Steel gate vibration signal noise reduction method based on multi-signal processing technology fusion

Abstract

The invention discloses a steel gate vibration signal noise reduction method based on multi-signal processing technology fusion, and belongs to the technical field of signal processing. The method comprises the following steps: acquiring vibration noise data of the arc-shaped steel gate in a discharge process by adopting an acceleration sensor; optimizing the variational mode decomposition method by adopting a multivariate universe optimization algorithm, and determining an optimal decomposition layer number and an optimal penalty factor according to the initial fitness distribution; decomposing the vibration noise data by adopting an optimized variational mode decomposition method to obtain a plurality of intrinsic mode components; calculating a multi-scale permutation entropy based on the intrinsic mode component to obtain a multi-scale permutation entropy curve; the intrinsic mode components with the multi-scale permutation entropy larger than the noise threshold are screened out, improved wavelet threshold denoising is carried out on the part, superposition reconstruction is carried out in combination with other intrinsic mode components, and denoised signals are obtained. According to the scheme, the decomposed modal function has a good narrowband characteristic, efficient signal decomposition is realized, and the denoising performance is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a method for reducing the noise of the vibration signal of a steel gate based on the fusion of multi-signal processing technologies. Background Art

[0002] Due to the harsh working environment, the vibration signal of the gate during flow discharge contains a large amount of noise signals, which seriously affects the extraction of the main information of the gate and the evaluation of the operating condition of the gate. Therefore, a denoising method is needed to denoise the collected vibration signal.

[0003] Traditional signal denoising methods mainly include mean filtering, median filtering, etc. These methods are based on the principle of statistics and remove noise based on the local statistical characteristics of the signal. However, the effect may be limited for non-stationary signals or cases where the noise characteristics change greatly. In recent years, with the development of non-stationary signal processing technologies, signal processing methods such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Wavelet Threshold Denoising (WTD) have the ability of multi-scale analysis and can effectively screen or remove noises in different frequency ranges. However, when using the above methods alone to process non-linear and non-stationary time series, and there are problems such as mode mixing, sensitive parameter setting, and end effect, the separation effect of the characteristic frequency and noise in the signal is not satisfactory. Summary of the Invention

[0004] The purpose of the present invention is to address the problem of poor separation effect of the characteristic frequency and noise in traditional single signal processing. This solution can solve the problem that the decomposition layer number and penalty factor of variational mode decomposition have a great influence on the result, and can select the optimal decomposition layer number and penalty factor to improve the decomposition ability and denoising ability, so as to realize the noise removal of the measured signal of the arc-shaped steel gate.

[0005] Specifically, a method for reducing the noise of the vibration signal of a steel gate based on the fusion of multi-signal processing technologies is proposed, including the following steps:

[0006] S1. Use an acceleration sensor to collect the vibration noise data of the arc-shaped steel gate during the flow discharge process;

[0007] S2. Optimize the variational mode decomposition method using the multi-universe optimization algorithm, and determine the optimal decomposition layer number and the optimal penalty factor according to the initial fitness distribution;

[0008] S3. Use the optimized variational mode decomposition method to decompose the vibration noise data to obtain a number of intrinsic mode components;

[0009] S4. Calculate the multi-scale permutation entropy based on the intrinsic mode components to obtain a multi-scale permutation entropy curve;

[0010] S5. Screen out the intrinsic mode components whose multi-scale permutation entropy is greater than the noise threshold, perform improved wavelet threshold denoising on this part, and combine with other intrinsic mode components for superposition and reconstruction to obtain the denoised signal.

[0011] Preferably, the S2 specifically includes the following steps:

[0012] S21. Input the vibration noise data and determine the optimization objective of variational mode decomposition;

[0013] S22. Through the multi-universe optimization algorithm, randomly generate a set of candidate solutions composed of the decomposition layer number and the penalty factor in the solution space, apply the variational mode decomposition method to decompose the signal for each candidate solution, calculate and record its corresponding fitness value, and obtain the initial fitness distribution;

[0014] S23. Use the inflation and contraction mechanism to perform global and local searches on the solution space, and continuously update the decomposition layer number and the penalty factor in the candidate solutions;

[0015] S24. Based on the initial fitness distribution, through fitness evaluation and iterative optimization, when the iteration process reaches the predetermined termination condition, the multi-universe optimization algorithm outputs the optimal combination of the decomposition layer number and the penalty factor parameters.

[0016] Preferably, the optimization objective of the variational mode decomposition is determined by minimizing the variational problem, and is specifically expressed as follows:

[0017]

[0018] where, u k (t) is the k-th modal signal, ω k is the center frequency of the k-th mode, δ(t) is the Dirac function, used to represent the position of the signal in the time domain; j is the imaginary unit; α is the penalty factor, controlling the sparsity and bandwidth of the modal function; represents the gradient of the modal function, and t represents time.

[0019] Preferably, the specific expression of the intrinsic mode component is:

[0020]

[0021] In the formula, K represents the number of intrinsic mode components.

[0022] Preferably, the S4 specifically includes the following steps:

[0023] S41. Coarsely granulate the intrinsic mode components to generate signal sequences of different scales;

[0024] S42. Calculate the permutation entropy at each scale through the single-scale permutation entropy calculation method based on the time series to obtain a permutation entropy set;

[0025] S43. Based on the permutation entropy set, obtain a multi-scale permutation entropy sequence, and further obtain a multi-scale permutation entropy curve.

[0026] Preferably, the coarse-graining process is specifically expressed as:

[0027]

[0028] In the formula, s is the scale factor, is the coarse-grained signal at scale s, and c is the time segment index after coarse-graining.

[0029] Preferably, the multi-scale permutation entropy sequence is specifically expressed as:

[0030]

[0031] In the formula, PE is the permutation entropy; s max is the maximum scale.

[0032] Preferably, the improved wavelet threshold denoising is specifically expressed as:

[0033]

[0034] Among them, τ is the calculation threshold, m is a variable value; d j is the signal strength of the signal component of the original input.

[0035] Preferably, the superimposed reconstruction is specifically expressed as:

[0036]

[0037] In the formula, IMF m (t) are multiple intrinsic mode components after wavelet threshold denoising, and IMF n (t) are multiple intrinsic mode components without wavelet threshold denoising; m is the number of intrinsic mode components using wavelet threshold denoising, and n is the number of intrinsic mode components not using wavelet threshold denoising.

[0038] Compared with the prior art, the beneficial effects of the present invention are:

[0039] 1. The proposed scheme automatically optimizes the decomposition layer number K and the penalty factor α of VMD through the MVO algorithm, avoiding the cumbersome process of manual parameter adjustment, ensuring the accuracy and stability of signal decomposition, and realizing automatic parameter selection.

[0040] 2. The optimized VMD proposed in this solution can decompose signals with optimal parameter configurations, enabling the decomposed mode functions to have good narrowband characteristics, reducing the overlap and interference between modes, achieving efficient signal decomposition, and effectively improving the denoising performance.

[0041] 3. This solution is applicable to the processing of various complex signals, including but not limited to mechanical vibration signals, biomedical signals, seismic wave signals, etc., and has wide applicability. Description of the Drawings

[0042] Figure 1 is the flowchart of the method of the present invention;

[0043] Figure 2 is the flowchart of the MVO optimization algorithm in the present invention;

[0044] Figure 3 is the waveform diagram of a pure signal and a noisy signal formed by adding random white noise in an embodiment of the present invention;

[0045] Figure 4 is the MVO-optimized VMD iterative convergence curve in an embodiment of the present invention;

[0046] Figure 5 is the convergence trend curve of the VMD decomposition parameters under the MVO optimization algorithm in an embodiment of the present invention;

[0047] Figure 6 is the IMF component curve diagram of the noisy signal decomposed by VMD in an embodiment of the present invention;

[0048] Figure 7 is the multi-scale permutation entropy histogram of each IMF after VMD decomposition in an embodiment of the present invention;

[0049] Figure 8 The waveform diagram of the denoised signal and the pure signal obtained after processing the noisy signal with the denoising method of the present invention in an embodiment of the present invention. Detailed Embodiments

[0050] Traditional signal denoising methods mainly include mean filtering, median filtering, etc. These methods are based on the principles of statistics and remove noise based on the local statistical characteristics of the signal. However, their effectiveness may be limited for non-stationary signals or cases where the noise characteristics change significantly. In recent years, with the development of non-stationary signal processing techniques, signal processing methods such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Wavelet Threshold Denoising (WTD) have the ability of multi-scale analysis and can effectively screen or remove noise in different frequency ranges. The EMD method is suitable for processing non-linear and non-stationary time series, but there are problems such as mode mixing, sensitive parameter setting, and end effect. Therefore, when using EMD decomposition, the separation effect between the characteristic frequency and noise in the signal is not satisfactory. Compared with the EMD method, the VMD method has better sampling and noise robustness, can effectively suppress the mode mixing phenomenon, and makes the decomposition result more accurate.

[0051] The Multi-Verse Optimizer (MVO) is a meta-heuristic optimization algorithm based on the theory of cosmic inflation. Its core idea is to simulate the interaction of multiple universes (candidate solutions) in the universe and gradually converge to the optimal solution. The optimization process of MVO is divided into three key steps: inflation, contraction, and wormhole transmission. The MVO algorithm has good global search and local development capabilities and has considerable superiority for complex optimization problems.

[0052] Multiscale Permutation Entropy (MPE) is a statistical method for analyzing the complexity and non-linear characteristics of time series through multi-scale analysis. It can reveal the dynamic behavior of data at different scales and is widely used in the field of signal processing. In signal denoising, it can effectively improve the signal processing quality by distinguishing the complexity characteristics of the signal and noise.

[0053] Wavelet threshold denoising is a classic denoising method based on wavelet transform. With its multi-scale decomposition ability of the signal, it can process both the local and global characteristics of the signal in the time-frequency domain and is suitable for denoising non-stationary signals. However, the traditional soft threshold and hard threshold methods of wavelet threshold denoising have their own advantages and disadvantages in the denoising process, and there are problems such as signal distortion or noise residue. Improving the threshold processing technology helps to improve the denoising effect, enhance signal fidelity, and reduce problems such as signal over-smoothing or detail loss.

[0054] Compared with single denoising methods, joint denoising methods have the advantages of multi-level noise separation ability, high signal fidelity, strong self-adaptability, good robustness, and high computational efficiency. Especially when dealing with complex and non-stationary signals, joint denoising methods can remove noise more accurately and retain the key feature information of the signal, making this method more widely applicable and having more superior performance in a variety of practical applications.

[0055] Example 1: As Figure 1 - Figure 8 shown, the present invention discloses a method for reducing the noise of the vibration signal of a steel gate based on the fusion of multi-signal processing technologies, including the following steps:

[0056] Step S101: Initialization and problem definition.

[0057] The input signal f(t) is defined as the target signal to be decomposed. The goal of VMD is to decompose the signal f(t) into K narrow-band mode functions u k (t), that is:

[0058]

[0059] where K is the decomposition level; u k (t) is the mode function, and w k is the center frequency of each mode.

[0060] The optimization goal of VMD decomposition is determined by minimizing the variational problem, that is

[0061]

[0062] where u k (t) is the k-th mode signal, ω k is the center frequency of the k-th mode, δ(t) is the Dirac function, which is used to represent the position of the signal in the time domain. j is the imaginary unit. α is the penalty factor, which controls the sparsity and bandwidth of the mode function. represents the gradient of the mode function, and t represents time.

[0063] Step S102: Initialization and fitness evaluation of the MVO algorithm.

[0064] Through the MVO algorithm, a group of candidate solutions are randomly generated in the solution space, and each candidate solution is composed of the decomposition level K and the penalty factor α.

[0065] The fitness function is defined according to indexes such as the spectral concentration and mode reconstruction error of the VMD decomposition result, and is used to evaluate the quality of each candidate solution. Apply VMD to each candidate solution for signal decomposition, calculate and record its fitness value, and obtain the initial fitness distribution.

[0066] Step S103: Iterative optimization of the MVO algorithm During the iterative process of the MVO algorithm, a dilation and contraction mechanism is used to perform global and local searches on the solution space, continuously updating the K and α parameters in the candidate solutions. Through fitness evaluation, candidate solutions with higher fitness are selected to drive the entire solution space to converge towards the global optimal solution. Through multiple iterations, the decomposition layer number and penalty factor combination of VMD are gradually optimized, continuously improving the decomposition effect of the signal.

[0067] Step S104: Selection of optimal parameters and signal decomposition When the iterative process reaches the predetermined termination condition, the MVO algorithm outputs the optimal combination of K and α parameters.

[0068] Figure 2 is the flowchart of the MVO optimization algorithm in the present invention. As Figure 2 shown, this flowchart is the specific implementation process of the general MVO optimization algorithm:

[0069] The MVO optimization algorithm first performs an initialization step, that is, initializing the universe matrix U. This matrix U represents the set of variables or parameters to be optimized in the algorithm. Then, the algorithm sets the standard inflation rate of the universe. This standard inflation rate is a threshold or reference value used for subsequent comparison and judgment of whether the inflation rate of each universe reaches the optimization goal. Then, the algorithm enters the judgment node, that is, checking whether the current state or condition meets the preset termination condition. Among them, this termination condition can be reaching a certain number of iterations, finding a solution that meets the requirements, etc. If the termination condition is met, the algorithm ends; if not, the subsequent steps are continued.

[0070] When the termination condition is not met, the algorithm first searches for variables through the spiral mechanism. This spiral mechanism can be a heuristic search strategy used to find potential high-quality solutions in the solution space. Then, the algorithm uses the fast classification algorithm mechanism to classify or screen these variables for further processing.

[0071] Subsequently, the algorithm enters the exploitation stage. In this stage, the algorithm divides the variables into two categories: high inflation rate pass and low inflation rate pass according to the level of the inflation rate. Variables with high inflation rates may be regarded as potential optimal solutions or candidate solutions, while variables with low inflation rates may be eliminated or ignored.

[0072] During the exploitation process, the algorithm also involves the operations of sending objects of white holes and black holes. These operations can be understood here as part of the operations used by the algorithm to update or optimize the solution.

[0073] Next, the algorithm will find the balance point between the optimal complexity and the worst complexity. This balance point may represent that while the algorithm pursues the optimization goal, it also needs to consider the trade-off between the complexity and feasibility of the solution. Update the inflation rate of the universe through the transfer of solutions or candidate solutions.

[0074] Finally, the algorithm will perform exploration mechanism coefficient processing. This step may involve adjusting or optimizing parameters such as the WEP coefficient and the TDR coefficient. These coefficients represent key parameters or weights in the algorithm, and by adjusting them, the quality or performance of the solution can be further improved. The above is the specific implementation process of the general MVO optimization algorithm.

[0075] Use the optimized parameters to perform the final VMD decomposition on the input signal f(t). At this time, the decomposed modal signals have the best narrowband characteristics and the smallest reconstruction error.

[0076] Step S105: K IMF components can be obtained by MVO-VMD decomposition:

[0077]

[0078] Step S106: Coarsen the IMF components to generate signal sequences Y(s) of different scales, where s is the scale factor. The coarsened signal at scale s is defined as:

[0079]

[0080] where s is the scale factor, is the coarsened signal at scale s, and c is the index of the coarsened time segment.

[0081] Step S107: Calculate the permutation entropy PE(s) at each scale s for each coarsened time series Y(s) through the single-scale permutation entropy calculation method.

[0082] Step S108: Calculate the permutation entropy at multiple scales to obtain a multi-scale permutation entropy sequence as:

[0083]

[0084] In the formula, PE is the permutation entropy; s max is the maximum scale. The multi-scale permutation entropy provides information on the distribution of signal complexity at different time scales. Low scales correspond to fine-grained time series features, and high scales correspond to coarse-grained features. The value of MPE is lower at high scales, usually indicating that the signal is more stable or regular at larger time scales, while a high MPE value at low scales indicates that the signal has more details and complexity at smaller time scales. In signal denoising applications, MPE can be used to distinguish noise from useful signals because noise usually has a higher entropy value, while the entropy value of useful signals is lower. By analyzing MPE at multiple scales, useful signal components can be effectively identified and retained.

[0085] Finally, a multi-scale permutation entropy curve is generated.

[0086] Step S109: Classify the IMFs into noisy IMFs and pure IMFs according to whether the MPE of each IMF is greater than 0.6.

[0087] It should be noted that the 0.6 here is a noise threshold index formulated by comprehensively considering actual project situations, engineering experience, relevant specifications and other factors, and it is not unique.

[0088] Step S110: Improve the wavelet threshold function, and the expression of the improved wavelet threshold function is:

[0089]

[0090] where τ is the calculated threshold, m is a variable value, and d j is the signal strength of the signal component of the original input.

[0091] Step S111: Adopt the wavelet threshold denoising method with an improved threshold to denoise the noisy classification with MPE greater than 0.6.

[0092] Step S112: Superimpose the classification after the improved wavelet threshold denoising on the components with MPE less than 0.6 to obtain the denoised signal.

[0093] Among them, the denoised IMF components are superimposed and reconstructed with other IMF components to obtain the denoised signal. The reconstruction formula is:

[0094]

[0095] In the formula, IMF m (t) are multiple IMF components after wavelet threshold denoising, and IMF n (t) are multiple IMF components that do not require wavelet threshold denoising.

[0096] After obtaining the denoised signal, the artificial noise simulation effect can be verified by using the signal-to-noise ratio and the root mean square error. Specifically, the signal-to-noise ratio formula is:

[0097]

[0098] In the formula: P s is the pure signal power, and P n is the noise power;

[0099] The root mean square error calculation formula is:

[0100]

[0101] In the formula: N is the signal length, x iis the signal after noise reduction, is the noisy signal. The higher the SNR, the less noise component in the signal. MSE reflects the mean square error between the original signal and the signal after noise reduction. The smaller the MSE, the better the noise reduction effect.

[0102] In addition, the noise reduction error ratio is used to judge the noise reduction quality of the actual signal. The calculation formula of the noise reduction error ratio is as follows:

[0103] dnSNR = 10lg(Ps / Pg);

[0104] In the formula: P s is the signal power before noise reduction, P g is the signal power after noise reduction. The smaller the noise reduction error ratio, the better the noise reduction effect.

[0105] Example 2, as Figure 1 shown, the present invention optimizes the VMD decomposition method by introducing the MVO optimization method and establishes a joint noise reduction model by introducing multi-scale permutation entropy and wavelet threshold noise reduction, effectively improving the denoising performance.

[0106] The method includes the following steps 1-7:

[0107] Step 1, artificially construct a pure signal and add artificial random white noise to obtain a noisy signal. Figure 3 shows the comparison between the pure signal and the noisy signal. It can be found that the pure signal becomes disordered after adding noise, and the original signal pattern is submerged.

[0108] Step 2, use the MVO optimization method to optimize the VMD decomposition method to obtain the key parameters of VMD decomposition, the decomposition layer number K and the penalty factor α, Figure 4 shows the MVO optimization convergence curve. It is found that after the number of iterations reaches 8 times, the fitness value tends to be stable. Figure 5 shows the curve of the hyperparameters of VMD changing with the number of iterations. It can be found that the penalty factor after iteration stabilization is 1850, and the number of modes is 12. So the VMD decomposition parameters are α = 5, K = 12.

[0109] Step 3, use the VMD decomposition algorithm optimized in Step 2 to decompose the signal in Step 1, and a total of K IMF intrinsic mode components are obtained, Figure 6 shows the 12 intrinsic mode components in the case. The original data in the figure is the case data, which is decomposed into IMF1-IMF12 with frequencies from low to high.

[0110] Step 4, calculate the multi-scale permutation entropy MPE of the K IMF intrinsic mode components obtained by the decomposition in Step 3, Figure 7The MPE of 12 intrinsic mode components in the case is shown, and it is found that the MPE of IMF1 and IMF2 is less than 0.6, while the MPE of the remaining IMF components is greater than 0.6.

[0111] Step 5: According to whether the MPE calculated in Step 4 is greater than the threshold value of 0.6, decompose the K IMFs into noisy IMFs and pure IMFs. That is, IMF1 and IMF2 are pure IMFs, and IMF3 to IMF12 are noisy IMFs.

[0112] Step 6: Perform improved wavelet threshold denoising on the noisy IMFs in Step 5, namely IMF3 to IMF12.

[0113] Step 7: Superimpose the IMF components after wavelet threshold denoising in Step 6 on the pure IMF components in Step 4 to obtain the denoised signal. Figure 8 The waveform comparison between the denoised signal and the original pure signal is shown, and it is found that the waveforms of the denoised signal and the original pure signal tend to be consistent, and the noise signal is well removed.

Claims

1. A steel gate vibration signal noise reduction method based on multi-signal processing technology fusion, characterized in that: The steps include: S1. Use acceleration sensors to collect vibration and noise data of the arc steel gate during the discharge process; S2. The variational mode decomposition method is optimized using the multiverse optimization algorithm, and the optimal number of decomposition layers and the optimal penalty factor are determined according to the initial fitness distribution; S3, using the optimized variational mode decomposition method to decompose the vibration noise data to obtain a number of eigenmode components; S4. Calculating a multi-scale permutation entropy based on the intrinsic mode component to obtain a multi-scale permutation entropy curve; S5. Screen out the intrinsic mode components whose multi-scale permutation entropy is greater than the noise threshold and perform improved wavelet threshold denoising on the part, combine with other intrinsic mode components for superposition reconstruction, and obtain a denoised signal.

2. The steel gate vibration signal denoising method based on multi-signal processing technology fusion according to claim 1 is characterized in that: The S2 specifically includes the following steps: S21, input vibration noise data and determine the optimization target of variational mode decomposition; S22. A set of candidate solutions consisting of decomposition levels and penalty factors are randomly generated in the solution space by using a multiverse optimization algorithm. A variational mode decomposition method is applied to each candidate solution to perform signal decomposition, and its corresponding fitness value is calculated and recorded to obtain an initial fitness distribution. S23, using the expansion and contraction mechanism to search the solution space globally and locally, and continuously updating the number of decomposition levels and penalty factors in the candidate solutions; S24. Based on the initial fitness distribution, through fitness evaluation and iterative optimization, when the iterative process reaches a predetermined termination condition, the multiverse optimization algorithm outputs the optimal combination of decomposition levels and penalty factor parameters.

3. The method for reducing the noise of steel gate vibration signals based on the fusion of multi-signal processing technology according to claim 2 is characterized in that: The optimization goal of the variational mode decomposition is determined by minimizing the variational problem, which is specifically expressed as follows: Among them, u k (t) is the kth modal signal, ω k is the center frequency of the kth mode, δ(t) is the Dirac function used to represent the position of the signal in the time domain; j is the imaginary unit; α is the penalty factor that controls the sparsity and bandwidth of the modal function; represents the gradient of the mode function, and t represents time.

4. The steel gate vibration signal noise reduction method based on multi-signal processing technology fusion according to claim 1 is characterized in that: The specific expression of the eigenmode component is: Where K represents the number of eigenmode components.

5. The method for reducing noise of steel gate vibration signal based on multi-signal processing technology fusion according to claim 1 is characterized in that: The S4 specifically includes the following steps: S41, performing coarse-graining processing on the intrinsic mode components to generate signal sequences of different scales; S42, based on the time series, calculating the permutation entropy at each scale by a single-scale permutation entropy calculation method to obtain a permutation entropy set; S43. Based on the permutation entropy set, a multi-scale permutation entropy sequence is obtained, and then a multi-scale permutation entropy curve is obtained.

6. The method for reducing the noise of steel gate vibration signals based on the fusion of multi-signal processing technology according to claim 5 is characterized in that: The coarse-graining process is specifically expressed as follows: Where s is the scale factor, is the coarse-grained signal at scale s, and c is the index of the time segment after coarse-graining.

7. The method for reducing noise of steel gate vibration signal based on multi-signal processing technology fusion according to claim 5 is characterized in that: The multi-scale permutation entropy sequence is specifically expressed as: Where PE is the permutation entropy; s max is the maximum size.

8. The method for reducing noise of steel gate vibration signal based on multi-signal processing technology fusion according to claim 1 is characterized in that: The improved wavelet threshold denoising is specifically expressed as: Among them, τ is the calculation threshold, m is a variable value, and d j is the signal strength of the original input signal component.

9. The method for reducing noise of steel gate vibration signal based on multi-signal processing technology fusion according to claim 8 is characterized in that: The superposition reconstruction is specifically expressed as: In the formula, IMF m (t) are multiple intrinsic mode components after wavelet threshold denoising, IMF n (t) is a number of intrinsic mode components that do not require wavelet threshold denoising, m is the number of intrinsic mode components that use wavelet threshold denoising, and n is the number of intrinsic mode components that do not use wavelet threshold denoising.

Images