of the present invention;

[0042] Figure 9 This is a structural diagram of a specific embodiment of a Rydberg microwave sensor denoising device based on self-supervised learning, according to a specific embodiment of the present invention. Detailed Implementation

[0043] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0044] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, and / or combinations thereof.

[0045] like Figure 8 As shown, Figure 8 This is a flowchart of the self-supervised learning-based Rydberg microwave sensor denoising method of the present invention. It includes the following steps:

[0046] Step 101: Data Acquisition and Preprocessing. Using the Rydberg atomic microwave sensing system, under the same experimental conditions, multiple sets of independent measurement data of the target microwave signal are acquired. Each set of data contains a time-domain or frequency-domain sequence consisting of the signal and additive noise. The acquired data undergoes standardized preprocessing. The Rydberg atomic microwave sensing system, based on the principles of electromagnetic induction transparency and atomic heterodyne detection, converts the microwave electric field to be measured into an intermediate-frequency electrical signal for acquisition.

[0047] Step 102: Construct the training dataset. Select a first set of noisy data as the training input and a second set of noisy data as the training label from the multiple sets of data. The signal components in the first set of data and the second set of data are the same or highly correlated, and the noise components are independent and identically distributed. The test set is noisy measurement data independent of the training data.

[0048] Specifically, two sets of data are selected from the multiple sets of measurement data as training inputs. and training labels ,in and This represents the ideal clean signal components. and The noise components are independently sampled from the same statistical distribution; the clean signal components corresponding to the training input and training labels are... and Physically identical or highly correlated, their differences stem solely from noise from independently sampled samples.

[0049] Step 103: Build and train a self-supervised deep learning model. Construct a deep learning model based on the Transformer architecture. With the training input As input to the model, the training labels As a supervision objective, this is achieved by minimizing the loss function between the predicted output and the training labels. To optimize model parameters The model learns the mapping relationship of recovering signal components from noisy input, wherein the loss function is preferably mean squared error loss; the deep learning model is a Transformer encoder structure based on multi-head self-attention mechanism, including an input projection layer, a sinusoidal position encoding layer, at least one encoder block and an output projection layer, wherein the encoder block includes a multi-head self-attention sub-layer, a feedforward neural network sub-layer and residual connections and normalization operations.

[0050] Step 104: Signal Denoising. The noisy signal from a single measurement to be denoised... Input the trained model The denoised signal output is obtained. .

[0051] Step 105: Performance evaluation. The denoised output signal is compared with the average result of a large number of measurement data under the same signal conditions, and the mean square error is used as the quantitative evaluation index.

[0052] like Figure 9 The diagram shown is a structural diagram of the Rydberg microwave sensor denoising system based on self-supervised learning according to the present invention. The system includes:

[0053] Data acquisition module 901: Configured for acquiring multiple sets of independent noisy measurement data of the target microwave signal using the Rydberg atomic microwave sensing system;

[0054] Preprocessing module 902: Configured for standardizing the acquired measurement data;

[0055] Data preparation module 903: Configured to construct a self-supervised training dataset from preprocessed data, including training input data and corresponding training label data, which are measurement pairs with the same signal components and independent and identically distributed noise;

[0056] Model training module 904: Configured to build a Transformer-based self-supervised deep learning model and train the model using the training dataset to optimize model parameters;

[0057] Denoising module 905: Configured to input the signal to be denoised from a single measurement into the trained model and output the denoised signal.

[0058] Output module 906: Configured for outputting or storing the denoised signal.

[0059] In a specific embodiment 1 of the present invention, a complete method for denoising Rydberg microwave sensor signals based on self-supervised deep learning is provided, combined with... Figure 1 The system shown is in operation.

[0060] Step 1: Experimental data collection.

[0061] A Rydberg atom microwave detection system was constructed, comprising a cesium atom glass bulb, a probe light module, a coupling light module, an electrode module, a balanced detection module, an attenuation adjustment module, and a signal acquisition module. The probe light module generates 852 nm probe light, and the coupling light module generates 510 nm coupling light. The probe light and coupling light work together to excite cesium atoms to the Rydberg state. The electrode module applies the measured microwave signal and a local oscillator signal, generating an intermediate frequency (IF) signal through the atomic heterodyne effect. The IF signal is obtained by the Rydberg microwave sensor through the atomic heterodyne effect. The time-domain signal and the frequency-domain signal are two different representations of this IF signal. The time-domain signal is the amplitude variation curve of the IF signal over time, and the frequency-domain signal is the frequency distribution characteristic of the IF signal; they can be converted to each other through Fourier transform. The attenuation adjustment module applies different intensities of attenuation to the generated IF signal, simulating various noise scenarios and acquiring noisy measurement data with different noise intensities. The balance detection module performs balance detection on the probe light, and the signal acquisition module simultaneously acquires time-domain and frequency-domain signals to obtain multiple sets of independent noisy measurement data in both time and frequency domains.

[0062] Specifically, a cesium atom vapor chamber is used, and an electromagnetically induced transparent (EIT) structure is constructed using an 852 nm probe light and a 510 nm coupling light. An arbitrary waveform generator generates the microwave signal to be measured (SUT, 63 MHz) and a local oscillator signal (LO, 63.05 MHz), which are applied to the EIT structure through parallel plate electrodes. The AC Stark shift of the atomic energy levels is detected by the change in the transmittance of the probe light and converted into a 50 kHz intermediate frequency (IF) electrical signal. The atomic system, i.e., cesium atoms, is confined in a room-temperature glass bulb. The 852 nm probe light excites the cesium atoms from the ground state (6S¹ / ²) to an intermediate state (6P³ / ²), and then the 510 nm coupling light further excites the atoms to the Rydberg state (60S¹ / ²); at this point, the atoms are in a high-energy state sensitive to the microwave electric field. The probe light is split into two beams: one beam serves as a reference beam outside the glass bulb, while the other beam, along with the coupling beam, propagates in the opposite direction inside the bulb, forming an electromagnetically induced transparent (EIT) structure. In this structure, the coupling beam modulates the atomic transmittance and absorptivity of the probe light. The microwave signal applied by the electrodes, along with the local oscillator signal, acts on the Rydberg-state atoms, causing a shift in their energy levels. This energy level shift alters the atomic transmittance of the probe light, producing the electromagnetically induced transparent (EIT) effect, where changes in the microwave signal are converted into changes in the intensity of the probe light.

[0063] The intermediate frequency (IF) electrical signal is received by a balanced photodetector and simultaneously recorded by an oscilloscope (time domain) and a spectrum analyzer (frequency domain). In a shielded anechoic chamber, different scenarios in which the signal is gradually submerged by noise are simulated by varying the amplitude of the SUT signal applied to the electrodes (e.g., attenuating from 200 mV to 3 mV). For each scenario, 10,000 sets of independent and identically distributed noisy measurement data are collected.

[0064] Step 2: Dataset construction and preprocessing.

[0065] The 10,000 collected data sets were randomly divided into a training set (4,000 sets), a label set (4,000 sets), and a test set (2,000 sets). For training, a set of measurement data was randomly selected from the training set as input x. train Another set of measurement data is randomly selected from the label set as label y. train These two sets of data correspond to the same physical signal source and contain only independently sampled noise. Each data sequence is standardized as follows: x′=(x-μ) / σ, where x is the original noisy data, μ is the data mean, σ is the data standard deviation, and x′ is the standardized data.

[0066] Step 3: Training the self-supervised deep learning model.

[0067] 31. Transformer model training:

[0068] Build as Figure 6 The Transformer model shown. The model includes, in sequence:

[0069] Fully connected layer: projects the input one-dimensional sequence onto a 64-dimensional feature space.

[0070] Sine positional coding layer: Generates a unique coding vector for each position in the sequence to inject sequence information.

[0071] Three stacked encoder blocks: each block contains an 8-head multi-head self-attention sublayer, a 128-dimensional feedforward neural network (GELU activation function), and each sublayer is followed by a normalization layer and a residual connection. The dropout rate is set to 0.1 to prevent overfitting.

[0072] Output fully connected layer: Maps the 64-dimensional features back to one dimension to obtain the denoised sequence.

[0073] Using the Adam optimizer (β1=0.9, β2=0.999, ε=10) -7 Training was conducted with a learning rate set to 1.0 × 10⁻⁶. -5 The loss function uses mean squared error (MSE):

[0074] Where N is the number of data points, y i For noise reduction output, This is the average reference value (as the true value) for the corresponding 10,000 measurements.

[0075] Training continues until the loss no longer decreases significantly after 10 consecutive epochs, at which point the optimal model parameters θ are obtained. * .

[0076] The deep learning model in the model training unit has a parameter size of 4.50×10⁵. The training time for each epoch is 2000 s, and the model inference time is in the millisecond range.

[0077] 32. U-net model training

[0078] To explore the impact of model complexity on performance and to provide a more lightweight alternative, this embodiment simultaneously builds and trains models such as... Figure 7 The U-Net model is shown below. Its specific structure is as follows:

[0079] Encoder (Downsampling Path): First Convolutional Block: Contains a one-dimensional convolutional layer with 24 kernels, followed by a LeakyReLU activation function. Then, a max-pooling layer (pooling size 2) is applied to halve the sequence length. Second Convolutional Block: Another one-dimensional convolutional layer is applied to the pooled features to extract higher-level features.

[0080] Decoder (upsampling path) and skip connections: The sequence length is recovered using a one-dimensional upsampling layer (scale factor of 2). Through skip connections, the upsampled features are concatenated with the high-resolution features output from the corresponding intermediate layer of the encoder to form feature fusion, thus preserving low-level detail information.

[0081] Final output layer: After feature concatenation, the data is fused and output through a final one-dimensional convolutional layer. This layer uses 48 convolutional kernels of size 3, followed by the LeakyReLU activation function.

[0082] The total number of parameters in the U-Net model is approximately 1.59 × 10⁻⁶. 4 Significantly fewer than the Transformer model (4.50 × 10⁻⁶). 5 On the same hardware and dataset, its training time per epoch is only about 10 seconds (compared to about 2000 seconds for Transformer), demonstrating extremely high training efficiency. This model could be considered a potential candidate for deployment in computationally limited embedded systems.

[0083] Step 4: Signal denoising and performance evaluation.

[0084] The noisy signal from a single measurement in the test set x test Input the trained model f θ* To obtain the denoised output To evaluate performance, The mean square error (MSE) is calculated by comparing it with the average of 10,000 measurements of the corresponding signal (as an approximate "ground truth"). Simultaneously, it is compared with the denoising results obtained using parameter-optimized wavelet transform and Kalman filtering methods.

[0085] In a specific embodiment of the application of the present invention, such as Figure 2 As shown, under different attenuation levels, the denoising results of the method of the present invention (blue curve) can effectively recover the 50 kHz intermediate frequency signal and its sideband and other characteristic components that were submerged by noise. The effect is highly consistent with the 10,000-times average (green curve) and is significantly better than a single measurement (gray curve).

[0086] like Figure 3 As shown, with the increase of training data, the denoised MSE decreases rapidly and tends to stabilize, indicating that the data utilization efficiency of this method is high.

[0087] like Figure 4 As shown in Table 1, in the task of time-domain signal denoising, the MSE of the method of this invention (blue curve) is two orders of magnitude lower than that of the traditional wavelet transform and Kalman filtering methods, and is closer to the average result (black dashed line), and the processing speed is extremely fast.

[0088] Table 1. Mean square error of time-domain data for different denoising methods at Vpp=200 mV and 100 mV.

[0089] like Figure 5 As shown, under the same self-supervised framework, the more complex Transformer model (blue curve) preserves weak signal features better than the U-Net model (orange curve), proving that performance can be further improved by increasing model complexity.

[0090] In a specific embodiment 2 of the present invention, a noise reduction system for implementing the above method is provided. This system can be integrated into a Rydberg sensor device or used as a standalone post-processing unit. The system includes:

[0091] Data acquisition interface: Connects to devices such as oscilloscopes and spectrum analyzers to receive raw noisy signal data in real time or offline.

[0092] Preprocessing unit: Performs necessary preprocessing operations such as format conversion and standardization on the input signal.

[0093] Model storage and loading unit: Stores pre-trained self-supervised deep learning models.

[0094] Model inference unit: Loads the model, performs forward propagation on the input single measurement signal, and outputs a denoised signal.

[0095] Control and output unit: coordinates the system process and outputs the denoised signal to the display, storage device or subsequent analysis module.

[0096] The system can be deployed on general-purpose computers, embedded GPU platforms, or dedicated AI chips.

[0097] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0098] Except for the technical features described in the specification, all other technologies are known to those skilled in the art.

Claims

1. A denoising method for Rydberg microwave sensors based on self-supervised learning, characterized in that, The self-supervised learning-based Rydberg microwave sensor denoising method includes: Step 1: Acquire multiple sets of independent, noisy measurement data of the same microwave signal using the Rydberg atomic microwave sensing system; Step 2: Preprocess multiple sets of independent noisy measurement data to obtain training set, label set and test set; Step 3: Construct a Transformer-based deep learning model, train the Transformer-based deep learning model, and obtain the optimized denoising model. Step 4: Input the noisy signal from the Rydberg microwave sensor to be processed into the optimized denoising model to obtain the denoised clean signal.

2. The Rydberg microwave sensor denoising method based on self-supervised learning according to claim 1, characterized in that, In step 1, the Rydberg atom microwave sensing system includes a cesium atom glass bulb, a probe light module, a coupling light module, an electrode module, a balanced detection module, an attenuation adjustment module, and a signal acquisition module. The probe light module generates a probe light, and the coupling light module generates a coupling light. The probe light and the coupling light work together to excite the cesium atoms in the cesium atom glass bulb to the Rydberg state. The electrode module applies the microwave signal to be measured and the local oscillator signal, generating an intermediate frequency (IF) signal through the atomic heterodyne effect. The IF signal includes a time-domain signal and a frequency-domain signal. The attenuation adjustment module applies different intensities of attenuation to the generated IF signal to simulate various noise scenarios and acquire noisy measurement data with different noise intensities. The balanced detection module performs balance detection on the probe light, and the signal acquisition module simultaneously acquires the time-domain signal and the frequency-domain signal to obtain multiple sets of independent noisy measurement data containing both time-domain and frequency-domain signals.

3. The Rydberg microwave sensor denoising method based on self-supervised learning according to claim 1, characterized in that, In step 2, the preprocessing of multiple sets of independent noisy measurement data includes standardization, and the standardization formula is: Where x is the original noisy data, μ is the data mean, σ is the data standard deviation, and x′ is the standardized data.

4. The Rydberg microwave sensor denoising method based on self-supervised learning according to claim 1, characterized in that, In step 2, a first set of noisy data is selected from the preprocessed multiple sets of independent noisy measurement data as the training input, i.e., the training set, and a second set of noisy data is selected as the training label, i.e., the label set. The signal components in the first set of noisy data and the second set of noisy data are the same or highly correlated, and the noise components are independently and identically distributed. The test set is noisy measurement data independent of the training data.

5. The Rydberg microwave sensor denoising method based on self-supervised learning according to claim 1, characterized in that, In step 3, the Transformer-based deep learning model is constructed. The training set is used as input and the label set is used as the supervision target for training. The model parameters are optimized by minimizing the loss function until the training converges, and the optimized denoising model is obtained.

6. The Rydberg microwave sensor denoising method based on self-supervised learning according to claim 5, characterized in that, In step 3, the structure of the Transformer-based deep learning model includes: an input layer, a fully connected projection layer, a sinusoidal coding layer, a stacked encoder block, and an output layer; the stacked encoder block includes a multi-head self-attention mechanism, a feedforward neural network with GELU activation function, residual connections, and a dropout layer.

7. The Rydberg microwave sensor denoising method based on self-supervised learning according to claim 6, characterized in that, In step 3, during model training, the Transformer-based deep learning model uses the mean squared error function as the loss function. Training continues until it is verified that the loss no longer decreases significantly for 10 consecutive epochs, thus obtaining the optimal model parameters θ. * .

8. The Rydberg microwave sensor denoising method based on self-supervised learning according to claim 7, characterized in that, In step 3, the optimizer for the Transformer-based deep learning model is the Adam optimizer, with a first-order momentum decay coefficient β1 = 0.9, a second-order momentum decay coefficient β2 = 0.999, and a stability parameter ε = 10. -7 The learning rate is 1.0 × 10⁻⁶. -5 .

9. The Rydberg microwave sensor denoising method based on self-supervised learning according to claim 1, characterized in that, The method further includes, after step 4, performing a performance evaluation, comparing the obtained denoised clean signal with the average result of a large number of measurement data under the same signal conditions, and using the mean square error as a quantitative evaluation index.

10. A Rydberg microwave sensor denoising system based on self-supervised learning, characterized in that, This self-supervised learning-based Rydberg microwave sensor denoising system includes: The data acquisition module acquires multiple sets of independent, noisy measurement data of the same microwave signal through the Rydberg atomic microwave sensing system; The preprocessing module preprocesses multiple sets of independent noisy measurement data; The data preparation module divides the preprocessed multiple sets of independent noisy measurement data into training set, label set and test set; The model training module constructs a Transformer-based deep learning model, trains the Transformer-based deep learning model, and obtains an optimized denoising model. The denoising module inputs the noisy signal from the Rydberg microwave sensor to be processed into the optimized denoising model to obtain a clean signal after denoising.

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