Laser Doppler signal non-sparse compressed sensing method and system

Abstract

The invention provides a laser Doppler signal non-sparse compressed sensing method and system, and belongs to the technical field of compressed sensing, and the method comprises the steps: constructing a Bernoulli sensing matrix, and carrying out the data compression of a laser Doppler signal, and obtaining a first compressed signal; inputting the first compressed signal into a multi-resolution feature fused signal reconstruction teacher model to obtain a first reconstruction signal; the signal reconstruction teacher model extracts a local time sequence mode of a signal through a time domain convolution feature extraction mechanism, and learns time-frequency features in combination with a frequency domain attention guidance mechanism; and constructing a lightweight signal reconstruction student model based on the output of the signal reconstruction teacher model, and inputting the first compressed signal into the signal reconstruction student model to obtain a final reconstruction signal. According to the method, the technical problems of high signal sparsity requirement, poor reconstruction real-time performance and large deep learning model parameter quantity of the traditional compressed sensing technology are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of compressed sensing, and in particular relates to a laser Doppler signal non-sparse compressed sensing method and system. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] With the rapid development of industrial intelligence and precision measurement, laser Doppler vibrometer technology plays a key role in mechanical vibration monitoring, structural health diagnosis, aerospace testing and other fields.

[0004] However, the high sampling rate (kHz level) of traditional laser vibrometer systems leads to massive data storage and transmission pressure. For example, a single-channel 40kHz sampling for one hour can generate 2.3GB of data, which seriously restricts the application of long-term monitoring at multiple measurement points. Although compressed sensing (CS) theory can reduce the sampling rate, traditional CS methods rely on signal sparsity, and laser vibrometer signals exhibit non-sparse characteristics due to factors such as multimodal coupling, environmental noise, and nonlinear vibration, resulting in insufficient reconstruction accuracy. In addition, although the CS method based on deep learning improves the reconstruction performance, the model parameters are huge and difficult to deploy on resource-constrained terminal devices. In summary, existing technologies mostly focus on single data compression or model compression, lack collaborative optimization solutions, and traditional evaluation indicators are difficult to comprehensively measure the quality of signal reconstruction. Summary of the Invention

[0005] In order to overcome the shortcomings of the above-mentioned existing technologies, the present invention proposes a non-sparse compressed sensing method and system for laser Doppler signals, and designs an ultra-lightweight, non-sparse-dependent compressed sensing method that takes into account high compression ratio, low computational complexity and high reconstruction accuracy. It is of great significance to improve the real-time performance of laser Doppler vibrometer systems, reduce storage costs, and promote the intelligent upgrading of domestic instruments and equipment. It solves the technical difficulties of traditional compressed sensing technology in terms of high signal sparsity requirements, poor reconstruction real-time performance, and large number of deep learning model parameters.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0007] In a first aspect, a non-sparse compressed sensing method for laser Doppler signals is disclosed, comprising:

[0008] Collecting laser Doppler signals;

[0009] Constructing a Bernoulli sensing matrix to perform data compression on the laser Doppler signal to obtain a first compressed signal;

[0010] The first compressed signal is input into a signal reconstruction teacher model with multi-resolution feature fusion to obtain a first reconstructed signal; the signal reconstruction teacher model extracts the local temporal pattern of the signal through a time domain convolution feature extraction mechanism, and learns the time-frequency features in combination with a frequency domain attention guidance mechanism;

[0011] Building a lightweight signal reconstruction student model based on the output of the signal reconstruction teacher model, and inputting the first compressed signal into the signal reconstruction student model to obtain a final reconstructed signal;

[0012] A distillation loss function is constructed according to the first reconstructed signal and the second reconstructed signal, a fusion loss function is constructed based on the distillation loss function, and the teacher model knowledge is distilled and transferred to the student model based on the fusion loss function.

[0013] In a second aspect, a laser Doppler signal non-sparse compressed sensing system is disclosed, comprising:

[0014] A signal acquisition module is configured to: acquire laser Doppler signals;

[0015] A signal compression module is configured to: construct a Bernoulli sensing matrix to perform data compression on the laser Doppler signal to obtain a first compressed signal;

[0016] A first reconstruction module is configured to: input the first compressed signal into a signal reconstruction teacher model with multi-resolution feature fusion to obtain a first reconstructed signal; the signal reconstruction teacher model extracts the local temporal pattern of the signal through a time domain convolution feature extraction mechanism, and learns the time-frequency features in combination with a frequency domain attention guidance mechanism;

[0017] a second reconstruction module, configured to: construct a lightweight signal reconstruction student model based on the output of the signal reconstruction teacher model, and input the first compressed signal into the signal reconstruction student model to obtain a final reconstructed signal;

[0018] A distillation loss function is constructed according to the first reconstructed signal and the second reconstructed signal, a fusion loss function is constructed based on the distillation loss function, and the teacher model knowledge is distilled and transferred to the student model based on the fusion loss function.

[0019] In a third aspect, an electronic device is disclosed, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps of the above-mentioned laser Doppler signal non-sparse compressed sensing method are completed.

[0020] In a fourth aspect, a computer-readable storage medium is disclosed for storing computer instructions. When the computer instructions are executed by a processor, the steps of the above-mentioned laser Doppler signal non-sparse compressed sensing method are completed.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] The present invention proposes a teacher model of multi-resolution feature fusion, which expands the signal to a high-dimensional feature space through an input projection module, uses a time-frequency fusion encoder to simultaneously extract local details and global patterns of the signal, and maps the features back to the target signal space through an output processing module. It effectively overcomes the dependence of traditional compressed sensing on signal sparsity, and achieves high-fidelity reconstruction of compressed signals through joint optimization of a dual-domain loss function. It can directly process complex characteristics such as multimodal coupling and noise interference in laser Doppler vibrometer signals, significantly improving the reconstruction accuracy under high compression ratios.

[0023] The present invention adopts knowledge distillation technology to transfer the knowledge of a complex teacher model to a student model containing only three fully connected layers. While maintaining high accuracy, it achieves 96.32% compression of model parameters and reduces the model size to 0.08MB, making it suitable for deployment on resource-constrained embedded devices.

[0024] Compared with traditional compressed sensing algorithms, the signal reconstruction time of this invention is only 0.01-0.44 seconds at a compression ratio of 10% to 90%, which meets the needs of industrial real-time monitoring and greatly improves data processing efficiency.

[0025] This paper innovatively proposes the NSEP evaluation metric, combining absolute error and dynamic characteristics to assess reconstruction quality, enabling a more accurate assessment of reconstruction performance. Even with a data compression ratio of 10% and a model compression ratio of 96.32%, the NSEP remains below 8%, outperforming existing lightweight networks and suitable for high-fidelity reconstruction of vibration signals of varying frequencies.

[0026] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0028] Figure 1 This is an overall framework diagram of the non-sparse compressed sensing method for laser Doppler signals described in Example 1 of the present invention.

[0029] Figure 2 Schematic diagram of the compressed sensing process described in Example 1 of the present invention.

[0030] Figure 3 This is a schematic diagram of the teacher model structure described in Example 1 of the present invention.

[0031] Figure 4 This is a schematic diagram of the student model structure described in Example 1 of the present invention.

[0032] Figure 5 Schematic diagram of the laser vibration measurement experimental platform described in Example 1 of the present invention.

[0033] Figure 6 This is a visualization of the comparative experimental results of the compressed sensing method described in Example 1 of the present invention with MobileNetV1, ShuffleNetV2 and SqueezeNet.

[0034] Figure 7 This is a visualization of the fitting results of the compressed sensing method described in Example 1 of the present invention.

[0035] Figure 8 The figure shows the comparison experimental results between the compressed sensing method described in the first embodiment of the present invention and OMP, Mco and SP. DETAILED DESCRIPTION

[0036] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0037] It should be noted that the terms used herein are for describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present invention.

[0038] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0039] Example 1

[0040] In one or more embodiments, a non-sparse compressed sensing method for laser Doppler signals is disclosed, such as Figure 1 As shown, the following steps are included:

[0041] Step S1, collecting laser Doppler signals;

[0042] Laser Doppler velocimetry (LDV) was used to collect laser Doppler vibrometer signals.

[0043] Step S2: constructing a Bernoulli sensing matrix to perform data compression on the laser Doppler signal to obtain a first compressed signal;

[0044] The process of compressed sensing, such as Figure 2As shown in FIG, compressed sensing (CS) is a technology that utilizes the sparsity or compressibility of signals to efficiently acquire and reconstruct signals with a number of samples far less than that required by the Nyquist sampling theorem.

[0045] Step S2-1: Perform sliding window sampling on the four groups of long sequence laser Doppler signal data respectively, with the sampling window size set to 2048, and discard the data that is less than a complete window at the end.

[0046] Step S2-2, construct the corresponding Bernoulli perception matrix Φ (dimension is M×N, where N=2048, M=round(N×CR)) with compression ratios of 10%, 30%, 50%, 70% and 90%, and the matrix elements are randomly generated by ±1. For each data segment x (length is N) after sliding window sampling, the compressed observation vector y (length is M) is obtained by matrix multiplication y=Φx, that is, the first compressed signal, thereby achieving data compression, and an adjustable data compression ratio of 10% to 90% can be achieved.

[0047] Step S3: inputting the first compressed signal into the signal reconstruction teacher model with multi-resolution feature fusion to obtain a first reconstructed signal; the signal reconstruction teacher model extracts the local temporal pattern of the signal through the time domain convolution feature extraction mechanism, and learns the time-frequency features in combination with the frequency domain attention guidance mechanism;

[0048] like Figure 3 As shown in the figure, the signal reconstruction teacher model of multi-resolution feature fusion has an overall structure of a composite mapping process, including an unsqueeze layer, an input projection module, a time-frequency fusion encoder, an output convolution module, and a linear transformation layer. The original input of the teacher model is the compressed laser Doppler vibrometer signal. The corresponding reconstructed output is The entire model can be viewed as a mapping from the input signal to the reconstructed signal:

[0049]

[0050] in, It is a compound operator, which means taking the output of one function as the input of another function to obtain a new function; in is an input projection module, which is used to expand the original input into a high-dimensional channel space; δ is a time-frequency fusion encoder, which contains multiple serially connected HybridBlocks; P out is the output convolution module, which is used to generate a one-dimensional reconstruction sequence; L is a linear transformation layer, which is used to adjust the final output to the target dimension K.

[0051] Step S3-1: The first compressed signal passes through the unsqueeze layer to obtain a first input signal;

[0052] Specifically, this layer is used to add a dimension of size 1 to the specified dimension to adjust the shape of the tensor so as to meet the requirements of subsequent operations (such as convolution, matrix multiplication, etc.) on the input tensor shape.

[0053] In this embodiment, the function of this module is to determine if x is a two-dimensional tensor (i.e., shape [B, L], where B is the batch size and L is the sequence length), then add a new dimension of size 1 to the first dimension (index 1) so that its shape becomes [B, 1, L]. If x is already a three-dimensional or higher-dimensional tensor, the original tensor is directly used to obtain the first input signal.

[0054] Step S3-2: The first input signal passes through the input projection module, and the first output signal is projected from the single-channel space into a feature space with stronger representation capability:

[0055]

[0056] Among them, X0 is the output feature of the input projection module; B is the batch size; C is the number of channels; L is the signal length; Conv1D is a one-dimensional convolution operation; BN represents batch normalization; ReLU is a nonlinear function that improves the model's ability to perceive nonlinear patterns.

[0057] Step S3-3: After the output features of the input projection module enter the encoder module, they will pass through multiple HybridBlocks in sequence. Each HybridBlock contains both a time domain path and a frequency domain path to extract multi-scale information and improve feature integrity through fusion.

[0058] Among them, the time domain path uses a standard one-dimensional convolution stacking structure:

[0059] X time =BN2(Conv1D2(ReLU(BN1(Conv1D1(X0))))) (3)

[0060] Among them, Conv1D1 is the first convolution layer; BN1 is the first batch normalization layer; Conv1D2 is the second one-dimensional convolution layer; BN2 is the second batch normalization layer; X time is the output feature of the time domain path. This path extracts the short-term dependency pattern of the sequence signal using a local window sliding method and improves its stability and nonlinear modeling capability through normalization and nonlinear mapping.

[0061] The design of the frequency domain path is based on the combination of Fourier transform and channel attention mechanism, which mainly enhances the representation of periodic structures and global patterns in the input signal.

[0062] First, the Fourier transform of the input signal along the last dimension is applied:

[0063]

[0064] Then the complex result in the Fourier domain is extracted into its real and imaginary parts:

[0065]

[0066] in, is the real part; The two channels are then feature mapped by a one-dimensional convolution with shared weights:

[0067]

[0068] In order to focus on key frequencies in the frequency domain, a lightweight channel attention mechanism is designed. Its core calculation logic is:

[0069] α=σ(W2·ReLU(W1·GAP(|F(X0)|))) (7)

[0070] Where GAP is the global average pooling operation; |F(X0)| is the complex modulus long spectral density; W1 and W2 are the convolution kernel weights; σ is the Sigmoid activation. The attention vector acts on the real and imaginary parts:

[0071]

[0072] Then restore it to the time domain through the inverse Fourier transform:

[0073]

[0074] The features of the final output of the frequency domain path will be spliced ​​and fused with the output of the time path:

[0075] X fused =ReLU(Conv1D 1×1 ([X time ;X freq ])) (10)

[0076] Using residual connection structure to enhance the stability of deep training:

[0077] X out =X0+X fused (11)

[0078] Among them, X out Output features for the time-frequency fusion encoder.

[0079] Step S3-4: The output features of the time-frequency fusion encoder are compressed into a single channel through the output convolution module, and the feature length is adjusted through linear mapping. This can reduce the dimension of the feature, thereby reducing the computational complexity and the number of parameters, while retaining the most important feature information:

[0080] Z = Conv1D1(ReLU(Conv1D2(X out ))) (12)

[0081]

[0082] in, is the final LDV signal reconstruction result of the teacher model. By compressing the output to a one-dimensional vector space, this module completes the restoration mapping from deep high-dimensional features to the target space.

[0083] In this embodiment, the signal reconstruction teacher model adopts a dual-domain loss function during training to measure the reconstruction errors in the time domain and the frequency domain respectively.

[0084] The time domain loss is:

[0085]

[0086] Where n is the number of signal samples; y i is the true value of the i-th signal; is the predicted value of the i-th signal.

[0087] The frequency domain loss performs a fast Fourier transform (FFT) on the prediction and label, and calculates the mean square error in the real and imaginary parts respectively:

[0088]

[0089] Among them, F(y i ) is the true value of the signal in the frequency domain; is the predicted value of the signal in the frequency domain.

[0090] Furthermore, we introduce a scaling factor λ freq :

[0091]

[0092] Here, ε is an infinitesimal constant factor of 1e-8, which is used to ensure that the denominator is not 0. The scaling factor ensures dynamic stability during training and prevents the teacher model from having a single loss that dominates during iterations.

[0093] Through this scaling factor, the teacher model can adaptively unify the magnitude of the two losses during training, so the final total loss function is:

[0094] Lteacher =L time +λ freq ·L freq (17)

[0095] Among them, L teacher is the total loss of the teacher model, L time is the time domain loss, L freq is the frequency domain loss, λ freq is a scaling factor. The proposed dynamic adaptive training mechanism balances time and frequency domain losses using a scaling factor, preventing a single loss from dominating the optimization process and improving model robustness. The dual-domain loss function enhances frequency domain structural fidelity. With this mechanism, the training loss function no longer maintains a fixed bias toward a specific domain during optimization. Instead, it dynamically adjusts the optimization direction based on task difficulty and model adaptability, improving the balance and multimodal robustness of feature distribution learning. The introduction of the frequency domain loss significantly enhances the model's sensitivity to the signal's spectral structure, reduces blurring and leakage of high-frequency information, and effectively preserves the frequency domain sparsity prior used in compressed sensing recovery. From the perspective of information fidelity, frequency domain modeling captures more global structure, while the time domain loss is more sensitive to local details. Combining the two helps achieve high-quality reconstruction. Furthermore, since signal distortion is often more pronounced in the frequency domain, a single time domain loss cannot easily discern subtle spectral shifts. The dual-domain loss design allows the model to simultaneously acquire error information from both domains, thereby improving the perceptual consistency and interference resistance of the training signal, and promoting robust reconstruction performance under low signal-to-noise ratios and high compression rates.

[0096] The compression ratio (CR) is an indicator of the degree of signal compression. The calculation formula is:

[0097]

[0098] Where M is the dimension of the signal after projection through the measurement matrix. By adjusting the value of M, the reconstruction performance under different compression rates can be tested.

[0099] Step S4: constructing a lightweight signal reconstruction student model based on the output of the signal reconstruction teacher model, and inputting the first compressed signal into the signal reconstruction student model to obtain a final reconstructed signal;

[0100] like Figure 4As shown in the figure, the lightweight signal reconstruction student model consists of only three fully connected layers, using a multilayer perceptron (MLP). The hidden layer of the student model consists of only three fully connected layers, with the first and third fully connected layers having 8 neurons, and the second fully connected layer having 16 neurons. This student model, constructed using fully connected layers, significantly reduces the number of parameters and computational cost while maintaining a certain level of representational capability.

[0101] The first compressed signal is input through a linear transformation, mapping the original dimension input to a smaller latent space dimension:

[0102] h1=ReLU(W1x+b1) (19)

[0103] Here, x is the student model input, W1 and b1 represent the weight and bias of the first layer respectively. Then, this representation is further stacked into a deeper network structure, forming the following forward propagation process:

[0104] h2=ReLU(W2h1+b2)

[0105] h3=ReLU(W3h2+b3)

[0106]

[0107] Among them, W i ,b i Represent the weight and bias of the i-th layer, h i is the intermediate activation result of each layer, The LDV reconstructed signal is the final output of the student model. Through this layer-by-layer linear mapping and activation stacking structure, the student model can extract key pattern information from the compressed laser vibrometer displacement data with low complexity, thereby achieving the effect of model compression and accelerated inference.

[0108] A distillation loss function is constructed according to the first reconstructed signal and the second reconstructed signal, a fusion loss function is constructed based on the distillation loss function, and the time-frequency domain knowledge distillation of the teacher model is transferred to the student model based on the fusion loss function;

[0109] Specifically, this embodiment adopts a distillation training mechanism and utilizes the knowledge distillation method to optimize the training of the lightweight student model. The knowledge distillation training process mainly includes three parts: generation of teacher output, construction of distillation loss, and definition of the overall objective function.

[0110] First, let the input sample be x and the output of the teacher model be z t =f teacher (x), the output of the student model is zs =f student (x).

[0111] Perform softmax normalization on the model output to obtain the probability distribution:

[0112]

[0113] Among them, z t and z s is the output logits vector of the teacher model and the student model; p t and p s is the temperature-scaled softmax output probability distribution; T is the temperature coefficient, which adjusts the degree of variance between logits, thereby amplifying the fine-grained information about inter-class relationships in the teacher model. The normalized probability distribution can extract richer soft target information, which primarily refers to the fine-grained information about the relative relationships between classes provided by the teacher model's softmax output probability distribution.

[0114] The distillation loss function is defined using the Kullback–Leibler (KL) divergence:

[0115]

[0116] Where C is the number of signal dimensions; and are the probability values ​​on the i-th dimension respectively. This loss term measures how well the student model imitates the teacher distribution, forcing the student model to more accurately fit the teacher model's distributed cognitive results of the samples, thereby learning the knowledge contained in the teacher model.

[0117] In addition, the mean square error loss function MSE is used for joint modeling:

[0118]

[0119] The mean square error loss function is used to enhance the student model's direct perception of the true label, avoiding relying solely on the distillation signal which will weaken the student model's direct perception of the true label.

[0120] The final total loss function is a weighted fusion of the two:

[0121] L student =α·L distill +(1-α)·L MSE (twenty four)

[0122] Among them, L student is the loss function of the student model; α∈[0,1] is the loss weight coefficient, which is used to control the fusion ratio of distillation and supervision signals.

[0123] In this embodiment, the student model is trained through a knowledge distillation training mechanism, thereby enhancing its expressive power and improving the predictive performance of compressed signal recovery.

[0124] Step S5: Normalized Signal Error Percentage (NSEP) is used to represent the normalized relative error between the reconstructed signal and the original signal, where the original signal is the laser Doppler signal after sliding window sampling. The calculation formula is:

[0125]

[0126] Here, max(y) and min(y) are the maximum and minimum values ​​of the original signal, respectively. NSEP not only considers the absolute error between the reconstructed and original signals but also, through normalization, compares this error with the dynamic range of the signal. Even if two signals have the same absolute error but different dynamic ranges, NSEP can more accurately reflect the relative error between them. Therefore, NSEP combines both absolute and relative error assessments to provide a comprehensive reconstruction quality metric, more comprehensively reflecting the quality of the reconstructed signal.

[0127] In this embodiment, the value range of NSEP is generally between 0 and 100. When the reconstructed signal is completely different from the original signal and the error is extremely large, NSEP will exceed 100.

[0128] This embodiment also verifies the above technical solution by example:

[0129] In order to verify the effectiveness of the proposed method, a laser Doppler vibration monitoring platform was built. Figure 5 As shown. The vibration table displacement data with vibration frequencies of 50Hz, 100Hz, 500Hz and 1kHz were collected at sampling rates of 4kHz, 12.5kHz, 40kHz and 80kHz respectively. The acquisition time of each sample is 200s, and the data is saved as a .csv file through the host computer. The size of each file is 12.9MB, 40.9MB, 132MB and 270MB respectively. The hardware environment for model verification is AMD Ryzen 98945HS CPU, 32G memory, RTX4060 graphics card and 8G video memory. The software environment is Python 3.12.2, Pytorch 2.6.0 and MATLABR2021a.

[0130] First, the collected data is compressed with different CRs. Then, for the laser Doppler shift signals with different CRs in the four frequency bands, the teacher model is fully trained, and the number of training iterations is set to 3000 generations. Then, the student model is trained by offline distillation, and the number of iterations is set to 1000 generations. The ratio of the training set to the test set is 8:2, with 312 samples in the training set and 78 samples in the test set. In order to verify the robustness and effectiveness of the proposed model under different CRs and signal frequencies, this embodiment evaluates the performance of the teacher model and the student model under four signal frequency conditions of 50Hz, 100Hz, 500Hz, and 1000Hz. 2 , SNR, NSEP, RMSE and other indicators. At the same time, in order to further verify the comprehensive performance of the proposed distilled student model in terms of lightweight and reconstruction accuracy, this embodiment introduces three lightweight network structures MobileNetV1, ShuffleNetV2 and SqueezeNet as comparison models. The number of iterations of the comparison model is consistent with that of the student model. The comparison experimental results are visualized as follows Figure 6 shown.

[0131] In the low frequency band test, the student model can maintain performance close to that of the teacher model regardless of the compression rate level. At 50Hz frequency and CR of 90%, R 2 The value only dropped by 0.0001, the NSEP index increased by 0.26%, the RMSE increased by about 292.02, and the SNR dropped by 4.55dB. Even in the case of an extremely high CR of 10%, R 2 The value only dropped by 0.0004, the NSEP index increased by 1.14%, the RMSE increased by about 1047.26, the SNR decreased by 7.68dB, and the parameter compression ratio was as high as 96.32% (that is, Params was reduced to 3.68%). At a frequency of 100Hz, when the CR reached 90%, the student model R 2 It decreases by 0.001, NSEP increases by 2.72%, and RMSE increases by about 756.60, indicating that low-frequency signals have better tolerance for model compression and the student model can effectively learn low-frequency features without losing reconstruction quality.

[0132] And the proposed student model is 2 , SNR, NSEP and RMSE indicators are significantly better than traditional lightweight networks. For example, at 50Hz frequency and CR of 50%, MobileNetV1 only achieves R 2 =0.9239, SNR=11.23dB, while the student model of this method achieves R 2=0.9997, SNR=35.24dB. At 100Hz frequency and CR of 30%, the NSEP of ShuffleNetV2 is 8.1%, while that of the student model is only 2.43%, with a significant improvement in accuracy. In terms of parameter scale, although the number of parameters of traditional lightweight network models is generally less than 300,000 and the model volume is 0.4-1.05MB, the distilled student model proposed in this invention shows higher reconstruction accuracy at a volume close to or even smaller (minimum 0.08MB). Especially at 100Hz and 90% CR, the R of SqueezeNet is 2 The R of the student model of this method is only 0.3068, and the RMSE is as high as 21103.27. 2 The accuracy is 0.9989 and the RMSE is 805.17, achieving better signal reconstruction performance at a smaller parameter scale.

[0133] In the mid-high frequency band test, when the frequency is 500Hz and the CR is 90%, the student model R 2 The NSEP increases by 1.49%, the RMSE increases by about 24.70, and the SNR decreases by 4.24dB. 2 The performance of the student model decreased by 0.0045, NSEP increased by 4.88%, RMSE increased by 11.12, and SNR decreased by 9.48dB. Compared with low-frequency signals, high-frequency components place higher demands on the reconstruction ability of the small model. This is because high-frequency signals contain more rapidly changing and weak details, which are easily lost during the compression process. However, the performance degradation of the student model is still controlled within a small range, and R 2 All of them are kept above 0.9980, and the NSEP is lower than 10%, which fully verifies the robustness of the method proposed in this invention.

[0134] And when the frequency is 500Hz and the CR is 30%, the RMSE of MobileNetV1 and SqueezeNet are 570.27 and 1080.20 respectively, while the student model of this method is 41.99. Similarly, when the frequency is 1000Hz and the CR is 50%, the NSEP of ShuffleNetV2 is as high as 47.22% and the RMSE is 112.69, while the student model is only 7.54% and 18.74, indicating that it still has stable accuracy at higher frequencies. In terms of parameters and model size, when the frequency is 1000Hz and the CR is 90%, the RMSE of SqueezeNet is as high as 173.71, while the student model is controlled at 16.74, and the model is only 0.13MB.

[0135] Comprehensive comparison shows that although the traditional lightweight model has a compact structure, it is difficult to effectively handle high-fidelity signal reconstruction tasks. The proposed student network achieves better capture of the details of the laser Doppler shift signal with extremely low parameter counts by integrating teacher knowledge and frequency domain modeling mechanisms, taking into account the dual requirements of compression rate and accuracy, and showing significant potential in laser Doppler shift signal compressed sensing and model deployment tasks. Under all frequency and compression rate conditions, the parameter compression ratio is basically above 96% (the lowest is 96.32%), and the model size is reduced to 0.86% to 3.67% of the original teacher model, achieving extremely high structural compression and storage savings. In addition, the higher the frequency, the greater the performance loss caused by compression, but by introducing the frequency domain attention mechanism and optimizing the distillation process, the student model can still maintain excellent reconstruction effects. This fully demonstrates that the designed training framework based on time-frequency fusion structure and spectrum consistency constraints greatly alleviates the performance degradation problem caused by compression while ensuring the lightweight of the model. The signal fitting results of the teacher model and the student model in four frequency bands are visualized as shown in the figure below. Figure 7 shown.

[0136] Figure 7 The comparison between the real signal and the reconstructed signal in the time domain and frequency domain at four different frequencies of 50Hz, 100Hz, 500Hz and 1000Hz is shown. As can be seen from the figure, no matter it is low frequency or high frequency, the reconstructed signal and the real signal have a high degree of fit in the time domain waveform and frequency domain spectrum, indicating that the reconstruction method proposed in the present invention can accurately reproduce the characteristics of the original laser Doppler shift signal. The Pearson correlation coefficient shows that there is a complete positive correlation between the two, and the p value of the t-test is 0.00, indicating that there is no significant difference between the two. It shows that the method proposed in the present invention has good consistency and stability at different frequencies and can effectively reconstruct the compressed signal. Then, the proposed method is compared with the traditional compressed sensing algorithms OMP, MCo and SP. Based on the assumption of signal sparsity, the three algorithms all use the Fourier domain as the sparse domain, and the test time is the time for each model to compress and reconstruct the test set. The comparison results are shown in the figure. Figure 8 shown.

[0137] Experimental results show that the proposed method significantly outperforms traditional methods across multiple compression ratios (CRs). For example, at a CR of 10%, the teacher model achieves a high SNR of 40.68 dB and a NSEP of only 0.92%, while the OMP achieves an SNR of 13.50 dB and an NSEP of 21.28%. Furthermore, the proposed method is significantly more computationally efficient. The runtimes of both the teacher and student models range from 0.01 to 0.44 seconds, while the OMP and MCo models consume tens or even hundreds of seconds. In particular, at a CR of 90%, the OMP runtime exceeds 200 seconds. This demonstrates that the proposed method not only offers significant performance advantages but also significantly reduces computational costs. Performance at different compression ratios demonstrates the robustness of the proposed method. While the performance of the OMP, MCo, and SP models improves with increasing CR, it remains significantly inferior to the teacher-student model. For example, at a CR of 90%, the teacher model's SNR remains above 45.49 dB, while the OMP's SNR is only 28.03 dB. The Student model maintains excellent performance despite its lightweight design, with SNR and NSEP metrics approaching those of the Teacher model, but with significantly fewer parameters and computation time. In contrast, the SP method performs the worst, with its SNR becoming negative at a CR of 10%, completely failing to meet practical requirements. In summary, the proposed method demonstrates significant advantages in performance, efficiency, and adaptability, making it particularly suitable for real-time signal processing tasks in high-compression scenarios.

[0138] Example 2

[0139] In one or more embodiments, a laser Doppler signal non-sparse compressed sensing system is disclosed, specifically comprising:

[0140] A signal acquisition module is configured to: acquire laser Doppler signals;

[0141] A signal compression module is configured to: construct a Bernoulli sensing matrix to perform data compression on the laser Doppler signal to obtain a first compressed signal;

[0142] A first reconstruction module is configured to: input the first compressed signal into a signal reconstruction teacher model with multi-resolution feature fusion to obtain a first reconstructed signal; the signal reconstruction teacher model extracts the local temporal pattern of the signal through a time domain convolution feature extraction mechanism, and learns the time-frequency features in combination with a frequency domain attention guidance mechanism;

[0143] a second reconstruction module, configured to: construct a lightweight signal reconstruction student model based on the output of the signal reconstruction teacher model, and input the first compressed signal into the signal reconstruction student model to obtain a final reconstructed signal;

[0144] A distillation loss function is constructed according to the first reconstructed signal and the second reconstructed signal, a fusion loss function is constructed based on the distillation loss function, and the teacher model knowledge is distilled and transferred to the student model based on the fusion loss function.

[0145] Example 3

[0146] This embodiment provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps of the above-mentioned laser Doppler signal non-sparse compressed sensing method are completed.

[0147] Example 4

[0148] This embodiment provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the above-mentioned laser Doppler signal non-sparse compressed sensing method are completed.

[0149] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0150] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0151] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide the functions for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0152] The description of each embodiment in the above embodiments has different emphases. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0153] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A non-sparse compressed sensing method for laser Doppler signals, characterized in that: include: Collecting laser Doppler signals; Constructing a Bernoulli sensing matrix to perform data compression on the laser Doppler signal to obtain a first compressed signal; The first compressed signal is input into a signal reconstruction teacher model with multi-resolution feature fusion to obtain a first reconstructed signal; the signal reconstruction teacher model extracts the local temporal pattern of the signal through a time domain convolution feature extraction mechanism, and learns the time-frequency features in combination with a frequency domain attention guidance mechanism; Building a lightweight signal reconstruction student model based on the output of the signal reconstruction teacher model, and inputting the first compressed signal into the signal reconstruction student model to obtain a final reconstructed signal; A distillation loss function is constructed according to the first reconstructed signal and the second reconstructed signal, a fusion loss function is constructed based on the distillation loss function, and the teacher model knowledge is distilled and transferred to the student model based on the fusion loss function.

2. The laser Doppler signal non-sparse compressed sensing method according to claim 1, wherein: The signal reconstruction teacher model includes a time-frequency fusion encoder; The time-frequency fusion encoder includes multiple HybridBlocks, each HybridBlock includes a time domain path and a frequency domain path; The time domain path is a one-dimensional convolution stack structure, which obtains the output features of the time domain path; The frequency domain path first applies a Fourier transform to its input signal along the last dimension, extracts the real and imaginary parts, performs one-dimensional convolution on the real and imaginary parts respectively, multiplies the convolved features with the attention vector obtained by the frequency domain attention guidance mechanism, and restores them to the time domain through an inverse Fourier transform to obtain the frequency domain path output features; The output features of the time domain path and the frequency domain path are fused and then added to the input feature residual of HybridBlock to obtain the output features of HybridBlock.

3. The laser Doppler signal non-sparse compressed sensing method according to claim 1, wherein: The frequency domain attention guidance mechanism is: α=σ(W2·ReLU(W1·GAP(|F(X0)|))) Where GAP is the global average pooling operation; |F(X0)| is the complex modulus long spectral density; W1 and W2 are the convolution kernel weights; σ is the Sigmoid activation.

4. The laser Doppler signal non-sparse compressed sensing method according to claim 1, wherein: The signal reconstruction teacher model adopts a dual-domain loss function during training: L teacher =L time +λ freq ·L freq Among them, L teacher is the total loss of the teacher model, L time is the time domain loss, L freq is the frequency domain loss, λ freq is the scaling factor.

5. The laser Doppler signal non-sparse compressed sensing method according to claim 4, characterized in that: The time domain loss is: Where n is the number of signal samples; y i is the true value of the i-th signal; is the predicted value of the i-th signal; The frequency domain loss is: Among them, F(y i ) is the true value of the signal in the frequency domain; is the predicted value of the signal in the frequency domain; The scaling factor is: Here, ε is an infinitesimal constant factor.

6. The laser Doppler signal non-sparse compressed sensing method according to claim 1, wherein: The fusion loss function is a weighted fusion of the distillation loss function and the mean square error loss function: L student =α·L distill +(1-a)·L MSE Among them, L student is the loss function of the student model; α∈[0,1] is the loss weight coefficient; L distill is the distillation loss function; The distillation loss function is: Where C is the number of signal dimensions; and are the probability values ​​on the i-th dimension respectively; T is the temperature coefficient.

7. The laser Doppler signal non-sparse compressed sensing method according to claim 1, characterized in that: The normalized signal error percentage is used to express the normalized relative error between the reconstructed signal and the original signal. The formula is: Where max(y) and min(y) are the maximum and minimum values ​​of the original signal respectively; n is the number of signal samples; y i is the true value of the i-th signal; is the predicted value of the i-th signal.

8. A laser Doppler signal non-sparse compressed sensing system, characterized in that: include: A signal acquisition module is configured to: acquire laser Doppler signals; A signal compression module is configured to: construct a Bernoulli sensing matrix to perform data compression on the laser Doppler signal to obtain a first compressed signal; A first reconstruction module is configured to: input the first compressed signal into a signal reconstruction teacher model with multi-resolution feature fusion to obtain a first reconstructed signal; the signal reconstruction teacher model extracts the local temporal pattern of the signal through a time domain convolution feature extraction mechanism, and learns the time-frequency features in combination with a frequency domain attention guidance mechanism; a second reconstruction module, configured to: construct a lightweight signal reconstruction student model based on the output of the signal reconstruction teacher model, and input the first compressed signal into the signal reconstruction student model to obtain a final reconstructed signal; A distillation loss function is constructed according to the first reconstructed signal and the second reconstructed signal, a fusion loss function is constructed based on the distillation loss function, and the teacher model knowledge is distilled and transferred to the student model based on the fusion loss function.

9. An electronic device, characterized in that: The method comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the laser Doppler signal non-sparse compressed sensing method according to any one of claims 1 to 7 is completed.

10. A computer-readable storage medium, characterized in that Used to store computer instructions, which, when executed by a processor, complete the laser Doppler signal non-sparse compressed sensing method according to any one of claims 1 to 7.

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