CN108095722B - Improved EEMD algorithm based on electroencephalogram signals - Google Patents

Improved EEMD algorithm based on electroencephalogram signals Download PDF

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CN108095722B
CN108095722B CN201810093526.7A CN201810093526A CN108095722B CN 108095722 B CN108095722 B CN 108095722B CN 201810093526 A CN201810093526 A CN 201810093526A CN 108095722 B CN108095722 B CN 108095722B
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张学军
王龙强
何涛
成谢锋
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Nanjing University Of Posts And Telecommunications Institute At Nantong Co ltd
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Abstract

The invention discloses an improved EEMD algorithm based on electroencephalogram signals, which is characterized in that firstly, based on the priori knowledge of the electroencephalogram signals, a mu rhythm frequency band (8-12Hz) and a beta rhythm frequency band (18-26Hz) are selected to respectively design two band-pass filters; carrying out filtering processing on the full-band white Gaussian noise by using the band-pass filter to obtain two band-limited white Gaussian noises; and finally, adding the band-limited white Gaussian noise w (t) into the original electroencephalogram signal, and performing empirical mode decomposition. The method is applied to decompose the electroencephalogram signals to obtain inherent mode function signals with relatively concentrated frequencies, the inherent mode functions of all frequency bands are distinguished, and the mode aliasing problem caused by empirical mode decomposition is greatly restrained.

Description

Improved EEMD algorithm based on electroencephalogram signals
Technical Field
The invention relates to an improved EEMD algorithm based on an electroencephalogram signal, and belongs to the technical field of intelligent information processing.
Background
Empirical Mode Decomposition (EMD) is a novel adaptive signal time-frequency processing method, and is suitable for analyzing and processing nonlinear and non-stationary signals. The EMD algorithm is based on local characteristics of signals, complex original signals can be decomposed into a series of finite sums of Intrinsic Mode Functions (IMFs) with small data volume through repeated screening, and then Hilbert transformation is carried out on each IMF to solve the instantaneous frequency of each IMF, so that the instantaneous frequency has practical physical significance, and time-frequency distribution of nonlinear and non-stationary signals is obtained.
The major drawback of the EMD algorithm is the modal aliasing problem. To solve this problem, the Ensemble empirical mode decomposition algorithm (EEMD) introduces a Noise-Assisted Data Analysis (NA-DA) method. When the original signal is added with a white noise background which is uniformly distributed, signal areas with different scales are automatically mapped to an appropriate scale related to the white noise of the background, so that the problem of mode aliasing is effectively overcome. Since EEMD has been proposed, EEMD has been widely used in many fields such as mechanical failure diagnosis, voice signal processing, image processing, oceanography, geological survey and the like.
Motor imagery means that only limb motor imagery is performed without actual limb movement. The movement-sensing rhythms consist of mu and beta rhythms, which are fluctuations in brain activity located in the mu (7-13) and beta (19-26Hz) bands. When the brain's activity and motor tasks are related, the sensorimotor rhythm changes, and more importantly, merely making motor imagery will also be reflected in the changes in sensorimotor rhythm. During motor imagery, the sensory motor cortex of the brain generates an event-related synchronization/desynchronization (ERS/ERD) phenomenon, and thus, the generated electroencephalogram signal is a nonlinear and non-stationary signal.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention provides an improved EEMD algorithm based on electroencephalogram signals, which improves the conventional EEMD algorithm.
In order to achieve the purpose, the invention adopts the following technical scheme:
an improved EEMD algorithm based on electroencephalogram signals comprises the following steps:
step 1: respectively designing a band-pass filter for different rhythm frequency bands of the electroencephalogram signal x (t);
step 2: filtering the full-band white Gaussian noise by using the band-pass filter to obtain a band-limited white Gaussian noise sequence wi(t)(i＝1,2,…,N)；
And step 3: adding the band-limited white Gaussian noise into the electroencephalogram signal x (t) respectivelyAcoustic sequence wi(t) (i ═ 1,2, …, N) to obtain an input signal xi(t)＝x(t)+wi(t), (i ═ 1,2, …, N), for xi(t) empirical mode decomposition, N input signals xi(t) obtaining an n-order natural mode function and a residual function ri,n(t)；
And 4, step 4: carrying out set average on each order of the obtained N input signals to obtain the j order intrinsic mode function c of the electroencephalogram signal x (t)j(t)；
Figure GDA0003005748330000021
The electroencephalogram signal x (t) can be represented as:
Figure GDA0003005748330000022
wherein, ci,jAnd (t) represents a j-th order intrinsic mode function obtained by adding band-limited white Gaussian noise to the electroencephalogram signal for the ith time and carrying out empirical mode decomposition.
Preferably, the different rhythm frequency bands of the electroencephalogram signal x (t) comprise a mu rhythm frequency band and a beta rhythm frequency band, and the frequency ranges are 8-12Hz and 18-26Hz respectively.
Preferably, in step 3, the step of empirical mode decomposition includes:
step 3.1: determining each input signal xi(t) local maxima, curve fitting using cubic spline curve, local maxima forming an upper envelope emax(t) local minima form the lower envelope emin(t)；
Step 3.2: find emax(t) and eminMean value of (t):
Figure GDA0003005748330000023
step 3.3: calculating an input signal xiDifference between (t) and m (t):
ci,1(t)＝xi(t)-m(t) (4)
if c isi,1(t) failing to meet the defined cutoff condition for IMF, repeating steps 3.1-3.3, otherwise, extracting ci,1(t) as a 1 st order natural mode function, a residual function ri,1(t) is calculated as follows:
ri,1(t)＝xi(t)-ci,1(t) (5)
step 3.4: the residual function ri,1(t) repeating steps 3.1-3.3 as a new input signal;
step 3.5: repeating steps 3.1-3.4 until the residual function ri,n(t) is a monotonic function or only one extremum, the decomposition process is stopped, where N input signals xi(t) obtaining n-order natural mode functions ci,1(t),…,ci,n(t) and a residual function ri,n(t)。
Preferably, n is 8.
Has the advantages that: the method is applied to decompose the electroencephalogram signals to obtain inherent mode function signals with relatively concentrated frequencies, the inherent mode functions of all frequency bands are distinguished, and the mode aliasing problem caused by empirical mode decomposition is greatly restrained. The introduction of band-limited noise effectively extracts a plurality of aliasing modes in a single IMF component into different IMFs, so that the effective separation of the modes is realized to a certain extent, the improved algorithm is proved to be feasible and effective to be used in the special field of electroencephalogram, and the problem of mode aliasing of the EMD decomposition of the electroencephalogram signal can be better solved. The algorithm is applied to the classification recognition of imagining left and right hands, and the improved EEMD algorithm can be used for distinguishing all the frequencies of the electroencephalogram signals as far as possible, so that all the components obtained by decomposition of the electroencephalogram signals are mainly single group of frequencies, and the method is beneficial to extracting feature vectors with more distinct features, thereby greatly improving the accuracy of the classification recognition.
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FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a graph of bandlimited white Gaussian noise generation in the method of the present invention.
FIG. 3 is a time-frequency diagram (upper time-domain diagram and lower frequency-domain diagram) of the original EEG signal.
FIG. 4 is a time-frequency diagram (left is a time-domain diagram and right is a frequency-domain diagram) of a classical EMD decomposition electroencephalogram signal.
FIG. 5 is a time-frequency diagram (left is a time-domain diagram, and right is a frequency-domain diagram) of the electroencephalogram signal decomposed by the algorithm of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings.
As shown in fig. 1, the method of the present invention comprises the following steps:
step 1: based on the priori knowledge of the electroencephalogram signals, selecting a mu rhythm frequency band (8-12Hz) and a beta rhythm frequency band (18-26Hz) and respectively designing two band-pass filters;
step 2: performing filtering processing on the full-band white gaussian noise by using the band-pass filter to obtain two band-limited white gaussian noises, as shown in fig. 2;
and step 3: adding the band-limited white Gaussian noise into the original electroencephalogram signal, and performing empirical mode decomposition;
the specific steps of carrying out empirical mode decomposition on the electroencephalogram signals are as follows:
(1) adding the band-limited white Gaussian noise sequence w into the electroencephalogram signal x (t) respectivelyi(t) (i ═ 1,2, …, N) to obtain an input signal xi(t)＝x(t)+wi(t), i is 1,2, …, N, and each x is determinedi(t) local maxima, curve fitting using cubic spline curve, local maxima forming an upper envelope emax(t) local minima form the lower envelope emin(t)。
(2) Find emax(t) and eminMean value of (t):
Figure GDA0003005748330000041
(3) calculating an input signal xiDifference between (t) and m (t):
ci,1(t)＝xi(t)-m(t) (2)
if c isi,1(t) failing to satisfy the IMF-defining cutoff condition, repeating the above processes (1) - (3), otherwise, extracting ci,1(t) as a function of the 1 st natural mode, the residual ri,1(t) is calculated as follows:
ri,1(t)＝xi(t)-ci,1(t) (3)
(4) the residual is passed through the same screening process as a new datum to obtain the next lower frequency eigenmode function. Until a residual function ri,n(t) is a monotonic function or only an extremum, the decomposition process is stopped. Suppose that at this time the input signal xi(t) is decomposed into n natural mode functions and a residual function number ri,n(t)。
And 4, step 4: carrying out set averaging on the obtained intrinsic mode functions of each order;
Figure GDA0003005748330000042
wherein, ci,j(t) j order intrinsic mode function obtained by adding band-limited white Gaussian noise to the original brain electrical signal for the ith time and carrying out empirical mode decomposition, cj(t) represents a j-th order natural mode function.
The reconstructed signal of the original input signal x (t) is:
Figure GDA0003005748330000043
the first 8 th order natural mode functions are taken for algorithm comparison in the embodiment. As shown in fig. 3, the original electroencephalogram signal is mainly 12Hz and 24Hz, and components of other frequencies are aliased; as shown in fig. 4, in the classical EMD decomposition, a component IMF1 aliases a plurality of frequency harmonics, mainly 12Hz and 24Hz, and a component IMF2 aliases 8Hz and 12 Hz; in the algorithm decomposition of the invention, the IMF1 component only contains the high-frequency harmonic component of 24Hz, and the IMF2 component only contains the low-frequency harmonic component of 12Hz, as shown in FIG. 5. The introduction of band-limited noise effectively extracts a plurality of aliasing modes in a single IMF component into different IMFs, so that the effective separation of the modes is realized to a certain extent, the improved algorithm is proved to be feasible and effective to be used in the special field of electroencephalogram, and the problem of mode aliasing of the EMD decomposition of the electroencephalogram signal can be better solved.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto. Changes and substitutions that can be easily made within the technical scope of the invention disclosed should be covered by the technical scope of the invention disclosed. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. An improved EEMD algorithm based on electroencephalogram signals is characterized by comprising the following steps:
step 1: based on the priori knowledge of the electroencephalogram signals, selecting a mu rhythm frequency band and a beta rhythm frequency band to respectively design two band-pass filters, wherein the frequency ranges of the mu rhythm frequency band and the beta rhythm frequency band are respectively 8-12Hz and 18-26 Hz;
step 2: the band-pass filter is used for filtering the full-band white Gaussian noise to obtain a sequence w containing two band-limited white Gaussian noisesi(t), i ═ 1,2, …, N indicates the number of EMD decompositions;
and step 3: adding the band-limited white Gaussian noise sequence w into the electroencephalogram signal x (t) respectivelyi(t) each of which is an input signal xi(t)＝x(t)+wi(t) for the input signal xi(t) empirical mode decomposition, N input signals xi(t) obtaining an n-order natural mode function and a residual function ri,n(t)；
And 4, step 4: for the obtained N input signals xi(t) carrying out ensemble averaging on the n-order intrinsic mode functions to obtain the j-th order intrinsic mode function c of the electroencephalogram signal x (t)j(t) is:
Figure FDA0003012109100000011
the electroencephalogram signal x (t) can be represented as:
Figure FDA0003012109100000012
wherein, ci,jAnd (t) represents a j-th order intrinsic mode function obtained by adding band-limited white Gaussian noise to the electroencephalogram signal for the ith time and carrying out empirical mode decomposition.
2. The EEMD signal-based improved EEMD algorithm as recited in claim 1, wherein in step 3, said step of empirical mode decomposition comprises:
step 3.1: determining each input signal xi(t) local maxima, curve fitting using cubic spline curve, local maxima forming an upper envelope emax(t) local minima form the lower envelope emin(t)；
Step 3.2: find emax(t) and eminMean value of (t):
Figure FDA0003012109100000013
step 3.3: calculating an input signal xiDifference between (t) and m (t):
ci,1(t)＝xi(t)-m(t) (4)
if c isi,1(t) failing to meet the defined cutoff condition for IMF, repeating steps 3.1-3.3, otherwise, extracting ci,1(t) as a 1 st order natural mode function, a residual function ri,1(t) is calculated as follows:
ri,1(t)＝xi(t)-ci,1(t) (5)
step 3.4: the residual function ri,1(t) repeating steps 3.1-3.3 as a new input signal;
step 3.5: repeating steps 3.1-3.4 until the residual function ri,n(t) is a monotonic function or only one extremum, the decomposition process is stopped, where N input signalsxi(t) obtaining n-order natural mode functions ci,1(t),…,ci,n(t) and a residual function ri,n(t)。
3. The EEMD signal-based improved EEMD algorithm of claim 2, wherein n-8.
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