CN114098656B - Signal noise reduction method and system based on empirical mode decomposition and bit plane conversion - Google Patents

Signal noise reduction method and system based on empirical mode decomposition and bit plane conversion Download PDF

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CN114098656B
CN114098656B CN202210093782.2A CN202210093782A CN114098656B CN 114098656 B CN114098656 B CN 114098656B CN 202210093782 A CN202210093782 A CN 202210093782A CN 114098656 B CN114098656 B CN 114098656B
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陈丹妮
丁俊涛
凌永权
王淑云
刘庆
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Guangdong University of Technology
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Abstract

The invention provides a signal noise reduction method and a system based on empirical mode decomposition and bit plane conversion, relates to the technical field of bioelectrical signal noise reduction processing, solves the problem that the current method for signal noise reduction only by EMD has poor noise reduction effect, firstly uses the empirical mode decomposition to quickly decompose the original signal to be processed, then, noise degree evaluation is carried out after reconstruction, the reconstruction signal to be denoised is positioned in a broad sense, then, by means of the mode of carrying out bit plane conversion on the reconstruction signal to be denoised to obtain a bit plane matrix, the local amplitude denoising processing of the signal is realized, the denoising process of the signal is ensured to be more detailed, and then, the bit plane matrix is restored to obtain a quantized signal, and then empirical mode decomposition is carried out again to remove a quantization error, so that signal refinement and noise reduction are realized on the whole, and the noise reduction effect is improved.

Description

Signal noise reduction method and system based on empirical mode decomposition and bit plane conversion
Technical Field
The invention relates to the technical field of bioelectrical signal noise reduction processing, in particular to a signal noise reduction method and a signal noise reduction system based on empirical mode decomposition and bit plane conversion.
Background
Electrocardiosignals, electroencephalogram signals and the like are typical non-stable and weak bioelectric signals, the signals are often accompanied by very serious high-frequency and low-frequency noises, and noise frequency bands are often overlapped with original frequency bands of the signals, so that the noise reduction processing is very difficult. In addition, in the signal acquisition and transmission process, noise is inevitably mixed due to the influence of external environment interference and instruments, the noise can influence target signal detection, feature extraction and regression prediction, and particularly in the analysis of some high-precision data, very weak noise can also have great influence on an analysis result, so that the noise reduction processing is of great importance in the signal analysis process.
The noise reduction processing method needs to adapt to different signals, wherein Empirical Mode Decomposition (EMD) has been widely used in biomedical fields, such as electrocardiogram signal analysis, blood pressure signal denoising, heartbeat signal analysis, etc., due to its good adaptability when analyzing nonlinear and non-stationary signals. The EMD decomposes the complex signal into a finite number of Intrinsic Mode Functions (IMFs), namely, the signal is decomposed into signals of different frequency bands, and each decomposed IMF component comprises local characteristic signals of different frequencies of the original signal; then, the high-frequency eigenmode function IMF is regarded as noise, after the high-frequency eigenmode function IMF is removed, the residual IMF component is reconstructed to obtain a denoised signal, in the process, any basis function does not need to be preset, the method is suitable for analyzing a nonlinear and non-stationary signal sequence, the non-stationary data can be subjected to stationary processing, and the method has a high signal-to-noise ratio, so that a certain denoising processing effect is achieved. However, the removed high-frequency eigenmode function IMF may include original signal information, which may result in a signal to be reconstructed subsequently being free of noise but the original signal information is seriously insufficient, and in the remaining IMF components remaining, there may be residual noise, which may result in a poor noise reduction effect.
The method includes the steps of firstly obtaining an energy curve based on IMF energy of each order after EMD decomposition, calculating orders of a first maximum point and a first minimum point of the energy curve except for a boundary point, determining IMF order change points needing denoising by combining the tolerance value instead of directly discarding IMF components of certain orders in the traditional method, then denoising each order of IMF before the IMF order change points in a threshold manner, reconstructing each order of IMF after threshold denoising, IMF without threshold denoising and residual errors, and completely keeping original signal characteristics of the part larger than the threshold, and is beneficial to improvement of denoising quality. But is limited to retaining the original signal information for more than a threshold portion and may also have residual noise. .
Disclosure of Invention
In order to solve the problem that the noise reduction effect of the current signal noise reduction method only by adopting EMD is poor, the invention provides a signal noise reduction method and system based on empirical mode decomposition and bit plane conversion, which realize the detailed noise reduction processing of signals and improve the noise reduction effect.
In order to achieve the technical effects, the technical scheme of the invention is as follows:
a signal noise reduction method based on empirical mode decomposition and bit plane conversion comprises the following steps:
s1, acquiring an original signal to be processed, and performing empirical mode decomposition on the original signal to obtain a signal component and reconstruct the signal component;
s2, evaluating the noise degree of the reconstructed signal, judging whether the reconstructed signal has noise or not, and if so, executing a step S3; otherwise, ending;
s3, carrying out bit plane conversion on the reconstructed signal to obtain a bit plane matrix;
s4, determining noise amplitude according to the reconstructed signal, and determining the bit number occupied by the noise according to the noise amplitude;
s5, local amplitude noise reduction is carried out: obtaining a bit plane matrix corresponding to the local amplitude noise reduction signal according to the bit number occupied by the noise and the bit plane matrix;
s6, restoring a bit plane matrix corresponding to the local amplitude noise reduction signal to obtain a quantized signal;
and S7, carrying out empirical mode decomposition on the quantized signal to obtain a final noise reduction signal.
In the technical scheme, the method for signal noise reduction only by adopting EMD is considered to have poor noise reduction effect, but the EMD has unique advantages, so that firstly, the original signal to be processed is quickly decomposed by using empirical mode decomposition to obtain a signal component, then, the signal component is reconstructed and then noise degree is evaluated, the reconstructed signal to be noise reduced is positioned in a broad sense (because the actually acquired signal does not know whether the signal completely does not contain noise, but the time, labor and material cost are required for blindly denoising all the acquired signals, so that the noise degree is evaluated under the set condition when the signal is smooth enough and is taken as the boundary of noise reduction in a broad sense) according to the requirement, then, the local amplitude noise reduction processing of the signal is realized by means of carrying out bit plane conversion on the reconstructed signal to be noise reduced to obtain a bit plane matrix, the noise reduction process of the signals is ensured to be more careful, then the bit plane matrix is restored, after the quantized signals are obtained, empirical mode decomposition is carried out again to remove quantization errors, the signal careful noise reduction processing is integrally realized, and the noise reduction effect is improved.
Preferably, in step S1, the empirical mode decomposition is performed on the original signal, and the process of obtaining and reconstructing the signal component is as follows:
s11, setting y (t) to represent an original signal to be processed, wherein t represents a time sequence, and fitting a local maximum value and a local minimum value of the original signal by utilizing a cubic spline interpolation method to form a smooth envelope line;
s12, extracting an upper envelope emax (t) and a lower envelope emin (t) of the smooth envelope, calculating an average value m1(t) of the upper envelope and the lower envelope, and calculating an expression as follows:
m1(t)=[emax(t)+emin(t)]/2；
s13, calculating the difference between the original signal and the average value to obtain a middle signal time sequence h1 (t);
s14, judging whether a negative local maximum value and a positive local minimum value exist in the intermediate signal time h1(t), if so, taking the intermediate signal h1(t) as a new original signal, and returning to the step S11; otherwise, the intermediate signal h1(t) is the first eigenmode function IMF of the original signal y (t), and step S15 is executed;
s15, subtracting the intermediate signal h1(t) from the original signal y (t) to obtain a first residual signal r1 (t);
s16, taking the first remainder signal r1(t) as a new original signal to be processed, returning to the step S11, repeating the steps S11-S15, sequentially obtaining a middle signal time sequence hi (t) as an eigenmode function IMF until obtaining a remainder signal sequence rn (t) which is monotonous or has a value smaller than a preset threshold value A, completing empirical mode decomposition, and obtaining a signal component hi (t), wherein n represents the number of the eigenmode function IMF;
s17, reconstructing the signal component hi (t) to obtain a reconstructed signal
Figure 387181DEST_PATH_IMAGE001
And satisfies the following conditions:
Figure 465864DEST_PATH_IMAGE002
where k represents the number of selected signal components and fi (t) represents the signal components. Typically selected by human experience depending on the particular signal application.
Preferably, the noise degree evaluation is performed on the reconstructed signal, and the process of determining whether noise exists in the reconstructed signal satisfies the following conditions:
assuming that the length of the reconstructed signal is U, the reconstructed signal is characterized as:
Figure 747591DEST_PATH_IMAGE003
;
detecting maximum and minimum points of the reconstructed signal sequence, setting the number of the detection points corresponding to the obtained maximum and minimum points as z, and setting the judgment threshold of the detection points as num _ peaks, wherein the judgment threshold of the detection points is determined by the signal noise reduction processing requirement;
when z < num _ peaks, the signal sequence is reconstructed
Figure 789496DEST_PATH_IMAGE004
No noise exists in the process; otherwise, reconstructing the signal sequence
Figure 398201DEST_PATH_IMAGE004
There is noise.
Here, since the actually acquired signals are not known whether the actually acquired signals completely do not contain noise, but time, labor and material costs are required for blindly denoising all the acquired signals, conditions are set for noise degree evaluation when the signals are smooth enough according to needs, and the noise degree evaluation is broadly used as a boundary for denoising, that is, a judgment threshold num _ peaks of a detection point is set, so that whether noise exists in a reconstructed signal sequence is determined in a broad sense, and the efficiency of signal denoising processing is further improved.
Preferably, assuming that the bit-plane transformation is performed on the reconstructed signal in step S3, the obtained bit-plane matrix is represented as an M × N matrix B, and the process of obtaining the bit-plane matrix is as follows:
reconstructing each decimal data point in the signal sequence
Figure 336201DEST_PATH_IMAGE005
And converting into binary data points, and satisfying the following conditions:
Figure 633452DEST_PATH_IMAGE006
wherein, M represents the converted binary digit number, depends on the bit depth parameter set when the hardware stores the signal data, and is also the row number of the matrix B;
is provided with
Figure 10207DEST_PATH_IMAGE007
Wherein, in the step (A),
Figure 207839DEST_PATH_IMAGE008
，
Figure 64543DEST_PATH_IMAGE009
p =1, …, N, then the bit-plane matrix is represented as:
Figure 98358DEST_PATH_IMAGE010
each column of the bit plane matrix B is a binary representation vector bp corresponding to each decimal data point of the reconstructed signal sequence, and binary bits from high to low are represented in the vector bp from top to bottom;
any element value in the M-th row element of the bit plane matrix B is greater than or equal to 0 and less than or equal to 1, and the other row elements except the M-th row element are 0 or 1.
Preferably, the process of determining the noise amplitude according to the reconstructed signal in step S4 is:
s41, recording coordinates corresponding to the detection points of q maximum and minimum points in the reconstructed signal sequence, sequencing the coordinates corresponding to all the detection points in an ascending order according to the size of an abscissa to obtain an abscissa sequence vx and an ordinate sequence vy, wherein,
Figure 996913DEST_PATH_IMAGE011
，
Figure 65363DEST_PATH_IMAGE012
,
Figure 95899DEST_PATH_IMAGE013
;
s42, calculating the difference value of the longitudinal coordinate values of the corresponding coordinates of every two adjacent detection points to obtain a difference sequence
Figure 617010DEST_PATH_IMAGE014
Wherein, in the step (A),
Figure 319255DEST_PATH_IMAGE015
；
s43, taking absolute values of all elements in the difference sequence d, counting the absolute values into a histogram, and taking the middle value of the interval corresponding to the square column with the highest histogram frequency as Noise amplitude Noise.
Preferably, the expression for determining the bit number occupied by the noise according to the noise amplitude is as follows:
Figure 242212DEST_PATH_IMAGE016
wherein, the first and the second end of the pipe are connected with each other,
Figure 434859DEST_PATH_IMAGE017
representing the bit number occupied by noise; noise represents the Noise amplitude. This process determines the noise amplitude in the signal.
Preferably, when the local amplitude noise reduction is performed in step S5, according to the bit number occupied by the noise and the bit plane matrix, the bit plane matrix corresponding to the local amplitude noise reduction signal is obtained as
Figure 958113DEST_PATH_IMAGE018
，
Figure 152466DEST_PATH_IMAGE018
Element (1) of
Figure 680661DEST_PATH_IMAGE019
Satisfies the following conditions:
Figure 364583DEST_PATH_IMAGE020
。
in this case, after the noise amplitude in the signal has been determined, this part of the noise has to be removed, so that the noise amplitude is determined in the signal
Figure 843975DEST_PATH_IMAGE021
And forcibly setting the bit number corresponding to the noise amplitude to zero to realize the noise reduction of the local amplitude.
Preferably, in step S6, the process of restoring the bit plane matrix corresponding to the local amplitude noise reduction signal to obtain the quantized signal satisfies:
Figure 638756DEST_PATH_IMAGE022
wherein the content of the first and second substances,
Figure 221790DEST_PATH_IMAGE023
representing a quantized signal sequence;
Figure 60302DEST_PATH_IMAGE018
representing a bit plane matrix corresponding to the local amplitude noise reduction signal;
Figure 43302DEST_PATH_IMAGE008
. In the process, bit plane conversion is introduced, the original signal data points are converted into binary data, and quantized signals corresponding to the decimal data points are recovered by means of a reduction process.
The present application further provides a signal noise reduction system based on empirical mode decomposition and bit plane transformation, where the system is configured to implement the signal noise reduction method based on empirical mode decomposition and bit plane transformation, and the system includes:
the signal acquisition processing module is used for acquiring an original signal to be processed, and performing empirical mode decomposition on the original signal to obtain a signal component and reconstruct the signal component;
the noise degree evaluation module is used for evaluating the noise degree of the reconstructed signal and judging whether the reconstructed signal has noise;
the bit plane conversion module is used for carrying out bit plane conversion on the reconstructed signal to obtain a bit plane matrix when noise exists in the reconstructed signal;
the noise bit calculation module is used for determining the noise amplitude according to the reconstructed signal and determining the bit number occupied by the noise according to the noise amplitude;
the local amplitude noise reduction module is used for obtaining a bit plane matrix corresponding to the local amplitude noise reduction signal according to the bit number occupied by the noise and the bit plane matrix;
the restoring module is used for restoring the bit plane matrix corresponding to the local amplitude noise reduction signal to obtain a quantized signal;
and the output module is used for carrying out empirical mode decomposition on the quantized signal to obtain a final noise reduction signal.
In the technical scheme, a signal noise reduction system for realizing the signal noise reduction method is packaged, firstly, a signal acquisition processing module acquires an original signal to be processed, empirical mode decomposition is carried out on the original signal to obtain a signal component and reconstruct the signal component, a primary processing process is completed, then, a noise degree evaluation module carries out noise degree evaluation on the reconstructed signal component after reconstructing the signal component, the reconstructed signal to be noise reduced is positioned in a broad sense, then, a bit plane matrix is obtained by means of bit plane transformation of the reconstructed signal by means of bit plane transformation module, local amplitude noise reduction processing of the signal is realized by the cooperation of a noise bit calculation module and a local amplitude noise reduction module, the noise reduction process of the signal is ensured to be more detailed, then, the bit plane matrix is restored by a restoration module, the quantized signal is obtained, and then, empirical mode decomposition is carried out through an output module again to remove quantization errors, all modules are matched with each other on the whole, signal careful noise reduction processing is realized, and the noise reduction effect is improved.
Preferably, a first empirical mode decomposition module is arranged in the signal acquisition processing module and is used for performing empirical mode decomposition on the original signal; and the output module is provided with a second empirical mode decomposition module used for carrying out empirical mode decomposition on the quantized signal.
In the scheme, the empirical mode decomposition algorithm is packaged in each of the first empirical mode decomposition module and the second empirical mode decomposition module, and the method considers that the noise reduction effect of the current method for signal noise reduction only by adopting the EMD is poor, but the EMD has unique advantages, and fully utilizes the advantages.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention provides a signal noise reduction method and a system based on empirical mode decomposition and bit plane conversion.
Drawings
Fig. 1 is a schematic flowchart of a signal noise reduction method based on empirical mode decomposition and bit plane transformation according to embodiment 1 of the present invention;
fig. 2 is a schematic diagram illustrating a process of performing bit plane transformation on a reconstructed signal to obtain a bit plane matrix according to embodiment 2 of the present invention;
fig. 3 is a block diagram of a signal noise reduction system based on empirical mode decomposition and bit plane conversion according to embodiment 3 of the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for better illustration of the present embodiment, certain parts of the drawings may be omitted, enlarged or reduced, and do not represent actual dimensions;
it will be understood by those skilled in the art that certain well-known descriptions of the figures may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
example 1
The embodiment provides a signal noise reduction method based on empirical mode decomposition and bit plane conversion for fully utilizing the unique advantage of the current method for signal noise reduction only by using the EMD, which has a poor noise reduction effect, and the flow schematic diagram of the method is shown in fig. 1, and specifically includes the following steps:
s1, acquiring an original signal to be processed, and performing empirical mode decomposition on the original signal to obtain a signal component and reconstruct the signal component;
s2, evaluating the noise degree of the reconstructed signal, judging whether the reconstructed signal has noise or not, and if so, executing a step S3; otherwise, ending;
s3, carrying out bit plane conversion on the reconstructed signal to obtain a bit plane matrix;
s4, determining noise amplitude according to the reconstructed signal, and determining the bit number occupied by the noise according to the noise amplitude;
s5, local amplitude noise reduction is carried out: obtaining a bit plane matrix corresponding to the local amplitude noise reduction signal according to the bit number occupied by the noise and the bit plane matrix;
s6, restoring a bit plane matrix corresponding to the local amplitude noise reduction signal to obtain a quantized signal;
and S7, carrying out empirical mode decomposition on the quantized signal to obtain a final noise reduction signal.
On the whole, firstly, the original signal to be processed is rapidly decomposed by using empirical mode decomposition to obtain a signal component, then, the noise degree is evaluated after the signal component is reconstructed, the reconstructed signal to be denoised is positioned in a broad sense, then, a bit plane matrix is obtained by means of bit plane conversion of the reconstructed signal to be denoised, so that the local amplitude denoising processing of the signal is realized, the denoising process of the signal is ensured to be more careful, then, the bit plane matrix is restored, the quantized signal is obtained, and then, the empirical mode decomposition is carried out again to remove quantization errors, so that the careful denoising processing of the signal is realized on the whole, and the denoising effect is improved.
Example 2
In this embodiment, the signal noise reduction method based on empirical mode decomposition and bit plane conversion proposed in embodiment 1 is further described, first, the process of performing empirical mode decomposition on an original signal to be processed to obtain a signal component and reconstructing the signal component is as follows:
s11, setting y (t) to represent an original signal to be processed, wherein t represents a time sequence, and fitting a local maximum value and a local minimum value of the original signal by utilizing a cubic spline interpolation method to form a smooth envelope line; in the step, the spline function corresponding to the cubic spline belongs to piecewise smooth interpolation, and the basic idea is to use a low-order polynomial to approximate in each small interval formed by two adjacent nodes, and ensure that the connection of each node is smooth (i.e. the derivative is continuous), so that a smooth envelope curve can be fitted for the original signal sequence.
S12, extracting an upper envelope emax (t) and a lower envelope emin (t) of the smooth envelope, calculating an average value m1(t) of the upper envelope and the lower envelope, and calculating an expression as follows:
m1(t)=[emax(t)+emin(t)]/2；
s13, calculating the difference between the original signal and the average value to obtain a middle signal time sequence h1 (t);
s14, judging whether a negative local maximum value and a positive local minimum value exist in the intermediate signal time h1(t), if so, taking the intermediate signal h1(t) as a new original signal, and returning to the step S11; otherwise, the intermediate signal h1(t) is the first eigenmode function IMF of the original signal y (t), and step S15 is executed;
s15, subtracting the intermediate signal h1(t) from the original signal y (t) to obtain a first residual signal r1 (t);
s16, taking the first remainder signal r1(t) as a new original signal to be processed, returning to the step S11, repeating the steps S11 to S15, sequentially obtaining a time sequence hi (t) of the intermediate signal as an eigenmode function IMF until obtaining a remainder signal sequence rn (t) which is monotonous or has a value smaller than a preset threshold value A, completing empirical mode decomposition to obtain a signal component hi (t), wherein n represents the number of the eigenmode function IMF; in this case, the original signal y (t) is represented as:
Figure 392506DEST_PATH_IMAGE024
general remainder
Figure 82244DEST_PATH_IMAGE025
The trend component representing the signal is not regarded as a reconstruction component in noise reduction, and therefore, step S16 is executed.
S17, reconstructing the signal component hi (t) to obtain a reconstructed signal
Figure 622816DEST_PATH_IMAGE026
And satisfies the following conditions:
Figure 827532DEST_PATH_IMAGE002
where k represents the number of selected signal components and fi (t) represents the signal components. In practical implementation, for k selection, the last few signal components of the low frequency are typically selected, as determined empirically.
In this embodiment, in the actual signal analysis process, it is considered that, for the acquired signals, no one knows whether the acquired signals completely do not contain noise, but it takes time, labor and material costs to blindly denoise all the acquired signals, so as to set conditions for noise degree evaluation when the signals are smooth enough as required, and the conditions are broadly used as the limit of whether to denoise the signals or not. Specifically, the method comprises the following steps: and evaluating the noise degree of the reconstructed signal, and judging whether the process of the noise in the reconstructed signal meets the following requirements:
assuming that the length of the reconstructed signal is U, the reconstructed signal is characterized as:
Figure 655461DEST_PATH_IMAGE003
；
detecting maximum and minimum points of the reconstructed signal sequence, setting the number of the detection points corresponding to the obtained maximum and minimum points as z, and setting the judgment threshold of the detection points as num _ peaks, wherein the judgment threshold of the detection points is determined by the signal noise reduction processing requirements, and if the number of the signal characteristic points needing to be extracted can be considered; the maximum and minimum detection of the reconstructed signal sequence can be directly solved by the inherent function in python or Matlab, which is not described herein again.
When z < num _ peaks, the signal sequence is reconstructed
Figure 511290DEST_PATH_IMAGE027
No noise exists in the process; otherwise, reconstructing the signal sequence
Figure 707916DEST_PATH_IMAGE027
There is noise.
In this embodiment, assuming that the bit-plane transformation is performed on the reconstructed signal in step S3, the obtained bit-plane matrix is represented as an M × N matrix B, and the process of obtaining the bit-plane matrix is as follows:
reconstructing each decimal data point in the signal sequence
Figure 150661DEST_PATH_IMAGE028
Converting into binary data points, and satisfying:
Figure 90935DEST_PATH_IMAGE029
wherein M represents the number of converted binary bits, depends on the bit depth parameter set when the hardware stores the signal data, and is also the number of rows of the matrix B;
is provided with
Figure 4534DEST_PATH_IMAGE030
Wherein, in the step (A),
Figure 106482DEST_PATH_IMAGE031
，
Figure 299172DEST_PATH_IMAGE032
p =1, …, N, then the bit-plane matrix is represented as:
Figure 777558DEST_PATH_IMAGE033
each column of the bit plane matrix B is a binary representation vector bp corresponding to each decimal data point of the reconstructed signal sequence, and binary bits from high to low are represented in the vector bp from top to bottom;
in the bit plane transformation process, referring to fig. 2, a schematic diagram corresponding to the above process, where any one element value in the M-th row element of the bit plane matrix B satisfies the condition that is greater than or equal to 0 and less than or equal to 1, and the other row elements except the M-th row element are 0 or 1.
In this embodiment, the process of determining the noise amplitude from the reconstructed signal in step S4 is:
s41, recording coordinates corresponding to the detection points of q maximum and minimum points in the reconstructed signal sequence, sequencing the coordinates corresponding to all the detection points according to the ascending order of the size of an abscissa to obtain an abscissa sequence vx and an ordinate sequence vy, wherein,
Figure 545663DEST_PATH_IMAGE034
，
Figure 834824DEST_PATH_IMAGE012
,
Figure 501429DEST_PATH_IMAGE035
;
s42, calculating the difference value of the longitudinal coordinate values of the corresponding coordinates of every two adjacent detection points to obtain a difference sequence
Figure 32773DEST_PATH_IMAGE036
Wherein, in the step (A),
Figure 671696DEST_PATH_IMAGE037
；
s43, taking absolute values of all elements in the difference sequence d, counting the absolute values into a histogram, and taking the middle value of the interval corresponding to the square column with the highest histogram frequency as Noise amplitude Noise.
The expression for determining the bit number occupied by the noise according to the noise amplitude is as follows:
Figure 880828DEST_PATH_IMAGE038
wherein the content of the first and second substances,
Figure 300308DEST_PATH_IMAGE039
representing the bit number occupied by noise; noise represents the Noise amplitude.
When local amplitude noise reduction is carried out, according to the bit number occupied by noise and the bit plane matrix, obtaining the bit plane matrix corresponding to the local amplitude noise reduction signal as
Figure 369764DEST_PATH_IMAGE040
，
Figure 613926DEST_PATH_IMAGE040
Element (1) of
Figure 228578DEST_PATH_IMAGE041
Satisfies the following conditions:
Figure 853463DEST_PATH_IMAGE042
。
the process of reducing the bit plane matrix corresponding to the local amplitude noise reduction signal to obtain the quantized signal in step S6 satisfies:
Figure 742922DEST_PATH_IMAGE043
wherein the content of the first and second substances,
Figure 635398DEST_PATH_IMAGE023
representing a quantized signal sequence;
Figure 889793DEST_PATH_IMAGE040
representing a bit plane matrix corresponding to the local amplitude noise reduction signal;
Figure 1974DEST_PATH_IMAGE031
。
in this embodiment, in step S7, the empirical mode decomposition process involved in obtaining the final noise reduction signal is performed on the quantized signal, and the quantized signal also satisfies the conditions and process for performing the empirical mode decomposition specifically in step S1
Figure 429544DEST_PATH_IMAGE023
It is represented by a series of step signals, which have a plurality of abrupt changes and no change in amplitude, so that important feature points (most extreme points) of the signals cannot be detected, and therefore, a smoothing process is also required to eliminate quantization errors. Because the sudden change can be regarded as instantaneous high-frequency oscillation, empirical mode decomposition can be continuously used for obtaining high-frequency and low-frequency components through decomposition, the high-frequency components are removed, the low-frequency components are selected for reconstruction, and the smoothed eliminated quantization error signal can be obtained.
The specific process is as follows:
s71. for quantized signals
Figure 445036DEST_PATH_IMAGE044
Fitting the signal using a cubic spline difference method
Figure 667070DEST_PATH_IMAGE044
Forming a smooth envelope by the local maximum and minimum values of the envelope;
s72, taking an upper envelope curve Eemax (t) and a lower envelope curve Eemin (t) of the smooth envelope curve, and calculating an average value Em1(t) of the upper envelope curve and the lower envelope curve, wherein the calculation expression is as follows:
Em1(t)=[Eemax(t)+Eemin(t)]/2；
s73, calculating the difference between the quantized signal and the average value to obtain an intermediate signal time sequence Eh1 (t);
s74, judging whether the intermediate signal time Eh1(t) has negative local maximum and positive local minimum, if yes, using the intermediate signal Eh1(t) as new quantized signal, returning to step S71(ii) a Otherwise, the intermediate signal Eh1(t) is the signal
Figure 204231DEST_PATH_IMAGE045
The first eigenmode function IMF of step S75 is performed;
s75, slave signal
Figure 923575DEST_PATH_IMAGE045
Subtracting the intermediate signal Eh1(t) to obtain a first residual signal Er1 (t);
s76, taking the first remainder signal Er1(t) as a new signal to be processed, returning to the step S71, repeating the steps S71 to S75, sequentially obtaining a middle signal time sequence Ehi (t) as an eigenmode function IMF until obtaining a remainder signal sequence Ern (t) which is monotonous or has a value smaller than a preset threshold value A, completing empirical mode decomposition to obtain a signal component Ehi (t), wherein n represents the number of the eigenmode functions IMF, and the frequency of the IMF is gradually reduced along with the increase of a decomposition order;
and S77, selecting the number of the selected low-frequency signal components by manual experience according to specific signal application, and reconstructing the signal components Ehi (t) to obtain a reconstructed signal as a signal subjected to noise reduction.
Example 3
In this embodiment, a signal noise reduction system based on empirical mode decomposition and bit plane transformation is provided, a structural diagram of the system is shown in fig. 3, the system is used for implementing the signal noise reduction method based on empirical mode decomposition and bit plane transformation, which is provided in embodiments 1 and 2, and referring to fig. 3, the system includes:
the signal acquisition processing module 101 is configured to acquire an original signal to be processed, perform empirical mode decomposition on the original signal, obtain a signal component, and reconstruct the signal component;
the noise degree evaluation module 102 is configured to perform noise degree evaluation on the reconstructed signal and determine whether noise exists in the reconstructed signal;
a bit plane conversion module 103, configured to perform bit plane conversion on the reconstructed signal when noise exists in the reconstructed signal, so as to obtain a bit plane matrix;
the noise bit calculation module 104 determines the noise amplitude according to the reconstructed signal and determines the bit number occupied by the noise according to the noise amplitude;
the local amplitude noise reduction module 105 is used for obtaining a bit plane matrix corresponding to the local amplitude noise reduction signal according to the bit number occupied by the noise and the bit plane matrix;
the restoring module 106 is configured to restore a bit plane matrix corresponding to the local amplitude noise reduction signal to obtain a quantized signal;
and the output module 107 is configured to perform empirical mode decomposition on the quantized signal to obtain a final noise reduction signal.
The embodiment packages a signal noise reduction system for implementing a signal noise reduction method, first, a signal acquisition processing module 101 acquires an original signal to be processed, and performs empirical mode decomposition on the original signal to obtain a signal component and reconstruct the signal component to complete a preliminary processing process, then a noise degree evaluation module 102 performs noise degree evaluation on the signal component after reconstructing the signal component to position a reconstructed signal to be noise reduced in a broad sense, then a bit plane conversion module 103 performs bit plane conversion on the reconstructed signal to obtain a bit plane matrix, a noise bit calculation module 104 and a local amplitude noise reduction module 105 are matched to implement local amplitude noise reduction processing on the signal to ensure that the noise reduction process of the signal is more detailed, then a reduction module 105 is used to reduce the bit plane matrix to obtain a quantized signal, and then an output module 106 performs empirical mode decomposition to remove quantization errors, all modules are mutually matched on the whole, and the signal refinement and noise reduction processing is realized.
The signal acquisition processing module 101 is provided with a first empirical mode decomposition module for performing empirical mode decomposition on the original signal; the output module 106 is provided with a second empirical mode decomposition module for performing an empirical mode decomposition on the quantized signal. The empirical mode decomposition algorithm is packaged in each of the first empirical mode decomposition module and the second empirical mode decomposition module, and the method considers that the noise reduction effect is poor in the current method of only adopting EMD to perform signal noise reduction, but the EMD has unique advantages, and the advantages are fully utilized.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (6)

1. A signal noise reduction method based on empirical mode decomposition and bit plane conversion is characterized by comprising the following steps:
s1, acquiring an original signal to be processed, and performing empirical mode decomposition on the original signal to obtain a signal component and reconstruct the signal component;
s2, evaluating the noise degree of the reconstructed signal, judging whether the reconstructed signal has noise or not, and if so, executing a step S3; otherwise, ending;
s3, carrying out bit plane conversion on the reconstructed signal to obtain a bit plane matrix;
let the bit-plane transformation of the reconstructed signal as described in step S3, and the obtained bit-plane matrix is expressed asM×NOf (2) matrixBThe process of obtaining the bit plane matrix is as follows:
each decimal data point in the reconstructed signal
Figure 331731DEST_PATH_IMAGE001
And converting into binary data points, and satisfying the following conditions:
Figure 75696DEST_PATH_IMAGE002
wherein the content of the first and second substances,Mrepresenting the converted number of binary bits, depending on the bit depth parameter set when the hardware stores the signal data, also in the form of a matrixBThe number of rows of (c);
is provided with
Figure 613774DEST_PATH_IMAGE003
Wherein, in the step (A),
Figure 152203DEST_PATH_IMAGE004
，
Figure 536917DEST_PATH_IMAGE005
，p=1，…,Nthen the bit-plane matrix is represented as:
Figure 507409DEST_PATH_IMAGE006
wherein, the bit plane matrixBIs a binary representation vector corresponding to each decimal data point of the reconstructed signalb p Vector of motionb p The middle from top to bottom represents binary bits from high order to low order;
bit plane matrixBAny element value of the M-th row element of (1) is greater than or equal to 0 and less than or equal to 1, and the other row elements except the M-th row element are 0 or 1;
s4, determining noise amplitude according to the reconstructed signal, and determining the bit number occupied by the noise according to the noise amplitude;
the process of determining the noise amplitude from the reconstructed signal described in step S4 is:
s41. recording the reconstructed signalqCoordinates corresponding to the detection points of the maximum value point and the minimum value point are sorted according to the ascending order of the horizontal coordinate size to obtain a horizontal coordinate sequencev x With ordinate seriesv y Wherein, in the step (A),
Figure 661179DEST_PATH_IMAGE007
，
Figure 573771DEST_PATH_IMAGE008
,
Figure 944316DEST_PATH_IMAGE009
;
s42, calculating the difference value of the longitudinal coordinate values of the corresponding coordinates of every two adjacent detection points to obtain a difference sequence
Figure 279352DEST_PATH_IMAGE010
Wherein, in the step (A),
Figure 38360DEST_PATH_IMAGE011
；
s43, pair of difference sequencesdTaking absolute value of all elements in the histogram, counting the absolute value as a histogram, and taking the middle value of the interval corresponding to the square column with the highest histogram frequency as the noise amplitudeNoise；
The expression for determining the bit number occupied by the noise according to the noise amplitude is as follows:
Figure 872586DEST_PATH_IMAGE012
wherein the content of the first and second substances,
Figure 966313DEST_PATH_IMAGE013
representing the bit number occupied by noise;Noiserepresenting the noise amplitude;
s5, local amplitude noise reduction is carried out: obtaining a bit plane matrix corresponding to the local amplitude noise reduction signal according to the bit number occupied by the noise and the bit plane matrix;
when the local amplitude noise reduction is performed in step S5, according to the bit number occupied by the noise and the bit plane matrix, a bit plane matrix corresponding to the local amplitude noise reduction signal is obtained as
Figure 824415DEST_PATH_IMAGE014
，
Figure 703509DEST_PATH_IMAGE014
Element (1) of
Figure 207172DEST_PATH_IMAGE015
Satisfies the following conditions:
Figure 289660DEST_PATH_IMAGE016
；
s6, restoring a bit plane matrix corresponding to the local amplitude noise reduction signal to obtain a quantized signal;
and S7, carrying out empirical mode decomposition on the quantized signal to obtain a final noise reduction signal.
2. The method of claim 1, wherein the step S1 of performing empirical mode decomposition on the original signal to obtain signal components and reconstructing the signal components comprises:
s11. sety(t) Which represents the original signal to be processed and,trepresenting a time sequence, and fitting a local maximum value and a local minimum value of an original signal by utilizing a cubic spline interpolation method to form a smooth envelope line;
s12, extracting an upper envelope line of the smooth envelope linee max (t) And a lower envelopee min (t) Calculating the mean of the upper and lower envelopesm 1(t), calculating the expression as:
m 1(t)=[e max (t)+e min (t)]/2；
s13, calculating the difference between the original signal and the average value to obtain an intermediate signal time sequenceh 1(t)；
S14, judging the time sequence of the intermediate signalh 1(t) whether there are still negative local maxima and positive local minima, if so, time-sequencing the intermediate signalh 1(t) returning to step S11 as a new original signal; otherwise, the intermediate signal time sequenceh 1(t) is the original signaly(t) The first eigenmode function IMF of step S15 is performed;
s15, slave signaly(t) Time series of intermediate signals subtracted inh 1(t) obtaining a first remainderNumber (C)r 1(t)；
S16, the first remainder signalr 1(t) as a new original signal to be processed, returning to the step S11, and repeating the steps S11-S15 to obtainiTime series of secondary intermediate signalsh i (t) as an eigenmode function, IMF, until a monotonic remainder signal sequence is obtainedr n(t) or a remainder signal sequence having a value less than a predetermined threshold Ar n(t), completing empirical mode decomposition to obtain signal components, wherein n represents the number of Intrinsic Mode Functions (IMFs), and the frequency of the IMFs is gradually reduced along with the increase of the decomposition order;
s17, reconstructing the signal component to obtain a reconstructed signal
Figure 904181DEST_PATH_IMAGE017
And satisfies the following conditions:
Figure 434519DEST_PATH_IMAGE018
wherein the content of the first and second substances,kindicating the number of selected signal components,f i(t) represents a signal component.
3. The signal noise reduction method based on empirical mode decomposition and bit plane conversion according to claim 2, wherein the process of evaluating the noise degree of the reconstructed signal and judging whether the reconstructed signal has noise satisfies the following steps:
assuming that the length of the reconstructed signal is U, the reconstructed signal is characterized as:
Figure 404356DEST_PATH_IMAGE019
；
detecting maximum and minimum points of the reconstructed signal, and setting the number of the detection points corresponding to the obtained maximum and minimum points aszThe judgment threshold value of the detection point isnum_peaksThe judgment threshold of the detection point is determined by the signal noise reduction processing requirement;
when in usez＜num_peaksWhen the temperature of the water is higher than the set temperature,then the signal is reconstructed
Figure 957828DEST_PATH_IMAGE020
No noise exists in the process; otherwise, reconstructing the signal
Figure 172777DEST_PATH_IMAGE020
There is noise.
4. The signal noise reduction method based on empirical mode decomposition and bit-plane transformation according to claim 3, wherein the process of restoring the bit-plane matrix corresponding to the local amplitude noise reduction signal to obtain the quantized signal in step S6 satisfies the following steps:
Figure 246038DEST_PATH_IMAGE021
wherein the content of the first and second substances,
Figure 638973DEST_PATH_IMAGE022
representing the quantized signal;
Figure 991326DEST_PATH_IMAGE014
representing a bit plane matrix corresponding to the local amplitude noise reduction signal;
Figure 698382DEST_PATH_IMAGE023
。
5. a signal noise reduction system based on empirical mode decomposition and bit plane transformation, wherein the signal noise reduction system is configured to implement the signal noise reduction method based on empirical mode decomposition and bit plane transformation according to claim 1, and the signal noise reduction system includes:
the signal acquisition processing module is used for acquiring an original signal to be processed, and performing empirical mode decomposition on the original signal to obtain a signal component and reconstruct the signal component;
the noise degree evaluation module is used for evaluating the noise degree of the reconstructed signal and judging whether the reconstructed signal has noise;
the bit plane conversion module is used for carrying out bit plane conversion on the reconstructed signal to obtain a bit plane matrix when noise exists in the reconstructed signal;
the noise bit calculation module is used for determining the noise amplitude according to the reconstructed signal and determining the bit number occupied by the noise according to the noise amplitude;
the local amplitude noise reduction module is used for obtaining a bit plane matrix corresponding to the local amplitude noise reduction signal according to the bit number occupied by the noise and the bit plane matrix;
the restoring module is used for restoring the bit plane matrix corresponding to the local amplitude noise reduction signal to obtain a quantized signal;
and the output module is used for carrying out empirical mode decomposition on the quantized signal to obtain a final noise reduction signal.
6. The system according to claim 5, wherein the signal acquisition and processing module includes a first empirical mode decomposition module for performing empirical mode decomposition on the original signal; and the output module is provided with a second empirical mode decomposition module used for carrying out empirical mode decomposition on the quantized signal.
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