CN101661752B - Signal processing method and device - Google Patents

Abstract

The embodiment of the invention relates to a signal processing method and a device. The method includes the following steps: in a period of time, receiving a mixed signal and obtaining the amplitude information of the received mixed signal; according to the third-order cumulant and the fourth-order cumulant of the amplitude information of the mixed signal, obtaining objective function through calculation; and using the objective function to obtain an independent signal in the mixed signal. The method can cause ICA algorithm to be applicable to unmixing treatment of various signals. Another method includes the following steps: using Newton iteration formula with a regulatory factor that can cause the objective function to descend according to given norm to conduct iterative treatment on initial weight vector until the iterated weight vector is converged, and obtaining the converged weight vector; receiving the mixed signal in a period of time and acquiring the amplitude information of the received mixed signal; and according to the converged weight vector, conducting unmixing treatment on the mixed signal and acquiring the independent signal in the mixed signal. The method has little restraint in selection of the initial value of the weight vector in partitioning matrix and high operation efficiency.

Description

Signal processing method and device

Technical field

The present invention relates to a kind of signal processing method and device, relate in particular to that a kind of (Independent Component Analysis is hereinafter to be referred as signal processing method ICA) and device based on independent component analysis.

Background technology

ICA is in recent years by the multi channel signals disposal route of signal separation techniques development, is a kind ofly having only observation data and signal source to mix repeatedly a kind of signal processing method that under the method condition of unknown signal independent source is extracted.The Blind Signal Separation that realizes through ICA has potential advantages at speech recognition, communication, processing of biomedical signals, image processing method mask.

For any ICA algorithm, can be summed up as: ICA algorithm=objective function+optimized Algorithm.Suppose to observe n stochastic variable x ₁, x ₂... X _n, and these variablees are by other n stochastic variable s ₁, s ₂... S _nLinear combination obtains, i.e. x _i=a _I1s ₁+ a _I2s ₂+ ... + a _Ins _n, i=1,2 ... N.Wherein, a _Ij, i, j=1,2 ... N is a real coefficient, s _iStatistics is independent each other, independent component s _iBe called as hidden variable.In addition, mixing constant a _IjAlso be that hypothesis is unknown, unique that can observe is stochastic variable x _iTherefore, must only use x _iJust mixing constant a _IjWith independent component s _iEstimate simultaneously to come out, this process must be carried out under general as much as possible hypothesis.Above-mentioned formula x _i=a _I1s ₁+ a _I2s ₂+ ... + a _Ins _n, i=1,2 ... N can be expressed as x=As.Behind estimated mixing matrix A, need to calculate the contrary of hybrid matrix A, i.e. separation matrix W=A ^-1Thereby, obtain the estimation y of isolated component s, i.e. y=Wx.Therefore; In order to estimate y; Just need an objective function L (W); When

can make L () function reach maximum or minimum value; What

asked for independent component analysis separates, and y this moment perhaps approximately equivalent promptly of equal value is in s.

In realizing process of the present invention; The inventor finds to exist at least in the prior art following problem: existing ICA method; Can be directed against respectively inferior gaussian signal, this signal of superelevation, probability density function for symmetry or asymmetrical signal etc. source signal is separated; And can't all have good separating property, thereby cause existing ICA algorithm to be suitable for the limitation of range of signal to these signals.And existing ICA method is responsive to choosing of weight vector initial value in the separation matrix, and constringency performance is relatively poor, and efficient is lower.

Summary of the invention

The embodiment of the invention provides a kind of signal processing method and device, to improve the extraction efficiency to the independent signal in the mixed signal.

The embodiment of the invention provides a kind of signal processing method, comprising:

In a period of time, receive mixed signal, obtain the amplitude information of the mixed signal of reception;

According to three rank semi-invariant and fourth order cumulants of the amplitude information of said mixed signal, calculate and obtain objective function;

Use said objective function and obtain the independent signal in the said mixed signal.

Correspondingly, the embodiment of the invention also provides a kind of signal processing apparatus, comprising:

First receiver module is used in a period of time, receiving mixed signal, obtains the amplitude information of the mixed signal of reception;

The computing module, three rank semi-invariant and fourth order cumulants of the amplitude information of the mixed signal that is used for obtaining according to first receiver module calculate and obtain objective function;

Obtain processing module, be used for using the independent signal that objective function that said computing module obtains obtains said mixed signal.

The embodiment of the invention is through combining the three rank semi-invariants and the fourth order cumulant of the amplitude information of mixed signal in objective function; Separating of different mixed signals mixed processing have very strong conformability; Both can handle inferior gaussian signal or/and this signal of superelevation; Be the good performance performance that also has symmetry or asymmetrical to probability density function again, therefore, overcome the limitation of existing ICA algorithm on the signal scope of application.

The embodiment of the invention provides another kind of signal processing method, comprising:

Application has makes objective function carry out iterative processing by the Newton iteration formula of the regulatory factor of given norm decline to initial weight vector, till the convergence of the weight vector after the iteration, obtains the convergent weight vector;

In a period of time, receive mixed signal, obtain the amplitude information of the mixed signal of reception;

According to said convergent weight vector said mixed signal is separated hybrid processing, obtain the independent signal in the said mixed signal.

Correspondingly, the embodiment of the invention also provides a kind of signal processing apparatus, comprising:

The iterative processing module is used to use have and makes the Newton iteration formula of the regulatory factor that objective function descends by given norm carry out iterative processing to initial weight vector, till the convergence of the weight vector after the iteration, obtains the convergent weight vector;

Second receiver module is used in a period of time, receiving mixed signal, obtains the amplitude information of the mixed signal of reception;

Separate mixed processing module, the convergent weight vector that is used for obtaining according to said iterative processing module is separated hybrid processing to the mixed signal that second receiver module receives, and obtains the independent signal in the said mixed signal.

The embodiment of the invention is through being introducing regulatory factor λ in the FastICA algorithm; Objective function is descended by given norm; Begin thereby impel from certain weight vector; Objective function can get into the convergence region of Newton iteration method, thereby can separate hybrid processing to mixed signal according to the weight vector after the convergence, obtains each independent signal in the mixed signal.In the present embodiment,, improved ICA convergence of algorithm performance, thereby improved the operation efficiency that mixed signal is carried out signal Processing because the speed of convergence of objective function is linear speed of convergence.

Through accompanying drawing and embodiment, technical scheme of the present invention is done further detailed description below.

Description of drawings

Fig. 1 is the process flow diagram of an embodiment of signal processing method of the present invention;

Fig. 2 is the structural representation of an embodiment of signal processing apparatus of the present invention;

Fig. 3 is the process flow diagram of another embodiment of signal processing method of the present invention;

Fig. 4 is the structural representation of another embodiment of signal processing apparatus of the present invention.

Embodiment

Signal processing method embodiment of the present invention receives mixed signal in a period of time, obtain the amplitude information of the mixed signal of reception; According to three rank semi-invariant and fourth order cumulants of the amplitude information of said mixed signal, calculate and obtain objective function; Use said objective function and obtain the independent signal in the said mixed signal.Signal processing method embodiment of the present invention is through combining the three rank semi-invariants and the fourth order cumulant of the amplitude information of the mixed signal that receives in objective function; Separating of different mixed signals mixed processing have very strong conformability; Both can handle inferior gaussian signal or/and this signal of superelevation; Again to probability density function for symmetry or asymmetrical the performance of good performance arranged also, therefore, overcome existing ICA algorithm when signal Processing to the limitation on the signal properties scope of application.

Fig. 1 is the process flow diagram of an embodiment of signal processing method of the present invention, and as shown in Figure 1, the method for present embodiment comprises:

Step 101, confirm rotation matrix auxiliary variable, mixed signal auxiliary variable and rotation matrix required when the application target function obtains each independent signal in the mixed signal.

For instance, confirm this rotation matrix auxiliary variable Q ' and mixed signal auxiliary variable y ', being rotation matrix auxiliary variable Q ' is for subsequent applications rotation matrix Q with the initialized effect of mixed signal auxiliary variable y ' ^UvRotation matrix auxiliary variable Q ' and mixed signal auxiliary variable y ' are carried out the iteration update processing respectively, thereby obtain the isolated component in the mixed signal.This rotation matrix Q ^UvIn u, v represents the two dimensional surface component, this rotation matrix Q ^UvCan picked at random also can choose according to a definite sequence.

In the present embodiment, can suppose Q '=I _n, y '=y.

Step 102, according to three rank semi-invariant and fourth order cumulants of mixed signal, calculate and obtain objective function.

For instance, present embodiment can be provided with an objective function based on three rank semi-invariants and fourth order cumulant, shown in formula (3):

${\stackrel{\‾}{\mathrm{\Ψ}}}_{34}\left(x\right)=\frac{1}{3!}\underset{\mathrm{\α\β\γ}\≠\mathrm{\α\α\α}}{\mathrm{\Σ}}{\left(C_{\mathrm{\α\β\γ}}\left(x\right)\right)}^2+\frac{1}{4!}\underset{\mathrm{\α\β\γ\δ}\≠\mathrm{\α\α\α\α}}{\mathrm{\Σ}}{\left(C_{\mathrm{\α\β\γ\δ}}\left(x\right)\right)}^2---\left(3\right)$

C in the formula _{α β γ}(x) expression three rank semi-invariants, C _{α β γ δ}(x) expression fourth order cumulant, a, beta, gamma, δ=1 or 2 is respectively three rank semi-invariant and fourth order cumulants of mixed signal.The quadratic sum of formula (3) expression three rank semi-invariants and fourth order cumulant off-diagonal element,

and

is by x being asked the K-L divergence launch the coefficient that obtains.

Minimize the objective function shown in the formula (3), also promptly be equivalent to the maximization diagonal element with, promptly obtain following formula (4):

${\mathrm{\Φ}}_{34}\left(x\right)=\frac{1}{3!}\underset{\mathrm{\α}}{\mathrm{\Σ}}{\left(C_{\mathrm{\α\α\α}}\left(x\right)\right)}^2+\frac{1}{4!}\underset{\mathrm{\α}}{\mathrm{\Σ}}{\left(C_{\mathrm{\α\α\α\α}}\left(x\right)\right)}^2---\left(4\right)$

Suppose that it is y that later mixed signal is handled in albefaction, have a rotation matrix Q, satisfy x=Qy, can obtain following formula (5) by formula (4):

${\mathrm{\ψ}}_{34}(Q,y)=\frac{1}{3!}\underset{\mathrm{\α}}{\mathrm{\Σ}}{\left(\underset{\mathrm{\β\γ\δ}}{\mathrm{\Σ}}{Q}_{\mathrm{\α\β}}{Q}_{\mathrm{\α\γ}}{Q}_{\mathrm{\α\δ}}{C}_{\mathrm{\β\γ\δ}}\left(y\right)\right)}^2+\frac{1}{4!}\underset{\mathrm{\α}}{\mathrm{\Σ}}{\left(\underset{\mathrm{\β\γ\δ\ϵ}}{\mathrm{\Σ}}{Q}_{\mathrm{\α\β}}{Q}_{\mathrm{\α\γ}}{Q}_{\mathrm{\α\δ}}{Q}_{\mathrm{\α\ϵ}}{C}_{\mathrm{\β\γ\δ\ϵ}}\left(y\right)\right)}^2---\left(5\right)$

Q is the Givens rotation matrix in the formula, around two dimensional surface u and v, obtains following formula (6):

$Q^{\mathrm{uv}}=\left[\begin{array}{cc}\cos \mathrm{\φ}& \sin \mathrm{\φ}\\ -\sin \mathrm{\φ}& \cos \mathrm{\φ}\end{array}\right]---\left(6\right)$

Wherein, φ is the anglec of rotation of rotation matrix.

In formula (6) substitution formula (5), can formula (3) formula be rewritten into following formula (7):

ψ ₃₄(φ，y)＝ψ ₃(φ，y)+ψ ₄(φ，y) (7)

Wherein, ${\mathrm{\ψ}}_n(\mathrm{\φ},y)=\frac{1}{n!}\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{d}_m\left(\mathrm{Cos}{\left(\mathrm{\φ}\right)}^{(2n-i)}\mathrm{Sin}{\left(\mathrm{\φ}\right)}^i\right)+\frac{1}{n!}\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{d}_m\left({\mathrm{Cos}\left(\mathrm{\φ}\right)}^{\left(i\right)}\mathrm{Sin}{\left(\mathrm{\φ}\right)}^{(2n-i)}\right),$ d _mBe only with the relevant constant of semi-invariant C (y), d _mDefinition following:

$d_{30}=({c_{111}^y}^2+{c_{222}^y}^2)$

${\mathrm{<figure-callout\; id="31"\; label="d"\; filenames="H2009100930194E00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_{31}=6({c_{111}^y}^2{c_{112}^y}^2-{c_{122}^y}^2{c_{222}^y}^2)$

${\mathrm{<figure-callout\; id="32"\; label="d"\; filenames="H2009100930194E00012.png"\; state="\{\{state\}\}">d</figure-callout>}}_{32}=9({c_{112}^y}^2+{c_{122}^y}^2)+6({c_{111}^y}^2{c_{122}^y}^2+{c_{112}^y}^2{c_{222}^y}^2)$

$d_{33}=2{c_{111}^y}^2{c_{222}^y}^2+18{c_{112}^y}^2{c_{122}^y}^2$

$d_{41}=8({c_{1111}^y}^2{c_{1112}^y}^2-{c_{1222}^y}^2{c_{2222}^y}^2)$

$d_{42}=16({c_{1112}^y}^2+{c_{1222}^y}^2)+12({c_{1111}^y}^2{c_{1122}^y}^2+{c_{1122}^y}^2{c_{2222}^y}^2)$

$d_{43}=48({c_{1112}^y}^2{c_{1112}^y}^2-{c_{1122}^y}^2{c_{1222}^y}^2)+8({c_{1111}^y}^2{c_{1222}^y}^2-{c_{1112}^y}^2{c_{2222}^y}^2)$

$d_{44}=36{c_{1122}^y}^2+32{c_{1112}^y}^2{c_{1222}^y}^2+2{c_{1111}^y}^2{c_{2222}^y}^2$

In order to simplify above-mentioned formula (7), can be provided with auxiliary variable: θ=tan (φ) and $\mathrm{\&xi;}=\mathrm{\&theta;}-\frac{1}{\mathrm{\&theta;}},$ Thereby obtain: ${\mathrm{\&Psi;}}_3(\mathrm{\&theta;},y)=\frac{1}{3!}{(\mathrm{\&theta;}+\frac{1}{\mathrm{\&theta;}})}^{-3}\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{a}_i({\mathrm{\&theta;}}^i-(-{\mathrm{\&theta;}}^{-i}))$ With ${\mathrm{\&Psi;}}_4(\mathrm{\&theta;},y)=\frac{1}{4!}{({\mathrm{\&xi;}}^2+4)}^{-3}\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_i{\mathrm{\&xi;}}^i.$

In order to reach the optimization effect, need find an objective function that can combine three rank semi-invariants and fourth order cumulant, and mathematical form is wanted simple, intuitive, optimization easily.Therefore, can obtain following formula (8):

ψ ₃₄(φ，y)＝A ₀+A ₄cos(4φ+φ ₄)+A ₈cos(8φ+φ ₈) (8)

Wherein, A ₀=a ₃₀+ a ₄₀

$A_4=\sqrt{{(c_{34}+c_{44})}^2+{(s_{34}+s_{44})}^2};$

$A_8=\sqrt{{c_{48}}^2+{s_{48}}^2};$

$\tan \left({\mathrm{\&phi;}}_4\right)=-\frac{s_{34}+s_{44}}{c_{34}+c_{44}};$

$\tan \left({\mathrm{\&phi;}}_8\right)=-\frac{s_{48}}{c_{48}};$

$a_{30}=\frac{1}{3!}\frac{1}{8}[5({c_{111}^y}^2+{c_{222}^y}^2)+9({c_{112}^y}^2+{c_{122}^y}^2)+6({c_{111}^y}^2{c_{122}^y}^2+{c_{112}^y}^2{c_{222}^y}^2)]$

$a_{40}=\frac{1}{4!}\frac{1}{64}[35({c_{1111}^y}^2+{c_{2222}^y}^2)+80({c_{1112}^y}^2+{c_{1222}^y}^2)+60(c_{1111}^y{c}_{1122}^y+c_{1122}^y{c}_{2222}^y)]$

$s_{34}=\frac{1}{3!}\frac{1}{4}\left[6(c_{111}^y{c}_{112}^y-c_{122}^y{c}_{222}^y)\right]$

$a_{34}=\frac{1}{3!}\frac{1}{8}[3({c_{111}^y}^2+{c_{222}^y}^2)-9({c_{112}^y}^2+{c_{122}^y}^2)-6{(c}_{111}^y{c}_{112}^y+c_{112}^y{c}_{222}^y)]$

$s_{44}=\frac{1}{4!}\frac{1}{32}[56(c_{1111}^y{c}_{1112}^y-c_{1222}^y{c}_{2222}^y)+48(c_{1112}^y{c}_{1122}^y-c_{1122}^y{c}_{1222}^y)+8(c_{1111}^y{c}_{1222}^y-c_{1112}^y{c}_{1222}^y)]$

$c_{44}=\frac{1}{4!}\frac{1}{16}[7({c_{1111}^y}^2+{c_{2222}^y}^2)-16({c_{1112}^y}^2+{c_{2222}^y}^2)-12(c_{1111}^y{c}_{1122}^y+c_{1122}^y{c}_{2222}^y)-36{c_{1122}^y}^2-32c_{1112}^y{c}_{1222}^y-2c_{1111}^y{c}_{2222}^y]$

$s_{48}=\frac{1}{4!}\frac{1}{64}[8(c_{1111}^y{c}_{1112}^y-c_{1222}^y{c}_{2222}^y)+48(c_{1112}^y{c}_{1122}^y-c_{1122}^y{c}_{1222}^y)-8(c_{1111}^y{c}_{1222}^y-c_{1112}^y{c}_{2222}^y)]$

The inventor finds through the calculating and the simulating, verifying of real data: in the objective function shown in the formula (8), and parameter A ₈Compare A ₄A little one magnitude, this just shows the 3rd that can ignore in the formula (8), therefore, the objective function shown in the formula (8) can further be reduced to formula as follows (1):

ψ ₃₄(φ，y)＝A ₀+A ₄cos(4φ+φ ₄) (1)

Therefore, according to three rank semi-invariant and fourth order cumulants of mixed signal, calculating is obtained objective function and can be thought in the step 102: application of formula (1) is calculated and is obtained said objective function.

In the present embodiment; This step 102 can at first be calculated three required rank semi-invariant and fourth order cumulants of the objective function shown in definite formula (1); In the mixed signal auxiliary variable y ' substitution formula (1) that three rank semi-invariants of then calculating being obtained and fourth order cumulant and step 101 initialization are obtained, thereby confirm this objective function.

Step 103, when confirming that the functional value of said objective function is maximum, the extreme value of relevant parameter in this objective function;

For instance, step 103 can be specially: confirm objective function ψ ₃₄When the functional value of (φ, y ') is maximum, the extreme value φ of relevant parameter φ in this objective function _Max, wherein y ' is said mixed signal auxiliary variable.

After step 102 utilizes formula (1) to confirm objective function, can obtain objective function ψ ₃₄(φ, y ').This objective function ψ ₃₄(φ, y ') can ask for this objective function ψ to the φ differentiate ₃₄The extreme value of (φ, y '), thus confirm φ corresponding under this extreme value _Max

Step 104, that whether the extreme value of judging parameter satisfies is pre-conditioned, if execution in step 105 then, otherwise execution in step 101 again.

For instance, present embodiment can be provided with the pre-conditioned φ that is _Max＞ε.This ε can select arbitrarily as required.

Step 105, with the product of said rotation matrix and said rotation matrix auxiliary variable as current rotation matrix auxiliary variable; The product of said rotation matrix and said mixed signal auxiliary variable as current mixed signal auxiliary variable, and is obtained said independent signal according to said current rotation matrix auxiliary variable and current mixed signal auxiliary variable.

The process of step 105 is at φ _MaxSatisfy when pre-conditioned, when promptly objective function is optimum, utilize rotation matrix to upgrade rotation matrix auxiliary variable and mixed signal auxiliary variable, and the process of obtaining independent signal according to the rotation matrix auxiliary variable after upgrading and mixed signal auxiliary variable.

For instance, step 105 can be specially: at extreme value φ _MaxDuring greater than predetermined threshold value ε, with rotation matrix Q ^UvWith the product of rotation matrix auxiliary variable Q ' as current rotation matrix auxiliary variable Q ', with rotation matrix Q ^UvWith the product of mixed signal auxiliary variable y ' as current mixed signal auxiliary variable y ', and, obtain independent signal with the multiplying each other of current rotation matrix auxiliary variable Q ' and current mixed signal auxiliary variable y '.Promptly utilize Q '=Q ^UvQ ' renewal Q ' utilizes y '=Q ^UvY ' upgrades y ', obtains isolated component x with x=Q ' y ' at last.

Do not satisfy when pre-conditioned in the extreme value of parameter, confirm said rotation matrix auxiliary variable, mixed signal auxiliary variable and rotation matrix again.Again execution in step 101～104 then, satisfy up to the extreme value of parameter pre-conditioned, φ for example _MaxFinish during＞ε.

Present embodiment is through combine three rank semi-invariants and fourth order cumulant fully; Effectively solved the circumscribed problem of separating property of source signal; Solved effectively the strict problem of the selectivity of signal type, solved the probability density function symmetry and asymmetrical restricted problem of mixed signal effectively.The objective function form simple, intuitive of present embodiment is easy to optimize, thereby has simplified the process that mixed signal is separated into independent signal.It is in extensive range that the method for present embodiment is used; Comprise that voice, image, CDMA etc. relate to fields such as field and the metal defect detection of signal Processing, heart and brain electric treatment; Not only can be used for the source signal condition of unknown; While can be used for the situation of known signal, not only can be used for the processing and the increased functionality of mobile phone signal, also can be used for the signal Processing and the increased functionality thereof of like product.

Correspondingly, the embodiment of the invention also provides a kind of signal processing apparatus corresponding with said method embodiment.This device comprises: first receiver module, computing module and obtain processing module, and first receiver module is used in a period of time, receiving mixed signal, obtains the amplitude information of the mixed signal of reception; Three rank semi-invariant and fourth order cumulants of the amplitude information of the mixed signal that this computing module is used for obtaining according to first receiver module calculate and obtain objective function; This obtains processing module and is used for using the independent signal that objective function that said computing module obtains obtains said mixed signal.Signal processing apparatus embodiment of the present invention combines through three rank semi-invariants and the fourth order cumulant with mixed signal; Separating of different mixed signals mixed processing have very strong conformability; Both can handle inferior gaussian signal or/and this signal of superelevation; Be the good performance performance that also has symmetry or asymmetrical to probability density function again, therefore, overcome the limitation of existing ICA algorithm on the signal scope of application.

Fig. 2 is the structural representation of an embodiment of signal processing apparatus of the present invention, and as shown in Figure 2, the device of this instance comprises:

First receiver module 1, computing module 2 and obtain processing module 3, the first receiver modules 1 and be used in a period of time, receiving mixed signal are obtained the amplitude information of the mixed signal of reception; Three rank semi-invariant and fourth order cumulants of the amplitude information of the mixed signal that this computing module 2 is used for obtaining according to first receiver module 1 calculate and obtain objective function; This obtains processing module 3 and is used for using the independent signal that objective function that said computing module 2 obtains obtains said mixed signal.

Further; The device of present embodiment also comprises: select processing module 4, this selections processing module 4 to be used for definite said rotation matrix auxiliary variable, mixed signal auxiliary variable and rotation matrix required when obtaining processing module and using said objective function and obtain each independent signal of said mixed signal.

Further, in the device of present embodiment, obtain processing module 3 and comprise: when first processing unit 31 and second processing unit 32, this first processing unit 31 are used for confirming that said objective function is maximum, the extreme value of relevant parameter in this objective function; Second processing unit 32 satisfies when pre-conditioned in the extreme value of said parameter; With the product of said rotation matrix and said rotation matrix auxiliary variable as current rotation matrix auxiliary variable; The product of said rotation matrix and said mixed signal auxiliary variable as current mixed signal auxiliary variable, and is obtained said independent signal according to said current rotation matrix auxiliary variable and current mixed signal auxiliary variable.

The realization principle of the device of present embodiment is identical with the realization principle of signal processing method embodiment of the present invention shown in Figure 1, repeats no more.

The device of present embodiment is through combine three rank semi-invariants and fourth order cumulant fully; Effectively solved the circumscribed problem of separating property of source signal; Solved effectively the strict problem of the selectivity of signal type, solved the probability density function symmetry and asymmetrical restricted problem of mixed signal effectively.Objective function form simple, intuitive in the present embodiment is easy to optimize, thereby has simplified the process that mixed signal is separated into independent signal.It is in extensive range that the device of present embodiment is used; Comprise that voice, image, CDMA etc. relate to fields such as field and the metal defect detection of signal Processing, heart and brain electric treatment; Not only can be used for the source signal condition of unknown; While can be used for the situation of known signal, not only can be used for the processing and the increased functionality of mobile phone signal, also can be used for the signal Processing and the increased functionality thereof of like product.

The embodiment of the invention also provides another kind of signal processing method; This method comprises: application has makes objective function carry out iterative processing by the Newton iteration formula of the regulatory factor of given norm decline to initial weight vector; Till the convergence of the weight vector after the iteration, obtain the convergent weight vector; In a period of time, receive mixed signal, obtain the amplitude information of the mixed signal of reception; According to said convergent weight vector mixed signal is separated hybrid processing, obtain the independent signal in the said mixed signal.

In the original FastICA algorithm; Initial weight vector generally is a picked at random, so the value difference of weight vector can cause each iteration efficient different, thereby the isolated component that obtains also can be slightly different; Especially for the bad situation of source signal independence; To the weight vector initial value choose the comparison sensitivity, different initial weight vectors possibly cause constringency performance different, even convergence can occur and not restrain two kinds of opposite extreme situations.Though prior art can be chosen the major component that obtains in the albefaction process value as initial weight vector, algorithm is easy to converge to this albefaction initial value, though good constringency performance is arranged, separating effect is not good.To this problem, signal processing method embodiment of the present invention proposes a kind of point of fixity based on regulatory factor λ (Fix Point) algorithm through for introducing regulatory factor λ in the FastICA algorithm; Through selecting λ; Objective function is descended by given norm, begin thereby impel from certain weight vector, objective function can get into the convergence region of Newton iteration method; Thereby can separate hybrid processing to mixed signal according to the weight vector after the convergence, obtain each independent signal in the mixed signal.Present embodiment under any circumstance all can make objective function reach convergence.Newton iteration method behind the introducing regulatory factor has been relaxed many for the selection of initial value condition of weight vector, speed of convergence is linear speed of convergence, has improved ICA convergence of algorithm performance, thereby has improved the operation efficiency that mixed signal is carried out signal Processing.

Further, owing in above-mentioned iterative process, need the Jacobi matrix of double counting objective function; To accomplish iterative algorithm, in the iterative process of present embodiment, when can all using iterative processing for the first time, calculates in said Jacobi matrix the Jacobi matrix that obtains; Thereby when iteration repeatedly; Under the situation of a Jacobi matrix of demand, the purpose of the data variation that adapts to iteration can also be reached, thereby the speed of convergence of iteration can be improved greatly.Because repeatedly iterative process combines, and can increase the correction of each iteration, makes algorithm obtain better constringency performance.Therefore, through improving iterative process, present embodiment can also reduce the calculation times of Jacobi matrix, has reduced calculated amount, has improved iteration speed; And the each iteration of this method is equivalent to the repeatedly effect of iteration of common Newton iteration method; The oscillatory occurences that can avoid common Newton iteration to produce effectively, the independence of each independent signal is not to obtain to restrain preferably the result under the good situation yet in mixed signal.

In concrete application process, both can only in the FastICA method, introduce regulatory factor, thereby solve the problem of choosing of the weight vector initial value in the former FastICA algorithm effectively; Improve algorithm iteration efficient and constringency performance; Also can only expand the general improvement of the Newton iteration in the FastICA algorithm, repeatedly iteration combines, and the iteration of back is all used the result of the Jacobi matrix that calculates for the first time; Thereby improve the speed of convergence of iteration; Can also above-mentioned two kinds of improvement all be incorporated in the FastICA algorithm, obtain dual improved FastICA algorithm, that is: the Newton iteration method of utilizing the band regulatory factor earlier is to the insensitive characteristic of initial value; Try to achieve approximate value preferably, the fast convergence with improved FastICA obtains isolated component again.

Fig. 3 is the process flow diagram of another embodiment of signal processing method of the present invention, and as shown in Figure 3, the method for present embodiment comprises:

Step 301, mixed signal is carried out centralization handle, obtain average and be 0 mixed signal.

The process of centralization is for deducting the expectation value of this mixed signal with mixed signal.

Step 302, the mixed signal after the centralization is carried out albefaction handle.

The purpose that albefaction is handled is uncorrelated mutually between each component in the mixed signal after feasible the processing.

The weight vector initialization value w that step 303, selection have unit norm.

Step 304, calculating Jacobi matrix J F (w _n), wherein F () is an objective function.

In the successive iterations processing procedure of present embodiment, Jacobi matrix J F (w _n) calculate the Jacobi matrix J F (w that obtains in the time of can all using iterative processing for the first time _n), and need not to recomputate.

Step 305, application of formula (2) are confirmed regulatory factor:

$\underset{\mathrm{\&lambda;}}{\min }\left|\right|F(w_n-\mathrm{\&lambda;F}\left(w_n\right)/\mathrm{JF}\left(w_n\right))\left|\right|---\left(2\right)$

Wherein, λ is a regulatory factor, and F () is an objective function, w _nBe n initial weight vector, JF (w _n) be the Jacobi matrix.

Selecting the purpose of regulatory factor λ is under certain normal form, to meet the demands:

$\left|\right|E\left\{\mathrm{xg}\left({w_n}^{T}x\right)\right\}-\mathrm{\&beta;}{w_{m+1}}^T\left|\right|<\left|\right|E\left\{\mathrm{xg}\left({w_n}^{T}x\right)\right\}-\mathrm{\&beta;}{w_n}^T\left|\right|,n=\mathrm{0,1},...$

W in the formula _nBe the value before upgrading, w _N+1It is the value after upgrading.

Step 306, application have makes objective function carry out iterative processing by the Newton iteration formula of the regulatory factor of given norm decline to initial weight vector.

For instance, step 306 can be carried out iterative processing to initial weight vector for application of formula (3):

w←w-λ[E{zg(w ^Tz)}+βw]/[E{g′(w ^Tz)}+β] (3)

Wherein, w is the weight vector in the separation matrix, and g () is a nonlinear function, and g ' () is the derivative of g (), and E () is for averaging, and z is a mixed signal, and β is a constant.

Step 307, the weight vector w that iteration is obtained carry out standardization.

This standardization promptly can be obtained divided by the norm of this weight vector through the weight vector that iteration is obtained.

Step 308, judge whether the weight vector w after the iteration restrains, if restrain then execution in step 309, otherwise execution in step 305.

Step 309, mixed signal is separated hybrid processing, obtain the independent signal in the said mixed signal according to the convergent weight vector.

This step 309 is that available convergent weight vector multiply by mixed signal and obtains the independent signal in this mixed signal.

Present embodiment combines two kinds of improvement, and the Newton iteration method of utilizing the band regulatory factor is earlier tried to achieve approximate value preferably to the insensitive characteristic of initial value, and the fast convergence with improved FastICA obtains isolated component again; Through introducing regulatory factor, can effectively solve the problem of choosing of the initial weight vector in the original FastICA algorithm, improve iteration efficient and convergence signal performance; Combine through inciting somebody to action repeatedly iteration, the iteration of back is all used the result of the Jacobi matrix that calculates for the first time, thereby can improve the speed of convergence of iteration greatly.Because repeatedly iterative process combines, and has increased the correction of each iteration, the oscillatory occurences that can avoid common Newton iteration to produce effectively, the independence of the independent signal in mixed signal is not to obtain to restrain preferably the result under the good situation yet.

Correspondingly, the embodiment of the invention also provides a kind of signal processing apparatus corresponding with said method embodiment.This device comprises: iterative processing module, second receiver module are conciliate and are mixed processing module; This iterative processing module is used to use have makes objective function carry out iterative processing by the Newton iteration formula of the regulatory factor of given norm decline to initial weight vector; Till the convergence of the weight vector after the iteration, obtain the convergent weight vector; Second receiver module is used in a period of time, receiving mixed signal, obtains the amplitude information of the mixed signal of reception; This is separated and mixes the convergent weight vector that processing module is used for obtaining according to said iterative processing module the mixed signal that second receiver module receives is separated hybrid processing, obtains the independent signal in the said mixed signal.

Further, said iterative processing module in iterative process, said Jacobi matrix J F (w _n) calculate the Jacobi matrix that obtains when all using iterative processing for the first time.

Present embodiment is through being introducing regulatory factor λ in the FastICA algorithm; Objective function is descended by given norm; Begin thereby impel from certain weight vector; Objective function can get into the convergence region of Newton iteration method, thereby can separate hybrid processing to mixed signal according to the weight vector after the convergence, obtains each independent signal in the mixed signal.In the present embodiment,, improved ICA convergence of algorithm performance, thereby improved the operation efficiency that mixed signal is carried out signal Processing because the speed of convergence of objective function is linear speed of convergence.

Owing in above-mentioned iterative process, need the Jacobi matrix of double counting objective function, to accomplish iterative algorithm; The iterative processing module of present embodiment is in iterative process; When can all using iterative processing for the first time, calculates in employed Jacobi matrix the Jacobi matrix that obtains, thereby when iteration repeatedly, under the situation of a Jacobi matrix of a demand; The purpose of the data variation that adapts to iteration can also be reached, thereby the speed of convergence of iteration can be improved greatly.Because repeatedly iterative process combines, and can increase the correction of each iteration, makes algorithm obtain better constringency performance.Therefore, through improving iterative process, present embodiment can also reduce the calculation times of Jacobi matrix, has reduced calculated amount, has improved iteration speed; And the each iteration of this method is equivalent to the repeatedly effect of iteration of common Newton iteration method; The oscillatory occurences that can avoid common Newton iteration to produce effectively, the independence of each independent signal is not to obtain to restrain preferably the result under the good situation yet in mixed signal.

In concrete application process, this iterative processing module both can only be introduced regulatory factor in the FastICA method, thereby solved the problem of choosing of the weight vector initial value in the former FastICA algorithm effectively; Improve algorithm iteration efficient and constringency performance; Also can only expand the general improvement of the Newton iteration in the FastICA algorithm, repeatedly iteration combines, and the iteration of back is all used the result of the Jacobi matrix that calculates for the first time; Thereby improve the speed of convergence of iteration; Can also above-mentioned two kinds of improvement all be incorporated in the FastICA algorithm, obtain dual improved FastICA algorithm, that is: the Newton iteration method of utilizing the band regulatory factor earlier is to the insensitive characteristic of initial value; Try to achieve approximate value preferably, the fast convergence with improved FastICA obtains isolated component again.

Fig. 4 is the structural representation of another embodiment of signal processing apparatus of the present invention; As shown in Figure 4; The device of present embodiment comprises: iterative processing module 5, second receiver module 6 are conciliate and are mixed processing module 7; This iterative processing module 5 is used to use have makes objective function carry out iterative processing by the Newton iteration formula of the regulatory factor of given norm decline to initial weight vector, till the convergence of the weight vector after the iteration, obtains the convergent weight vector; Second receiver module 6 is used in a period of time, receiving mixed signal, obtains the amplitude information of the mixed signal of reception; This is separated and mixes the convergent weight vector that processing module 7 is used for obtaining according to said iterative processing module 5 mixed signal that second receiver module 6 receives is separated hybrid processing, obtains the independent signal in the said mixed signal.

Further, the device of present embodiment also comprises: acquisition module 8, this acquisition module 8 are used for the regulatory factor that application of formula (2) confirms that said iterative processing module 5 is required:

$\underset{\mathrm{\&lambda;}}{\min }\left|\right|F(w_n-\mathrm{\&lambda;F}\left(w_n\right)/\mathrm{JF}\left(w_n\right))\left|\right|---\left(2\right)$

Wherein, λ is a regulatory factor, and F () is an objective function, w _nBe n initial weight vector, JF (w _n) be the Jacobi matrix.

Said iterative processing module 5 in iterative process, said Jacobi matrix J F (w _n) calculate the Jacobi matrix that obtains when all using iterative processing for the first time.Said iterative processing module 5 application of formula (3) are carried out iterative processing to initial weight vector:

w←w-λ[E{zg(w ^Tz)}+βw]/[E{g′(w ^Tz)}+β] (3)

Wherein, w is the vector in the separation matrix, and g () is a nonlinear function, and g ' () is the derivative of g (), and E () is for averaging, and z is a mixed signal, and β is a constant.

The realization principle of the device of present embodiment is identical with the realization principle of signal processing method embodiment of the present invention shown in Figure 3, repeats no more.

The device of present embodiment combines two kinds of improvement, and the Newton iteration method of utilizing the band regulatory factor is earlier tried to achieve approximate value preferably to the insensitive characteristic of initial value, and the fast convergence with improved FastICA obtains isolated component again; Introduce regulatory factor through the iterative processing module, can effectively solve the problem of choosing of the initial weight vector in the original FastICA algorithm, improve iteration efficient and convergence signal performance; To repeatedly iteration through the iterative processing module and combine, the iteration of back is all used the result of the Jacobi matrix that calculates for the first time, thereby can improve the speed of convergence of iteration greatly.Because repeatedly iterative process combines, and has increased the correction of each iteration, the oscillatory occurences that can avoid common Newton iteration to produce effectively, the independence of the independent signal in mixed signal is not to obtain to restrain preferably the result under the good situation yet.

What should explain at last is: above embodiment is only in order to technical scheme of the present invention to be described but not limit it; Although the present invention has been carried out detailed explanation with reference to preferred embodiment; Those of ordinary skill in the art is to be understood that: it still can make amendment or be equal to replacement technical scheme of the present invention, also can not make amended technical scheme break away from the spirit and the scope of technical scheme of the present invention and these are revised or be equal to replacement.

Claims (5)

1. a signal processing method is characterized in that, comprising:

In a period of time, receive mixed signal, obtain the amplitude information of the mixed signal of reception;

According to three rank semi-invariant and fourth order cumulants of the amplitude information of said mixed signal, calculate and obtain objective function;

Confirm rotation matrix auxiliary variable, mixed signal auxiliary variable and rotation matrix required when using said objective function obtains each independent signal in the said mixed signal;

When confirming the functional value maximum of said objective function, the extreme value of relevant parameter in this objective function;

Satisfy when pre-conditioned in the extreme value of said parameter; With the product of said rotation matrix and said rotation matrix auxiliary variable as current rotation matrix auxiliary variable; The product of said rotation matrix and said mixed signal auxiliary variable as current mixed signal auxiliary variable, and is obtained said independent signal according to said current rotation matrix auxiliary variable and current mixed signal auxiliary variable.

2. signal processing method according to claim 1 is characterized in that, does not satisfy when pre-conditioned in the extreme value of said parameter, also comprises:

Again confirm said rotation matrix auxiliary variable, mixed signal auxiliary variable and rotation matrix.

3. signal processing method according to claim 1 and 2 is characterized in that, objective function is obtained in said calculating, comprising:

Application of formula (1) is calculated and is obtained said objective function:

Ψ ₃₄(φ，y)＝A ₀+A ₄?cos(4φ+φ ₄) (1)

Wherein, $A_0=a_{30}+a_{40},A_4=\sqrt{{(c_{34}+c_{44})}^2+{(s_{34}+s_{44})}^2},$

$\tan \left({\mathrm{\&phi;}}_4\right)=-\frac{s_{34}+s_{44}}{c_{34}+c_{44}}$

$a_{30}=\frac{1}{3!}\frac{1}{8}[5({c_{111}}^2+{c_{222}}^2)+9({c_{112}}^2+{c_{122}}^2)+6({c_{111}}^2{c_{122}}^2+{c_{112}}^2{c_{222}}^2)]$

$a_{40}=\frac{1}{4!}\frac{1}{64}[35({c_{1111}}^2+{c_{2222}}^2)+80({c_{1112}}^2+{c_{1222}}^2)+60(c_{1111}{c}_{1122}+c_{1122}{c}_{2222})]$

$s_{34}=\frac{1}{3!}\frac{1}{4}\left[6(c_{111}{c}_{112}-c_{122}{c}_{222})\right]$

$c_{34}=\frac{1}{3!}\frac{1}{8}[3({c_{111}}^2+{c_{222}}^2)-9({c_{112}}^2+{c_{122}}^2)-6(c_{111}{c}_{112}+c_{112}{c}_{222})]$

$s_{44}=\frac{1}{4!}\frac{1}{32}[56(c_{1111}{c}_{1112}-c_{1222}{c}_{2222})+48(c_{1112}{c}_{1122}-c_{1122}{c}_{1222})+8(c_{1111}{c}_{1222}-c_{1112}{c}_{1222})]$

$c_{44}=\frac{1}{4!}\frac{1}{16}[7({c_{1111}}^2+{c_{2222}}^2)-16({c_{1112}}^2+{c_{2222}}^2)-12(c_{1111}{c}_{1122}+c_{1122}{c}_{2222})-36{c_{1122}}^2-32c_{1112}{c}_{1222}-2c_{1111}{c}_{2222}]$

c _{α β γ}And c _{α β γ δ}, α, beta, gamma, δ=1 or 2 is respectively three rank semi-invariant and fourth order cumulants of mixed signal.

4. signal processing method according to claim 3 is characterized in that, the said objective function of said application obtains the independent signal in the said mixed signal, comprising:

Confirm objective function Ψ ₃₄When the functional value of (φ, y ') is maximum, the extreme value φ of relevant parameter φ in this objective function _Max, wherein y ' is said mixed signal auxiliary variable;

At extreme value φ _MaxDuring greater than predetermined threshold value, with rotation matrix Q ^UvWith the product of rotation matrix auxiliary variable Q ' as current rotation matrix auxiliary variable Q ', with rotation matrix Q ^UvWith the product of mixed signal auxiliary variable y ' as current mixed signal auxiliary variable y ', and, obtain independent signal with the multiplying each other of current rotation matrix auxiliary variable Q ' and current mixed signal auxiliary variable y '.

5. a signal processing apparatus is characterized in that, comprising:

First receiver module is used in a period of time, receiving mixed signal, obtains the amplitude information of the mixed signal of reception;

The computing module, three rank semi-invariant and fourth order cumulants of the amplitude information of the mixed signal that is used for obtaining according to first receiver module calculate and obtain objective function;

Select processing module, be used for confirming said rotation matrix auxiliary variable, mixed signal auxiliary variable and rotation matrix required when obtaining processing module and using said objective function and obtain each independent signal of said mixed signal;

Obtain processing module, comprising:

First processing unit, when being used for confirming the functional value maximum of said objective function, the extreme value of relevant parameter in this objective function;

Second processing unit; Satisfy when pre-conditioned in the extreme value of said parameter; With the product of said rotation matrix and said rotation matrix auxiliary variable as current rotation matrix auxiliary variable; The product of said rotation matrix and said mixed signal auxiliary variable as current mixed signal auxiliary variable, and is obtained said independent signal according to said current rotation matrix auxiliary variable and current mixed signal auxiliary variable.

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