Pulse signal denoising method based on combination of lifting wavelet transform and morphological filtering

Abstract

The invention discloses a pulse signal denoising method based on combination of lifting wavelet transform and morphological filtering, and belongs to the field of digital signal processing. According to the method, lifting wavelet transformation and morphological filtering are coupled, and baseline removal processing of morphological filtering is introduced between lifting wavelet decomposition and lifting wavelet reconstruction, so that the number of layers required by lifting wavelet decomposition and reconstruction is reduced. In a digital circuit, wavelet transform needs to use a large number of multipliers, and a morphological filtering method can be realized through an adder and a subtractor, so that when the digital circuit is designed based on the pulse signal denoising method, the circuit area can be greatly reduced, the demand on hardware resources is relatively small, and the real-time performance is also obviously improved.

Description

Technical Field

[0001] The invention belongs to the field of signal processing, and in particular relates to a pulse signal denoising method based on a combination of lifting wavelet transform and morphological filtering. Background Art

[0002] Pulse is one of the physiological signals of human beings. It is generated by the activity of the heart cycle and is affected by the human heart, blood vessels, internal organs, etc. The health status of a person can be diagnosed by checking the pulse. The pulse signal is a typical non-stationary weak signal with the characteristics of small amplitude and low frequency. It is easily interfered during the acquisition process. In the collected pulse signal data, the noise mainly includes (1) electromyographic noise; (2) power frequency interference; (3) baseline drift. Electromyographic noise is usually high-frequency noise. Power frequency interference is affected by the mains power supply and is usually 50Hz. Baseline drift is generally caused by factors such as body movement and breathing of the collector, and the frequency is usually 0~1Hz.

[0003] Therefore, the original collected pulse signal needs to be denoised before it can be used for subsequent data analysis. Wavelet transform is a time-frequency analysis method commonly used in pulse analysis. It achieves noise processing, feature analysis, data compression and other effects by decomposing and processing the signal layer by layer. Wavelet transform can effectively process myoelectric noise, power frequency interference and other noise in pulse signal data, but it cannot effectively process baseline drift that overlaps with the pulse signal frequency.

[0004] In the invention patent with application number CN201410665880.4, a "method for denoising ECG signals based on morphological filtering and lifting wavelet transform" is provided. Although the lifting wavelet and morphological filtering methods reduce the amount of calculation and hardware resources to a certain extent, the morphological filtering operation is only used to denoise the reconstructed signal, and the two algorithms cannot be effectively combined to overcome the calculation delay problem caused by morphological filtering. Therefore, if this method is used for denoising pulse signals, it still needs to perform a large number of levels of wavelet decomposition and reconstruction in actual implementation, and the amount of calculation and hardware resource consumption are still large.

[0005] Therefore, how to reduce the amount of calculation and hardware resource consumption in the process of pulse signal denoising so that it is suitable for implementation through digital circuits is a technical problem that needs to be solved urgently. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that pulse signal denoising processing in the prior art consumes a large amount of calculation and hardware resources, and to provide a pulse signal denoising method based on a combination of lifting wavelet transform and morphological filtering.

[0007] The specific technical solutions adopted by the present invention are as follows:

[0008] The present invention provides a pulse signal denoising method based on a combination of lifting wavelet transform and morphological filtering, which comprises:

[0009] S1. Perform multi-layer lifting wavelet decomposition on the pulse signal to be processed, and the decomposition results obtained in each layer include two parts: an approximate signal and a detail signal. The approximate signal is input to the next layer to continue the lifting wavelet decomposition, and the detail signal is input to the threshold function for processing so that the signal value less than the specified threshold is set to zero, thereby obtaining the processed detail signal; the total number of layers of the multi-layer lifting wavelet decomposition must satisfy the frequency bandwidth of the approximate signal obtained by the last layer of lifting wavelet decomposition is less than 16 Hz;

[0010] S2, applying one-dimensional morphological filtering to the approximate signal obtained by the last layer of lifting wavelet decomposition, extracting the baseline in the approximate signal, and then performing baseline removal processing on the approximate signal obtained by the last layer of lifting wavelet decomposition according to the extracted baseline to obtain the approximate signal after drift is filtered out;

[0011] S3. Reversely use the detail signal processed by the threshold function obtained in each layer of the multi-layer lifting wavelet decomposition to perform multi-layer lifting wavelet reconstruction on the approximate signal after drift is filtered out, wherein the reconstructed signal of the first layer of lifting wavelet reconstruction is the approximate signal after drift is filtered out, and the input of each of the remaining layers of lifting wavelet reconstruction is the reconstructed signal obtained in the previous layer and the processed detail signal of the corresponding scale; the total number of layers of the multi-layer lifting wavelet reconstruction is the same as the total number of layers of the multi-layer lifting wavelet decomposition, and the reconstructed signal obtained by the last layer of lifting wavelet reconstruction is used as the pulse signal after denoising.

[0012] Preferably, the total number of layers of the multi-layer lifting wavelet decomposition needs to satisfy the frequency bandwidth of the approximate signal obtained by the last layer of lifting wavelet decomposition is 0.5-16 Hz.

[0013] Preferably, the total number of layers of the multi-layer lifting wavelet reconstruction and the multi-layer lifting wavelet decomposition are both 6 layers.

[0014] Preferably, the threshold function adopts a hard threshold function, in which the relative size of the detail signal coefficient at each moment in the detail signal and the specified threshold needs to be determined. If the detail signal coefficient at a moment is less than the specified threshold, the detail signal coefficient at this moment is set to zero, otherwise the detail signal coefficient at this moment is not processed.

[0015] Preferably, the threshold function adopts a soft threshold function, in which the relative size of the detail signal coefficient at each moment in the detail signal and the specified threshold needs to be determined. If the detail signal coefficient at a moment is less than the specified threshold, the detail signal coefficient at this moment is set to zero, otherwise the detail signal coefficient at this moment is transformed into the product of the sgn function output value of the detail signal coefficient and the coefficient difference, and the coefficient difference is the difference obtained by subtracting the absolute value of the detail signal coefficient from the specified threshold.

[0016] Preferably, the wavelet basis used in the multi-layer lifting wavelet decomposition is Symlets wavelet.

[0017] Preferably, the Symlets wavelet adopts the sym6 wavelet.

[0018] Preferably, the method for extracting the baseline from the approximate signal obtained by the last layer of lifting wavelet decomposition through one-dimensional morphological filtering is as follows: the approximate signal obtained by the last layer of lifting wavelet decomposition is used as the input of the first filter branch and the second filter branch respectively; in the first filter branch, the input approximate signal is first opened and then closed to obtain a first output signal; in the second filter branch, the input approximate signal is first closed and then opened to obtain a second output signal; the first output signal and the second output signal are averaged, and the average signal obtained is the baseline.

[0019] Preferably, the opening operation is to first perform an expansion operation on the signal using a structure element, and then perform an erosion operation on the expansion operation result, and the structure element used is a triangular structure element whose length is greater than one pulse signal cycle.

[0020] Preferably, the closing operation is to first perform an erosion operation on the signal using a structure element and then perform an expansion operation on the result of the erosion operation, and the structure element used is a triangular structure element whose length is greater than one pulse signal cycle.

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

[0022] 1) The present invention couples lifting wavelet transform with morphological filtering, and reduces the number of layers required for lifting wavelet decomposition and reconstruction by introducing morphological filtering baseline removal processing between lifting wavelet decomposition and lifting wavelet reconstruction. Since wavelet transform requires a large number of multipliers in digital circuits, while morphological filtering methods can be implemented through adders and subtractors, when designing digital circuits based on the pulse signal denoising method of the present invention, the circuit area can be greatly reduced, and the demand for hardware resources can be reduced.

[0023] 2) Since the kernel function length of the morphological method needs to match the signal period, the approximate signal of the present invention has been pre-decomposed by wavelet transform before morphological filtering so that the signal is compressed layer by layer. Therefore, the kernel function length used in the morphological filtering is also greatly shortened. At this time, the clock period required by the morphological filter is greatly reduced, which can further ensure the real-time performance of the filter.

[0024] 3) The present invention organically combines the advantages of lifting wavelet transform and morphological filtering, and can greatly reduce the area of ​​digital circuits designed based on the denoising method without substantially losing the denoising effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of the steps of the pulse signal denoising method of the present invention;

[0026] Figure 2 Schematic diagram for lifting wavelet decomposition;

[0027] Figure 3 Schematic diagram for lifting wavelet reconstruction;

[0028] Figure 4 Flow chart of the method for extracting baseline by one-dimensional morphological filtering;

[0029] Figure 5 It is the overall flow chart of the pulse signal denoising method;

[0030] Figure 6 The figure is a comparison diagram of the original pulse signal and the approximate signal obtained under two different methods;

[0031] Figure 7 Schematic diagram of the triangular structural element selected in the opening operation and the closing operation;

[0032] Figure 8 The figure is a comparison of the area of ​​the digital circuit layouts of the present invention and the comparison group. DETAILED DESCRIPTION

[0033] In order to make the above-mentioned purpose, features and advantages of the present invention more obvious and easy to understand, the specific implementation mode of the present invention is described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. The technical features in each embodiment of the present invention can be combined accordingly without conflicting with each other.

[0034] like Figure 1As shown, in a preferred embodiment of the present invention, a pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering is provided. The pulse signal denoising method organically combines lifting wavelet transform and morphological filtering, and overcomes the calculation delay problem caused by morphological filtering by combining their respective advantages, while greatly saving the calculation amount and hardware resource consumption required for signal denoising, and can be well applied to the design of digital circuits capable of realizing pulse signal denoising. The specific implementation of each of steps S1 to S3 of the pulse signal denoising method is described in detail below.

[0035] S1. Perform multi-layer lifting wavelet decomposition on the pulse signal to be processed. The decomposition results obtained in each layer include two parts: an approximate signal and a detail signal. The approximate signal is input to the next layer to continue the lifting wavelet decomposition, and the detail signal is input to the threshold function for processing so that the signal value less than the specified threshold is set to zero, so as to obtain the processed detail signal. The total number of layers of the multi-layer lifting wavelet decomposition must satisfy that the frequency bandwidth of the approximate signal obtained by the last layer of lifting wavelet decomposition is less than 16 Hz.

[0036] It should be noted that lifting wavelet, also known as the second generation wavelet, is a wavelet transform method that has a significant computational advantage over traditional wavelet transform. Lifting wavelet decomposition belongs to the existing technology and can be implemented using the existing technology. The algorithm process of lifting wavelet decomposition is divided into three operations: splitting, prediction, and updating. Figure 2 As shown, when each layer performs lifting wavelet decomposition, the splitting operation divides the input signal Xin into odd and even sequences, namely d0=x(2n-1) and s0=x(2n); the prediction operation uses one of the sequences to perform prediction operations on the other sequence; the update operation uses the prediction results to update the predicted sequence. The prediction and update operations can be repeated and iterated continuously, and finally the scaling factor K is used to scale the updated approximate signal and detail signal (the approximate signal is amplified K times, and the detail signal is reduced K times) to ensure the data smoothness of the calculation results and output the final approximate signal cA and detail signal cD. Corresponding to the lifting wavelet decomposition is the lifting wavelet reconstruction, which is the inverse operation of the lifting wavelet decomposition. The lifting wavelet reconstruction process of each layer is as follows. Figure 3 As shown, for the approximate signal cA and detail signal cD that need to be reconstructed, the scaling factor K can be reused to scale both (the approximate signal cA is reduced by K times, and the detail signal cD is enlarged by K times), and then after repeated iterative reverse update and reverse prediction operations, the final merging operation is performed to output the reconstructed result Xout.

[0037] For ease of description, the total number of decomposition layers in the multi-layer lifting wavelet decomposition is recorded as n, the approximate signal output by the first layer of lifting wavelet decomposition is cA1, and the detail signal is recorded as cD1, the approximate signal output by the second layer of lifting wavelet decomposition is cA2, and the detail signal is recorded as cD2, and so on, the approximate signal output by the nth layer of lifting wavelet decomposition is cAn, and the detail signal is recorded as cDn. Therefore, the input of the first layer of lifting wavelet decomposition is the original pulse signal to be processed, and the input of the subsequent n-1 layers of lifting wavelet decomposition is the approximate signal output by the previous layer of lifting wavelet decomposition, and finally the approximate signal cAn output by the nth layer of lifting wavelet decomposition is no longer decomposed, but needs to enter the next step of morphological filtering.

[0038] Unlike the traditional wavelet decomposition and reconstruction denoising algorithm, the present invention does not set too many layers to decompose the pulse signal to be processed. The total number of layers n of the multi-layer lifting wavelet decomposition only needs to satisfy that the frequency bandwidth of the approximate signal cAn obtained by the last layer of lifting wavelet decomposition is lower than 16 Hz. This is because the present invention introduces a one-dimensional morphological filtering operation to remove the baseline in the subsequent process. Combining the respective advantages of lifting wavelet transform and morphological filtering, the number of layers required for wavelet decomposition can be greatly reduced, thereby maintaining a good denoising effect without consuming too much computational effort and hardware resources.

[0039] Because in the process of multi-layer lifting wavelet decomposition, the approximate signal obtained by each layer of decomposition occupies most of the energy of the previous layer of signal, and retains the trend and low-frequency information of the signal, while the detail signal retains the detail changes and high-frequency information of the signal. Therefore, if the total number of decomposition layers n is too large or too small, the denoising effect of the signal will be affected. Since the signal information of the pulse wave is mainly distributed in the frequency range of 0.5~16 Hz, the high-frequency noise frequency that may be introduced is greater than 16 Hz, the power frequency interference is 50 Hz, and the baseline drift is below 1 Hz. The present invention needs to control the approximate signal cAn obtained by the last layer of lifting wavelet decomposition to be lower than 16 Hz. Preferably, the total number of layers n needs to satisfy the frequency bandwidth of the approximate signal obtained by the last layer of lifting wavelet decomposition to be 0.5~16 Hz. In the embodiment of the present invention, the collected pulse wave signal is 1000 Hz. After reasonable optimization, the total number of layers n of the final multi-layer lifting wavelet decomposition can be preferably set to 6 layers. At this time, the approximate signal frequency bandwidth is 0~15.625 Hz, and the detail signal frequency bandwidth is 15.625~31.25 Hz.

[0040] In addition, wavelet transform uses a wavelet basis with limited length and decay to replace the infinite length trigonometric function basis in Fourier transform to analyze the signal in time and frequency domain. Therefore, the focus of wavelet transform is to select a suitable wavelet basis. Common wavelet basis functions include Haar wavelet, Morlet wavelet, Daubenchies wavelet, Coiflets wavelet, Biorthogonal wavelet, Mexicanhat wavelet, Symlets wavelet, etc. Haar wavelet is the simplest but non-continuous in time domain; Morlet wavelet has symmetry, but is non-orthogonal and cannot reconstruct signals; Daubenchies wavelet has symmetry only at the first order, and other orders do not have nonlinear phase relationship, and phase distortion will occur in the process of decomposing and reconstructing signals; Symlets wavelet is a wavelet function improved on the basis of Daubenchies wavelet, with better symmetry, reducing the phase distortion problem in the process of signal decomposition and reconstruction, and it also has good compactness and orthogonality, suitable as a wavelet basis function for processing pulse signal noise. In the multi-layer lifting wavelet decomposition of the present invention, the wavelet basis used is Symlets wavelet, and when the pulse signal is analyzed by Symlets wavelet, it is found that the sym6 wavelet uses fewer update prediction operations to obtain a good noise reduction effect. Therefore, it is further preferred to use the sym6 wavelet as the wavelet basis used in the lifting wavelet decomposition.

[0041] In the present invention, each layer of detail signal is a one-dimensional vector composed of a series of detail signal coefficients at different times. All detail signals cD1~cDn obtained by n-layer lifting wavelet decomposition need to be processed by threshold function to obtain processed detail signals cD1'~cDn'. The threshold function in the present invention can be a hard threshold function or a soft threshold function. Both of them need to set the detail signal coefficients less than the threshold to zero, but there are certain differences in the processing of detail signal coefficients not less than the threshold by the two functions. The specific threshold function can be designed and optimized according to the actual situation, so as to achieve better noise reduction and feature extraction effects according to the characteristics of the pulse signal.

[0042] In the embodiment of the present invention, if the threshold function adopts a hard threshold function, then the relative size of the detail signal coefficient at each moment in the detail signal and the specified threshold needs to be determined in the hard threshold function. If the detail signal coefficient at a moment is less than the specified threshold, the detail signal coefficient at this moment is set to zero, otherwise the detail signal coefficient at this moment is not processed. The corresponding hard threshold function It can be expressed by the formula:

[0043]

[0044] Where: It represents the detail signal coefficient at a moment in the detail signal, and T is a specified threshold that can be controlled according to actual conditions.

[0045] In the embodiment of the present invention, if the threshold function adopts a soft threshold function, then the relative size of the detail signal coefficient at each moment in the detail signal and the specified threshold needs to be determined in the soft threshold function. If the detail signal coefficient at a moment is less than the specified threshold, the detail signal coefficient at this moment is set to zero. Otherwise, the detail signal coefficient at this moment is transformed into the product of the output value of the sgn function of the detail signal coefficient and the coefficient difference. The coefficient difference is the difference obtained by subtracting the absolute value of the detail signal coefficient from the specified threshold. The corresponding soft threshold function It can be expressed by the formula:

[0046]

[0047] Where: represents the detail signal coefficient at a moment in the detail signal, and T is a specified threshold value that can be controlled according to actual conditions; So is the input sgn function (i.e., symbolic function), the expression is:

[0048]

[0049] In the present invention, the threshold function can adopt either a hard threshold function or a soft threshold function. The hard threshold function uses a fixed threshold. When the detail signal coefficient amplitude is greater than or equal to the threshold T, the coefficient is retained, and when it is less than the threshold T, the coefficient is directly set to zero. This scheme will cause the signal to oscillate after the lifting wavelet reconstruction. The soft threshold function performs a difference and transformation process on the detail signal coefficients greater than or equal to the threshold T, and retains the result as a new detail signal coefficient. The detail signal coefficients less than the threshold T are directly set to zero. The soft threshold scheme avoids the possibility of oscillation, but it will lose the characteristics of the signal to a certain extent, and the threshold is difficult to select. Therefore, the specific choice of threshold function can be reasonably selected based on the results of actual tests.

[0050] For the detail signal cDi obtained by lifting wavelet decomposition of any layer, i=1,2,…,n, the detail signal coefficient w at each moment is processed by the threshold function and can be re-concatenated in order to form the processed detail signal cDi'.

[0051] S2. The approximate signal obtained by the last layer of lifting wavelet decomposition is filtered through one-dimensional morphology to extract the baseline in the approximate signal. Then, the approximate signal obtained by the last layer of lifting wavelet decomposition is subjected to baseline removal processing according to the extracted baseline to obtain the approximate signal cAn' after drift is filtered out.

[0052] In the present invention, the lifting wavelet decomposition does not execute too many layers, but stops after the approximate signal cAn is lower than 16Hz. In order to reduce the noise of the signal finally reconstructed under this decomposition method, the present invention introduces a one-dimensional morphological filter to extract the baseline part of the approximate signal obtained by the last layer of lifting wavelet decomposition, and then removes the drift in the approximate signal by removing the baseline, and then performs multi-layer lifting wavelet reconstruction on the approximate signal cAn' after filtering out the drift. The present invention can reduce the amount of calculation by using a morphological filter to replace part of the lifting wavelet decomposition layer and reconstruction layer, but can still maintain a good denoising effect.

[0053] In an embodiment of the present invention, the method flow of extracting the baseline from the approximate signal obtained by the last layer of lifting wavelet decomposition by one-dimensional morphological filtering is as follows: Figure 4 As shown, the details are as follows:

[0054] The approximate signal obtained by the last layer of lifting wavelet decomposition is used as the input of the first filter branch and the second filter branch respectively; in the first filter branch, the input approximate signal is first opened and then closed to obtain a first output signal; in the second filter branch, the input approximate signal is first closed and then opened to obtain a second output signal; the first output signal and the second output signal are averaged, and the average signal obtained is the aforementioned baseline.

[0055] It should be noted that the above-mentioned opening operation and closing operation are common operations in morphological filtering, and both are composed of expansion and erosion operations. In the embodiment of the present invention, the opening operation is to use the structure element to first perform an expansion operation on the signal, and then perform an erosion operation on the expansion operation result, and the structure element used is a triangular structure element with a length greater than one pulse signal cycle. The closing operation is to use the structure element to first perform an erosion operation on the signal, and then perform an expansion operation on the erosion operation result, and the structure element used is a triangular structure element with a length greater than one pulse signal cycle.

[0056] It should be further explained that the expansion and corrosion operations constituting the above-mentioned opening and closing operations are one of the basic operations in mathematical morphology, and the corresponding functions are realized by the most basic addition and subtraction, which will not be elaborated. When designing a digital circuit based on the pulse signal denoising method of the present invention, it is easier to implement by adders and subtractors than multipliers, and the circuit area is small, which is conducive to reducing the area and complexity of the digital circuit and improving the calculation efficiency.

[0057] In the opening and closing operations used in the above-mentioned one-dimensional morphological filtering, the selection of the structural element is crucial to the effect of the opening and closing operations. Smaller structural elements may only affect small details in the signal, while larger structural elements may significantly change the overall shape of the signal. Since the structural element determines the filtering effect, the shape of the structural element used in the present invention needs to match the geometric shape of the processed signal as much as possible, and the length of the structural element is slightly wider than the signal to be retained. The preferred structural element of the present invention is a triangular structural element, whose length is slightly larger than one pulse cycle.

[0058] In the above step S2, after the baseline is extracted, the approximate signal cAn obtained by the last layer of lifting wavelet decomposition is subtracted from the baseline to achieve baseline removal and obtain the approximate signal cAn' after drift filtering. This process belongs to the prior art and will not be described in detail.

[0059] S3. Reversely use the detail signal processed by the threshold function obtained in each layer of the multi-layer lifting wavelet decomposition to perform multi-layer lifting wavelet reconstruction on the approximate signal cAn' after drift is filtered out, wherein the reconstructed signal of the first layer of lifting wavelet reconstruction is the approximate signal cAn' after drift is filtered out, and the input of each of the remaining layers of lifting wavelet reconstruction is the reconstructed signal obtained in the previous layer and the processed detail signal of the corresponding scale; the total number of layers of the multi-layer lifting wavelet reconstruction is the same as the total number of layers of the multi-layer lifting wavelet decomposition, and the reconstructed signal obtained by the last layer of lifting wavelet reconstruction is used as the pulse signal after denoising.

[0060] Since lifting wavelet decomposition and lifting wavelet reconstruction are a set of corresponding inverse operations, the multi-layer lifting wavelet reconstruction in S3 and the multi-layer lifting wavelet reconstruction in S1 are actually one-to-one corresponding layer by layer. If the total number of layers of multi-layer lifting wavelet decomposition is n, then the total number of layers of multi-layer lifting wavelet reconstruction is also n. The input of each layer of lifting wavelet reconstruction is the reconstructed signal obtained in the previous layer and the detail signal processed by the threshold function of the corresponding scale. However, it should be noted that according to the corresponding relationship between the signal scales, when performing lifting wavelet reconstruction layer by layer, it is necessary to use the detail signal processed by the threshold function obtained in each layer of the multi-layer lifting wavelet decomposition in reverse order. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering described in S1~S3 above can be expressed as follows Figure 5The process shown. After n-layer lifting wavelet decomposition, threshold function processing and morphological filtering, the data required for n-layer lifting wavelet reconstruction can be obtained. The process of n-layer lifting wavelet reconstruction can be expressed as follows: the input of the first-layer lifting wavelet reconstruction is the approximate signal cAn' after drift is filtered out in S2 and the detail signal cDn obtained by the last layer of lifting wavelet decomposition is processed by the threshold function and output as the processed detail signal cDn'; the input of the second-layer lifting wavelet reconstruction is the reconstructed signal cA(n-1)' output by the first-layer lifting wavelet reconstruction and the detail signal cD(n-1) obtained by the last second layer of lifting wavelet decomposition is processed by the threshold function and output as the processed detail signal cD(n-1) ', the input of the third layer of lifting wavelet reconstruction is the reconstructed signal cA(n-2)' output by the second layer of lifting wavelet reconstruction and the processed detail signal cD(n-2)' output by the detail signal cD(n-2) decomposed by the third layer of lifting wavelet after being processed by the threshold function. Similarly, the input of the last layer of lifting wavelet reconstruction is the reconstructed signal cA1' output by the n-1th layer of lifting wavelet reconstruction and the processed detail signal cD(1)' output by the detail signal cD(1) decomposed by the first layer of lifting wavelet after being processed by the threshold function. The reconstructed signal output by the last layer of lifting wavelet reconstruction is recorded as the processed pulse signal, and the noise in the original pulse signal has been basically removed.

[0061] The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering described in S1 to S3 of the present invention couples the lifting wavelet transform with the morphological filtering, and reduces the number of layers required for lifting wavelet decomposition and reconstruction by introducing the baseline removal processing of morphological filtering between lifting wavelet decomposition and lifting wavelet reconstruction. Since wavelet transform requires a large number of multipliers in digital circuits, while the morphological filtering method can be implemented by adders and subtractors, when designing a denoising digital circuit based on the pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering described in S1 to S3, the circuit area can be greatly reduced, the demand for hardware resources can be reduced, and the real-time performance and efficiency of denoising can be improved.

[0062] The following is a specific example to demonstrate the specific implementation and denoising effect of the pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering described in S1 to S3 above.

[0063] Example

[0064] In this embodiment, a pulse signal with a sampling rate of 1000 Hz is used as an example of pulse information to be processed. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering described in S1 to S3 above is specifically implemented as follows:

[0065] 1) The pulse signal to be processed is subjected to multi-layer lifting wavelet decomposition. The decomposition results obtained at each layer contain two parts: the approximate signal and the detail signal. The approximate signal is input into the next layer to continue the lifting wavelet decomposition, while the detail signal is input into the threshold function for processing so that the signal value less than the specified threshold is set to zero, and the processed detail signal is obtained.

[0066] For a pulse signal with a sampling rate of 1000 Hz, Table 1 shows the frequency bandwidth of each layer coefficient obtained by performing 10-layer wavelet decomposition on the signal.

[0067] Table 1 Frequency bandwidth at each decomposition level

[0068]

[0069] As can be seen from Table 1, high-frequency noise has disappeared in the approximate signal of the 6th layer decomposition, power frequency interference is concentrated in the detail signal of the 5th layer, and baseline drift is concentrated in the approximate signal of the 10th layer wavelet decomposition. Therefore, in this embodiment, the pulse signal to be processed is subjected to multi-layer lifting wavelet decomposition with a total number of layers n of 6 layers, and the wavelet base adopts sym6 wavelet, so as to obtain the approximate signal and detail signal of the 6 layers of lifting wavelet decomposition, wherein the frequency bandwidth of the approximate signal obtained by the last layer of lifting wavelet decomposition is 0~15.625Hz, and the bandwidth is lower than 16 Hz.

[0070] In this embodiment, the approximate signal obtained by each layer of lifting wavelet decomposition needs to be processed using a hard threshold function. In the hard threshold function, the relative size of the detail signal coefficient at each moment in the detail signal and the specified threshold needs to be determined. If the detail signal coefficient at a moment is less than the specified threshold, the detail signal coefficient at this moment is set to zero, otherwise the detail signal coefficient at this moment is not processed. In this embodiment, the specified threshold is set to 0.5, so the corresponding hard threshold function It is expressed by the formula:

[0071]

[0072] 2) The approximate signal obtained by the last layer of lifting wavelet decomposition is filtered through one-dimensional morphology to extract the baseline in the approximate signal. Then, the approximate signal obtained by the last layer of lifting wavelet decomposition is de-baselined according to the extracted baseline to obtain the approximate signal after drift is filtered out.

[0073] In this embodiment, if Figure 6As shown in the figure, the original pulse signal (referred to as the original signal) and the approximate signals obtained in two different ways are shown. In the "wavelet transform denoising" group, the original signal is directly decomposed by lifting wavelet using 10 layers of sym6 wavelet basis to obtain the approximate signal, while in the "wavelet transform combined with morphological denoising" group, the original signal is first decomposed by lifting wavelet using 6 layers of sym6 wavelet basis to obtain the approximate signal with a bandwidth of 0~15.625Hz according to the above steps S1 and S2, and then the approximate signal is further processed by morphological filtering. Figure 4 As shown, in this embodiment, the opening operation is to use the structure element to first perform an expansion operation on the signal, and then perform an erosion operation on the expansion operation result, and the structure element used is a triangular structure element with a length greater than one pulse signal cycle; and the closing operation is to use the structure element to first perform an erosion operation on the signal, and then perform an expansion operation on the erosion operation result, and the structure element used is a triangular structure element with a length greater than one pulse signal cycle. In this embodiment, the selected structure elements in the opening operation and the closing operation are as follows Figure 7 As shown, it is a triangle with a height of 2.5 and a width of 1024 (corresponding to the signal length), and its length is slightly larger than one pulse cycle.

[0074] Finally, from Figure 6 It can be seen that after the present invention introduces morphological filtering processing, even if only 6 layers of lifting wavelet decomposition are used, its filtering result is still close to the approximate signal obtained by using 10 layers of lifting wavelet decomposition. However, wavelet transform requires the use of a large number of multipliers, while the morphological method can be implemented through adders and subtractors. Therefore, "wavelet transform combined with morphological denoising" can effectively reduce the circuit area required for subsequent digital circuit design. At the same time, the kernel function length of the morphological method needs to match the signal period, which is the main reason affecting the real-time performance of the morphological filter. However, after wavelet transform decomposition, the signal is compressed layer by layer, and the kernel function length used in morphological filtering is greatly shortened. At this time, the clock cycle required by the morphological filter in "wavelet transform combined with morphological denoising" is greatly reduced, which can further ensure the real-time performance of the filter.

[0075] 3) Reversely use the detail signal processed by the threshold function obtained in each layer of the multi-layer lifting wavelet decomposition to perform multi-layer lifting wavelet reconstruction on the approximate signal after drift filtering, where the reconstructed signal of the first layer of lifting wavelet reconstruction is the approximate signal after drift filtering, and the input of each of the remaining layers of lifting wavelet reconstruction is the reconstructed signal obtained in the previous layer and the processed detail signal of the corresponding scale.

[0076] In this embodiment, the overall decomposition, filtering and reconstruction process is as described above. Figure 5As shown in FIG. 1 , the total number of layers of multi-layer lifting wavelet reconstruction is the same as the total number of layers of multi-layer lifting wavelet decomposition, both of which are 6 layers. Lifting wavelet reconstruction is the inverse operation of lifting wavelet recombination. The reconstructed signal obtained by the last layer of lifting wavelet reconstruction is used as the pulse signal after denoising.

[0077] This embodiment is based on the above Figure 5 The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering is shown. The pulse signal denoising filter digital circuit of the pulse signal denoising method is implemented by System Verilog hardware language design, and verified by using Xilinx's xc7k325tffg676-2 chip. At the same time, for intuitive comparison, this embodiment also directly uses the lifting wavelet decomposition of 10 layers of sym6 wavelet basis to directly decompose the original signal according to the method in the aforementioned "wavelet transform denoising" group to obtain an approximate signal, and then uses 10 layers of lifting wavelet to reconstruct the restored signal. This method is recorded as the comparison group.

[0078] The results show that this method can effectively filter out high-frequency noise and baseline, reduce hardware resource consumption, and ensure the real-time performance of the algorithm. Figure 8 a) shows the digital circuit layout obtained on the FPGA chip model xc7k325tffg676-2 according to the comparison group method, and b) shows the digital circuit layout obtained according to the method of this embodiment. It can be clearly seen that the area of ​​the digital circuit of the present invention is greatly reduced compared with the comparison group. For the pulse signal data with a data length of 66541, it takes about 4.658016631 seconds to process the data segment after the test digital circuit. The returned data is plotted and it can be seen that the signal high-frequency noise and baseline drift are well filtered out. Compared with the traditional wavelet filter, the present invention reduces the use of LUT from 79.84% to 50.52%, and the use of DSP from 38.10% to 22.86%, effectively saving hardware resources.

[0079] The above-described embodiments are only some preferred implementations of the present invention, but are not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims

1. A pulse signal denoising method based on a combination of lifting wavelet transform and morphological filtering, characterized in that: include: S1. Perform multi-layer lifting wavelet decomposition on the pulse signal to be processed, and the decomposition results obtained in each layer include two parts: an approximate signal and a detail signal. The approximate signal is input to the next layer to continue the lifting wavelet decomposition, and the detail signal is input to the threshold function for processing so that the signal value less than the specified threshold is set to zero, thereby obtaining the processed detail signal; the total number of layers of the multi-layer lifting wavelet decomposition must satisfy the frequency bandwidth of the approximate signal obtained by the last layer of lifting wavelet decomposition is less than 16 Hz; S2, applying one-dimensional morphological filtering to the approximate signal obtained by the last layer of lifting wavelet decomposition, extracting the baseline in the approximate signal, and then performing baseline removal processing on the approximate signal obtained by the last layer of lifting wavelet decomposition according to the extracted baseline to obtain the approximate signal after drift is filtered out; S3. Reversely use the detail signal processed by the threshold function obtained in each layer of the multi-layer lifting wavelet decomposition to perform multi-layer lifting wavelet reconstruction on the approximate signal after drift is filtered out, wherein the reconstructed signal of the first layer of lifting wavelet reconstruction is the approximate signal after drift is filtered out, and the input of each of the remaining layers of lifting wavelet reconstruction is the reconstructed signal obtained in the previous layer and the processed detail signal of the corresponding scale; the total number of layers of the multi-layer lifting wavelet reconstruction is the same as the total number of layers of the multi-layer lifting wavelet decomposition, and the reconstructed signal obtained by the last layer of lifting wavelet reconstruction is used as the pulse signal after denoising.

2. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 1, characterized in that: The total number of layers of the multi-layer lifting wavelet decomposition must satisfy the frequency bandwidth of the approximate signal obtained by the last layer of lifting wavelet decomposition is 0.5~16 Hz.

3. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 1, characterized in that: The total number of layers of the multi-layer lifting wavelet reconstruction and the multi-layer lifting wavelet decomposition are both 6 layers.

4. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 1, characterized in that: The threshold function adopts a hard threshold function, in which the relative size of the detail signal coefficient at each moment in the detail signal and the specified threshold needs to be judged. If the detail signal coefficient at a moment is less than the specified threshold, the detail signal coefficient at this moment is set to zero, otherwise the detail signal coefficient at this moment is not processed.

5. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 1, characterized in that: The threshold function adopts a soft threshold function, in which the relative size of the detail signal coefficient at each moment in the detail signal and the specified threshold needs to be determined. If the detail signal coefficient at a moment is less than the specified threshold, the detail signal coefficient at this moment is set to zero, otherwise the detail signal coefficient at this moment is transformed into the product of the sgn function output value of the detail signal coefficient and the coefficient difference, and the coefficient difference is the difference obtained by subtracting the absolute value of the detail signal coefficient from the specified threshold.

6. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 1, characterized in that: The wavelet basis used in the multi-layer lifting wavelet decomposition is the Symlets wavelet.

7. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 6, characterized in that: The Symlets wavelet adopts the sym6 wavelet.

8. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 1, characterized in that: The method for extracting the baseline from the approximate signal obtained by the last layer of lifting wavelet decomposition by one-dimensional morphological filtering is as follows: the approximate signal obtained by the last layer of lifting wavelet decomposition is used as the input of the first filter branch and the second filter branch respectively; in the first filter branch, the input approximate signal is first opened and then closed to obtain a first output signal; in the second filter branch, the input approximate signal is first closed and then opened to obtain a second output signal; The first output signal and the second output signal are averaged, and the obtained average signal is the baseline.

9. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 8, characterized in that: The opening operation is to use a structure element to first perform an expansion operation on the signal, and then perform an erosion operation on the expansion operation result, and the structure element used is a triangular structure element with a length greater than one pulse signal cycle.

10. The pulse signal denoising method based on the combination of lifting wavelet transform and morphological filtering as claimed in claim 8, characterized in that: The closing operation is to use a structure element to first perform an erosion operation on the signal, and then perform an expansion operation on the result of the erosion operation, and the structure element used is a triangular structure element whose length is greater than one pulse signal cycle.

Images