Signal denoising method based on superimposition and single instance of collection
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-02-11
- Publication Date
- 2026-08-13
Smart Images
Figure CN2025076853_13082026_PF_FP_ABST
Abstract
Description
Methods for signal superposition and noise reduction in a single acquisition Technical Field
[0001] This invention belongs to the field of signal processing technology, and in particular relates to a method for signal superposition and noise reduction in a single acquisition. Background Technology
[0002] Existing signal noise reduction methods include: (1) Multiple acquisition averaging method, which involves repeatedly acquiring the same signal and averaging it. Although this method can effectively suppress random noise, it requires that the signal be repeatedly acquired and is costly; (2) Time-frequency domain filtering method, which filters based on the difference in time-frequency characteristics of the signal and noise. Although this method is simple to implement and has a small computational load, it is difficult to preserve signal details and has poor effect on overlapping spectrum noise; (3) Adaptive filtering, which dynamically adjusts the filter parameters according to the statistical characteristics of the signal. Although this method can adaptively track signal changes, it requires a lot of prior knowledge and the parameter adjustment is complex.
[0003] To address the aforementioned problems in existing technologies, there is an urgent need to propose a method for signal superposition and noise reduction using a single acquisition for signals that are difficult to acquire repeatedly, such as seismic waves and electrocardiogram signals. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention proposes a method for signal superposition and noise reduction through single acquisition, thereby resolving the issues present in the prior art.
[0005] To achieve the above objectives, the present invention provides a method for signal superposition and noise reduction based on a single acquisition, comprising the following steps:
[0006] Acquire noisy signals, and perform normalization processing on the noisy signals to obtain normalized signals;
[0007] The normalized signal is subjected to spectral analysis, adaptive sparsity estimation, and sampling point configuration optimization, selecting fixed sampling points and random sampling points;
[0008] Iterative noise reduction is performed based on selected fixed and random sampling points;
[0009] When the preset maximum number of iterations is reached, the noise reduction ends, and the OMP algorithm is used to reconstruct the signal to obtain the reconstructed signal.
[0010] The signal-to-noise ratio (SNR) of the reconstructed signal is obtained, and the parameters of the noise reduction method are optimized based on the trend of SNR variation.
[0011] The optimal reconstruction result is obtained based on the optimized denoising method.
[0012] Optionally, the process of normalizing the noisy signal to obtain a normalized signal includes:
[0013] The noisy signal is processed by signal vectorization, amplitude normalization and length standardization to obtain a normalized signal.
[0014] Optionally, the process of performing spectral analysis on the normalized signal includes:
[0015] The normalized signal is subjected to spectral analysis using Fast Fourier Transform to obtain frequency distribution characteristics; the energy contribution of each frequency point is calculated based on the frequency distribution characteristics to establish a frequency-energy mapping relationship; and spectral features are quantized based on the frequency-energy mapping relationship to provide a basis for adaptive sparsity estimation.
[0016] Optionally, the process of adaptive sparsity estimation includes:
[0017] Based on the Pareto principle, the cumulative distribution function of spectral energy is calculated; based on the inflection point characteristics of the cumulative distribution function of spectral energy, the energy coverage threshold is determined; based on the energy coverage threshold, the number of effective frequency points is determined, and the sparsity estimate is dynamically updated.
[0018] Optionally, the process of optimizing the sampling point configuration includes:
[0019] The energy of the determined number of effective frequency points is sorted, and several high-energy frequency points are selected as fixed sampling points, while the remaining frequency points are used as random sampling points.
[0020] Optionally, the iterative noise reduction process based on selected fixed and random sampling points includes:
[0021] When the number of iterations is even, a mixed sampling strategy is implemented by combining fixed sampling points and random sampling points; when the number of iterations is odd, a random sampling strategy is implemented.
[0022] Optionally, the process of signal reconstruction using the OMP algorithm includes:
[0023] An improved atom selection strategy is adopted to achieve an adaptive stopping criterion; soft threshold filtering is applied to achieve coefficient screening; the signal is reconstructed based on the screened coefficients, and momentum smoothing is performed on the reconstructed signal.
[0024] Optionally, the process of optimizing the parameters of the denoising method based on the trend of signal-to-noise ratio variation includes:
[0025] Based on the trend of signal-to-noise ratio change, the sparsity of the denoising method is dynamically adjusted and the number of samples is updated to obtain an optimized denoising method.
[0026] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.
[0027] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.
[0028] Compared with the prior art, the present invention has the following advantages and technical effects:
[0029] This invention overcomes many limitations of traditional noise reduction methods through signal processing technology, demonstrating broad technical advantages. First, for signals that cannot be repeatedly acquired, this invention breaks through the limitations of traditional multiple acquisition averaging methods, achieving efficient noise reduction with a single acquisition, solving key problems in scenarios such as clinical diagnosis and emergency event recording. Second, this invention excels in economics, avoiding the high costs associated with multiple acquisitions, making it particularly suitable for scenarios with expensive acquisition equipment or high acquisition costs, significantly reducing resource consumption and improving cost-effectiveness. Furthermore, this invention not only improves the signal-to-noise ratio but also preserves the detailed features of the signal, ensuring high fidelity and effectively solving the problem of signal detail loss in existing single acquisition methods. Simultaneously, this invention introduces an adaptive parameter control mechanism, reducing reliance on prior knowledge of signal and noise characteristics, simplifying the parameter adjustment process, and improving processing flexibility and adaptability. Finally, this invention possesses high computational efficiency, meeting the needs of real-time signal processing and rapid response.
[0030] In summary, this invention provides an efficient, economical, and widely applicable signal noise reduction solution, effectively addressing the shortcomings of existing methods in terms of applicability, economy, signal fidelity, and operational complexity, and has significant technical effects and application value. Attached Figure Description
[0031] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:
[0032] Figure 1 is a schematic diagram of the method flow according to an embodiment of the present invention;
[0033] Figure 2 is a comparison diagram of the effects of Example 1 of the present invention;
[0034] Figure 3 is a comparison diagram of the effects of Example 2 of the present invention;
[0035] Figure 4 is a comparison diagram of the effects of Example 3 of the present invention;
[0036] Figure 5 is a comparison diagram of the effects of Example 4 of the present invention;
[0037] Figure 6 is a comparison diagram of the effects of Example 5 of the present invention. Detailed Implementation
[0038] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.
[0039] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.
[0040] Example 1
[0041] As shown in Figure 1, this embodiment provides a method for signal superposition and noise reduction through a single acquisition, including the following steps:
[0042] Acquire noisy signals, and perform normalization processing on the noisy signals to obtain normalized signals;
[0043] The normalized signal is subjected to spectral analysis, adaptive sparsity estimation, and sampling point configuration optimization, selecting fixed sampling points and random sampling points;
[0044] Iterative noise reduction is performed based on selected fixed and random sampling points;
[0045] When the preset maximum number of iterations is reached, the noise reduction ends, and the OMP algorithm is used to reconstruct the signal to obtain the reconstructed signal.
[0046] The signal-to-noise ratio (SNR) of the reconstructed signal is obtained, and the parameters of the noise reduction method are optimized based on the trend of SNR variation.
[0047] The optimal reconstruction result is obtained based on the optimized denoising method.
[0048] Through the rigorous algorithm design described above, this solution achieves efficient noise reduction of noisy signals. The various stages are closely integrated, forming a complete closed-loop optimization system. This process not only ensures the stability and reliability of the algorithm but also provides clear implementation guidance for practical applications.
[0049] As an feasible approach, the noisy signal is normalized to obtain a normalized signal, establishing a unified data format and computational foundation for subsequent processing. The specific process includes:
[0050] Signal vectorization: Obtain the noisy signal and convert the input noisy signal into an N×1 column vector form to facilitate subsequent matrix operations;
[0051] Amplitude normalization: By scaling the amplitude, the signal range is normalized to the [-1,1] interval, which improves the stability of numerical calculation;
[0052] Length normalization: Calculate the signal length N and pad with zeros or truncate it as needed to ensure that the length is a power of 2, thereby optimizing the FFT calculation efficiency.
[0053] As an feasible approach, system parameter initialization specifically includes:
[0054] Iteration control parameters: set the maximum number of iterations to ensure that the algorithm converges within a finite number of steps;
[0055] Sampling strategy parameters: Set the initial sampling ratio to min(4K / N, 0.5), where K is the estimated sparsity;
[0056] Sparse representation parameters: The initial sparsity level is set based on empirical values and is subsequently adjusted through an adaptive mechanism.
[0057] As one feasible approach, the process of performing spectral analysis on the normalized signal includes:
[0058] FFT calculation: The Fast Fourier Transform is used to perform spectral analysis on the normalized signal to obtain frequency distribution characteristics;
[0059] Energy distribution analysis: Calculate the energy contribution at each frequency point and establish a frequency-energy mapping relationship;
[0060] Spectral feature quantization: Extracting characteristic parameters such as spectral concentration and bandwidth to provide a basis for parameter adaptation.
[0061] As an feasible approach, the process of adaptive sparsity estimation includes:
[0062] Cumulative energy calculation: Based on the Pareto principle, calculate the cumulative energy distribution function of the spectrum;
[0063] Threshold adaptation: Determine the energy coverage threshold based on the inflection point characteristics of the cumulative energy distribution function of the spectrum;
[0064] Actual sparsity determination: The number of effective frequency points is determined based on a threshold, and the sparsity estimate is dynamically updated.
[0065] As an feasible approach, the process of optimizing sampling point configuration includes:
[0066] Fixed sampling point selection:
[0067] Select the top-K high-energy frequency points based on energy sorting; ensure stable sampling of key frequency components; and establish a fixed sampling point index table.
[0068] Random sampling point strategy: Construct a sampling pool for remaining frequency points; implement a probability-based dynamic sampling mechanism; ensure sufficient coverage of the sampling space.
[0069] As an implementable approach, the iterative noise reduction process based on selected fixed and random sampling points includes:
[0070] During this stage, the system achieves signal reconstruction and noise suppression through multiple iterative optimizations:
[0071] (1) Adaptive sampling process:
[0072] Even-numbered iterations: Execute a hybrid sampling strategy; combine fixed and random sampling points; construct the complete sampling matrix;
[0073] Odd iteration rounds: Perform pure random sampling; update sampling positions; keep the number of samples constant;
[0074] (2) Improved signal reconstruction mechanism:
[0075] Optimized OMP algorithm implementation: An improved atomic selection strategy is adopted to implement an adaptive stopping criterion, thereby improving reconstruction accuracy and efficiency;
[0076] Reconstruction coefficient optimization: Apply soft threshold filtering to select coefficients and suppress the influence of noise;
[0077] Signal reconstruction process: The signal is reconstructed based on the filtered coefficients, and momentum smoothing is applied to maintain signal continuity.
[0078] (3) Parameter dynamic update mechanism:
[0079] Signal-to-noise ratio (SNR) evaluation and tracking: Calculate the signal-to-noise ratio (SNR) of the current reconstructed signal, record the SNR change trend, and evaluate the noise reduction effect;
[0080] Momentum parameter adjustment: Adjust the momentum factor based on SNR changes to balance convergence speed and stability;
[0081] Sampling parameter optimization: dynamically adjust sparsity K, update sampling quantity M, and optimize sampling strategy.
[0082] As an feasible approach, during the convergence control phase:
[0083] This stage employs a rigorous convergence judgment mechanism to ensure that the algorithm outputs the optimal result:
[0084] (1) SNR dynamic tracking:
[0085] Current SNR calculation: The sliding window method is used to update the SNR value in real time;
[0086] SNR Change Analysis: Record historical SNR data, analyze the trend of change, and evaluate the convergence.
[0087] (2) Termination condition determination:
[0088] SNR stability test: Calculate the rate of change of SNR in multiple consecutive iterations, set a stability threshold, and determine whether a stable state has been reached;
[0089] Iteration count control: Check if the maximum number of iterations has been reached to prevent excessive iterations and ensure the algorithm can terminate.
[0090] As an feasible approach, final stage completion results processing and performance evaluation can be performed during the output processing phase:
[0091] (1) Noise reduction result generation:
[0092] Optimal signal selection: Select the optimal reconstruction result based on SNR, apply post-processing optimization, and ensure the quality of the output signal;
[0093] Performance metrics recording: Record the degree of SNR improvement, save iteration process data, and generate performance reports;
[0094] (2) Comprehensive performance evaluation:
[0095] SNR Improvement Analysis: Calculate the overall SNR improvement and evaluate the noise reduction effect;
[0096] Signal correlation analysis: Calculate the correlation coefficient with the original signal to assess the degree of signal distortion;
[0097] Error statistical analysis: Calculate the mean square error, assess the reconstruction accuracy, and generate an error distribution report.
[0098] As an implementable approach, the basic principles of this implementation include:
[0099] Useful signals are typically sparsity:
[0100] In an appropriate transform domain (such as the Fourier domain or wavelet domain), the signal has a sparse representation:
[0101] x(t) = Ψα, where α is a sparse vector.
[0102] Non-sparseness of noise:
[0103] The noise n(t) is not sparsity in most transform domains and exhibits broad-spectrum characteristics.
[0104] Incoherence of random sampling:
[0105] Random sampling of noise results in reconstructed noise that is uncorrelated with the original noise; while for sparse signals, compressed sensing reconstruction can recover the original signal better.
[0106] Based on the mathematical theory of compressed sensing, this embodiment establishes the following mathematical model:
[0107] Basic signal model construction:
[0108] This embodiment first establishes a complete mathematical description of the characteristics of noisy signals. It is assumed that the observed signal x(t) can be expressed as: x(t) = s(t) + n(t),
[0109] Where: s(t) is the original signal to be reconstructed, which has K-sparseness under a specific orthogonal basis Ψ. This sparsity means that the signal has only K significant non-zero components in the transform domain, where K is much smaller than the signal length N. n(t) is additive noise, which does not have sparse characteristics under any orthogonal basis and exhibits broad-spectrum features.
[0110] Sparse representation and transformation:
[0111] Under the orthogonal basis Ψ, the signal can be expressed as s(t)=Ψα,
[0112] Where α is a K-sparse vector containing only K non-zero elements. Correspondingly, the noise under this basis is represented as:
[0113] n(t) = Ψβ, where β is not sparse.
[0114] Hybrid sampling strategy:
[0115] This embodiment proposes a novel hybrid sampling strategy that combines the advantages of deterministic sampling and random sampling.
[0116] The i-th sampling process can be represented as:
[0117] The i-th random sample can be represented as: y i =Φ i (s+n)=Φ i Ψα+Φ i Ψβ,
[0118] Where: Φ i Let be the sampling matrix for the i-th iteration. The construction of this sampling matrix employs an adaptive mechanism, dynamically adjusting the ratio of fixed to random sampling points based on signal characteristics. This hybrid strategy ensures stable acquisition of the main components of the signal while providing noise suppression capabilities through random sampling. Where Φ i It is the random sampling matrix of the i-th iteration.
[0119] Signal reconstruction and noise suppression:
[0120] Basic principles of signal reconstruction:
[0121] For each sampled data point, an improved Orthogonal Matching Pursuit (OMP) algorithm is used for signal reconstruction. Its mathematical model is expressed as: min α′ |α′|1subject to|y i -Φ i Ψα′|2≤ε,
[0122] Where: y i Φ represents the measurement value obtained from the i-th sampling. i Let Ψ be the measurement matrix of the i-th sampling, Ψ be the sparse representation basis of the signal, α' be the sparse coefficient vector to be solved, and ε be the upper bound of the allowed reconstruction error.
[0123] Reconstruction theory guarantees:
[0124] For a K-sparse signal s(t), according to compressed sensing theory, when the number of samples M satisfies:
[0125] When M≥CKlog(N / K), accurate reconstruction of signal components can be guaranteed;
[0126] Where: C is a constant related to reconstruction accuracy, N is the signal dimension, and K is the signal sparsity.
[0127] Noise handling mechanism:
[0128] For non-sparse noise, the noise estimate obtained in each reconstruction The original noise n has the following statistical properties:
[0129] The noise estimates between different reconstruction times are approximately uncorrelated, and this statistical property provides a theoretical basis for subsequent noise suppression.
[0130] Superposition effect and final reconstruction:
[0131] The final reconstructed signal is obtained by weighted averaging of the L reconstruction results:
[0132] Key theoretical properties include:
[0133] Signal components:
[0134] This indicates that the average value of multiple reconstructions will converge to the true signal;
[0135] Noise components:
[0136] It was demonstrated that noise can be effectively suppressed through multiple reconstructions, and the suppression effect is inversely proportional to the square root of the number of reconstructions L.
[0137] Adaptive parameter control mechanism:
[0138] System parameter adaptive adjustment strategy:
[0139] Adaptive sparsity: The K value is dynamically adjusted according to the signal spectrum characteristics. When the spectrum is highly concentrated, the K value is decreased; when the spectrum is dispersed, the K value is appropriately increased.
[0140] Adaptive sampling rate: The M value is dynamically adjusted based on the reconstruction quality. A target reconstruction error threshold is set, and the sampling rate is dynamically adjusted according to the actual reconstruction error.
[0141] Momentum parameter adaptation: The momentum factor is adjusted according to the degree of SNR improvement, and a mapping relationship between the SNR improvement and the momentum factor is established to ensure system stability while optimizing the convergence speed.
[0142] Closed-loop optimization mechanism:
[0143] The system achieves dynamic parameter optimization through the following feedback mechanism:
[0144] When the reconstruction quality improves: appropriately reduce the sparsity K and the number of samples M, and increase the momentum factor to accelerate convergence;
[0145] When reconstruction quality deteriorates: increase K and M to improve reconstruction accuracy, and decrease momentum factor to enhance stability;
[0146] This adaptive mechanism achieves a dynamic balance between computational efficiency and reconstruction quality.
[0147] As an implementable approach, the adaptive mechanism mainly involves three aspects:
[0148] Signal feature analysis:
[0149] Time-domain characteristics: signal variance, reflecting the degree of signal fluctuation; peak amplitude, reflecting signal strength; zero passthrough rate, reflecting the signal frequency characteristics;
[0150] Frequency domain characteristics: power spectral density distribution; spectral width (occupied bandwidth); number of main frequency components.
[0151] Parameters that need to be adapted:
[0152] Sparsity (K): Determines the number of basis functions used for reconstruction;
[0153] Sampling rate (ratio): determines the amount of data to be randomly sampled;
[0154] Number of iterations (M): determines the number of reconstructions;
[0155] Convergence threshold: determines the stopping condition of the iteration.
[0156] Adaptive rules:
[0157] Adaptive sparsity:
[0158] K = ceil(N * base_sparsity),
[0159] The base_sparsity is determined based on the spectral width: narrowband signal: 0.05; medium bandwidth: 0.1; wideband signal: 0.2.
[0160] Sampling rate adaptive:
[0161] ratio=base_ratio+α*spectral_width,
[0162] Where base_ratio = 0.3, α = 0.2 (adjustment coefficient), and the range is limited to [0.3, 0.7].
[0163] Iteration count adaptive:
[0164] M=base_iterations*(1+complexity_factor),
[0165] The complexity_factor is based on the signal variance and peak value ratio; for simple signals: 10th order, for medium complexity: 20th order, and for complex signals: 30th order.
[0166] As a specific example, the following illustrations are provided:
[0167] ECG signal:
[0168] Features: Narrow bandwidth, regular waveform;
[0169] Adaptive results:
[0170] Low sparsity (K≈0.05N);
[0171] A relatively low sampling rate (ratio≈0.3);
[0172] Fewer iterations (M≈10).
[0173] Earthquake signal:
[0174] Features: Broadband, irregular;
[0175] Adaptive results:
[0176] High sparsity (K≈0.2N);
[0177] A relatively high sampling rate (ratio≈0.6);
[0178] A relatively large number of iterations (M≈30).
[0179] Experimental verification:
[0180] Example 1: Verification of the algorithm's noise reduction effect in a purely noisy environment:
[0181] 1. Experimental Design and Parameter Configuration:
[0182] This embodiment aims to verify the algorithm's ability to process different types of pure noise. Three representative noise models were selected for the experiment:
[0183] Gaussian white noise: represents additive random noise;
[0184] Uniformly distributed noise: represents background noise;
[0185] Mixed noise: It is composed of the two types of noise mentioned above in a certain proportion and is used to simulate complex noise environments.
[0186] The key parameters for the experiment are configured as follows:
[0187] The random sampling rate is set to 0.5, which means that 50% of the original signal is sampled.
[0188] The algorithm iteration count was set to 20 to ensure a thorough optimization process.
[0189] The signal length was uniformly set to 1000 points to ensure the statistical significance of the experimental data.
[0190] 2. Analysis of experimental results:
[0191] The following key findings can be drawn from the comparative analysis of Figure 2:
[0192] (1) Time-domain waveform analysis (top left of Figure 2):
[0193] The blue line represents the original noisy signal, showing significant noise amplitude and a low signal-to-noise ratio.
[0194] The red line represents the signal after algorithm processing, where noise is significantly suppressed and the waveform is smoother;
[0195] The signal amplitude range converged from the original [-2,2] to [-0.5,0.5], indicating that the noise was effectively controlled.
[0196] (2) Power spectral density analysis (bottom left of Figure 2):
[0197] The power spectrum before processing (blue line) shows a high energy level across the entire frequency band;
[0198] The overall energy level of the processed power spectrum (red line) is reduced by approximately 10-15 dB;
[0199] The spectral shape maintained its original characteristics, indicating that the algorithm did not introduce significant frequency distortion.
[0200] (3) Comparison of energy distribution (top right of Figure 2):
[0201] The energy distribution of three noise types (Gaussian, uniform, and mixed) at different amplitudes is shown.
[0202] The algorithm exhibits stable suppression effects against different types of noise;
[0203] The energy ratio after processing remained at around 0.1, indicating that the noise was effectively attenuated.
[0204] (4) SNR progress curve (bottom right of Figure 2):
[0205] The horizontal axis represents the number of iterations (0-20 times), and the vertical axis represents the degree of SNR improvement (dB).
[0206] The SNR of all three noise types showed a significant upward trend;
[0207] It stabilized after about 10 iterations, and the final SNR improved by about 2.5-3dB;
[0208] The fast convergence speed indicates that the algorithm has good practicality.
[0209] 3. Summary of performance advantages:
[0210] This embodiment experimentally verifies that the algorithm has the following advantages when dealing with pure noise:
[0211] It has a significant suppression effect on various types of noise;
[0212] The energy decay is stable and exhibits consistent performance across different amplitudes.
[0213] It converges quickly, typically reaching a stable state in 10 iterations.
[0214] The basic characteristics of the signal were preserved during the processing, and no obvious distortion was introduced.
[0215] These experimental results fully demonstrate the applicability and effectiveness of the algorithm in a purely noisy environment, providing a reliable basis for its deployment in practical applications.
[0216] Example 2: Performance verification of the algorithm in simple signal denoising:
[0217] 1. Experimental Design and Parameter Configuration:
[0218] This embodiment includes a comprehensive experiment designed to verify the algorithm's ability to process noisy, simple signals. The specific experimental setup is as follows:
[0219] (1) Signal construction:
[0220] Original signal: A standard sine wave signal is selected as the reference signal, which has clear periodicity and frequency characteristics;
[0221] Noise synthesis: Three typical noises (Gaussian, uniform, and mixed noise) are superimposed to simulate real-world application scenarios;
[0222] Sampling design: A single-sampling method is adopted to ensure the continuity and integrity of the data.
[0223] (2) Key parameter configuration:
[0224] Random sampling rate: set to 0.5 to ensure that the sampled data can fully represent the original signal;
[0225] Number of iterations: fixed at 20, used to observe the convergence performance of the algorithm;
[0226] Signal length: 500 sampling points are used to cover multiple complete cycles.
[0227] 2. Analysis of experimental results:
[0228] The experimental results are fully presented and analyzed in Figure 3:
[0229] (1) Time-domain waveform comparison:
[0230] Blue line: Represents the original sinusoidal signal, showing standard periodic characteristics;
[0231] Red line: Represents the signal after noise is added, showing obvious random fluctuations;
[0232] Green line: Represents the signal after algorithm processing, which basically restores the periodic characteristics of the original signal;
[0233] Processing results: Noise is significantly suppressed while preserving the amplitude and phase information of the signal.
[0234] (2) Frequency domain feature analysis:
[0235] The spectral distribution of the signal in the range of 0-500Hz is displayed;
[0236] The original signal (blue line) has a significant energy concentration at the fundamental frequency;
[0237] The processed signal (red line) retains its main frequency components;
[0238] High-frequency noise is effectively suppressed, and the spectrum is clearer;
[0239] The energy distribution is concentrated in the effective frequency range, indicating that the algorithm has good frequency selectivity.
[0240] (3) SNR improvement curve:
[0241] The horizontal axis represents the number of iterations (0-20).
[0242] The vertical axis represents the degree of improvement in signal-to-noise ratio (range 7-8.5dB);
[0243] Curve characteristics:
[0244] Initial stage (0-2 times): SNR increases rapidly, by approximately 0.5 dB;
[0245] Mid-term stage (2-10 times): Continuous improvement, with the slope gradually slowing down;
[0246] Stable phase (10-20 times): The signal level tends to stabilize, and the final SNR improves by about 1.5dB.
[0247] Convergence characteristics:
[0248] The algorithm reaches a stable state after approximately 15 iterations.
[0249] The overall convergence process is smooth, without obvious oscillations;
[0250] The final SNR remained at around 8.5dB, indicating a significant noise reduction effect;
[0251] 3. Performance Advantage Analysis:
[0252] Through this embodiment, the algorithm demonstrates the following key advantages:
[0253] High signal fidelity: effectively preserves the periodic characteristics and amplitude information of the original signal;
[0254] Significant noise suppression: The time-domain waveform is smoother, and frequency-domain noise is effectively attenuated;
[0255] Good convergence performance: The iteration process is stable with no obvious oscillations;
[0256] High computational efficiency: Stable results can be achieved within 15 iterations;
[0257] Highly adaptable: It exhibits excellent processing capabilities for different types of superimposed noise.
[0258] These experimental results fully verify the effectiveness and stability of the algorithm in processing noisy, simple signals, providing a reliable experimental basis for its promotion in practical engineering applications. Furthermore, the analysis of various aspects of the experimental results provides important references for further optimization of the algorithm's performance.
[0259] Example 3: Application verification of the algorithm in ECG signal denoising:
[0260] 1. Experimental Design and Parameter Configuration:
[0261] This embodiment verifies the algorithm's performance in electrocardiogram (ECG) signal processing within a real-world medical scenario. The experimental design fully considers the unique characteristics of ECG signals:
[0262] (1) Data acquisition scheme:
[0263] Signal source: Clinical electrocardiogram data were used to ensure the authenticity and practicality of the experiment;
[0264] Data collection method: Multiple data collections cannot be performed, which meets the limitations of actual medical scenarios;
[0265] Data characteristics: Includes complete ECG characteristic waveforms (P wave, QRS complex, T wave);
[0266] (2) Experimental parameter settings:
[0267] Hybrid sampling strategy:
[0268] Random sampling rate: 0.5, to ensure basic acquisition of signal characteristics;
[0269] Fixed sampling rate: 0.5, to ensure stable acquisition of key feature points;
[0270] Algorithm iterations: set to 20 times to balance processing efficiency and computational cost;
[0271] Evaluation metrics: Focus on the degree of SNR improvement and the preservation of QRS group morphology;
[0272] 2. Analysis of experimental results:
[0273] A comprehensive analysis of the experimental results is presented in Figure 4:
[0274] (1) Time-domain waveform analysis (above figure):
[0275] Original signal (blue line):
[0276] Displays typical ECG waveform characteristics;
[0277] QRS groups are clearly identifiable;
[0278] The baseline fluctuates to some extent;
[0279] Noisy signal (red line):
[0280] Random noise interference was superimposed;
[0281] The signal details are contaminated by noise;
[0282] Processed signal (black line):
[0283] The QRS group morphology was well preserved;
[0284] Baseline drift was effectively suppressed;
[0285] The morphological characteristics of P waves and T waves are more clearly defined.
[0286] (2) Power spectral density analysis (Chinese figure):
[0287] Frequency range: 0-150Hz, covering the main frequency components of ECG signals;
[0288] Original signal spectrum (black line):
[0289] Low-frequency energy is concentrated;
[0290] High-frequency energy decays rapidly;
[0291] Noisy signal spectrum (blue line):
[0292] High-frequency noise is obvious;
[0293] Energy distribution is more dispersed;
[0294] Processed signal spectrum (red line):
[0295] It retains the effective components in the low-frequency range;
[0296] High-frequency noise is significantly suppressed;
[0297] The spectral shape is closer to the original signal.
[0298] (3) SNR improvement curve (see figure below):
[0299] Iterative process analysis:
[0300] Initial phase (0-4 times): SNR improves rapidly, from 6dB to 10dB;
[0301] Mid-term stage (4-12 times): Continued improvement, but the rate of improvement slows down;
[0302] Stable phase (12-20 iterations): asymptotic convergence, with the final SNR improvement reaching 14dB;
[0303] Convergence characteristics:
[0304] Overall, it shows a smooth upward trend;
[0305] No obvious fluctuations or oscillations;
[0306] It reaches a stable state after about 15 iterations.
[0307] 3. Summary of performance advantages:
[0308] This embodiment verifies that the algorithm has the following significant advantages in electrocardiogram signal processing:
[0309] Signal feature preservation:
[0310] The shape of the QRS group was accurately preserved;
[0311] The detailed features of the P wave and T wave are clearly distinguishable;
[0312] Baseline drift was effectively suppressed;
[0313] Noise suppression effect:
[0314] The overall SNR improvement is approximately 14 dB;
[0315] High-frequency noise is significantly attenuated;
[0316] It preserves the main frequency components of the signal;
[0317] Algorithm stability:
[0318] The convergence process was smooth;
[0319] No over-filtering phenomenon;
[0320] It has high computational efficiency.
[0321] These experimental results demonstrate that the algorithm can effectively process electrocardiogram (ECG) signals in real-world medical scenarios, achieving significant noise reduction while preserving key diagnostic features. This is of great significance for improving the diagnostic value of ECG signals and provides reliable technical support for the practical application of the algorithm in the medical field.
[0322] Example 4: Application verification of the algorithm in seismic waveform processing:
[0323] 1. Experimental Design and Parameter Configuration:
[0324] This embodiment is specifically designed to meet the unique requirements of seismic waveform data processing, and verifies the algorithm's performance in processing transient, non-periodic seismic signals:
[0325] (1) Data acquisition scheme:
[0326] Signal source: Actual seismic record data is used to ensure the practical significance of the experiment;
[0327] Data acquisition characteristics: Data acquired in a single instance, consistent with the sudden nature of seismic signals;
[0328] Signal characteristics: Contains complete waveform information of seismic waves, including key phases such as P-waves and S-waves;
[0329] (2) Optimization of experimental parameters:
[0330] Hybrid sampling strategy configuration:
[0331] Random sampling rate: 0.4, adapting to the non-stationary characteristics of seismic signals;
[0332] Fixed sampling rate: 0.6, to ensure stable acquisition of key seismic phases;
[0333] Number of iterations: Set to 20 to ensure the algorithm fully converges;
[0334] Evaluation focus: Pay attention to the degree of SNR improvement and the preservation of seismic wave phase information;
[0335] 2. Analysis of experimental results:
[0336] A detailed analysis can be conducted using Figure 5:
[0337] (1) Time-domain waveform analysis (above figure):
[0338] Original signal characteristics (black line):
[0339] It displays typical seismic waveform characteristics;
[0340] Includes arrival time information for multiple seismic phases;
[0341] The amplitude varies between [-0.5, 1.0].
[0342] Noisy signal representation (red line):
[0343] The background noise is obvious;
[0344] Seismic phase information was partially obscured;
[0345] Post-processing result (blue line):
[0346] The main seismic phases were clearly preserved;
[0347] Background noise is significantly reduced;
[0348] Signal continuity is well maintained;
[0349] (2) Power spectral density analysis (Chinese figure):
[0350] Frequency range coverage: 0-500Hz
[0351] Original signal spectrum (black line):
[0352] Low-frequency energy is concentrated;
[0353] High-frequency bands exhibit rapid attenuation characteristics;
[0354] Processed signal spectrum (blue line):
[0355] Main frequency components were preserved;
[0356] High-frequency noise is effectively suppressed;
[0357] The overall shape of the spectrum is close to that of the original signal;
[0358] It exhibits better noise suppression in the 250-500Hz range.
[0359] (3) SNR improvement curve (see figure below):
[0360] Iterative process analysis:
[0361] Initial phase (0-4 times): SNR improves rapidly, from 10dB to 12dB;
[0362] Mid-term stage (4-10 times): Continued improvement, but the rate of improvement gradually slows down;
[0363] Stable phase (10-20 times): The signal level tends to stabilize, and the final SNR improvement reaches 13dB;
[0364] Convergence characteristics:
[0365] The overall convergence process is smooth;
[0366] It reaches a stable state after about 12 iterations;
[0367] There was no obvious oscillation or instability.
[0368] 3. Summary of performance advantages:
[0369] This embodiment verifies that the algorithm has the following significant advantages in seismic waveform processing:
[0370] Signal feature preservation:
[0371] The main phase information of the seismic waves is fully preserved;
[0372] Waveform details are clearly discernible;
[0373] Phase information is accurately preserved;
[0374] Noise suppression effect:
[0375] The SNR was significantly improved, from 10dB to 23dB;
[0376] Background noise is effectively suppressed;
[0377] Algorithm stability:
[0378] The convergence process is smooth and controllable;
[0379] It has high computational efficiency;
[0380] The processing results are stable and reliable.
[0381] These experimental results fully demonstrate the superior performance of the algorithm in processing seismic waveform data. It not only effectively extracts seismic wave information from landslide curves but also preserves key signal characteristics. This has significant practical implications for the accurate analysis and interpretation of seismic data and provides reliable technical support for the widespread application of the algorithm in seismological research and engineering.
[0382] The success of this embodiment also demonstrates the algorithm's powerful ability to process non-stationary signals, laying the foundation for its application in a wider range of geophysical signal processing fields.
[0383] Example 5: Application verification of the algorithm in vibration signal processing of industrial equipment:
[0384] 1. Experimental Design and Parameter Configuration:
[0385] This embodiment focuses on an industrial equipment fault diagnosis scenario to verify the algorithm's performance in processing vibration signals:
[0386] (1) Data acquisition scheme:
[0387] Signal source: Fault diagnosis data from actual industrial equipment;
[0388] Signal characteristics: Includes typical vibration features of the equipment's operating status;
[0389] Data acquisition method: Real-time data is acquired using a standard vibration sensor;
[0390] (2) Experimental parameter settings:
[0391] Sampling strategy:
[0392] Random sampling rate: set to 0.6 to ensure sufficient acquisition of vibration characteristics;
[0393] Sampling duration: 1 second, covering multiple vibration cycles;
[0394] Algorithm iteration: Set 20 iterations to ensure convergence of processing results;
[0395] Evaluation metrics: Focus on maintaining the characteristic frequency of vibration and suppressing noise levels;
[0396] 2. Analysis of experimental results:
[0397] A detailed analysis is conducted using the three dimensions shown in Figure 6:
[0398] (1) Time-domain waveform analysis (above figure):
[0399] Original signal (black line):
[0400] It exhibits obvious periodic vibration characteristics;
[0401] The amplitude ranges between [-2, 2].
[0402] Includes complete vibration period information;
[0403] Noisy signal (red line):
[0404] Random noise interference was superimposed;
[0405] It has basically maintained its periodic characteristics;
[0406] Details are affected by noise;
[0407] Processed signal (blue line):
[0408] The periodicity of vibration is more clearly defined;
[0409] The waveform profile is smoother;
[0410] The amplitude range of the original signal was maintained.
[0411] (2) Power spectral density analysis (Chinese figure):
[0412] Frequency range: 0-500Hz, covering the main vibration frequencies;
[0413] Original signal spectrum (black line):
[0414] It exhibits distinct characteristic frequencies in the low-frequency range;
[0415] High-frequency bands have lower energy.
[0416] Processed signal spectrum (blue line):
[0417] It retains the main characteristic frequency components;
[0418] High-frequency noise is significantly suppressed;
[0419] The characteristic frequencies below 50Hz are even more prominent;
[0420] The spectral peaks are clearer, making it easier to identify fault characteristics;
[0421] (3) SNR improvement curve (see figure below):
[0422] Iterative process analysis:
[0423] Initial phase (0-4 times): SNR improves rapidly, from 9dB to 11dB;
[0424] Mid-term stage (4-10 times): Continuous improvement, but the rate of improvement slows down;
[0425] Stable phase (10-20 times): The signal level tends to stabilize, and the final SNR reaches 12dB;
[0426] Convergence characteristics:
[0427] It exhibits a smooth convergence process;
[0428] It reaches a stable state after about 12 iterations;
[0429] There was no obvious fluctuation.
[0430] 3. Summary of performance advantages:
[0431] This embodiment verifies that the algorithm has the following advantages in industrial vibration signal processing:
[0432] Feature preservation capability:
[0433] It accurately maintained the periodic characteristics of the vibration;
[0434] The characteristic frequency components are clearly identifiable;
[0435] Waveform details are well preserved;
[0436] Noise reduction effect:
[0437] Noise levels were significantly reduced;
[0438] SNR improvement reached 12dB;
[0439] High-frequency interference was effectively suppressed;
[0440] Processing stability:
[0441] The convergence process was smooth;
[0442] High computational efficiency;
[0443] The results show good reliability.
[0444] These experimental results demonstrate that the algorithm can effectively process vibration signals from industrial equipment, preserving the key characteristics required for fault diagnosis while achieving significant noise reduction. This is of great significance for improving the accuracy and reliability of equipment fault diagnosis and provides strong technical support for the practical application of the algorithm in the industrial field.
[0445] The successful verification of this embodiment further demonstrates the superior performance of the algorithm in processing periodic signals, laying a solid foundation for its widespread application in fields such as industrial equipment condition monitoring and fault diagnosis.
[0446] Example 2
[0447] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.
[0448] Example 3
[0449] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.
[0450] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for signal superposition and noise reduction based on a single acquisition, characterized in that, Includes the following steps: A noisy signal is acquired in a single acquisition, and the noisy signal is normalized to obtain a normalized signal; The normalized signal is subjected to spectral analysis, adaptive sparsity estimation, and sampling point configuration optimization, selecting fixed sampling points and random sampling points; Iterative noise reduction is performed based on selected fixed and random sampling points; When the preset maximum number of iterations is reached, the noise reduction ends, and the OMP algorithm is used to reconstruct the signal to obtain the reconstructed signal. The signal-to-noise ratio (SNR) of the reconstructed signal is obtained, and the parameters of the denoising method are optimized based on the trend of SNR variation; parameter optimization includes resetting the maximum number of iterations. The optimal reconstruction result is obtained based on the optimized denoising method.
2. The method according to claim 1, characterized in that, The process of normalizing the noisy signal to obtain a normalized signal includes: The noisy signal is processed by signal vectorization, amplitude normalization and length standardization to obtain a normalized signal.
3. The method according to claim 1, characterized in that, The process of performing spectral analysis on the normalized signal includes: The normalized signal is subjected to spectral analysis using Fast Fourier Transform to obtain frequency distribution characteristics; the energy contribution of each frequency point is calculated based on the frequency distribution characteristics to establish a frequency-energy mapping relationship; and spectral features are quantized based on the frequency-energy mapping relationship to provide a basis for adaptive sparsity estimation.
4. The method according to claim 3, characterized in that, The process of adaptive sparsity estimation includes: Based on the Pareto principle, the cumulative distribution function of spectral energy is calculated; based on the inflection point characteristics of the cumulative distribution function of spectral energy, the energy coverage threshold is determined; based on the energy coverage threshold, the number of effective frequency points is determined, and the sparsity estimate is dynamically updated.
5. The method according to claim 4, characterized in that, The process of optimizing sampling point configuration includes: The energy of the determined number of effective frequency points is sorted, and several high-energy frequency points are selected as fixed sampling points, while the remaining frequency points are used as random sampling points.
6. The method according to claim 1, characterized in that, The iterative noise reduction process based on selected fixed and random sampling points includes: When the number of iterations is even, a mixed sampling strategy is implemented by combining fixed sampling points and random sampling points; when the number of iterations is odd, a random sampling strategy is implemented.
7. The method according to claim 1, characterized in that, The process of signal reconstruction using the OMP algorithm includes: An improved atom selection strategy is adopted to achieve an adaptive stopping criterion; soft threshold filtering is applied to achieve coefficient screening; the signal is reconstructed based on the screened coefficients, and momentum smoothing is performed on the reconstructed signal.
8. The method according to claim 1, characterized in that, The process of optimizing the parameters of the noise reduction method based on the trend of signal-to-noise ratio changes includes: Based on the trend of signal-to-noise ratio change, the sparsity of the denoising method is dynamically adjusted and the number of samples is updated to obtain an optimized denoising method.
9. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-8.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-8.