CN108992062A - A kind of quadrature analysis and reconstructing method of electrocardiosignal - Google Patents
A kind of quadrature analysis and reconstructing method of electrocardiosignal Download PDFInfo
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- CN108992062A CN108992062A CN201810682068.0A CN201810682068A CN108992062A CN 108992062 A CN108992062 A CN 108992062A CN 201810682068 A CN201810682068 A CN 201810682068A CN 108992062 A CN108992062 A CN 108992062A
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- A61B5/318—Heart-related electrical modalities, e.g. electrocardiography [ECG]
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Abstract
The invention discloses a kind of quadrature analysis of electrocardiosignal and reconstructing method, includes the following steps: to carry out empirical mode decomposition to electrocardiosignal, obtain corresponding intrinsic mode function；Operation is standardized to intrinsic mode function, i.e., by each intrinsic mode function divided by its corresponding two norm of vector, and is arranged in a matrix in the form of column vector；Completely orthogonal intrinsic mode function is obtained by the method for singular value decomposition；Best projection of the electrocardiosignal on complete orthogonal intrinsic mode function is found using least square method；Electrocardiosignal is restored by best projection.The present invention is to carry out quadrature analysis and Accurate Reconstruction to electrocardiosignal based on empirical mode decomposition, to inherit the adaptivity of empirical mode decomposition；Compared with traditional empirical mode decomposition technology, the obtained intrinsic mode function of the present invention is completely orthogonal, therefore overcomes energy leakage problem existing for Conventional wisdom Mode Decomposition.
Description
Technical field
The present invention relates to ECG's data compression technical fields, and in particular to a kind of quadrature analysis of electrocardiosignal and reconstruct side
Method.
Background technique
Electrocardiosignal is a certain position that measuring electrode is placed on to human body surface, from macroscopically have recorded heart constantly into
The change in electric curve of capable rhythmical contraction and diastole campaign, electrocardiosignal have objectively responded heart to a certain extent
The physiological status at each position, thus it is significant in clinical medicine；But at present existing electrocardiosignal quadrature analysis with
The method of reconstruct mainly has the disadvantage that: (1) Fourier transformation: this method is by mutually orthogonal sine and cosine function to the heart
Electric signal is decomposed, and frequency content included in electrocardiosignal is obtained, and by Fourier inversion, electrocardiosignal can essence
Really reconstruct, but this method is to carry out under the assumed condition that signal has smooth performance, and electrocardiosignal is a kind of non-flat
Steady signal；(2) wavelet transformation: this method decomposes electrocardiosignal by mutually orthogonal wavelet basis, and this method has
Good Time-Frequency Localization characteristic is suitable for non-stationary signal, by inverse wavelet transform, electrocardiosignal energy Accurate Reconstruction, still,
There is also deficiencies for this method, such as how to choose suitable wavelet basis, and suitable parameter etc. how is arranged, further, since
Wavelet basis cannot change, so wavelet transformation also lacks adaptivity once selecting in the analysis of electrocardiosignal；(3) it passes through
Test Mode Decomposition: this method is a kind of NEW ADAPTIVE signal time frequency processing method, the time scale feature according to data itself
Signal decomposition is carried out, is very suitable to be analyzed and processed non-linear, non-stationary electrocardiosignal, by by all natural modes
State function is added, and enables electrocardiosignal Accurate Reconstruction, but this method decompose obtained intrinsic mode function be it is approximate just
It hands over, and it is simultaneously non-fully orthogonal, therefore will lead to serious energy leakage problem.
Summary of the invention
The purpose of the present invention is to overcome the shortcomings of the existing technology with it is insufficient, provide the quadrature analysis of electrocardiosignal a kind of with
Reconstructing method, this method obtain complete orthogonal intrinsic mode function by singular value decomposition, prevent energy leakage while can
Accurate Reconstruction electrocardiosignal.
The purpose of the invention is achieved by the following technical solution:
A kind of quadrature analysis and reconstructing method of electrocardiosignal, include the following steps:
S1 carries out empirical mode decomposition to electrocardiosignal, to obtain corresponding intrinsic mode function, specific steps are such as
Under:
S1.1, initialization residue signal are electrocardiosignal；
S1.2, initialization detail signal are residue signal；
S1.3 searches the maximum point and minimum point of detail signal；
S1.4, respectively in S1.3 maximum point and minimum point carry out cubic spline interpolation to obtaining upper lower envelope
Line；
S1.5 seeks the mean value of envelope above and below obtained in S1.4；
S1.6 uses the detail signal in S1.3 to subtract the signal that obtains after the mean value of envelope up and down in S1.5 as new
Detail signal, the new detail signal is for judging following situations: if the new detail signal meets preset natural mode of vibration letter
Several conditions then using the new detail signal as an intrinsic mode function, and carries out S1.7；Otherwise the new details is believed
Number as the detail signal in S1.3 and repeat S1.3-S1.6；
Residue signal in S1.2 is subtracted intrinsic mode function obtained in S1.6 as new residual signals by S1.7,
If the residual signals meet intrinsic mode function condition, terminate；Otherwise using the new residual signals as the remnants in S1.2
Signal repeats S1.2-S1.6；
S2 is standardized operation to intrinsic mode function obtained in S1, i.e., by each intrinsic mode function divided by
Its corresponding two norm of vector, and a matrix is arranged in the form of column vector；
S3 establishes the Optimized model of the completely orthogonal intrinsic mode function of electrocardiosignal, is obtained by the method for singular value decomposition
To the complete orthogonal intrinsic mode function of electrocardiosignal, and carry out Analysis on quadrature error, the specific steps are as follows:
The Optimized model of S3.1, the completely orthogonal intrinsic mode function of electrocardiosignal are indicated using following formula:
subject to UTU=I,
Wherein, U is the completely orthogonal intrinsic mode function of electrocardiosignal for needing to solve,For the standardization natural mode in S2
The matrix that state function is arranged in, | | | |FFor the Frobenius norm of matrix, UTU is the transposition of matrix U multiplied by matrix U, and I is
Unit matrix；
S3.2 is rightSingular value decomposition is carried out, its orthogonal matrix is obtainedWith diagonal matrix DA, then it is required completely just
Hand over intrinsic mode function U are as follows:
S3.3, using the quadrature error ε of the completely orthogonal intrinsic mode function of following formula analysis1:
ε1=| | UTU-I||F；
S4 finds best projection of the electrocardiosignal on complete orthogonal intrinsic mode function by least square method, specifically
Steps are as follows:
Best projection w of the electrocardiosignal on complete orthogonal intrinsic mode function is indicated with following formula:
W=(UTU)UTX,
Wherein x is former electrocardiosignal；
S5 reconstructs electrocardiosignal, and carries out the analysis of reconstructed error, the specific steps are as follows:
S5.1 acquires reconstruction signal according to the best projection w acquired in S4, and by following formula
S5.2, using the reconstructed error ε of the completely orthogonal intrinsic mode function of following formula analysis2:
The present invention have compared with prior art it is below the utility model has the advantages that
Compared with existing Fourier and wavelet technique, the present invention is to be carried out based on empirical mode decomposition to electrocardiosignal
Quadrature analysis and Accurate Reconstruction are suitable for analyzing non-stationary signal to inherit the adaptivity of empirical mode decomposition；With biography
The empirical mode decomposition technology of system is compared, the obtained intrinsic mode function of the present invention with trigonometric function base as wavelet basis,
It is completely orthogonal, therefore energy leakage can be prevented, and the present invention equally can be with Accurate Reconstruction electrocardiosignal；Experimental data
Show that quadrature error of the invention reaches the order of magnitude 10-15, reconstructed error reaches the order of magnitude 10-14, therefore error can be considered 0, institute
With and energy Accurate Reconstruction electrocardiosignal completely orthogonal by obtained intrinsic mode function of the invention.Pass through analysis electrocardiosignal
Completely orthogonal intrinsic mode function prevents the energy leakage problem of intrinsic mode function, is more completely separated in signal in mode,
Highlight signal characteristic.It allows the present invention can obtain the position of the QRS complex of the information of electrocardiosignal such as electrocardiosignal, electrocardio is believed
The information of number T wave, baseline drift situation of electrocardiosignal etc..
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is the waveform diagram of electrocardiosignal and first three resulting completely orthogonal intrinsic mode function of the invention,
In second orthogonal intrinsic mode function effectively reflect electrocardiosignal QRS complex position；
Fig. 3 is the waveform diagram of electrocardiosignal and resulting rear three completely orthogonal intrinsic mode functions of the invention,
In the 4th orthogonal intrinsic mode function contain the information of electrocardiosignal T wave, the 6th orthogonal intrinsic mode function reflects
The baseline drift situation of electrocardiosignal.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
As shown in Figures 1 to 3, the quadrature analysis and reconstructing method of a kind of electrocardiosignal, includes the following steps:
S1 carries out empirical mode decomposition to electrocardiosignal, to obtain corresponding intrinsic mode function, specific steps are such as
Under:
S1.1, initialization residue signal are electrocardiosignal；
S1.2, initialization detail signal are residue signal；
S1.3 searches the maximum point and minimum point of detail signal；
S1.4, respectively in S1.3 maximum point and minimum point carry out cubic spline interpolation to obtaining upper lower envelope
Line；
S1.5 seeks the mean value of envelope above and below obtained in S1.4；
S1.6 uses the detail signal in S1.3 to subtract the signal that obtains after the mean value of envelope up and down in S1.5 as new
Detail signal, the new detail signal is for judging following situations: if the new detail signal meets preset natural mode of vibration letter
Several conditions then using the new detail signal as an intrinsic mode function, and carries out S1.7；Otherwise the new details is believed
Number as the detail signal in S1.3 and repeat S1.3-S1.6；
Residue signal in S1.2 is subtracted intrinsic mode function obtained in S1.6 as new residual signals by S1.7,
If the residual signals meet intrinsic mode function condition, terminate；Otherwise using the new residual signals as the remnants in S1.2
Signal repeats S1.2-S1.6；
S2 is standardized operation to intrinsic mode function obtained in S1, i.e., by each intrinsic mode function divided by
Its corresponding two norm of vector, and a matrix is arranged in the form of column vector；
S3 establishes the Optimized model of the completely orthogonal intrinsic mode function of electrocardiosignal, is obtained by the method for singular value decomposition
To the complete orthogonal intrinsic mode function of electrocardiosignal, and carry out Analysis on quadrature error, the specific steps are as follows:
The Optimized model of S3.1, the completely orthogonal intrinsic mode function of electrocardiosignal are indicated using following formula:
subject to UTU=I,
Wherein, U is the completely orthogonal intrinsic mode function of electrocardiosignal for needing to solve,For the standardization natural mode in S2
The matrix that state function is arranged in, | | | |FFor the Frobenius norm of matrix, UTU is the transposition of matrix U multiplied by matrix U, and I is
Unit matrix；
S3.2 is right(For matrixTransposition multiplied by matrix) singular value decomposition is carried out, it is orthogonal to obtain its
MatrixWith diagonal matrix DA, then required orthogonal intrinsic mode function U completely are as follows:
S3.3, using the quadrature error ε of the completely orthogonal intrinsic mode function of following formula analysis1:
ε1=| | UTU-I||F；
S4 finds best projection of the electrocardiosignal on complete orthogonal intrinsic mode function by least square method, specifically
Steps are as follows:
Best projection w of the electrocardiosignal on complete orthogonal intrinsic mode function is indicated with following formula:
W=(UTU)UTX,
Wherein x is former electrocardiosignal；
S5 reconstructs electrocardiosignal, and carries out the analysis of reconstructed error, the specific steps are as follows:
S5.1 acquires reconstruction signal according to the best projection w acquired in S4, and by following formula
S5.2, using the reconstructed error ε of the completely orthogonal intrinsic mode function of following formula analysis2:
Compared with existing Fourier and wavelet technique, the present invention is to be carried out based on empirical mode decomposition to electrocardiosignal
Quadrature analysis and Accurate Reconstruction are suitable for analyzing non-stationary signal to inherit the adaptivity of empirical mode decomposition；With biography
The empirical mode decomposition technology of system is compared, the obtained intrinsic mode function of the present invention with trigonometric function base as wavelet basis,
It is completely orthogonal, therefore energy leakage can be prevented, and the present invention equally can be with Accurate Reconstruction electrocardiosignal；Experimental data
Show that quadrature error of the invention reaches the order of magnitude 10-15, reconstructed error reaches the order of magnitude 10-14, therefore error can be considered 0, institute
With and energy Accurate Reconstruction electrocardiosignal completely orthogonal by obtained intrinsic mode function of the invention.Pass through analysis electrocardiosignal
Completely orthogonal intrinsic mode function prevents the energy leakage problem of intrinsic mode function, is more completely separated in signal in mode,
Highlight signal characteristic.It allows the present invention can obtain the position of the QRS complex of the information of electrocardiosignal such as electrocardiosignal, electrocardio is believed
The information of number T wave, baseline drift situation of electrocardiosignal etc..
Above-mentioned is the preferable embodiment of the present invention, but embodiments of the present invention are not limited by the foregoing content,
His any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention, should be
The substitute mode of effect, is included within the scope of the present invention.
Claims (1)
1. the quadrature analysis and reconstructing method of a kind of electrocardiosignal, which is characterized in that include the following steps:
S1 carries out empirical mode decomposition to electrocardiosignal, to obtain corresponding intrinsic mode function, the specific steps are as follows:
S1.1, initialization residue signal are electrocardiosignal；
S1.2, initialization detail signal are residue signal；
S1.3 searches the maximum point and minimum point of detail signal；
S1.4, respectively to the maximum point and minimum point progress cubic spline interpolation in S1.3 to obtain envelope up and down；
S1.5 seeks the mean value of envelope above and below obtained in S1.4；
S1.6 uses the detail signal in S1.3 to subtract the signal that obtains after the mean value of envelope up and down in S1.5 as new details
Signal, the new detail signal is for judging following situations: if the new detail signal meets preset intrinsic mode function
Condition then using the new detail signal as an intrinsic mode function, and carries out S1.7；Otherwise the new detail signal is made
For the detail signal in S1.3 and repeat S1.3-S1.6；
Residue signal in S1.2 is subtracted intrinsic mode function obtained in S1.6 as new residual signals by S1.7, if should
Residual signals meet intrinsic mode function condition, then terminate；Otherwise using the new residual signals as the residue signal in S1.2
Repeat S1.2-S1.6；
S2 is standardized operation to intrinsic mode function obtained in S1, i.e., each intrinsic mode function is right divided by its
Two norm of vector answered, and a matrix is arranged in the form of column vector；
S3, establishes the Optimized model of the completely orthogonal intrinsic mode function of electrocardiosignal, obtains the heart by the method for singular value decomposition
The complete orthogonal intrinsic mode function of electric signal, and carry out Analysis on quadrature error, the specific steps are as follows:
The Optimized model of S3.1, the completely orthogonal intrinsic mode function of electrocardiosignal are indicated using following formula:
subject to UTU=I,
Wherein, U is the completely orthogonal intrinsic mode function of electrocardiosignal for needing to solve,For the standardization natural mode of vibration letter in S2
The matrix that number is arranged in, | | | |FFor the Frobenius norm of matrix, UTU is the transposition of matrix U multiplied by matrix U, and I is unit
Matrix；
S3.2 is rightSingular value decomposition is carried out, its orthogonal matrix is obtainedWith diagonal matrix DA, then required completely orthogonal solid
There is mode function U are as follows:
S3.3, using the quadrature error ε of the completely orthogonal intrinsic mode function of following formula analysis1:
ε1=| | | UTU-I||F；
S4 finds best projection of the electrocardiosignal on complete orthogonal intrinsic mode function, specific steps by least square method
It is as follows:
Best projection w of the electrocardiosignal on complete orthogonal intrinsic mode function is indicated with following formula:
W=(UTU)UTX,
Wherein x is former electrocardiosignal；
S5 reconstructs electrocardiosignal, and carries out the analysis of reconstructed error, the specific steps are as follows:
S5.1 acquires reconstruction signal according to the best projection w acquired in S4, and by following formula
S5.2, using the reconstructed error ε of the completely orthogonal intrinsic mode function of following formula analysis2:
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101782895A (en) * | 2009-01-12 | 2010-07-21 | 财团法人工业技术研究院 | Method and device thereof for performing hierarchical empirical mode decomposition on signal |
| CN102499670A (en) * | 2011-11-23 | 2012-06-20 | 北京理工大学 | Electrocardiogram baseline drifting correction method based on robust estimation and intrinsic mode function |
| US20160000346A1 (en) * | 2014-07-02 | 2016-01-07 | National Central University | Method and system for extracting ventricular fibrillation signals in electrocardiogram |
| CN106096236A (en) * | 2016-05-31 | 2016-11-09 | 广东工业大学 | A kind of one-dimensional signal quadrature analysis and precise reconstruction method |
| CN106798554A (en) * | 2017-01-12 | 2017-06-06 | 安徽大学 | A kind of denoising method of noisy IMF components and electrocardiosignal |
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2018
- 2018-06-27 CN CN201810682068.0A patent/CN108992062A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101782895A (en) * | 2009-01-12 | 2010-07-21 | 财团法人工业技术研究院 | Method and device thereof for performing hierarchical empirical mode decomposition on signal |
| CN102499670A (en) * | 2011-11-23 | 2012-06-20 | 北京理工大学 | Electrocardiogram baseline drifting correction method based on robust estimation and intrinsic mode function |
| US20160000346A1 (en) * | 2014-07-02 | 2016-01-07 | National Central University | Method and system for extracting ventricular fibrillation signals in electrocardiogram |
| CN106096236A (en) * | 2016-05-31 | 2016-11-09 | 广东工业大学 | A kind of one-dimensional signal quadrature analysis and precise reconstruction method |
| CN106798554A (en) * | 2017-01-12 | 2017-06-06 | 安徽大学 | A kind of denoising method of noisy IMF components and electrocardiosignal |
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Application publication date: 20181214 |