Failure Mode Classification for Rolling Element Bearings Using Time-Domain Transformer-Based Encoder.

In this paper, we propose a Transformer-based encoder architecture integrated with an unsupervised denoising method to learn meaningful and sparse representations of vibration signals without the need for data transformation or pre-trained data. Existing Transformer models often require transformed data or extensive computational resources, limiting their practical adoption. We propose a simple yet competitive modification of the Transformer model, integrating a trainable noise reduction method specifically tailored for failure mode classification using vibration data directly in the time domain without converting them into other domains or images. Furthermore, we present the key architectural components and algorithms underlying our model, emphasizing interpretability and trustworthiness. Our model is trained and validated using two benchmark datasets: the IMS dataset (four failure modes) and the CWRU dataset (four and ten failure modes). Notably, our model performs competitively, especially when using an unbalanced test set and a lightweight architecture.

A Smartphone-Based M-Health Monitoring System for Arrhythmia Diagnosis.

Deep learning technology has been widely adopted in the research of automatic arrhythmia detection. However, there are several limitations in existing diagnostic models, e.g., difficulties in extracting temporal information from long-term ECG signals, a plethora of parameters, and sluggish operation speed. Additionally, the diagnosis performance of arrhythmia is prone to mistakes from signal noise. This paper proposes a smartphone-based m-health system for arrhythmia diagnosis. First, we design a cycle-GAN-based ECG denoising model which takes real-world noise signals as input and aims to produce clean ECG signals. In order to train its two generators and two discriminators simultaneously, we explore an unsupervised pre-training strategy to initialize the generator and accelerate the convergence speed during training. Second, we propose an arrhythmia diagnosis model based on the time convolution network (TCN). This model can identify 34 common arrhythmia events using eight-lead ECG signals, and we deploy such a model on the Android platform to develop an at-home ECG monitoring system. Experimental results have demonstrated that our approach outperforms the existing noise reduction methods and arrhythmia diagnosis models in terms of denoising effect, recognition accuracy, model size, and operation speed, making it more suitable for deployment on mobile devices for m-health monitoring services.

Damage Monitoring and Localization Imaging of Aluminum Alloy Thin-Walled Structure Based on Remote Bonding Fiber Bragg Gratings Sensing.

In this paper, the damage monitoring investigation based on the remote bonding fiber Bragg grating sensing is performed on the aerospace aluminum alloy thin-walled structure with prefabricated damage. Firstly, an ultrasonic excitation-fiber Bragg gratings (UE-FBGs) sensing experimental platform is established for the simulation of defects monitoring, in which the sensors are placed at a certain distance from the bonding area. Secondly, different arrangements of exciters and receivers are utilized for the original signals and the damage signals. Subsequently, the raw signals are processed by filter and feature extraction in order to denoise the signals and acquire the parameters sensitive to the damage. Finally, an improved Reconstruction for Image Defects (RAPID) algorithm is used to locate and reconstruct the pre-existing damage. The results show that the proposed system improves the sensitivity of the FBG receiver signal and the accuracy of the damage imaging.

Efficient EEG motion artifact elimination framework for ambulatory epileptic seizure detection application.

Motion artifacts are a pervasive challenge in EEG ambulatory monitoring, often obscuring critical neurological signals and impeding accurate seizure detection. In this study, we propose a new approach of outlier based grouping of two level Singular Spectrum Analysis (SSA) decomposition combined with Relative Total Variation (RTV) filter for the effective removal of motion-induced noise from ambulatory EEG data. A two-stage SSA method was employed to decompose single-channel EEG signal, which had been interfered with, into various fre quency bands. The affected sub-band signal was then subjected to an RTV filter to estimate the artifact signal. Subtracting this estimated artifact signal from the contaminated sub-band signal yielded the filtered sub-band signal. Subse quently, the filtered sub-band signal was reintegrated with the other decomposed components from noise-free bands, culminating in the generation of the ultimate denoised EEG signal. Based on the comprehensive set of simulation results, it can be deduced that the algorithm described in the paper outperforms existing methods. It demonstrates superior metrics evaluation in terms of ΔSNR,η,MAE, andPSNRwhen compared to these alternatives. Our framework sig- nificantly enhances the quality of EEG data by successfully eliminating motion artifacts while preserving crucial brainwave information. To evaluate the prac tical impact of this noise reduction technique, we assess its performance in the context of seizure detection. The results reveal a substantial improvement in the accuracy and reliability of seizure detection algorithms when applied to EEG data preprocessed with proposed method.

Convolutional transformer-driven robust electrocardiogram signal denoising framework with adaptive parametric ReLU.

The electrocardiogram (ECG) is a widely used diagnostic tool for cardiovascular diseases. However, ECG recording is often subject to various noises, which can limit its clinical evaluation. To address this issue, we propose a novel Transformer-based convolutional neural network framework with adaptively parametric ReLU (APtrans-CNN) for ECG signal denoising. The proposed APtrans-CNN architecture combines the strengths of transformers in global feature learning and CNNs in local feature learning to address the inadequacy of learning with long sequence time-series features. By fully exploiting the global features of ECG signals, our framework can effectively extract critical information that is necessary for signal denoising. We also introduce an adaptively parametric ReLU that can assign a value to the negative information contained in the ECG signal, thereby overcoming the limitation of ReLU to retain negative information. Additionally, we introduce a dynamic feature aggregation module that enables automatic learning and retention of valuable features while discarding useless noise information. Results obtained from two datasets demonstrate that our proposed APtrans-CNN can accurately extract pure ECG signals from noisy datasets and is adaptable to various applications. Specifically, when the input consists of ECG signals with a signal-to-noise ratio (SNR) of -4 dB, APtrans-CNN successfully increases the SNR to more than 6 dB, resulting in the diagnostic model's accuracy exceeding 96%.

Multi-layer convolutional dictionary learning network for signal denoising and its application to explainable rolling bearing fault diagnosis.

As a vital mechanical sub-component, the health monitoring of rolling bearings is important. Vibration signal analysis is a commonly used approach for fault diagnosis of bearings. Nevertheless, the collected vibration signals cannot avoid interference from noises which has a negative influence on fault diagnosis. Thus, denoising needs to be utilized as an essential step of vibration signal processing. Traditional denoising methods need expert knowledge to select hyperparameters. And data-driven methods based on deep learning lack interpretability and a clear justification for the design of architecture in a "black-box" deep neural network. An approach to systematically design neural networks is by unrolling algorithms, such as learned iterative soft-thresholding (LISTA). In this paper, the multi-layer convolutional LISTA (ML-CLISTA) algorithm is derived by embedding a designed multi-layer sparse coder to the convolutional extension of LISTA. Then the multi-layer convolutional dictionary learning (ML-CDL) network for mechanical vibration signal denoising is proposed by unrolling ML-CLISTA. By combining ML-CDL network with a classifier, the proposed denoising method is applied to the explainable rolling bearing fault diagnosis. The experiments on two bearing datasets show the superiority of the ML-CDL network over other typical denoising methods.

Adaptive convolutional dictionary learning for denoising seismocardiogram to enhance the classification performance of aortic stenosis.

BACKGROUND: Aortic stenosis (AS) is the most prevalent type of valvular heart disease (VHD), traditionally diagnosed using echocardiogram or phonocardiogram. Seismocardiogram (SCG), an emerging wearable cardiac monitoring modality, is proved to be feasible in non-invasive and cost-effective AS diagnosis. However, SCG waveforms acquired from patients with heart diseases are typically weak, making them more susceptible to noise contamination. While most related researches focus on motion artifacts, sensor noise and quantization noise have been mostly overlooked. These noises pose additional challenges for extracting features from the SCG, especially impeding accurate AS classification. METHOD: To address this challenge, we present a convolutional dictionary learning-based method. Based on sparse modeling of SCG, the proposed method generates a personalized adaptive-size dictionary from noisy measurements. The dictionary is used for sparse coding of the noisy SCG into a transform domain. Reconstruction from the domain removes the noise while preserving the individual waveform pattern of SCG. RESULTS: Using two self-collected SCG datasets, we established optimal dictionary learning parameters and validated the denoising performance. Subsequently, the proposed method denoised SCG from 50 subjects (25 AS and 25 non-AS). Leave-one-subject-out cross-validation (LOOCV) was applied to 5 machine learning classifiers. Among the classifiers, a bi-layer neural network achieved a moderate accuracy of 90.2%, with an improvement of 13.8% from the denoising. CONCLUSIONS: The proposed sparsity-based denoising technique effectively removes stochastic sensor noise and quantization noise from SCG, consequently improving AS classification performance. This approach shows promise for overcoming instrumentation constraints of SCG-based diagnosis.

ECG Signal Denoising Using an Improved Hybrid DWT-ADTF Approach.

PURPOSE: The electrocardiogram signal (ECG) presents a fundamental source of information to consider for the diagnosis of a heart condition. Given its low-frequency features, this signal is quite susceptible to various noise and interference sources. This paper presents an improved hybrid approach to ECG signal denoising based on the DWT and the ADTF methods. METHODS: The proposed improvements consist of integrating an adaptive [Formula: see text] parameter into the ADTF approach, combining a soft thresholding ADTF-based process with the DWT details, along with employing the mean filter to handle the baseline wandering noise. Furthermore, the proposed approach incorporates several denoising measures based on various proposed noise features, which have also been introduced in this approach. Several real noises collected from the Noise Stress Test Database (NSTDB), as well as several synthetic noises at different SNR levels, are proposed to ensure a thorough assessment of the proposed method's performance. RESULTS: The evaluation focuses on the SN Rimp, PRD, and MSE parameters, as well as the SINAD parameter as a diagnostic distortion measurement. Furthermore, a time complexity evaluation is proposed. The proposed approach demonstrated promising results compared to a recent hybridization of the DWT and ADTF methods, as well as recently published ECG signal denoising-based approaches in various real and synthetic noise cases using different statistical evaluation metrics. CONCLUSION: In the vast majority of the study cases, the proposed approach outperforms the compared methods in terms of statistical results for real and synthetic noises. Furthermore, compared to these methods, it provides a fairly low time complexity. This is consistent with the ambition of embedding this approach in low-cost hardware architectures.

Radiation-induced acoustic signal denoising using a supervised deep learning framework for imaging and therapy monitoring.

Radiation-induced acoustic (RA) imaging is a promising technique for visualizing the invisible radiation energy deposition in tissues, enabling new imaging modalities and real-time therapy monitoring. However, RA imaging signal often suffers from poor signal-to-noise ratios (SNRs), thus requiring measuring hundreds or even thousands of frames for averaging to achieve satisfactory quality. This repetitive measurement increases ionizing radiation dose and degrades the temporal resolution of RA imaging, limiting its clinical utility. In this study, we developed a general deep inception convolutional neural network (GDI-CNN) to denoise RA signals to substantially reduce the number of frames needed for averaging. The network employs convolutions with multiple dilations in each inception block, allowing it to encode and decode signal features with varying temporal characteristics. This design generalizes GDI-CNN to denoise acoustic signals resulting from different radiation sources. The performance of the proposed method was evaluated using experimental data of x-ray-induced acoustic, protoacoustic, and electroacoustic signals both qualitatively and quantitatively. Results demonstrated the effectiveness of GDI-CNN: it achieved x-ray-induced acoustic image quality comparable to 750-frame-averaged results using only 10-frame-averaged measurements, reducing the imaging dose of x-ray-acoustic computed tomography (XACT) by 98.7%; it realized proton range accuracy parallel to 1500-frame-averaged results using only 20-frame-averaged measurements, improving the range verification frequency in proton therapy from 0.5 to 37.5 Hz; it reached electroacoustic image quality comparable to 750-frame-averaged results using only a single frame signal, increasing the electric field monitoring frequency from 1 fps to 1k fps. Compared to lowpass filter-based denoising, the proposed method demonstrated considerably lower mean-squared-errors, higher peak-SNR, and higher structural similarities with respect to the corresponding high-frame-averaged measurements. The proposed deep learning-based denoising framework is a generalized method for few-frame-averaged acoustic signal denoising, which significantly improves the RA imaging's clinical utilities for low-dose imaging and real-time therapy monitoring.

An efficient ECG denoising method by fusing ECA-Net and CycleGAN.

For wearable electrocardiogram (ECG) acquisition, it was easy to infer motion artifices and other noises. In this paper, a novel end-to-end ECG denoising method was proposed, which was implemented by fusing the Efficient Channel Attention (ECA-Net) and the cycle consistent generative adversarial network (CycleGAN) method. The proposed denoising model was optimized by using the ECA-Net method to highlight the key features and introducing a new loss function to further extract the global and local ECG features. The original ECG signal came from the MIT-BIH Arrhythmia Database. Additionally, the noise signals used in this method consist of a combination of Gaussian white noise and noises sourced from the MIT-BIH Noise Stress Test Database, including EM (Electrode Motion Artifact), BW (Baseline Wander) and MA (Muscle Artifact), as well as mixed noises composed of EM+BW, EM+MA, BW+MA and EM+BW+MA. Moreover, corrupted ECG signals were generated by adding different levels of single and mixed noises to clean ECG signals. The experimental results show that the proposed method has better denoising performance and generalization ability with higher signal-to-noise ratio improvement (SNRimp), as well as lower root-mean-square error (RMSE) and percentage-root-mean-square difference (PRD).

An Internal Defect Detection Algorithm for Concrete Blocks Based on Local Mean Decomposition-Singular Value Decomposition and Weighted Spatial-Spectral Entropy.

Within the scope of concrete internal defect detection via laser Doppler vibrometry (LDV), the acquired signals frequently suffer from low signal-to-noise ratios (SNR) due to the heterogeneity of the concrete's material properties and its rough surface structure. Consequently, these factors make the defect signal characteristics challenging to discern precisely. In response to this challenge, we propose an internal defect detection algorithm that incorporates local mean decomposition-singular value decomposition (LMD-SVD) and weighted spatial-spectral entropy (WSSE). Initially, the LDV vibration signal undergoes denoising via LMD and the SVD algorithms to reduce noise interference. Subsequently, the distribution of each frequency in the scan plane is analyzed utilizing the WSSE algorithm. Since the vibrational energy of the frequencies caused by the defect resonance is concentrated in the defect region, its energy distribution in the scan plane is non-uniform, resulting in a significant difference between the defect resonance frequencies' SSE values and the other frequencies' SSE values. This feature is used to estimate the resonant frequencies of internal defects. Ultimately, the defects are characterized based on the modal vibration patterns of the defect resonant frequencies. Tests were performed on two concrete blocks with simulated cavity defects, using an ultrasonic transducer as the excitation device to generate ultrasonic vibrations directly from the back of the blocks and applying an LDV as the acquisition device to collect vibration signals from their front sides. The results demonstrate the algorithm's capacity to effectively pinpoint the information on the location and shape of shallow defects within the concrete, underscoring its practical significance for concrete internal defect detection in practical engineering scenarios.

Global optimality analysis and solution of the ℓ0 total variation signal denoising model.

The total variation regularizer is diffusely emerged in statistics, image and signal processing to obtain piecewise constant estimator. The ℓ0 total variation (L0TV) regularized signal denoising model is a nonconvex and discontinuous optimization problem, and it is very difficult to find its global optimal solution. In this paper, we present the global optimality analysis of L0TV signal denoising model, and design an efficient algorithm to pursuit its solution. Firstly, we equivalently rewrite the L0TV denoising model as a partial regularized (PL0R) minimization problem by aid of the structured difference operator. Subsequently, we define a P-stationary point of PL0R, and show that it is a global optimal solution. These theoretical results allow us to find the global optimal solution of the L0TV model. Therefore, an efficient Newton-type algorithm is proposed for the PL0R problem. The algorithm has a considerably low computational complexity in each iteration. Finally, experimental results demonstrate the excellent performance of our approach in comparison with several state-of-the-art methods.

Deep learning-based protoacoustic signal denoising for proton range verification.

Proton therapy is a type of radiation therapy that can provide better dose distribution compared to photon therapy by delivering most of the energy at the end of range, which is called the Bragg peak (BP). The protoacoustic technique was developed to determine the BP locationsin vivo, but it requires a large dose delivery to the tissue to obtain a high number of signal averaging (NSA) to achieve a sufficient signal-to-noise ratio (SNR), which is not suitable for clinical use. A novel deep learning-based technique has been proposed to denoise acoustic signals and reduce BP range uncertainty with much lower doses. Three accelerometers were placed on the distal surface of a cylindrical polyethylene (PE) phantom to collect protoacoustic signals. In total, 512 raw signals were collected at each device. Device-specific stack autoencoder (SAE) denoising models were trained to denoise the noise-containing input signals, which were generated by averaging only 1, 2, 4, 8, 16, or 24 raw signals (low NSA signals), while the clean signals were obtained by averaging 192 raw signals (high NSA). Both supervised and unsupervised training strategies were employed, and the evaluation of the models was based on mean squared error (MSE), SNR, and BP range uncertainty. Overall, the supervised SAEs outperformed the unsupervised SAEs in BP range verification. For the high accuracy detector, it achieved a BP range uncertainty of 0.20 ± 3.44 mm by averaging over 8 raw signals, while for the other two low accuracy detectors, they achieved the BP uncertainty of 1.44 ± 6.45 mm and -0.23 ± 4.88 mm by averaging 16 raw signals, respectively. This deep learning-based denoising method has shown promising results in enhancing the SNR of protoacoustic measurements and improving the accuracy in BP range verification. It greatly reduces the dose and time for potential clinical applications.

Non-invasive detection of the content of white blood cells in the blood of humans based on dynamic spectrum.

Objective. Changes in white blood cell content have been shown to be useful in determining whether the body is in a healthy state. We propose an improved data processing and modeling approach, which helps to accommodate blood component content detection and improve prediction accuracy.Approach. In this experiment, the finger-end transmission method was used for spectral measurement, and we collected a total of 440 sample data. In this paper, we first use the method of CEEMDAN combined with wavelet threshold to denoise the PPG signal, and then use the integral method to extract the spectral features, which makes up for the defects of the single-edge method using incomplete data and the deviation of the slope of the rising segment from the actual signal. We further improve the screening of samples and wavelengths, and used PLS regression modeling combine the double nonlinear correction method to build the most stable and universal model.Main results. The model has been applied to 332 subjects' finger transmission spectral data to predict the concentration of leukocytes. The correlation coefficient of the final training set result was 0.927, and the root mean square error (RMSE) is 0.569×109l-1, the correlation coefficient of the prediction set result is 0.817, and the RMSE is 0.826×109l-1, which proves the practicability of the proposed method.Significance. We propose a non-invasive method for detecting leukocyte concentration in blood that can also be generalized to detect other blood components.

Dual Residual Denoising Autoencoder with Channel Attention Mechanism for Modulation of Signals.

Aiming to address the problems of the high bit error rate (BER) of demodulation or low classification accuracy of modulation signals with a low signal-to-noise ratio (SNR), we propose a double-residual denoising autoencoder method with a channel attention mechanism, referred to as DRdA-CA, to improve the SNR of modulation signals. The proposed DRdA-CA consists of an encoding module and a decoding module. A squeeze-and-excitation (SE) ResNet module containing one residual connection is modified and then introduced into the autoencoder as the channel attention mechanism, to better extract the characteristics of the modulation signals and reduce the computational complexity of the model. Moreover, the other residual connection is further added inside the encoding and decoding modules to optimize the network degradation problem, which is beneficial for fully exploiting the multi-level features of modulation signals and improving the reconstruction quality of the signal. The ablation experiments prove that both the improved SE module and dual residual connections in the proposed method play an important role in improving the denoising performance. The subsequent experimental results show that the proposed DRdA-CA significantly improves the SNR values of eight modulation types in the range of -12 dB to 8 dB. Especially for 16QAM and 64QAM, the SNR is improved by 8.38 dB and 8.27 dB on average, respectively. Compared to the DnCNN denoising method, the proposed DRdA-CA makes the average classification accuracy increase by 67.59∼74.94% over the entire SNR range. When it comes to the demodulation, compared with the RLS and the DnCNN denoising algorithms, the proposed denoising method reduces the BER of 16QAM by an average of 63.5% and 40.5%, and reduces the BER of 64QAM by an average of 46.7% and 18.6%. The above results show that the proposed DRdA-CA achieves the optimal noise reduction effect.

Signal denoising through topographic modularity of neural circuits.

Information from the sensory periphery is conveyed to the cortex via structured projection pathways that spatially segregate stimulus features, providing a robust and efficient encoding strategy. Beyond sensory encoding, this prominent anatomical feature extends throughout the neocortex. However, the extent to which it influences cortical processing is unclear. In this study, we combine cortical circuit modeling with network theory to demonstrate that the sharpness of topographic projections acts as a bifurcation parameter, controlling the macroscopic dynamics and representational precision across a modular network. By shifting the balance of excitation and inhibition, topographic modularity gradually increases task performance and improves the signal-to-noise ratio across the system. We demonstrate that in biologically constrained networks, such a denoising behavior is contingent on recurrent inhibition. We show that this is a robust and generic structural feature that enables a broad range of behaviorally relevant operating regimes, and provide an in-depth theoretical analysis unraveling the dynamical principles underlying the mechanism.

Motion Artifact Reduction in Electrocardiogram Signals Through a Redundant Denoising Independent Component Analysis Method for Wearable Health Care Monitoring Systems: Algorithm Development and Validation.

BACKGROUND: The quest for improved diagnosis and treatment in home health care models has led to the development of wearable medical devices for remote vital signs monitoring. An accurate signal and a high diagnostic yield are critical for the cost-effectiveness of wearable health care monitoring systems and their widespread application in resource-constrained environments. Despite technological advances, the information acquired by these devices can be contaminated by motion artifacts (MA) leading to misdiagnosis or repeated procedures with increases in associated costs. This makes it necessary to develop methods to improve the quality of the signal acquired by these devices. OBJECTIVE: We aimed to present a novel method for electrocardiogram (ECG) signal denoising to reduce MA. We aimed to analyze the method's performance and to compare its performance to that of existing approaches. METHODS: We present the novel Redundant denoising Independent Component Analysis method for ECG signal denoising based on the redundant and simultaneous acquisition of ECG signals and movement information, multichannel processing, and performance assessment considering the information contained in the signal waveform. The method is based on data including ECG signals from the patient's chest and back, the acquisition of triaxial movement signals from inertial measurement units, a reference signal synthesized from an autoregressive model, and the separation of interest and noise sources through multichannel independent component analysis. RESULTS: The proposed method significantly reduced MA, showing better performance and introducing a smaller distortion in the interest signal compared with other methods. Finally, the performance of the proposed method was compared to that of wavelet shrinkage and wavelet independent component analysis through the assessment of signal-to-noise ratio, dynamic time warping, and a proposed index based on the signal waveform evaluation with an ensemble average ECG. CONCLUSIONS: Our novel ECG denoising method is a contribution to converting wearable devices into medical monitoring tools that can be used to support the remote diagnosis and monitoring of cardiovascular diseases. A more accurate signal substantially improves the diagnostic yield of wearable devices. A better yield improves the devices' cost-effectiveness and contributes to their widespread application.

A Novel End-to-end Network Based on a bidirectional GRU and a Self-Attention Mechanism for Denoising of Electroencephalography Signals.

Electroencephalography (EEG) signals are nonlinear and non-stationary sequences that carry much information. However, physiological signals from other body regions may readily interfere with EEG signal capture, having a significant unfavorable influence on subsequent analysis. Therefore, signal denoising is a crucial step in EEG signal processing. This paper proposes a bidirectional gated recurrent unit (GRU) network based on a self-attention mechanism (BG-Attention) for extracting pure EEG signals from noise-contaminated EEG signals. The bidirectional GRU network can simultaneously capture past and future information while processing continuous time sequence. And by paying different levels of attention to the content of varying importance, the model can learn more significant feature of EEG signal sequences, highlighting the contribution of essential samples to denoising. The proposed model is evaluated on the EEGdenoiseNet data set. We compared the proposed model with a fully connected network (FCNN), the one-dimensional residual convolutional neural network (1D-ResCNN), and a recurrent neural network (RNN). The experimental results show that the proposed model can reconstruct a clear EEG waveform with a decent signal-to-noise ratio (SNR) and the relative root mean squared error (RRMSE) value. This study demonstrates the potential of BG-Attention in the pre-processing phase of EEG experiments, which has significant implications for medical technology and brain-computer interface (BCI) applications.

A New De-Noising Method Based on Enhanced Time-Frequency Manifold and Kurtosis-Wavelet Dictionary for Rolling Bearing Fault Vibration Signal.

The transient pulses caused by local faults of rolling bearings are an important measurement information for fault diagnosis. However, extracting transient pulses from complex nonstationary vibration signals with a large amount of background noise is challenging, especially in the early stage. To improve the anti-noise ability and detect incipient faults, a novel signal de-noising method based on enhanced time-frequency manifold (ETFM) and kurtosis-wavelet dictionary is proposed. First, to mine the high-dimensional features, the C-C method and Cao's method are combined to determine the embedding dimension and delay time of phase space reconstruction. Second, the input parameters of the liner local tangent space arrangement (LLTSA) algorithm are determined by the grid search method based on Renyi entropy, and the dimension is reduced by manifold learning to obtain the ETFM with the highest time-frequency aggregation. Finally, a kurtosis-wavelet dictionary is constructed for selecting the best atom and eliminating the noise and reconstruct the defective signal. Actual simulations showed that the proposed method is more effective in noise suppression than traditional algorithms and that it can accurately reproduce the amplitude and phase information of the raw signal.