Disclosure of Invention
The invention aims to provide a noise suppression method and a system, which can remove noise source signals, can also remove additive white noise in observation signals and have high noise removal efficiency; and the influence of additive white noise on the analysis and the processing of the independent component can be avoided, and the accuracy is high.
In order to solve the above technical problem, the present invention provides a noise suppression method, including:
acquiring M observation signals received by M detectors; wherein each of the observation signals is composed of N source signals independent of each other; m and N are positive integers;
performing additive white noise removal processing on the M observation signals to obtain M observation signals after the additive white noise is removed;
performing independent component analysis processing on the M observation signals from which the additive white noise is removed to obtain N source signals which are separated from each other;
and removing the noise source signals from the N source signals which are separated from each other to obtain effective signals.
Preferably, the performing the additive white noise removal processing on the M observation signals specifically includes:
and performing additive white noise removal processing on the M observation signals by adopting a two-step eigenvalue decomposition method.
Preferably, the process of performing additive white noise removal processing on the M observation signals by using the two-step eigenvalue decomposition method specifically includes:
step s 201: obtaining an observation signal vector X (k) from M observation signals, wherein X (k) is [ X ]1,x2,……,xM]T,x1、x2、……、xMRespectively carrying out sampling processing on the M observation signals to obtain corresponding vectors;
step s 202: centering the observation signal vector X (k) to make the average value of the observation signal vector X (k) be 0;
step s 203: based on the observed signal vector X (k) and the correlation matrix relationObtaining a correlation matrixWherein the correlation matrix relation is:
step s 204: according to the correlation matrixAnd obtaining the characteristic value Lambda by the first decomposition relationX;
Wherein the first decomposition relation is:
wherein, ΛX=diag{λ1,λ2,……,λN};
Step s 205: pre-whitening the observation signal vector X (k) according to a pre-whitening relational expression to obtain a pre-whitened vector Z (k);
wherein the pre-whitening relational expression is:
wherein,VSis ΛSA corresponding feature vector;
step s 206: obtaining a diagonal matrix according to a preset time lag value p and a second decomposition relation
ΣX(ii) a Wherein the second decomposition relation is:
wherein, UXFor the feature matrix, p is not equal to 0;
step s 207: judging the diagonal matrix ΣXIf all singular values in the data are different, if yes, the step s208 is carried out; otherwise, returning to the step s206, and presetting different time lag values p;
step s 208: according to the pre-whitening vector Z (k) and the feature matrix UXAnd obtaining the observation signal vector X after the additive white noise is removed by the pre-whitening relational expression1(k);
Wherein the observation signal vector X1(k) The method comprises M signal vectors, wherein the M signal vectors respectively correspond to the M observed signals after the additive white noise is removed.
Preferably, the time lag value p takes 1.
Preferably, the process of performing independent component analysis processing on the M observed signals from which the additive white noise is removed to obtain N source signals separated from each other specifically includes:
step s 401: setting the initial value of the iteration times q as 1;
step s 402: randomly generating an initial weight vector Wq;
Step s 403: vector X of the observed signal1(k) And the initial weight vector WqCarrying in a target relational expression, wherein the obtained result is a target weight vector W;
wherein the target relation is:
wherein E is the mean value operation, g is the nonlinear function;
step s 404: judging whether the target weight vector W is converged, if so, entering the step s405, otherwise, returning to the step s 403;
step s 405: adding 1 to the iteration number q, judging whether the iteration number q is greater than a preset iteration number threshold value, and if so, entering a step s 406; otherwise, return to step s 402;
step s 406: combining the target weight vector W and the observed signal vector X1(k) And substituting a separation relation to obtain a separation vector Y (k), wherein the separation relation is as follows:
Y(k)=WX1(k)
the separation vector Y (k) includes N source signal vectors separated from each other, and the N source signal vectors correspond to the N source signals, respectively.
Preferably, the non-linear function g [. cndot. ] may be:
g (y) tanh (ay) or g (y) yexp (-y)2Y is/2) or g (y)3Wherein a is more than or equal to 1 and less than or equal to 2.
In order to solve the above technical problem, the present invention further provides a noise suppression system, including:
the acquisition unit is used for acquiring M observation signals received by the M detectors; wherein each of the observation signals is composed of N source signals independent of each other; m and N are positive integers;
the noise removing unit is used for performing additive white noise removing processing on the M observation signals to obtain M observation signals after the additive white noise is removed;
an independent component analysis processing unit, configured to perform independent component analysis processing on the M observation signals from which the additive white noise is removed, to obtain N source signals that are separated from each other;
and an effective signal obtaining unit configured to remove a noise source signal from the N source signals separated from each other to obtain an effective signal.
The invention provides a noise suppression method and a system, which improve the traditional ICA algorithm. The method comprises the steps of firstly carrying out additive white noise removal processing on M observation signals received by M detectors to remove additive white noise in the observation signals, then carrying out independent component analysis processing on the M observation signals to separate and remove noise source signals in the observation signals, and thus obtaining effective signals. Namely, the invention not only can remove the noise source signal, but also can remove the additive white noise in the observation signal, and the efficiency of removing the noise is high; and the independent component analysis processing is carried out after the additive white noise is removed, so that the premise of 'noise neglect is not counted' in the independent component analysis processing is met, the influence of the additive white noise on the independent component analysis processing is avoided, and the accuracy of the result is improved.
Detailed Description
The core of the invention is to provide a noise suppression method and a system, which can remove noise source signals, can also remove additive white noise in observation signals, and has high noise removal efficiency; and the influence of additive white noise on the analysis and the processing of the independent component can be avoided, and the accuracy is high.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a noise suppression method, and as shown in fig. 1, fig. 1 is a flow chart of a process of the noise suppression method provided by the invention; the method comprises the following steps:
step s 101: acquiring M observation signals received by M detectors; wherein each observation signal is composed of N source signals which are independent of each other; m and N are positive integers;
step s 102: performing additive white noise removal processing on the M observation signals to obtain M observation signals after the additive white noise is removed;
step s 103: carrying out independent component analysis processing on the M observation signals from which the additive white noise is removed to obtain N source signals which are separated from each other;
step s 104: and removing the noise source signals from the N source signals which are separated from each other to obtain effective signals.
For ease of understanding, the noise suppression method of the present invention is described below with respect to a specific relationship:
the M observation signals received by the M detectors are xiI ═ 1,2, … …, M; each observation signal is composed of N mutually independent source signals SjJ is 1,2, … …, N (including effective wave, alternating current interference wave, single frequency noise, etc.) is obtained by linear mixing; the relationship between the observed signal and the additive white noise and the source signal can be represented by the following relationship:
X=A×S+N
wherein X is ═ X1,x2,……,xM]TIs an observed signal vector; s ═ S1,s2,……,sN]TIs an unknown independent source signal vector; n is an additive white noise vector; a is an m n unknown mixing matrix. The invention can remove the additive white noise vector N through the additive white noise removal processing, thereby meeting the assumption that the noise can be ignored in the ICA algorithm, and at the moment, the relational expression can be simplified as follows:
X=A×S
and then separating N source signals in X through independent component analysis processing, and removing noise source signals to obtain effective signals.
The noise source signal herein mainly refers to a single-frequency noise source signal, such as an alternating-current interference wave with a frequency, a phase and an amplitude that are substantially unchanged from a shallow layer to a deep layer of the ground. Of course, the present invention is not particularly limited to this.
It can be understood that the noise suppression method in the present invention is an improved ICA algorithm, the conventional ICA algorithm directly processes the observed signal, and the assumption of the ICA algorithm is that "noise is negligible", so that additive white noise present in the observed signal will affect the ICA algorithm, so that the result obtained after the independent component analysis processing is inaccurate. The invention adds additive white noise removal treatment on the basis of the original ICA algorithm, thereby improving the accuracy of the ICA algorithm.
The additive white noise herein generally refers to thermal noise, shot noise, and the like, and their relationship to the signal is additive, that is, the additive white noise exists regardless of whether the detector receives the observed signal.
The sources of additive white noise in a channel are generally classified into three types:
1. artifacts, which originate from unrelated other signal sources, such as: external station signals, switch contact noise, industrial ignition emissions, etc.
2. Natural noise, which refers to various electromagnetic wave sources existing in nature, such as: lightning, lightning strikes, electrical storms in the atmosphere, various cosmic noises, and the like.
3. Internal noise, which is various kinds of noise generated by the system device itself, such as: thermal movement of free electrons in the resistor and fluctuation of carriers in the semiconductor, etc.
Preferably, M and N are both positive integers not less than 2.
The method for removing the additive white noise of the M observation signals specifically comprises the following steps:
and (3) performing additive white noise removal processing on the M observation signals by adopting a two-step eigenvalue decomposition method.
It can be further known that the process of performing additive white noise removal processing on the M observation signals by using the two-step eigenvalue decomposition method specifically includes:
step s 201: obtaining an observation signal vector X (k) from the M observation signals, wherein X (k) ═ X1,x2,……,xM]T,x1、x2、……、xMRespectively carrying out sampling processing on the M observation signals to obtain corresponding vectors;
step s 202: centering the observation signal vector X (k) to make the average value of the observation signal vector X (k) be 0;
step s 203: obtaining a correlation matrix according to the observation signal vector X (k) and a correlation matrix relational expressionWherein, the relational expression of the correlation matrix is:
step s 204: according to a correlation matrixAnd obtaining the characteristic value Lambda by the first decomposition relationX;
Wherein the first decomposition relation is:
wherein, ΛX=diag{λ1,λ2,……,λN};
Step s 205: pre-whitening processing is carried out on the observation signal vector X (k) according to the pre-whitening relational expression to obtain a pre-whitened vector Z (k);
wherein, the prewhitening relational expression is:
wherein,VSis ΛSA corresponding feature vector;
step s 206: obtaining a diagonal matrix according to a preset time lag value p and a second decomposition relation
ΣX(ii) a Wherein the second decomposition relation is:
wherein, UXFor the feature matrix, p is not equal to 0;
step s 207: determining diagonal matrix ΣXIf all singular values in the data are different, if yes, the step s208 is carried out; otherwise, returning to the step s206, and presetting different time lag values p;
here, the singular value means the diagonal matrix ΣXThe value on the middle diagonal;
step s 208: according to the pre-whitening vector Z (k) and the feature matrix UXAnd obtaining the observation signal vector X after the additive white noise is removed by the pre-whitening relational expression1(k);
Wherein, observing a signal vector X1(k) The M signal vectors are respectively corresponding to the M observed signals after the additive white noise is removed.
Here, the time lag value p takes 1. Of course, the specific value of the time lag value is not limited, and the staff can set the value according to the actual situation.
In addition, the process of performing independent component analysis processing on the M observation signals from which the additive white noise is removed to obtain N source signals separated from each other specifically includes:
step s 401: setting the initial value of the iteration times q as 1;
step s 402: randomly generating an initial weight vector Wq;
Step s 403: will observe signal vector X1(k) And an initial weight vector WqCarrying in a target relational expression, wherein the obtained result is a target weight vector W;
wherein, the target relational expression is:
wherein E is the mean value operation, g is the nonlinear function; the target relation is a target relation based on negative entropy maximization;
step s 404: judging whether the target weight vector W is converged, if so, entering the step s405, otherwise, returning to the step s 403;
step s 405: adding 1 to the iteration number q, judging whether the iteration number q is greater than a preset iteration number threshold value, and if so, entering a step s 406; otherwise, return to step s 402;
step s 406: combining the target weight vector W and the observed signal vector X1(k) And substituting a separation relation to obtain a separation vector Y (k), wherein the separation relation is as follows:
Y(k)=WX1(k)
the separation vector Y (k) includes N source signal vectors separated from each other, and the N source signal vectors correspond to the N source signals, respectively.
The preset iteration threshold can be determined through multiple tests, and the preset iteration threshold is set to enable separation signals corresponding to the finally obtained separation vector Y (k) to be respectively equal to the N source signals as far as possible through multiple iteration processes. Of course, the present invention does not limit the specific value of the preset iteration threshold.
Preferably, the non-linear function g [. cndot. ] may be:
g (y) tanh (ay) or g (y) yexp (-y)2Y is/2) or g (y)3Wherein a is more than or equal to 1 and less than or equal to 2.
Of course, the present invention is not particularly limited as to the type of nonlinear function g [. cndot. ] specifically employed.
In order to facilitate understanding of the invention, a simulation test can be carried out on the process of independent component analysis processing in the invention by adopting a mode of simulating seismic signals, so that the effectiveness and the accuracy of the improved ICA algorithm can be verified.
First, a zero-phase signal S with a frequency of 60Hz is selected1As an active wave, a square wave signal S with a frequency of 100Hz2And a random signal S3As alternating current interference waves (i.e. noise source signals) constituting the source signal S(i.e. each observed signal is composed of three source signals S independent of each other1、S2、S3Linear mixing), as shown in fig. 2, fig. 2 is a schematic diagram of a source signal composition in a noise suppression method provided by the present invention, where a time sampling interval of the source signal is 1ms, and a signal length is 0.5 s; the abscissa represents the number of sampling points and the ordinate represents the amplitude.
The source signal passes through a random mixing matrix A5×3Then, 5 observation signals X are obtained1~X5Referring to fig. 3, fig. 3 is a schematic diagram of an observed signal composition in a noise suppression method according to the present invention;
at this time, assume that the source signal S and the random mixing matrix A5×3Are unknown, and separate signals Y corresponding to the separate vectors Y (k) are obtained by independent component analysis processing only according to the observed signals X1~Y3Referring to fig. 4, fig. 4 is a schematic diagram of a separation signal corresponding to a separation vector Y (k) in a noise suppression method according to the present invention.
Wherein the independent component analysis process has a convergence error accuracy of 10-7In this case, the iteration time is 0.0780 s. The correlation coefficients of the isolated signal and the corresponding source signal are calculated to be-0.9980, -1.0000/0.9763, respectively.
Referring to fig. 5 and fig. 6, fig. 5 is a schematic frequency spectrum diagram of a source signal in a noise suppression method according to the present invention; FIG. 6 is a schematic frequency spectrum diagram of a separated signal in a noise suppression method according to the present invention; separating two independent components Y in a signal1And Y2Respectively 100Hz and 60Hz, respectively corresponding to the source signal S2And S1In contrast, the frequency is unchanged. That is, when the observed signal does not contain additive white noise, the independent component analysis processing can accurately separate the observed signal to obtain separate signals respectively corresponding to the source signals, so as to separate the noise source signals and obtain effective signals.
The simulation results of the simulation experiments show that the improved ICA algorithm has high convergence speed and high calculation precision, does not need to perform filtering processing in a frequency domain, can effectively overcome the influence of additive white noise on the conventional ICA algorithm, and better separates out the noise source signals in the pre-stack seismic data, thereby achieving the purpose of suppressing the noise source signals in the pre-stack seismic data.
The invention provides a noise suppression method which improves the traditional ICA algorithm. The method comprises the steps of firstly carrying out additive white noise removal processing on M observation signals received by M detectors to remove additive white noise in the observation signals, then carrying out independent component analysis processing on the M observation signals to separate and remove noise source signals in the observation signals, and thus obtaining effective signals. Namely, the invention not only can remove the noise source signal, but also can remove the additive white noise in the observation signal, and the efficiency of removing the noise is high; and the independent component analysis processing is carried out after the additive white noise is removed, so that the premise of 'noise neglect is not counted' in the independent component analysis processing is met, the influence of the additive white noise on the independent component analysis processing is avoided, and the accuracy of the result is improved.
The invention further provides a noise suppression system, and fig. 7 is a schematic structural diagram of the noise suppression system provided by the invention. The system comprises:
an obtaining unit 11, configured to obtain M observation signals received by M detectors; wherein each observation signal is composed of N source signals which are independent of each other; m and N are positive integers;
the noise removing unit 12 is configured to perform additive white noise removal processing on the M observation signals to obtain M observation signals from which the additive white noise is removed;
an independent component analysis processing unit 13, configured to perform independent component analysis processing on the M observation signals from which the additive white noise is removed, so as to obtain N source signals that are separated from each other;
the effective signal acquisition unit 14 removes the noise source signal from the N source signals separated from each other, and obtains an effective signal.
The invention provides a noise suppression system which improves the traditional ICA algorithm. The method comprises the steps of firstly carrying out additive white noise removal processing on M observation signals received by M detectors to remove additive white noise in the observation signals, then carrying out independent component analysis processing on the M observation signals to separate and remove noise source signals in the observation signals, and thus obtaining effective signals. Namely, the invention not only can remove the noise source signal, but also can remove the additive white noise in the observation signal, and the efficiency of removing the noise is high; and the independent component analysis processing is carried out after the additive white noise is removed, so that the premise of 'noise neglect is not counted' in the independent component analysis processing is met, the influence of the additive white noise on the independent component analysis processing is avoided, and the accuracy of the result is improved.
It should be noted that, in the present specification, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.