CN103219998B - A kind of mixed parameter estimation method under multichannel CS framework - Google Patents

A kind of mixed parameter estimation method under multichannel CS framework Download PDF

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CN103219998B
CN103219998B CN201310101905.3A CN201310101905A CN103219998B CN 103219998 B CN103219998 B CN 103219998B CN 201310101905 A CN201310101905 A CN 201310101905A CN 103219998 B CN103219998 B CN 103219998B
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mixed
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matrix
entropy
mixed signal
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CN103219998A (en
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付宁
徐红伟
乔立岩
于伟
殷聪如
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Harbin Institute of Technology
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Harbin Institute of Technology
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Abstract

A mixed parameter estimation method under multichannel CS framework, relates to technical field of multichannel CS, and solve existing mixed parameter estimation and calculate and must first complete reconstruct mixed signal, source signal reconstructs inefficient problem.Gather mixed signal x icompression observation signal be y i, get nonlinear function g (), described function g () be input as yW l, export as Y, calculate the entropy of Y, calculate the gradient of entropy H (Y) gradient direction along entropy H (Y) upgrades back mixing and closes matrix W l+1, entropy H (Y) is increased gradually, and the formula that matrix W is closed in described renewal back mixing is: the value of iterations l being added 1, l=l+1, judges whether iterations l is greater than total iterations t of setting, closing matrix W according to upgrading through t iteration the back mixing obtained t, calculate the estimated value of hybrid matrix A the present invention can be widely used in the calculating to mixed parameter estimation.

Description

A kind of mixed parameter estimation method under multichannel CS framework
Technical field
The present invention relates to technical field of multichannel CS.
Background technology
Traditional signal acquisition based on nyquist sampling theorem, that is:, when the sampling rate of signal must be more than or equal to 2 times of signal highest frequency, undistortedly from the data collected could recover source signal.Along with people are to the increase of amount of information demand, the bandwidth of signal increases, and when the acquisition of signal is still based on nyquist sampling theorem, will bring great challenge to signal sampling and data storage etc.The novel sampling proposed for 2004 is theoretical---compressed sensing (CompressedSensing, CS) point out when signal meets openness, can to observe signal far below the speed of nyquist sampling rate, then by suitable restructing algorithm Restorer varieties signal from the less is more value of signal.Because CS theory can reduce sampling rate and the data storage capacity of signal greatly, be with a wide range of applications in multiple field.But in the application scenario of some multisensor, such as: the fields such as speech recognition, Network Abnormal detection, medical signals process, the one mixing of the multiple source signals often that transducer collects, and hybrid parameter and source signal parameter are all unknown.And the universal method under existing multichannel CS framework estimates that hybrid parameter existence first must complete reconstruct mixed signal, the inefficient problem of mixed parameter estimation.
Summary of the invention
In order to the universal method solved under existing multichannel CS framework, the present invention estimates that hybrid parameter first must reconstruct mixed signal, estimate the inefficient problem of hybrid parameter, thus provide a kind of mixed parameter estimation method under multichannel CS framework.
A mixed parameter estimation method under multichannel CS framework, it comprises the steps:
Step one: gather mixed signal x icompression observation signal be y i, 1≤i≤m;
Wherein, x ibe i-th mixed signal, m is the number of mixed signal, mixed signal x ilength be N, observation signal y ilength be M, namely and M < < N;
If: the real number array that matrix W is the capable m row of m is closed in back mixing, namely
Calculation matrix is Ф is the real number matrix that the capable N of M arranges, namely
The initial value of algorithm iteration number of times l is 1, and total iterations is L, and it is W that matrix setup values is closed in back mixing 0, renewal step-length is η;
Step 2, in (0,1) interior monotonically increasing function, choose Any Nonlinear Function g ();
Step 3, setting function g () be input as yW l-1, export as Y, i.e. Y=g (yW l-1), wherein y=[y 1, y 2..., y m], y irepresent the compression measured value of i-th mixed signal;
The entropy of step 4, calculating Y H ( Y ) = H ( y ) + E [ &Sigma; i = 1 m ln g &prime; ( y W l - 1 ) ] + ln | W l - 1 | ,
Wherein H (Y) represents the entropy of Y, and H (y) represents the entropy of mixed signal measured value y, and function ln is logarithmic function, the first derivative of g ' expression g, represent lng ' (yW l-1) average;
The gradient of step 5, calculating entropy H (Y) wherein it is the back mixing conjunction matrix W of the l-1 time cycle calculations l-1each element, that entropy is about variable partial derivative, it is the gradient of entropy;
Step 6, upgrade anti-hybrid matrix along the gradient direction of entropy H (Y), entropy H (Y) is increased gradually, and the formula of the anti-hybrid matrix of described renewal is: W l = W l - 1 + &eta; * &dtri; h ;
Step 7, judge whether iterations l is more than or equal to total iterations L of setting, and judged result is yes, then perform step 8, and judged result is no, then the value of iterations l is added 1, l=l+1, return step 3;
Step 8, close matrix W according to upgrading the back mixing obtained through L iteration l, calculate hybrid parameter
A ^ = ( W L ) - 1
Described hybrid parameter wherein a ijrepresent and produce mixed signal x itime, the weight of a jth source signal;
Above-mentioned mixed signal x irefer to the mixed signal of i-th multichannel source signal collected.
The present invention, by mixed signal measured value direct estimation hybrid parameter, does not need, through loaded down with trivial details signal reconstruction process, to greatly reduce amount of calculation.In the occasion of some multi-sensor cooperation work, when transducer compresses the one mixing that the signal collected is multiple source signal, and hybrid parameter and source signal parameter all unknown time, when only knowing the compression observation data of mixed signal, the inventive method can be used for calculating the hybrid parameter of source signal when different path generation mixing, the hybrid parameter calculated can be used in reconstructed source signal, and the computational accuracy of hybrid parameter affects the reconstruction accuracy of source signal.The inventive method estimates that the hybrid parameter time used is 0.1698s, be less than the 0.1834s that universal method estimates hybrid parameter process, and this method also eliminates the process of mixed signal reconstruct compared with universal method, as can be seen here, the inventive method amount of calculation is less.
The present invention is applicable in the signal processing technology fields such as speech recognition, Network Abnormal detection, medical signals process.
Accompanying drawing explanation
Fig. 1 is the theory diagram being carried out mixed parameter estimation by mixed signal compression measured value through general method;
Fig. 2 is the theory diagram of the mixed parameter estimation method under a kind of multichannel CS framework of the present invention;
Fig. 3 is the change curve of mixed parameter estimation effect with compression ratio,
With symbol the curve of mark is adopt the mixed parameter estimation effect of the described method acquisition of invention with the change curve of compression ratio;
Fig. 4 is the change curve of effect with compression ratio that the method for the invention and universal method estimate hybrid parameter,
With symbol the curve of mark is adopt the mixed parameter estimation effect of the described method acquisition of invention with the change curve of compression ratio;
With symbol the curve of mark is for adopting the mixed parameter estimation effect that obtains of universal method with the change curve of compression ratio.
Embodiment
Embodiment one, composition graphs 2 illustrate this embodiment.A mixed parameter estimation method under multichannel CS framework, it comprises the steps:
Step one: gather mixed signal x icompression observation signal be y i, 1≤i≤m;
Wherein, x ibe i-th mixed signal, m is the number of mixed signal, mixed signal x ilength be N, observation signal y ilength be M, namely and M < < N;
If: the real number array that matrix W is the capable m row of m is closed in back mixing, namely
Calculation matrix is Ф is the real number matrix that the capable N of M arranges, namely
The initial value of algorithm iteration number of times l is 1, and total iterations is L, and it is W that matrix setup values is closed in back mixing 0, renewal step-length is η;
Step 2, in (0,1) interior monotonically increasing function, choose Any Nonlinear Function g ();
Step 3, setting function g () be input as yW l-1export as Y, i.e. Y=g (yW l-1), wherein y=[y 1, y 2..., y m], y irepresent the compression measured value of i-th mixed signal;
The entropy of step 4, calculating Y H ( Y ) = H ( y ) + E [ &Sigma; i = 1 m ln g &prime; ( y W l - 1 ) ] + ln | W l - 1 | ,
Wherein H (Y) represents the entropy of Y, and H (y) represents the entropy of mixed signal measured value y, and function ln is logarithmic function, the first derivative of g ' expression g, represent lng ' (yW l-1) average;
The gradient of step 5, calculating entropy H (Y) wherein it is the back mixing conjunction matrix W of the l-1 time cycle calculations l-1each element, that entropy is about variable partial derivative, it is the gradient of entropy;
Step 6, upgrade anti-hybrid matrix along the gradient direction of entropy H (Y), entropy H (Y) is increased gradually, and the formula of the anti-hybrid matrix of described renewal is: W l = W l - 1 + &eta; * &dtri; h ;
Step 7, judge whether iterations l is more than or equal to total iterations L of setting, and judged result is yes, then perform step 8, and judged result is no, then the value of iterations l is added 1, l=l+1, return step 3;
Step 8, close matrix W according to upgrading the back mixing obtained through L iteration l, calculate hybrid parameter for:
A ^ = ( W L ) - 1
Described hybrid parameter wherein a ijrepresent and produce mixed signal x itime, the weight of a jth source signal;
Above-mentioned mixed signal x irefer to the mixed signal of i-th multichannel source signal collected.
Embodiment two, this embodiment and embodiment one is unlike a described m mixed signal x iform be , then m observation signal y iform be .
Embodiment three, this embodiment and embodiment one or two are unlike described mixed signal x ifor:
x 1 ( t ) = a 11 s 1 ( t ) + a 21 s 2 ( t ) + &CenterDot; &CenterDot; &CenterDot; + a m 1 s 2 ( t ) &CenterDot; &CenterDot; &CenterDot; x m ( t ) = a 1 m s 1 ( t ) + a 2 m s 2 ( t ) + &CenterDot; &CenterDot; &CenterDot; + a mm s 2 ( t )
To mixed signal x icarry out compression observation, x it () represents i-th mixed signal, wherein t=1,2 ..., N, represents the discrete value of time; By x it form that () is write as matrix is expressed as x i; s it () represents i-th source signal;
The model of compressed sensing processing signals is:
y i＝Фx i。
Embodiment four, this embodiment and embodiment one is unlike described calculation matrix Ф Gaussian distributed.
Embodiment five, this embodiment and embodiment one is 100 unlike described total iterations, and iteration step length is 0.25.
Embodiment six, this embodiment and embodiment one selects tanh function unlike described nonlinear function g ().
Adopt mixed parameter estimation method nonlinear function g () under a kind of multichannel CS framework of the present invention, this function is preferably close to the cumulative distribution function of source signal, in the method, choosing of function g () is not strict, and can choose some monotonic function and replace.
Adopt the mixed parameter estimation method under a kind of multichannel CS framework of the present invention, by the compression measured value y of mixed signal, through introducing nonlinear function g (), find optimum back mixing by gradient ascent method again and close matrix W, make the entropy of the output vector of function g () reach maximum, now, the inverse of matrix W is closed in optimum back mixing, be exactly the estimated value of hybrid parameter A, i.e. hybrid parameter
Verification method: calculate hybrid parameter respectively by the mixed parameter estimation method under a kind of multichannel CS framework of the present invention and prior art and the process of " the extensive cross (talk) error " GCE between hybrid matrix A is:
One, the random hybrid matrix A producing the capable m row of m, is mixed m voice simulation signal by the hybrid matrix generated, obtains m mixed signal;
Two, the random calculation matrix producing a Gaussian Profile respectively compression observation is carried out to each mixed signal, obtain m compression sensing signal, y i=Ф x i;
Three, by the observation signal y of mixed signal i, estimate hybrid parameter respectively by the method for method of the present invention and prior art
Four, the method for the method of the invention and prior art respectively runs 100 times, calculates hybrid matrix A and hybrid parameter between " extensive cross (talk) error " GCE, and minute book method estimates that the method for hybrid parameter process and prior art estimates the time required for hybrid parameter process (not comprising reconstruct mixed signal process).
In this proof procedure, adopt 2 sections of speech source signals, be respectively the recording that 2 different people speak, mixed by the hybrid matrix A of 2 × 2, obtain 2 tunnel mixed signal x 1, x 2.Carry out compression observation frame by frame to 2 mixed signals, every frame signal length is N=500, and observing matrix line number is M, and columns is N.The value of setting M is respectively 50,100 ..., 500, the compression ratio M/N namely compressing observation process respectively value is 0.1,0.2 ..., 1.0.For each value of M, run each 100 times of the method for method of the present invention and prior art respectively, estimate hybrid parameter , calculate hybrid matrix A and hybrid parameter between " extensive cross (talk) error " GCE, and record often kind of algorithm estimates the time required for hybrid parameter process.
Table 1
Experimental result is as shown in table 1, GCE arepresent that algorithm runs the mean value in the GCE calculated for 100 times, GCE minrepresent that algorithm runs the minimum value in 100 GCE calculated, GCE maxrepresent that algorithm runs the maximum in 100 GCE that calculate, Time represents that algorithm runs the mean value of time required for the estimation hybrid parameter process that records for 100 times.As can be seen from Table 1, the GCE that method of the present invention calculates is less than the method for prior art, and namely the method for the invention estimates that hybrid parameter is more accurate, and, estimate that hybrid parameter process time used is more less than the method for prior art.Time in table 1 only represents the time of estimated parameter process need, and from Fig. 1,2, the method for the invention is omitted the process of reconstruct mixed signal, and namely generally speaking, the time that this method is saved than the method for prior art is more.

Claims (6)

1. the mixed parameter estimation method under multichannel CS framework, is characterized in that it comprises the steps:
Step one: gather mixed signal x icompression observation signal be y i, 1≤i≤m;
Wherein, x ibe i-th mixed signal, m is the number of mixed signal, mixed signal x ilength be N, observation signal y ilength be M, namely , and M < < N;
If: the real number array that matrix W is the capable m row of m is closed in back mixing, namely
Calculation matrix is Ф is the real number matrix that the capable N of M arranges, namely
The initial value of algorithm iteration number of times l is 1, and total iterations is L, and it is W that matrix setup values is closed in back mixing 0, renewal step-length is η;
Step 2, in (0,1) interior monotonically increasing function, choose Any Nonlinear Function g ();
Step 3, setting function g () be input as yW l-1, export as Y, i.e. Y=g (yW l-1), wherein y=[y 1, y 2..., y m], y irepresent the compression measured value of i-th mixed signal;
The entropy of step 4, calculating Y H ( Y ) = H ( y ) + E [ &Sigma; i = 1 m ln g &prime; ( y W l - 1 ) ] + ln | W l - 1 | ,
Wherein H (Y) represents the entropy of Y, and H (y) represents the entropy of mixed signal measured value y, and function ln is logarithmic function, the first derivative of g ' expression g, represent lng ' (yW l-1) average;
The gradient of step 5, calculating entropy H (Y) wherein it is the back mixing conjunction matrix W of the l-1 time cycle calculations l-1each element, that entropy is about variable partial derivative, it is the gradient of entropy;
Step 6, upgrade anti-hybrid matrix along the gradient direction of entropy H (Y), entropy H (Y) is increased gradually, and the formula of the anti-hybrid matrix of described renewal is: W l = W l - 1 + &eta; * &dtri; h ;
Step 7, judge whether iterations l is more than or equal to total iterations L of setting, and judged result is yes, then perform step 8, and judged result is no, then the value of iterations l is added 1, l=l+1, return step 3;
Step 8, close matrix W according to upgrading the back mixing obtained through L iteration l, calculate hybrid parameter for:
A ^ = ( W L ) - 1
Described hybrid parameter wherein a ijrepresent and produce mixed signal x itime, the weight of a jth source signal;
Above-mentioned mixed signal x irefer to the mixed signal of i-th multichannel source signal collected.
2. the mixed parameter estimation method under a kind of multichannel CS framework according to claim 1, is characterized in that a described m mixed signal x iform be then m observation signal y iform be .
3. the mixed parameter estimation method under a kind of multichannel CS framework according to claim 1 and 2, is characterized in that described mixed signal x ifor:
x 1 ( t ) = a 11 s 1 ( t ) + a 21 s 2 ( t ) + &CenterDot; &CenterDot; &CenterDot; + a m 1 s 2 ( t ) &CenterDot; &CenterDot; &CenterDot; x m ( t ) = a 1 m s 1 ( t ) + a 2 m s 2 ( t ) + &CenterDot; &CenterDot; &CenterDot; + a mm s 2 ( t )
To mixed signal x icarry out compression observation, x it () represents i-th mixed signal, wherein t=1,2 ..., N, represents the discrete value of time; By x it form that () is write as matrix is expressed as x i; s it () represents i-th source signal;
The model of compressed sensing processing signals is:
y i＝Фx i。
4. the mixed parameter estimation method under a kind of multichannel CS framework according to claim 1, is characterized in that described calculation matrix Ф Gaussian distributed.
5. the mixed parameter estimation method under a kind of multichannel CS framework according to claim 1, it is characterized in that described total iterations is 100, iteration step length is 0.25.
6. the mixed parameter estimation method under a kind of multichannel CS framework according to claim 1, is characterized in that described nonlinear function g () selects tanh function.
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