Method for realizing signal superposition noise reduction through single acquisition

Abstract

The invention discloses a method for realizing signal superposition noise reduction through single acquisition, which comprises the following steps of: acquiring a noisy signal, and carrying out normalized processing on the noisy signal to obtain a normalized signal; performing spectral analysis, adaptive sparseness estimation and sampling point configuration optimization on the normalized signal, and selecting a fixed sampling point and a random sampling point; iterative noise reduction is carried out based on the selected fixed sampling points and random sampling points; when a preset maximum number of iterations is reached, noise reduction is ended, and an OMP algorithm is adopted to carry out signal reconstruction to obtain a reconstructed signal; obtaining the signal-to-noise ratio of the reconstructed signal, and optimizing the parameters of the noise reduction method based on the change trend of the signal-to-noise ratio; and obtaining an optimal reconstruction result based on the optimized noise reduction method. The method effectively overcomes the defects of an existing method in the aspects of applicability, economy, signal fidelity, operation complexity and the like, and has remarkable technical effects and application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a method for realizing signal superposition and noise reduction by single acquisition. Background Art

[0002] Existing signal noise reduction methods include: (1) the multiple acquisition averaging method, which repeatedly acquires the same signal multiple times and takes the average. Although this method can effectively suppress random noise, it requires that the signal must be repeatedly acquirable and has a high cost; (2) the time-frequency domain filtering method: filtering based on the difference in the time-frequency characteristics of the signal and noise. Although this method is simple to implement and has a small computational amount, it is difficult to maintain the signal details and has a poor effect on overlapping spectrum noise; (3) adaptive filtering: dynamically adjusting the filter parameters according to the statistical characteristics of the signal. Although this method can adaptively track the signal changes, it requires more prior knowledge and the parameter adjustment is complex.

[0003] In view of the above problems in the prior art, for signals such as seismic waves and electrocardiogram signals that are difficult to repeatedly acquire, there is an urgent need to propose a method for realizing signal superposition and noise reduction by single acquisition. Summary of the Invention

[0004] To solve the above technical problems, the present invention proposes a method for realizing signal superposition and noise reduction by single acquisition to solve the problems existing in the above prior art.

[0005] To achieve the above object, the present invention provides a method for realizing signal superposition and noise reduction by single acquisition, including the following steps:

[0006] Acquire a noisy signal, perform normalization processing on the noisy signal to obtain a normalized signal;

[0007] Perform spectrum analysis, adaptive sparsity estimation and sampling point configuration optimization on the normalized signal, and select fixed sampling points and random sampling points;

[0008] Perform iterative noise reduction based on the selected fixed sampling points and random sampling points;

[0009] When the preset maximum number of iterations is reached, the noise reduction ends, and the OMP algorithm is used for signal reconstruction to obtain a reconstructed signal;

[0010] Obtain the signal-to-noise ratio of the reconstructed signal, and optimize the parameters of the noise reduction method based on the change trend of the signal-to-noise ratio;

[0011] Based on the optimized noise reduction method, obtain the optimal reconstruction result.

[0012] Optionally, the process of performing normalization processing on the noisy signal to obtain a normalized signal includes:

[0013] Process the noisy signal through signal vectorization, amplitude normalization, and length standardization to obtain a normalized signal.

[0014] Optionally, the process of performing spectrum analysis on the normalized signal includes:

[0015] Perform spectrum analysis on the normalized signal using the fast Fourier transform to obtain frequency distribution characteristics; calculate the energy contribution of each frequency point based on the frequency distribution characteristics, and establish a frequency-energy mapping relationship; perform spectrum feature quantization based on the frequency-energy mapping relationship to provide a basis for adaptive sparsity estimation.

[0016] Optionally, the process of performing adaptive sparsity estimation includes:

[0017] Based on the Pareto principle, calculate the cumulative distribution function of spectrum energy; determine the energy coverage threshold based on the inflection point characteristics of the cumulative distribution function of spectrum energy; determine the number of effective frequency points based on the energy coverage threshold, and dynamically update the sparsity estimation value.

[0018] Optionally, the process of performing sampling point configuration optimization includes:

[0019] Perform energy sorting on the determined number of effective frequency points, select several high-energy frequency points as fixed sampling points, and the remaining frequency points as random sampling points.

[0020] Optionally, the process of performing iterative noise reduction based on the selected fixed sampling points and random sampling points includes:

[0021] When the number of iterations is even, combine the fixed sampling points and random sampling points and execute the hybrid sampling strategy; when the number of iterations is odd, execute the random sampling strategy.

[0022] Optionally, the process of performing signal reconstruction using the OMP algorithm includes:

[0023] Adopt an improved atom selection strategy to implement an adaptive stopping criterion; apply soft threshold filtering to implement coefficient screening; reconstruct the signal based on the screened coefficients, and perform momentum smoothing processing on the reconstructed signal.

[0024] Optionally, the process of optimizing the parameters of the noise reduction method based on the change trend of the signal-to-noise ratio includes:

[0025] Based on the change trend of the signal-to-noise ratio, dynamically adjust the sparsity of the noise reduction method, update the sampling quantity, and thus obtain an optimized noise reduction method.

[0026] The present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory, and the processor executes the computer program to implement the steps of the method.

[0027] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method are implemented.

[0028] Compared with the prior art, the present invention has the following advantages and technical effects:

[0029] Through signal processing technology, the present invention overcomes many limitations of traditional noise reduction methods and demonstrates extensive technical advantages. First, for signals that cannot be repeatedly collected, the present invention breaks through the limitation of the traditional multiple collection averaging method and can achieve efficient noise reduction through single collection, solving key problems in scenarios such as clinical diagnosis and emergency event recording. Second, the present invention performs well in terms of economy, avoiding the high costs brought by multiple collections, especially suitable for scenarios where the collection equipment is expensive or the collection cost is high, significantly reducing resource consumption and enhancing economy. In addition, the present invention not only improves the signal-to-noise ratio but also retains the detailed features of the signal, ensuring high fidelity and effectively solving the problem of signal detail loss in existing single collection methods. At the same time, the present invention introduces an adaptive parameter control mechanism, reducing the dependence on prior knowledge of signal and noise characteristics, simplifying the parameter adjustment process, and improving the flexibility and adaptability of processing. Finally, the present invention has high computational efficiency and can meet the requirements of real-time signal processing and rapid response.

[0030] In summary, the present invention provides an efficient, economical, and widely applicable signal noise reduction solution, effectively solving the deficiencies of existing methods in terms of applicability, economy, signal fidelity, and operation complexity, and having significant technical effects and application values. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0032] Figure 1 is a schematic flowchart of the method according to an embodiment of the present invention;

[0033] Figure 2 is a comparison diagram of the effects of Example 1 according to an embodiment of the present invention;

[0034] Figure 3 is a comparison diagram of the effects of Example 2 according to an embodiment of the present invention;

[0035] Figure 4 is a comparison diagram of the effects of Example 3 according to an embodiment of the present invention;

[0036] Figure 5 is a comparison diagram of the effects of Example 4 according to an embodiment of the present invention;

[0037] Figure 6 This is the comparison diagram of the effect of Example 5 of the embodiment of the present invention. Specific Embodiments

[0038] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The present application will be described in detail below with reference to the drawings and in conjunction with the embodiments.

[0039] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0040] Embodiment 1

[0041] As Figure 1 shown, in this embodiment, a method for realizing signal superposition and noise reduction by single acquisition is provided, including the following steps:

[0042] Collect the noisy signal, perform normalization processing on the noisy signal to obtain a normalized signal;

[0043] Perform spectrum analysis, adaptive sparsity estimation, and sampling point configuration optimization on the normalized signal, and select fixed sampling points and random sampling points;

[0044] Perform iterative noise reduction based on the selected fixed sampling points and random sampling points;

[0045] When the preset maximum number of iterations is reached, the noise reduction ends, and the OMP algorithm is used for signal reconstruction to obtain a reconstructed signal;

[0046] Obtain the signal-to-noise ratio of the reconstructed signal, and optimize the parameters of the noise reduction method based on the change trend of the signal-to-noise ratio;

[0047] Based on the optimized noise reduction method, obtain the optimal reconstruction result.

[0048] Through the above rigorous algorithm flow design, this solution realizes the efficient noise reduction processing of the noisy signal. Each stage is closely connected, 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 implementable method, performing normalization processing on the noisy signal to obtain a normalized signal, which establishes a unified data format and calculation basis for subsequent processing. The specific process includes:

[0050] Signal vectorization: Obtain the noisy signal, and convert the input noisy signal into a column vector form of N×1, which is convenient for subsequent matrix operations;

[0051] Amplitude normalization: Standardize the signal range to the interval [-1, 1] through amplitude scaling to improve the stability of numerical calculations;

[0052] Length normalization: Calculate the signal length N, and perform zero-padding or truncation processing as needed to ensure that the length meets the power of 2, optimizing the FFT calculation efficiency.

[0053] As an implementable method, initialize the system parameters, specifically including:

[0054] Iterative control parameter: Set the maximum number of iterations (maximum of iteration) to ensure the convergence of the algorithm within a finite number of steps;

[0055] Sampling strategy parameter: Set the initial sampling ratio sampling ratio to min(4K / N, 0.5), where K is the estimated sparsity;

[0056] Sparse representation parameter: The initial sparsity level is set based on empirical values and adjusted through an adaptive mechanism later.

[0057] As an implementable method, the process of performing spectral analysis on the normalized signal includes:

[0058] FFT calculation: Perform spectral analysis on the normalized signal using the fast Fourier transform to obtain the frequency distribution characteristics;

[0059] Energy distribution analysis: Calculate the energy contribution of each frequency point and establish a frequency-energy mapping relationship;

[0060] Spectrum feature quantization: Extract feature parameters such as spectral concentration and bandwidth to provide a basis for parameter adaptation.

[0061] As an implementable method, the process of performing adaptive sparsity estimation includes:

[0062] Cumulative energy calculation: Calculate the cumulative distribution function of spectral energy based on the Pareto principle;

[0063] Threshold adaptation: Determine the energy coverage threshold according to the inflection point characteristics of the cumulative distribution function of spectral energy;

[0064] Actual sparsity determination: Determine the number of effective frequency points based on the threshold and dynamically update the sparsity estimate value.

[0065] As an implementable method, the process of performing sampling point configuration optimization 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; establish a fixed sampling point index table.

[0068] Random sampling point strategy: construct a sampling pool for the remaining frequency points; implement a probability-based dynamic sampling mechanism; ensure full coverage of the sampling space.

[0069] As an implementable approach, the process of iterative noise reduction based on the selected fixed sampling points and random sampling points includes:

[0070] In this stage, the system realizes signal reconstruction and noise suppression through multiple iterative optimizations:

[0071] (1) Adaptive sampling process:

[0072] Even iteration rounds: execute a hybrid sampling strategy; combine fixed sampling points and random sampling points; construct a complete sampling matrix;

[0073] Odd iteration rounds: implement pure random sampling; update the sampling positions; keep the sampling quantity unchanged;

[0074] (2) Improved signal reconstruction mechanism:

[0075] Implementation of the optimized OMP algorithm: adopt an improved atom selection strategy, implement an adaptive stopping criterion, and improve the reconstruction accuracy and efficiency;

[0076] Optimization of reconstruction coefficients: apply soft threshold filtering to implement coefficient screening and suppress the influence of noise;

[0077] Signal reconstruction process: reconstruct the signal based on the screened coefficients, and apply momentum smoothing to maintain signal continuity.

[0078] (3) Parameter dynamic update mechanism:

[0079] Signal-to-noise ratio (SNR) evaluation and tracking: calculate the SNR of the current reconstructed signal, record the changing trend of SNR, and evaluate the noise reduction effect;

[0080] Adjustment of momentum parameter: adjust the momentum factor based on the change of SNR to balance the convergence speed and stability;

[0081] Optimization of sampling parameters: dynamically adjust the sparsity K, update the sampling quantity M, and optimize the sampling strategy.

[0082] As an implementable approach, in the convergence control stage:

[0083] This stage ensures the optimal output of the algorithm through a rigorous convergence judgment mechanism:

[0084] (1) SNR dynamic tracking:

[0085] Current SNR calculation: Adopt a sliding window method to update the SNR value in real time;

[0086] SNR variation analysis: Record historical SNR data, analyze the variation trend, and evaluate the convergence situation;

[0087] (2) Termination condition judgment:

[0088] SNR stability test: Calculate the SNR change rate for consecutive multiple iterations, set a stability threshold, and judge whether the stable state is reached;

[0089] Iteration count control: Check whether the maximum iteration count is reached, prevent over-iteration, and ensure the terminability of the algorithm.

[0090] As an implementable method, in the output processing stage, final stage result collation and performance evaluation are carried out:

[0091] (1) Denoising result generation:

[0092] Optimal signal selection: Select the optimal reconstruction result based on SNR, and apply post-processing optimization to ensure the output signal quality;

[0093] Performance metric recording: Record the degree of SNR improvement, save the iteration process data, and generate a performance report;

[0094] (2) Comprehensive performance evaluation:

[0095] SNR improvement analysis: Calculate the overall SNR improvement and evaluate the denoising effect;

[0096] Signal correlation analysis: Calculate the correlation coefficient with the original signal and evaluate the signal distortion degree;

[0097] Error statistical analysis: Calculate the mean square error, evaluate the reconstruction accuracy, and generate an error distribution report.

[0098] As an implementable method, the basic principle of this implementation includes:

[0099] Useful signals usually have sparsity:

[0100] In an appropriate transform domain (such as the Fourier domain, wavelet domain), the signal has a sparse representation:

[0101] x(t) = Ψα, where α is a sparse vector.

[0102] Non-sparsity of noise:

[0103] Noise n(t) does not have sparsity in most transform domains and shows a broad-spectrum characteristic.

[0104] Incoherence of random sampling:

[0105] Random sampling is performed on the noise, and the reconstructed noise is uncorrelated with the original noise; for a sparse signal, compressive sensing reconstruction can better recover the original signal.

[0106] Regarding the mathematical theory of compressive sensing, the following mathematical model is established in this embodiment:

[0107] Construction of the basic signal model:

[0108] In this embodiment, a complete mathematical description is first established for the characteristics of the noisy signal. It is assumed that the observed signal x(t) can be expressed as:

[0109] x(t) = s(t) + n(t),

[0110] where: s(t) is the original signal to be reconstructed, and this signal has K-sparsity in a specific orthogonal basis Ψ. This sparsity means that the signal has only K significant non-zero components in the transform domain, and K is much smaller than the signal length N. n(t) is additive noise, and this noise does not have sparse characteristics in any orthogonal basis and shows a broad-spectrum feature.

[0111] Sparse representation and transformation:

[0112] In the orthogonal basis Ψ, the signal can be expressed as

[0113] s(t) = Ψα,

[0114] where α is a K-sparse vector containing only K non-zero elements. Correspondingly, the representation of the noise in this basis is:

[0115] n(t) = Ψβ, where β is not sparse.

[0116] Hybrid sampling strategy:

[0117] This embodiment proposes a new type of hybrid sampling strategy that combines the advantages of deterministic sampling and random sampling.

[0118] The i-th sampling process can be expressed as:

[0119] The i-th random sampling can be expressed as:

[0120] y i = Φ i (s + n) = Φ i Ψα + Φ i Ψβ,

[0121] where: Φ iis the sampling matrix for the i-th time. The construction of the sampling matrix adopts an adaptive mechanism, dynamically adjusting the ratio of fixed sampling points and random sampling points according to the signal characteristics. This hybrid strategy ensures the stable acquisition of the main components of the signal, and at the same time provides noise suppression ability through random sampling, where Φ i is the random sampling matrix for the i-th time.

[0122] Signal reconstruction and noise suppression:

[0123] Basic principle of signal reconstruction:

[0124] For each sampling sample, an improved orthogonal matching pursuit (OMP) algorithm is used for signal reconstruction. Its mathematical model is expressed as:

[0125]

[0126] where: y i represents the measurement value obtained from the i-th sampling, Φ i is the measurement matrix for the i-th sampling, Ψ is the sparse representation basis of the signal, α' is the sparse coefficient vector to be solved, and ε is the upper bound of the allowable reconstruction error.

[0127] Reconstruction theory guarantee:

[0128] For a K-sparse signal s(t), according to the compressive sensing theory, when the number of samplings M satisfies:

[0129] M≥CKlog(N / K), the accurate reconstruction of the signal components can be guaranteed;

[0130] where: C is a constant related to the reconstruction accuracy, N is the signal dimension, and K is the signal sparsity.

[0131] Noise processing mechanism:

[0132] For non-sparse noise, the noise estimate obtained from each reconstruction has the following statistical characteristics with the original noise n:

[0133]

[0134] The noise estimates between different reconstruction times are approximately uncorrelated, and this statistical characteristic provides a theoretical basis for subsequent noise suppression.

[0135] Superposition effect and final reconstruction:

[0136] The final reconstructed signal is obtained by the weighted average of L reconstruction results:

[0137]

[0138] Among them, the important theoretical properties include:

[0139] Signal component:

[0140] It shows that the average value of multiple reconstructions will converge to the true signal;

[0141] Noise component:

[0142] It is proved that the 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.

[0143] Adaptive parameter control mechanism:

[0144] System parameter adaptive adjustment strategy:

[0145] Adaptive sparsity: Dynamically adjust the value of K according to the signal spectrum characteristics. When the spectrum concentration is high, decrease the value of K; when the spectrum is dispersed, appropriately increase the value of K;

[0146] Sampling rate adaptation: Dynamically adjust the value of M based on the reconstruction quality. Set the target reconstruction error threshold and dynamically adjust the sampling rate according to the actual reconstruction error;

[0147] Momentum parameter adaptation: Adjust the momentum factor according to the improvement degree of SNR, establish the mapping relationship between the improvement amount of SNR and the momentum factor, and optimize the convergence speed while ensuring the system stability.

[0148] Closed-loop optimization mechanism:

[0149] The system realizes the dynamic optimization of parameters through the following feedback mechanism:

[0150] When the reconstruction quality improves: Appropriately decrease the sparsity K and the number of samples M, and increase the momentum factor to accelerate the convergence;

[0151] When the reconstruction quality deteriorates: Increase K and M to improve the reconstruction accuracy, and decrease the momentum factor to enhance the stability;

[0152] Through this adaptive mechanism, a dynamic balance is achieved between the computational efficiency and the reconstruction quality.

[0153] As an implementable method, the adaptive mechanism mainly involves three aspects:

[0154] Signal feature analysis:

[0155] Time-domain features: Signal variance, reflecting the signal fluctuation degree; peak amplitude, reflecting the signal intensity; zero-crossing rate, reflecting the signal frequency characteristics;

[0156] Frequency-domain features: Power spectral density distribution; spectral width (occupied bandwidth); number of main frequency components.

[0157] Parameters to be adapted:

[0158] Sparsity (K): Determines the number of basis functions used for reconstruction;

[0159] Sampling rate (ratio): Determines the amount of randomly sampled data;

[0160] Number of iterations (M): Determines the number of reconstruction times;

[0161] Convergence threshold (threshold): Determines the iteration stop condition.

[0162] Adaptive rule:

[0163] Adaptive sparsity:

[0164] K = ceil(N * base_sparsity),

[0165] where base_sparsity is determined according to the spectral width: narrowband signal: 0.05; medium bandwidth: 0.1; wideband signal: 0.2;

[0166] Sampling rate adaption:

[0167] ratio = base_ratio + α * spectral_width,

[0168] where base_ratio = 0.3, α = 0.2 (adjustment coefficient), and the range is limited to [0.3, 0.7]

[0169] Number of iterations adaption:

[0170] M = base_iterations * (1 + complexity_factor),

[0171] where complexity_factor is based on the signal variance and peak ratio; simple signal: 10 times, medium complexity: 20 times, complex signal: 30 times;

[0172] As a specific embodiment, an example is given:

[0173] ECG signal:

[0174] Characteristics: Narrowband, regular waveform;

[0175] Adaptive result:

[0176] Lower sparsity (K ≈ 0.05N);

[0177] Lower sampling rate (ratio ≈ 0.3);

[0178] Fewer number of iterations (M ≈ 10).

[0179] Seismic signal:

[0180] Features: Wideband, irregular;

[0181] Adaptive result:

[0182] Higher sparsity (K≈0.2N);

[0183] Higher sampling rate (ratio≈0.6);

[0184] More iteration times (M≈30).

[0185] Experimental verification:

[0186] Example 1: Verification of the noise reduction effect of the algorithm in a pure noise environment:

[0187] 1. Experimental design and parameter configuration:

[0188] This embodiment aims to verify the processing ability of the algorithm for different types of pure noise. Three representative noise models are selected for the experiment:

[0189] Gaussian white noise: representing additive random noise;

[0190] Uniform distribution noise: representing background noise;

[0191] Mixed noise: composed of the above two types of noise compounded in a certain proportion, used to simulate a complex noise environment.

[0192] The key parameter configuration of the experiment is as follows:

[0193] The random sampling rate is set to 0.5, that is, 50% of the original signal is sampled;

[0194] The number of algorithm iterations is set to 20 times to ensure a sufficient optimization process;

[0195] The signal length is uniformly set to 1000 points to ensure the statistical significance of the experimental data.

[0196] 2. Analysis of experimental results:

[0197] Through Figure 2 Comparative analysis, the following key findings can be obtained:

[0198] (1) Time-domain waveform analysis ( Figure 2 Upper left):

[0199] The blue line represents the original noisy signal, and it can be seen that the noise amplitude is significant and the signal-to-noise ratio is low;

[0200] The red line represents the signal after algorithm processing, the noise is significantly suppressed, and the waveform is smoother;

[0201] The signal amplitude range converges from the original [-2, 2] to [-0.5, 0.5], indicating that the noise is effectively controlled.

[0202] (2) Power spectral density analysis ( Figure 2 lower left):

[0203] The power spectrum before processing (blue line) shows a high energy level across the entire frequency band;

[0204] The power spectrum after processing (red line) has an overall energy level reduction of approximately 10 - 15 dB;

[0205] The spectral shape maintains its original characteristics, indicating that the algorithm does not introduce significant frequency distortion.

[0206] (3) Energy distribution comparison ( Figure 2 upper right):

[0207] Shows the energy distribution of three types of noise (Gaussian, uniform, mixed) at different amplitudes;

[0208] The algorithm shows a stable suppression effect on different types of noise;

[0209] The energy ratio after processing remains at around 0.1, indicating that the noise is effectively attenuated.

[0210] (4) SNR progress curve ( Figure 2 lower right):

[0211] The abscissa represents the number of iterations (0 - 20 times), and the ordinate represents the degree of SNR improvement (dB);

[0212] The SNR of the three types of noise all shows a significant upward trend;

[0213] Tends to be stable after about 10 iterations, and the final SNR increases by about 2.5 - 3 dB;

[0214] The convergence speed is fast, indicating that the algorithm has good practicality.

[0215] 3. Summary of performance advantages:

[0216] This embodiment verifies through experiments that the algorithm has the following advantages when dealing with pure noise:

[0217] It has a significant suppression effect on various types of noise;

[0218] The energy attenuation is stable and shows the same performance at different amplitudes;

[0219] The convergence speed is fast, and generally 10 iterations can reach a stable state;

[0220] The basic characteristics of the signal are maintained during the processing, and no obvious distortion is introduced.

[0221] These experimental results fully demonstrate the applicability and effectiveness of the algorithm in a pure noise environment, providing a reliable basis for its deployment in practical applications.

[0222] Example 2: Performance verification of the algorithm in simple signal denoising:

[0223] 1. Experimental design and parameter configuration:

[0224] In this embodiment, a comprehensive experiment is designed to verify the processing ability of the algorithm for noisy simple signals. The specific experimental settings are as follows:

[0225] (1) Signal construction:

[0226] Original signal: The standard sine signal is selected as the reference signal, which has clear periodic and frequency characteristics;

[0227] Noise synthesis: Three typical noises (Gaussian, uniform, and mixed noise) are superimposed to simulate the actual application scenario;

[0228] Sampling design: The single acquisition method is adopted to ensure the continuity and integrity of the data.

[0229] (2) Key parameter configuration:

[0230] Random sampling rate: Set to 0.5 to ensure that the sampled data can fully represent the original signal;

[0231] Number of iterations: Fixed at 20 times to observe the convergence performance of the algorithm;

[0232] Signal length: 500 sampling points are used to cover multiple complete cycles.

[0233] 2. Analysis of experimental results:

[0234] The experimental results are Figure 3 fully presented and analyzed:

[0235] (1) Comparison of time-domain waveforms:

[0236] Blue line: Represents the original sine signal, showing standard periodic characteristics;

[0237] Red line: Represents the signal after adding noise, with obvious random fluctuations visible;

[0238] Green line: Represents the signal processed by the algorithm, which basically restores the periodic characteristics of the original signal;

[0239] Processing effect: The noise is significantly suppressed, while the amplitude and phase information of the signal are maintained.

[0240] (2) Frequency domain feature analysis:

[0241] It shows the spectral distribution of the signal in the range of 0 - 500 Hz;

[0242] The original signal (blue line) has significant energy concentration at the fundamental frequency;

[0243] The processed signal (red line) retains the main frequency components;

[0244] High - frequency noise is effectively suppressed and the spectrum is clearer;

[0245] The energy distribution is concentrated in the effective frequency range, indicating that the algorithm has good frequency selectivity.

[0246] (3) SNR improvement curve:

[0247] The horizontal axis represents the number of iterations (0 - 20 times);

[0248] The vertical axis represents the degree of SNR improvement (in the range of 7 - 8.5 dB);

[0249] Curve characteristics:

[0250] Initial stage (0 - 2 times): The SNR increases rapidly, about 0.5 dB improvement;

[0251] Middle stage (2 - 10 times): Continuous improvement with a gradually decreasing slope;

[0252] Stable stage (10 - 20 times): Tends to be stable, and finally the SNR increases by about 1.5 dB.

[0253] Convergence characteristics:

[0254] The algorithm reaches a stable state after about 15 iterations;

[0255] The overall shows a smooth convergence process without obvious oscillations;

[0256] The final SNR is maintained at about 8.5 dB, indicating significant noise reduction effect;

[0257] 3. Analysis of performance advantages:

[0258] Through this embodiment, the algorithm demonstrates the following key advantages:

[0259] High signal fidelity: Effectively maintains the periodic characteristics and amplitude information of the original signal;

[0260] Significant noise suppression: The time - domain waveform is smoother and the frequency - domain noise is effectively attenuated;

[0261] Good convergence performance: The iteration process is stable without obvious oscillations;

[0262] High computational efficiency: It can achieve a stable effect within 15 iterations;

[0263] Strong adaptability: It shows good processing ability for different types of superimposed noise.

[0264] These experimental results fully verify the effectiveness and stability of the algorithm in processing noisy simple signals, providing a reliable experimental basis for its popularization in practical engineering applications. At the same time, the analysis of all aspects of the experimental results also provides an important reference for the further optimization of the algorithm performance.

[0265] Example 3: Verification of the application of the algorithm in electrocardiogram signal denoising:

[0266] 1. Experimental design and parameter configuration:

[0267] In this embodiment, aiming at the actual medical scenario, the performance of the algorithm in electrocardiogram signal processing is verified. The experimental design fully considers the particularity of electrocardiogram signals:

[0268] (1) Data acquisition scheme:

[0269] Signal source: Clinical electrocardiogram data is used to ensure the authenticity and practicality of the experiment;

[0270] Acquisition method: Multiple acquisitions cannot be implemented, which meets the limiting conditions of the actual medical scenario;

[0271] Data characteristics: Include complete electrocardiogram characteristic wave groups (P wave, QRS wave group, T wave);

[0272] (2) Experimental parameter settings:

[0273] Hybrid sampling strategy:

[0274] Random sampling rate: 0.5, ensuring the basic acquisition of signal characteristics;

[0275] Fixed sampling rate: 0.5, ensuring the stable acquisition of key feature points;

[0276] Algorithm iteration: Set to 20 times, balancing the processing effect and computational overhead;

[0277] Evaluation index: Focus on the improvement degree of SNR and the morphology preservation of QRS wave groups;

[0278] 2. Analysis of experimental results:

[0279] By Figure 4 Conduct a comprehensive analysis of the experimental results:

[0280] (1) Time-domain waveform analysis (above figure):

[0281] Original signal (blue line):

[0282] Show typical electrocardiogram characteristic waveforms;

[0283] The QRS complex is clearly distinguishable;

[0284] There is a certain fluctuation in the baseline;

[0285] Noisy signal (red line):

[0286] Superimposed with random noise interference;

[0287] The detailed part of the signal is contaminated by noise;

[0288] Processed signal (black line):

[0289] The morphology of the QRS complex is well maintained;

[0290] The baseline drift is effectively suppressed;

[0291] The morphological characteristics of the P wave and T wave are clearer.

[0292] (2) Power spectral density analysis (middle figure):

[0293] Frequency range: 0 - 150 Hz, covering the main frequency components of the electrocardiogram signal;

[0294] Original signal spectrum (black line):

[0295] The energy is concentrated in the low - frequency band;

[0296] The energy in the high - frequency band decays rapidly;

[0297] Noisy signal spectrum (blue line):

[0298] High - frequency noise is obvious;

[0299] The energy distribution is more dispersed;

[0300] Processed signal spectrum (red line):

[0301] The effective components in the low - frequency band are maintained;

[0302] High - frequency noise is significantly suppressed;

[0303] The spectral morphology is closer to the original signal.

[0304] (3) SNR improvement curve (bottom figure):

[0305] Analysis of the iterative process:

[0306] Initial stage (0 - 4 times): The SNR increases rapidly, from 6 dB to 10 dB;

[0307] Mid - term stage (4 - 12 times): Continued improvement with a slowing down of the improvement rate;

[0308] Stable stage (12 - 20 times): Asymptotic convergence, and finally the SNR improvement reaches 14 dB; Convergence characteristics:

[0309] Overall, it shows a smooth upward trend;

[0310] There are no obvious fluctuations or oscillations;

[0311] It reaches a stable state after about 15 iterations.

[0312] 3. Summary of performance advantages:

[0313] This embodiment verifies that the algorithm has the following significant advantages in electrocardiogram signal processing:

[0314] Signal feature preservation:

[0315] The morphology of the QRS complex is accurately preserved;

[0316] The detailed features of the P wave and T wave are clearly distinguishable;

[0317] The baseline drift is effectively suppressed;

[0318] Noise suppression effect:

[0319] The overall SNR is increased by about 14 dB;

[0320] The high - frequency noise is significantly attenuated;

[0321] The main frequency components of the signal are maintained;

[0322] Algorithm stability:

[0323] The convergence process is stable;

[0324] There is no over - filtering phenomenon;

[0325] The calculation efficiency is relatively high.

[0326] These experimental results show that the algorithm can effectively process electrocardiogram signals in actual medical scenarios, achieving significant noise reduction while maintaining key diagnostic features. This is of great significance for improving the diagnostic value of electrocardiogram signals and provides reliable technical support for the practical application of the algorithm in the medical field.

[0327] Example 4: Application verification of the algorithm in seismic waveform processing:

[0328] 1. Experimental design and parameter configuration:

[0329] This example is specially designed for the special needs of seismic waveform data processing, and verifies the performance of the algorithm in processing transient and non-periodic seismic signals:

[0330] (1) Data collection plan:

[0331] Signal source: using actual earthquake record data to ensure the practical significance of the experiment;

[0332] Acquisition characteristics: Single data acquisition, in line with the sudden characteristics of seismic signals;

[0333] Signal characteristics: Contains complete waveform information of seismic waves, including key phases such as P waves and S waves; (2) Experimental parameter optimization:

[0334] Hybrid sampling strategy configuration:

[0335] Random sampling rate: 0.4, adapted to the non-stationary characteristics of seismic signals;

[0336] Fixed sampling rate: 0.6, to ensure stable acquisition of key seismic phases;

[0337] Iteration number: set to 20 to ensure that the algorithm fully converges;

[0338] Evaluation focus: Focus on the degree of SNR improvement and the preservation of seismic wave phase information;

[0339] 2. Experimental results analysis:

[0340] pass Figure 5 Expand detailed analysis:

[0341] (1) Time domain waveform analysis (above):

[0342] Original signal characteristics (black line):

[0343] Display typical earthquake waveform characteristics;

[0344] Contains multiple earthquake phase arrival information;

[0345] The amplitude range is between [-0.5, 1.0];

[0346] Noisy signal performance (red line):

[0347] The background noise is obvious;

[0348] The seismic phase information is partially obscured;

[0349] The effect after processing (blue line):

[0350] The main seismic phases are clearly maintained;

[0351] Background noise is significantly reduced;

[0352] The signal continuity is well maintained;

[0353] (2) Power spectral density analysis (middle figure):

[0354] Frequency range coverage: 0 - 500 Hz

[0355] Original signal spectrum (black line):

[0356] The energy is concentrated in the low - frequency band;

[0357] The high - frequency band shows the characteristic of rapid attenuation;

[0358] Processed signal spectrum (blue line):

[0359] The main frequency components are maintained;

[0360] The high - frequency noise is effectively suppressed;

[0361] The overall shape of the spectrum is close to that of the original signal;

[0362] It shows a better noise suppression effect in the range of 250 - 500 Hz.

[0363] (3) SNR improvement curve (lower figure):

[0364] Analysis of the iterative process:

[0365] Initial stage (0 - 4 times): The SNR increases rapidly, from 10 dB to 12 dB; Middle stage (4 - 10 times): It continues to improve, and the increasing rate gradually slows down;

[0366] Stable stage (10 - 20 times): It tends to be stable, and finally the SNR increases to 13 dB; Convergence characteristics:

[0367] The overall shows a smooth convergence process;

[0368] It reaches the stable state after about 12 iterations;

[0369] There is no obvious oscillation or instability;

[0370] 3. Summary of performance advantages:

[0371] This embodiment verifies that the algorithm has the following significant advantages in seismic waveform processing: Signal feature preservation:

[0372] The main phase information of seismic waves is completely retained;

[0373] The waveform detail features are clearly distinguishable;

[0374] The phase information is accurately maintained;

[0375] Noise suppression effect:

[0376] The SNR is significantly improved, from 10 dB to 23 dB;

[0377] The background noise is effectively suppressed;

[0378] Algorithm stability:

[0379] The convergence process is stable and controllable;

[0380] The computational efficiency is relatively high;

[0381] The processing results are stable and reliable.

[0382] These experimental results fully demonstrate the superior performance of the algorithm in processing seismic waveform data. It can not only effectively extract the seismic wave information in the landslide curve but also maintain the key features of the signal. This has important practical significance for the accurate analysis and interpretation of seismic data and provides reliable technical support for the promotion of the algorithm in seismological research and engineering applications.

[0383] The success of this embodiment also indicates that the algorithm has a powerful ability to process non-stationary signals, which lays a foundation for its application in a wider field of geophysical signal processing.

[0384] Example 5: Application verification of the algorithm in processing industrial equipment vibration signals:

[0385] 1. Experimental design and parameter configuration:

[0386] This embodiment targets the industrial equipment fault diagnosis scenario to verify the performance of the algorithm in processing vibration signals:

[0387] (1) Data acquisition scheme:

[0388] Signal source: The fault diagnosis data of actual industrial equipment is adopted;

[0389] Signal characteristics: Include typical vibration characteristics of the equipment operation state;

[0390] Acquisition method: Real-time data is acquired through standard vibration sensors;

[0391] (2) Experimental parameter settings:

[0392] Sampling strategy:

[0393] Random sampling rate: Set to 0.6 to ensure sufficient acquisition of vibration characteristics;

[0394] Sampling duration: 1 second, covering multiple vibration cycles;

[0395] Algorithm iteration: Set 20 iterations to ensure the convergence of the processing effect; Evaluation metrics: Pay attention to the preservation of vibration characteristic frequencies and the suppression of noise levels; 2. Analysis of experimental results:

[0396] Through Figure 6 Conduct a detailed analysis from three dimensions:

[0397] (1) Time-domain waveform analysis (upper figure):

[0398] Original signal (black line):

[0399] Exhibits obvious periodic vibration characteristics;

[0400] The amplitude range is between [-2, 2];

[0401] Contains complete vibration period information;

[0402] Noisy signal (red line):

[0403] Superimposed with random noise interference;

[0404] Basically maintains the periodic characteristics;

[0405] The details are affected by noise;

[0406] Processed signal (blue line):

[0407] The vibration periodicity is clearer;

[0408] The waveform profile is smoother;

[0409] Maintains the amplitude range of the original signal.

[0410] (2) Power spectral density analysis (middle figure):

[0411] Frequency range: 0 - 500 Hz, covering the main vibration frequencies;

[0412] Original signal spectrum (black line):

[0413] Shows obvious characteristic frequencies in the low-frequency band;

[0414] The energy in the high-frequency band is lower;

[0415] Processed signal spectrum (blue line):

[0416] Maintains the main characteristic frequency components;

[0417] The high-frequency noise is significantly suppressed;

[0418] The characteristic frequencies below 50 Hz are more prominent;

[0419] The spectral peaks are clearer, facilitating the identification of fault characteristics;

[0420] (3) SNR improvement curve (the following figure):

[0421] Analysis of the iterative process:

[0422] Initial stage (0 - 4 times): The SNR increases rapidly, from 9 dB to 11 dB; Middle stage (4 - 10 times): Continuous improvement with a slowing down of the improvement rate;

[0423] Stable stage (10 - 20 times): Tends to be stable, and finally the SNR reaches 12 dB; Convergence characteristics:

[0424] Shows a smooth convergence process;

[0425] Reaches a stable state after about 12 iterations;

[0426] There is no obvious oscillation phenomenon.

[0427] 3. Summary of performance advantages:

[0428] This embodiment verifies that the algorithm has the following advantages in industrial vibration signal processing: Feature retention ability:

[0429] Accurately retains the periodic characteristics of vibration;

[0430] The characteristic frequency components are clearly distinguishable;

[0431] The waveform details are well maintained;

[0432] Noise reduction effect:

[0433] The noise level is significantly reduced;

[0434] The SNR improvement reaches 12 dB;

[0435] High - frequency interference is effectively suppressed;

[0436] Processing stability:

[0437] The convergence process is stable;

[0438] High computational efficiency;

[0439] Good reliability of the results.

[0440] These experimental results show that the algorithm can effectively process industrial equipment vibration signals, both maintaining the key features required for fault diagnosis and achieving a significant noise reduction effect. 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.

[0441] The successful verification of this embodiment further proves the superior performance of the algorithm in processing periodic signals, laying a solid foundation for its popularization and application in the fields of industrial equipment condition monitoring, fault diagnosis, etc.

[0442] Embodiment 2

[0443] The present invention also provides a computer device, including a memory, a processor, and a computer program stored on the memory, and the processor executes the computer program to implement the steps of the method.

[0444] Embodiment 3

[0445] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method are implemented.

[0446] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for realizing signal superposition and noise reduction by single acquisition, characterized in that: The following steps are involved: Acquire a noisy signal once, and perform normalization processing on the noisy signal to obtain a normalized signal; Performing spectrum analysis, adaptive sparsity estimation, and sampling point configuration optimization on the normalized signal, and selecting fixed sampling points and random sampling points; Iterative noise reduction is performed based on selected fixed sampling points and random sampling points; When the preset maximum number of iterations is reached, the noise reduction is completed, and the OMP algorithm is used to reconstruct the signal to obtain the reconstructed signal; Acquiring a signal-to-noise ratio of the reconstructed signal, and optimizing parameters of a noise reduction method based on a variation trend of the signal-to-noise ratio; the parameter optimization includes resetting a maximum number of iterations; Based on the optimized denoising method, the best reconstruction result is obtained.

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 subjected to 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 spectrum analysis on the normalized signal includes: The normalized signal is subjected to spectrum analysis by using fast Fourier transform to obtain frequency distribution characteristics; based on the frequency distribution characteristics, the energy contribution of each frequency point is calculated to establish a frequency-energy mapping relationship; based on the frequency-energy mapping relationship, the spectrum characteristics are quantified to provide a basis for adaptive sparsity estimation.

4. The method according to claim 3, characterized in that The process of performing adaptive sparsity estimation includes: Based on the Pareto principle, the spectrum energy cumulative distribution function is calculated; based on the inflection point characteristics of the spectrum energy cumulative distribution function, the energy coverage threshold is determined; based on the energy coverage threshold, the number of effective frequency points is determined, and the sparsity estimation value is dynamically updated.

5. The method according to claim 4, characterized in that The process of optimizing the sampling point configuration includes: The determined number of effective frequency points is energy sorted, and several high-energy frequency points are selected as fixed sampling points, and the remaining frequency points are used as random sampling points.

6. The method according to claim 1, characterized in that The process of iterative denoising based on selected fixed sampling points and random sampling points includes: When the number of iterations is an even number, fixed sampling points and random sampling points are combined to implement a mixed sampling strategy; when the number of iterations is an odd number, 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 realize the adaptive stopping criterion. Soft threshold filtering is applied to realize 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 the signal-to-noise ratio includes: Based on the changing trend of the signal-to-noise ratio, the sparsity of the denoising method is dynamically adjusted and the number of samplings is updated to obtain the 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 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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