NL2026029B1

NL2026029B1 - Electrocardio noise removing method based on morphological component analysis and sparse representation

Info

Publication number: NL2026029B1
Application number: NL2026029A
Authority: NL
Inventors: Wang Yinglong; Shi Hao; Shu Minglei; Liu Ruixia; Liu Hui; Chen Chao
Original assignee: Shandong Artificial Intelligence Inst
Priority date: 2020-04-29
Filing date: 2020-07-09
Publication date: 2021-05-04
Also published as: CN111513679A; CN111513679B

Abstract

An electrocardio noise removing method based on morphological component analysis and sparse representation is provided, explanations are made through an ECG signal 5 repairing technology based on different components analysis and a sparse representation principle, and this method is not based on the amplitude and frequency spectrum generated by Fourier transform. The above method decomposes the signal to have different characteristic components, wherein one component consists of a plurality of simultaneously and continuously vibrated signals, and referred to as a high 10 resonance component. Another component consists of transient impact signals that do not have specific states and continuous time, and referred to as a low resonance component. Through, the electrocardio noise removing method based on morphological component analysis and sparse representation including morphological component analysis of signals, sparse representation and group sparse threshold 15 processing, so as to effectively remove interferences of noises at the same frequency band.

Description

-1-

ELECTROCARDIO NOISE REMOVING METHOD BASED ON MORPHOLOGICAL COMPONENT ANALYSIS AND SPARSE

REPRESENTATION Technical Field The present invention belongs to the technical field of electrocardio signal processing, and particularly relates to an electrocardio noise removing method based on morphological component analysis and sparse representation.

Background The electrocardio signal is an important physiological activity signal of a human body, and a waveform of the signal is an important basis of estimating a patient's heart health condition. In the process of collecting ECG signals, due to an outside interference for an electronic environment and a potential change of a body surface, the collected initial signals will be mixed together with various forms of noises. Due to the influence of these noises, waveforms of the initial ECG signals will be blurred and even key features in the waveforms may be covered, and cannot be used. The ECG signals are nonlinear and unsteady signals, since the noise has a modulating function for amplitudes of useful frequencies of the signals, and noise interference components usually exist in the whole frequency range, the noises of the signals are often represented. Generally, a method based on frequency cannot effectively remove interferences of transient components of the noises at the same frequency band. Summary The present invention, in order to overcome the above defects in technology, provides an electrocardio noise removing method based on morphological component analysis and sparse representation of effectively removing noise inferences at the same frequency band according to differences of oscillation characteristics of the signals in conjunction with the morphological component analysis.

The technical solution adopted by the present invention for overcoming the technical problem thereof is:

-2- an electrocardio noise removing method based on morphological component analysis and sparse representation, including the following steps: a) loading electrocardio data .§' containing noises; b) performing resonant sparse decomposition on the electrocardio data to form a high resonance signal $ ‚ and a low resonance signal S, ;

c) performing different group sparse threshold processing on the high resonance signal S, and the low resonance signal S, , respectively, and separating signals x,” and x,” respectively after removing noises in the high resonance signal S, and the low resonance signal S, ; and d) overlapping the signals x,” and x," , to obtain electrocardio data in which the noises are reduced.

Further, steps of a computer loading the electrocardio data in step a) are: inputting the electrocardio data containing Gaussian white noises in a form of matrix §, the matrix S is data on line #2 of column 1, and extracting the whole data of the matrix S through Formula N=length (5), wherein N is a length of the loaded data.

Further, steps of the resonant sparse decomposition in step b) are as follows: b-1) §=5,+3,, wherein S, is a high resonance component consisting of a plurality of simultaneously and continuously vibrated signals, and 5, is a low resonance component consisting of multiple transient impact signals that do not have specific states and continuous time; b-2) separating the signals S, and §, from the electrocardio data §, constructing an over-complete dictionary P, of a high resonant signal component and an over- complete dictionary P, of a low resonant signal component by using a wavelet base function having different quality factors through a TWQT adjustable Q factor wavelet transform algorithm, and denoting the electrocardio data through Formula S=Pw, + P,w,, wherein w, is a transformation coefficient of .S, under the over- complete dictionary P,, and w, is a transformation coefficient of §,, under the over- complete dictionary B, ;

-3- - 2 Î b-3) through Formula J (w,,w,) = |S pw, — Pow, |, + 4 wi, +4 Iw, I : calculating an objective function .J(w,,w,) , wherein 4, and A, in the formula are regularization coefficients; and b-4) through Formulas S, =P, w; and S; =P, w, , calculating and obtaining the decomposed high resonance signal 5, and low resonance signal §,, wherein w, in the formula is a transformation matrix of a minimum high resonance component obtained when iterating the objective function /(W,, W, ) through a SALSA iteration algorithm, and w, is a transformation matrix of a minimum low resonance component obtained when iterating the objective function J (w,, w,) through the SALSA iteration algorithm. Further, steps of step c) are as follows: c-1) the high resonance signal §, being formed by useful electrocardio data X, in the high resonance signal and noise data Z, in the high resonance signal, the low resonance signal S, being formed by useful electrocardio data X; in the low resonance signal and noise data 2; in the low resonance signal, S, (0) =X, (I) + zi) ieN , and S, (1) = xX, (0) + z,(7) ie N | N being a length of the loaded data, and l being a data reference number; le P | c-2) through Formula X, Mg min F(x,) = s- | + A R(x) , x, 5 calculating a signal X, , wherein R(x) in the formula is a penalty function, 1/2

A R(x,)= >| Sn (f + f)| | ‚ Tef0,..N-B, and J&{0,.. K-1}, whereinj iel | jeJ is a coefficient index of the I” group, 4, is a regularization parameter, and 4,=0.1;

-4- 12 3) when K=1, R(x.) = Xo [xy (Of | = [x O+" (V = 2) + fr, (¥ =D), ief performing an iteration calculation for the function F (x,) using MM minimum optimization algorithm, and returning the data x, back until the function is converged; Ig ’ ¢-3) through Formula xX, =arg min {rs 5 35 vB | + A RX ‚ calculating a signal X 8 , wherein R(x) in the formula is a penalty function, 1/2 R(x,) = >| She | , I€{0,...,N-1}, and Je{0,... K-1}, wherein j ie] | jeJ is a coefficient index of the ! group, A, is a regularization parameter, and 4,=0.1; c-4) when K=3, u2 R(x;)= > > |x, (i + Nf | = |x, (0)] Ty EP (0)] + x, (D+ |x, (2)| +...

ial | jeJ , X(N =3)+x,(N=-2)+x,(N-1) performing an iteration calculation for the function F(x 5) using MM minimum optimization algorithm, and returning the data X 8 back until the function is converged. Further, the overlapped electrocardio data Sis calculated through Formula OS =x,"+x, in step d). Advantageous effects of the present invention are as follows: explanations are made through an ECG signal repairing technology based on different components analysis and a sparse representation principle, and this method is not based on the amplitude and frequency spectrum generated by Fourier transform. The above method decomposes the signal to have different characteristic components, wherein one component consists of a plurality of simultaneously and continuously vibrated signals, and referred to as a high resonance component. Another component consists of transient impact signals that do not have specific states and continuous time, and

-5- referred to as a low resonance component. Through, the electrocardio noise removing method based on morphological component analysis and sparse representation including morphological component analysis of signals, sparse representation and group sparse threshold processing, the traditional decomposition method of dividing signals by frequency is broken. According to differences of oscillation characteristics of signals, and in conjunction with the morphological component analysis method, the components having the same oscillation characteristic and different forms are distinguished, and different process of group sparse thresholds (OGS, Overlapping Group Shrinkage) are set respectively, so as to effectively remove interferences of noises at the same frequency band. Brief Description of the Drawings Fig. 11s a method flowchart of the present invention.

Detailed Description of the Embodiments The present invention is further explained in conjunction with Fig. 1 below. An electrocardio noise removing method based on morphological component analysis and sparse representation, includes the following steps: a) loading electrocardio data § containing noises; b) performing resonant sparse decomposition on the electrocardio data to form a high resonance signal 5, and a low resonance signal Sj ; c) performing different group sparse threshold processing on the high resonance signal S, and the low resonance signal §,,, respectively, and separating signals x,” and x,’ respectively after removing noises in the high resonance signal 5, and the low resonance signal S, ; and d) overlapping the signals x,” and x,” , to obtain electrocardio data in which the noises are reduced. Explanations are made through an ECG signal repairing technology based on different components analysis and a sparse representation principle, and this method is not based on the amplitude and frequency spectrum generated by Fourier transform. The above method decomposes the signal to have different characteristic components,

-6- wherein one component consists of a plurality of simultaneously and continuously vibrated signals, and referred to as a high resonance component. Another component consists of transient impact signals that do not have specific states and continuous time, and referred to as a low resonance component. Through, the electrocardio noise removing method based on morphological component analysis and sparse representation including morphological component analysis of signals, sparse representation and group sparse threshold processing, the traditional decomposition method of dividing signals by frequency is broken. According to differences of oscillation characteristics of signals, and in conjunction with the morphological component analysis method, the components having the same oscillation characteristic and different forms are distinguished, and different process of group sparse thresholds (OGS, Overlapping Group Shrinkage) are set respectively, so as to effectively remove interferences of noises at the same frequency band.

Preferably, steps of a computer loading the electrocardio data in step a) are: inputting the electrocardio data containing Gaussian white noises in a form of matrix S, the matrix § is data on line 7 of column 1, and extracting the whole data of the matrix § through Formula N=length (5), wherein N is a length of the loaded data. Preferably, steps of the resonant sparse decomposition in step b) are as follows: b-1) S=S,+S,, wherein S, is a high resonance component consisting of a plurality of simultaneously and continuously vibrated signals, and $, is a low resonance component consisting of multiple transient impact signals that do not have specific states and continuous time; b-2) separating the signals S, and S, from the electrocardio data §, constructing an over-complete dictionary P, of a high resonant signal component and an over- complete dictionary P, of a low resonant signal component by using a wavelet base function having different quality factors through a TWQT adjustable Q factor wavelet transform algorithm, and denoting the electrocardio data through Formula S=Pw, +P,w,, wherein w, is a transformation coefficient of §, under the over- complete dictionary P,, and w, is a transformation coefficient of §, under the over- complete dictionary P,;

-7- - 2 Î b-3) through Formula J (w,,w,) = |S pw, — Pow, |, + 4 wi, +4 Iw, I. calculating an objective function / (3, Ww, ) , wherein A; and A: in the formula are regularization coefficients, the smaller value of ./ (3, ,) indicates that the decomposed result is sparse, and the minimized value 1s related to A; and Az; and b-4) through Formulas S, =P, w, and S; =P, w, | calculating and obtaining the decomposed high resonance signal 5, and low resonance signal 5, , wherein w, In the formula is a transformation matrix of a minimum high resonance component obtained when iterating the objective function /(w,, w,) through a SALSA iteration algorithm, and w, is a transformation matrix of a minimum low resonance component obtained when iterating the objective function J (w,, w,) through the SALSA iteration algorithm.

Preferably, steps of step c) are as follows: c-1) the high resonance signal §, being formed by useful electrocardio data X; in the high resonance signal and noise data Zz, in the high resonance signal, the low resonance signal 5, being formed by useful electrocardio data Xg in the low resonance signal and noise data Z; in the low resonance signal, Ss (i) =X, (1) + z‚() ie N and SD) = x, (1) + z, (i) ie N , N being a length of the loaded data, and [ being a data reference number; He F c-2) through Formula xX, arg min F(x) = Hs | + AR) , x. 2 ) calculating a signal X, , wherein R(x) in the formula is a penalty function, 1/2 : CAR R(x,)= >| Se + | | ‚ 1€{0,....N-1}, and Je{0,...,K-1}, wherein ief | jet

-8- J 1s a coefficient index of the I group, A, is a regularization parameter, and 4,=0.1 2 1/2 c-3) when K=1, R(x,)= >| ] = |x, (0)| +, (N- 2) + |x, (N _ 1) iel performing an iteration calculation for the function FV (x,) using MM minimum optimization algorithm, and returning the data x, back until the function is converged; I | c-3) through Formula Xp Ig min F(x) 7 2h ) * Ap R(x) , xg 2 calculating a signal X 2 , wherein R(x,) in the formula is a penalty function, 1/2

IN R(x,)= >| Shee | ‚ Tef0,..N-B, and J{0,...,K-1}, wherein j iel | jel is a coefficient index of the {™ group, A, is a regularization parameter, and 24=0.1; c-4) when K=3, 172 NT: : R(x) = | ZG + Ml | =|x, (0) Fy x, (0) + lr, (1)+ x, 2) +o. iel | jel ‚ NAN =3)+x,(N —2)+x;(N-]) performing an iteration calculation for the function F(x 2) using MM minimum optimization algorithm, and returning the data X 3 back until the function is converged. Preferably, the overlapped electrocardio data § is calculated through Formula § =x +x,” in step d).

Claims

-9- NL2026029 Conclusions

Electrocardio noise removal method based on morphological component analysis and sparse representation, characterized by the following steps: a) loading electrocardiodata S containing noise; b) performing resonant sparse decomposition on the electrocardio data from a high resonance signal Ss to a low resonance signal Sp, c) performing various group sparse threshold processing on the high resonance signal Ss and the low resonance signal Sp, respectively, and separating signals x, and, respectively, X; after removing noise in the high resonance signal Ssen, the low resonance signal Sz, and d) overlapping the signals x, and xp, to obtain electrocardio data with reduced noise.

Electrocardio noise removal method based on the morphological component analysis and sparse representation according to claim 1, characterized in that the steps of a computer loading the electrocardio data in step a) are as follows: inputting the electrocardio data representing Gaussian white noise in a form of matrix S, wherein the matrix S is data on line n of column 1, and extracting the entire data from the matrix S by Formula N = length (5), where N is a length of the loaded data.

Electrocardio noise removal method based on the morphological component analysis and sparse representation according to claim 1, characterized in that the steps of the resonant sparse decomposition in step b) are: b-1) § = S, + Sg, where S, is a high resonance component comprising a plurality of simultaneously and continuously vibrating signals, and Sg is a low resonance component comprising a plurality of multiple transient impact signals having no specific states and continuous time, b-2) separating the signals S, and Sp from the electrocardiodata S, constructing a crowded dictionary P; of a high resonance signal component and an overcrowded dictionary P2 of a low resonance signal component by a

- 10 - use NL2026029 wavelet base function that has different quality factors by a TWQT-adjustable Q-factor wavelet transformation algorithm, and designate the electrocardiodata by Formula § = P, w; + P, w, where wi is a transform coefficient of S, under the overcrowded dictionary Pi, and w, is a transform coefficient of Sg under the overcrowded dictionary P:; b-3) calculating, by Formula J (w‚w2) = || S - Paw - P2w; | {2 + Aillwilk + Azllwall ,, a target function J (w ;, wa), where A, and A, are regularization coefficients in the formula; and b-4), by Formulas SBP, and sB = p, w, calculating and obtaining the decompositioned high resonance signal S $; and low resonance signal Sp, where xk w in the formula is a transformation matrix of a minimum high resonance component 1 that is obtained when the target function J (w ,, w,) is iterated by a + k SALSA iteration algorithm, and where wy in the formula is a transformation matrix of a minimum low resonance component that is obtained if the target function J (wy, w,) is iterated by a SALSA iteration algorithm.

Electrocardio noise removal method based on the morphological component analysis and sparse representation according to claim 1, characterized in that the steps of step c) are: c-1) the high resonance signal S, which is formed from electrocardio useful data x; 1n the high resonance signal and noise data z, in the high resonance signal, the low resonance signal $; formed from electrocardio useful data xp in the low resonance signal and noise data Zg in the low resonance signal, Syiy = x, 0 + z, 00) ieN. Sz) = x) + z, (7) IEN where N is a length of the loaded data, and i is a data reference number; : fo Ue Fo ... | x, = arg minus 1 “(r = Sax) + ARC) c-2) calculating, by Formula / ©: J, a signal x, *, where R (x,) in the formula is a penalty function,

-11- NL2026029 1/2 R = Zhe), 1 € {0, .., N — 1}, and J € {0, ..., K - 1}, where j one cubit | your J coefficient index of the group, A4 is a regularization parameter, and 1 = 0.1; 1/2 c-3) it, if K = 1, R (x 1) = Xe] | = x, (0) + L | x (N = 2) + | x, (NV -D), ie! performing an iteration calculation for the function F (x4) using MM minimum optimization algorithm, and returning the data x, "back until the function is converged:, ooo ro Xp = arg mi Fl) = 3 Ss Xp) + AR) c-3) calculating, by Formula - u: I, a signal Xp ', where R (xg) in the formula is a penalty function, 12 Rs) = Stee |, 1 € {0, .., N —1}, and J {0, .., K — 1}, where j is an ief | je J coefficient index of the group, A is a regularization parameter, and Ap = 0.1; c-4) it, if K = 3, 1/2 R (x;) = | Z (i + pf | = 5500) + Yes (0) + e, (D + x, 2) + L ief | jet »JX, (N = 3) + x, (N = -2) + x, (N-1) perform an iteration calculation for the function F (xg) using MM minimum optimization algorithm, and return the data xz "back until the function converged is.

Electrocardio noise removal method based on the morphological component analysis and sparse representation according to claim 1, characterized in that the overlapping electrocardio data S "is calculated by Formula S = x4 * + x5" in step d).