CN103219998A - Hybrid parameter estimation method for use under multi-channel compressed sensing framework - Google Patents

Hybrid parameter estimation method for use under multi-channel compressed sensing framework Download PDF

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CN103219998A
CN103219998A CN2013101019053A CN201310101905A CN103219998A CN 103219998 A CN103219998 A CN 103219998A CN 2013101019053 A CN2013101019053 A CN 2013101019053A CN 201310101905 A CN201310101905 A CN 201310101905A CN 103219998 A CN103219998 A CN 103219998A
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mixed signal
entropy
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hybrid parameter
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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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Abstract

The invention discloses a hybrid parameter estimation method for use under a multi-channel compressed sensing framework, which relates to the technical field of multi-channel compressed sensing, and is used for solving the problem of low source signal reconstruction efficiency caused by the fact that reconstruction of a hybrid signal must be firstly finished in the conventional hybrid parameter estimation calculation. The method comprises the following steps of: acquiring a compressed observation signal yi of a hybrid signal xi; selecting a non-linear function g(.), wherein the input of the function g(.) is yWl while the output is Y; calculating the entropy of the Y; calculating the gradient of the entropy H(Y), and updating a reverse hybrid matrix Wl+1 along the gradient direction of the entropy H(Y) to make the entropy H(Y) increase gradually, wherein a formula for updating the reverse hybrid matrix W is: Wl=Wl-1+eta*nabla h adding 1 to the value of an iteration number l, namely, l=l+1; judging whether the iteration number l is larger than a set total iteration number t; and calculating an estimated value of a hybrid matrix A according to a reverse hybrid matrix Wt obtained by performing t times of iteration update. The hybrid parameter estimation method can be applied widely to the calculation of hybrid parameter estimation.

Description

Hybrid parameter method of estimation under a kind of multichannel compressed sensing framework
Technical field
The present invention relates to multichannel compressed sensing technical field.
Background technology
Traditional signal obtains based on nyquist sampling theorem, that is: when signals sampling speed must be more than or equal to 2 times of signal highest frequency, could be from the data that collect the undistorted source signal that recovers.Along with the increase of people to the amount of information demand, the bandwidth of signal increases, when signal obtain still based on nyquist sampling theorem the time, will bring great challenge to signal sampling and storage etc.Novel sampling theory---compressed sensing (the Compressed Sensing that proposed in 2004, CS) point out when signal satisfies sparse property, can from a small amount of projection value of signal, recover source signal by suitable restructing algorithm then signal is observed far below the speed of nyquist sampling rate.Because the CS theory can reduce signals sampling speed and data storage capacity greatly, is with a wide range of applications in a plurality of fields.But in the application scenario of some multisensor, such as: fields such as speech recognition, network abnormality detection, medical signals processing, a kind of mixing of the multiple source signals often that sensor acquisition arrives, and hybrid parameter and source signal parameter all are unknown.And the existence of the estimation of the universal method under existing multichannel compressed sensing framework hybrid parameter must be finished the reconstruct mixed signal earlier, the problem that the hybrid parameter estimated efficiency is low.
Summary of the invention
The present invention estimates the necessary first reconstruct mixed signal of hybrid parameter for the universal method that solves under the existing multichannel compressed sensing framework, estimates the inefficient problem of hybrid parameter, thereby the hybrid parameter method of estimation under a kind of multichannel compressed sensing framework is provided.
Hybrid parameter method of estimation under a kind of multichannel compressed sensing framework, it comprises the steps:
Step 1: gather mixed signal x iThe compression observation signal be y i, 1≤i≤m;
Wherein, x iBe i mixed signal, m is the number of mixed signal, mixed signal x iLength be N, observation signal y iLength be M, promptly
Figure BDA00002974544300011
And M＜＜N;
If: the real number array that matrix W is the capable m row of m is closed in back mixing, promptly
Figure BDA00002974544300012
Measuring matrix is that Ф is the real number matrix of the capable N row of M, promptly
The initial value of algorithm iteration number of times l is 1, and total iterations is L, and it is W that the matrix initial value is closed in back mixing 0, the renewal step-length is η;
Step 2, in (0,1) interior monotonically increasing function, choose any nonlinear function g ();
Step 3, set the yW that is input as of function g () L-1, be output as Y, i.e. Y=g (yW L-1), y=[y wherein 1, y 2..., y m], y iThe compression measured value of representing i mixed signal;
The entropy of step 4, calculating Y H ( Y ) = H ( y ) + E [ Σ i = 1 m ln g ′ ( y W l - 1 ) ] + ln | W l - 1 | ,
Wherein H (Y) represents the entropy of Y, the entropy of H (y) expression mixed signal measured value y, and function ln is a logarithmic function, the first derivative of g ' expression g, Expression ln g ' (yW L-1) average;
The gradient of step 5, calculating entropy H (Y)
Figure BDA00002974544300023
Figure BDA00002974544300024
Wherein
Figure BDA00002974544300025
Matrix W is closed in the back mixing that is the l-1 time cycle calculations L-1Each element,
Figure BDA00002974544300026
Be that entropy is about variable
Figure BDA00002974544300027
Partial derivative,
Figure BDA00002974544300028
It is the gradient of entropy;
Step 6, upgrade back mixing along the gradient direction of entropy H (Y) and close matrix, make entropy H (Y) increase gradually, the formula that matrix is closed in described renewal back mixing is: W l = W l - 1 + η * ▿ h ;
Step 7, judge iterations l whether more than or equal to the total iterations L that sets, judged result is for being, then execution in step eight, and judged result is for denying, and then the value with iterations l adds 1, and l=l+1 returns step 3;
Matrix W is closed in step 8, the back mixing that L iteration renewal obtains according to process L, calculate hybrid parameter
A ^ = ( W L ) - 1
Described hybrid parameter
Figure BDA000029745443000212
A wherein IjExpression produces mixed signal x iThe time, the weight of j source signal;
Above-mentioned mixed signal x iBe meant the mixed signal of i multichannel source signal that collects.
The present invention is not needed to have significantly reduced amount of calculation through loaded down with trivial details signal reconstruction process by mixed signal measured value direct estimation hybrid parameter.Occasion in some multisensor collaborative works, the signal that collects when the transducer compression is a kind of mixing of multiple source signal, and when hybrid parameter and source signal parameter are all unknown, under the situation of the compression observation data of only knowing mixed signal, hybrid parameter when the inventive method can be used for calculating source signal through the generation mixing of different paths, the hybrid parameter that calculates can be used in the reconstructed source signal, and the computational accuracy of hybrid parameter influences the reconstruction accuracy of source signal.The inventive method estimates that the used time of hybrid parameter is 0.1698s, less than the 0.1834s of universal method estimation hybrid parameter process, and this method is compared the process of also having saved mixed signal reconstruct with universal method, this shows that the inventive method amount of calculation is littler.
The present invention is applicable in the signal processing technology fields such as speech recognition, network abnormality detection, medical signals processing.
Description of drawings
Fig. 1 carries out hybrid parameter estimation principles block diagram by mixed signal compression measured value through method in common;
Fig. 2 is the theory diagram of the hybrid parameter method of estimation under a kind of multichannel compressed sensing framework of the present invention;
Fig. 3 is the change curve of hybrid parameter estimation effect with compression ratio,
Have symbol
Figure BDA00002974544300031
The curve of mark is invented the change curve of the hybrid parameter estimation effect of described method acquisition with compression ratio for employing;
Fig. 4 is that the method for the invention and universal method are estimated the change curve of the effect of hybrid parameter with compression ratio,
Have symbol
Figure BDA00002974544300032
The curve of mark is invented the change curve of the hybrid parameter estimation effect of described method acquisition with compression ratio for employing;
Have symbol
Figure BDA00002974544300033
The curve of mark is the change curve of the employing hybrid parameter estimation effect that universal method obtained with compression ratio.
Embodiment
Embodiment one, this embodiment is described in conjunction with Fig. 2.Hybrid parameter method of estimation under a kind of multichannel compressed sensing framework, it comprises the steps:
Step 1: gather mixed signal x iThe compression observation signal be y i, 1≤i≤m;
Wherein, x iBe i mixed signal, m is the number of mixed signal, mixed signal x iLength be N, observation signal y iLength be M, promptly
Figure BDA00002974544300034
And M＜＜N;
If: the real number array that matrix W is the capable m row of m is closed in back mixing, promptly
Measuring matrix is that Ф is the real number matrix of the capable N row of M, promptly
Figure BDA00002974544300036
The initial value of algorithm iteration number of times l is 1, and total iterations is L, and it is W that the matrix initial value is closed in back mixing 0, the renewal step-length is η;
Step 2, in (0,1) interior monotonically increasing function, choose any nonlinear function g ();
Step 3, set the yW that is input as of function g () L-1Be output as Y, i.e. Y=g (yW L-1), y=[y wherein 1, y 2..., y m], y iThe compression measured value of representing i mixed signal;
The entropy of step 4, calculating Y H ( Y ) = H ( y ) + E [ Σ i = 1 m ln g ′ ( y W l - 1 ) ] + ln | W l - 1 | ,
Wherein H (Y) represents the entropy of Y, the entropy of H (y) expression mixed signal measured value y, and function ln is a logarithmic function, the first derivative of g ' expression g,
Figure BDA00002974544300042
Expression ln g ' (yW L-1) average;
The gradient of step 5, calculating entropy H (Y)
Figure BDA00002974544300043
Wherein
Figure BDA00002974544300045
Matrix W is closed in the back mixing that is the l-1 time cycle calculations L-1Each element,
Figure BDA00002974544300046
Be that entropy is about variable
Figure BDA00002974544300047
Partial derivative,
Figure BDA000029745443000413
It is the gradient of entropy;
Step 6, upgrade back mixing along the gradient direction of entropy H (Y) and close matrix, make entropy H (Y) increase gradually, the formula that matrix is closed in described renewal back mixing is: W l = W l - 1 + η * ▿ h ;
Step 7, judge iterations l whether more than or equal to the total iterations L that sets, judged result is for being, then execution in step eight, and judged result is for denying, and then the value with iterations l adds 1, and l=l+1 returns step 3;
Matrix W is closed in step 8, the back mixing that L iteration renewal obtains according to process L, calculate hybrid parameter
Figure BDA00002974544300049
For:
A ^ = ( W L ) - 1
Described hybrid parameter
Figure BDA000029745443000411
A wherein IjExpression produces mixed signal x iThe time, the weight of j source signal;
Above-mentioned mixed signal x iBe meant the mixed signal of i multichannel source signal that collects.
That embodiment two, this embodiment and embodiment one are different is described m mixed signal x iForm be , m observation signal y then iForm be
Figure BDA000029745443000415
That embodiment three, this embodiment are different with embodiment one or two is described mixed signal x iFor:
x 1 ( t ) = a 11 s 1 ( t ) + a 21 s 2 ( t ) + · · · + a m 1 s 2 ( t ) · · · x m ( t ) = a 1 m s 1 ( t ) + a 2 m s 2 ( t ) + · · · + a mm s 2 ( t )
To mixed signal x iCompress observation, x i(t) i mixed signal of expression, t=1 wherein, 2 ..., N, the discrete value of express time; With x i(t) form of the matrix of being write as is expressed as x is i(t) i source signal of expression;
The model of compressed sensing processing signals is:
y i＝Фx i。
What embodiment four, this embodiment and embodiment one were different is described measurement matrix Ф Gaussian distributed.
What embodiment five, this embodiment and embodiment one were different is that described total iterations is 100, and iteration step length is 0.25.
What embodiment six, this embodiment and embodiment one were different is that described nonlinear function g () selects the tanh function for use.
Adopt the hybrid parameter method of estimation nonlinear function g () under a kind of multichannel compressed sensing framework of the present invention, this function is preferably near 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 hybrid parameter method of estimation under a kind of multichannel compressed sensing framework of the present invention, compression measured value y by mixed signal, through introducing nonlinear function g (), seek optimum back mixing by the gradient climb procedure again and close matrix W, make the entropy of output vector of function g () reach maximum, at this moment, the contrary of matrix W closed in optimum back mixing, be exactly the estimated value of hybrid parameter A, i.e. hybrid parameter
Figure BDA00002974544300051
Verification method: calculate hybrid parameter by hybrid parameter method of estimation under a kind of multichannel compressed sensing of the present invention framework and prior art respectively
Figure BDA00002974544300052
And the process of " the extensive cross (talk) error " GCE between the hybrid matrix A is:
One, produces the hybrid matrix A of the capable m row of m at random, m voice simulation signal mixed, obtain m mixed signal by the hybrid matrix that generates;
Two, produce the measurement matrix of a Gaussian Profile at random
Figure BDA00002974544300054
Respectively each mixed signal is compressed observation, obtain m compression sensing signal, y i=Ф x i
Three, by the observation signal y of mixed signal i, estimate hybrid parameter by the method for method of the present invention and prior art respectively
Figure BDA00002974544300053
Four, the method for the method of the invention and prior art is respectively moved 100 times, calculates hybrid matrix A and hybrid parameter
Figure BDA00002974544300061
Between " extensive cross (talk) error " GCE, and the minute book method estimates that the method for hybrid parameter process and prior art estimates the needed time of hybrid parameter process (not comprising reconstruct mixed signal process).
In this proof procedure, adopt 2 sections speech source signals, be respectively the recording that 2 different people speak, mix, obtain 2 tunnel mixed signal x by one 2 * 2 hybrid matrix A 1, x 22 mixed signals are compressed observation frame by frame, and every frame signal length is N=500, and the 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 that promptly compresses observation process value respectively is 0.1,0.2 ..., 1.0.For each value of M, move the method each 100 times of method of the present invention and prior art respectively, estimate hybrid parameter
Figure BDA00002974544300062
, calculate hybrid matrix A and hybrid parameter
Figure BDA00002974544300063
Between " extensive cross (talk) error " GCE, and write down every kind of algorithm and estimate the hybrid parameter needed time of process.
Table 1
Experimental result is as shown in table 1, GCE aMean value among the GCE that the operation of expression algorithm is calculated for 100 times, GCE MinMinimum value among expression algorithm operation 100 GCE that calculated, GCE MaxMaximum among expression algorithm operation 100 GCE that calculated, Time represents the mean value of the estimation hybrid parameter required time of process that the algorithm operation is write down for 100 times.As can be seen from Table 1, the GCE that method of the present invention is calculated is littler than the method for prior art, and promptly the method for the invention estimates that hybrid parameter is more accurate, and the method for the time ratio prior art that estimation hybrid parameter process is used still less.Time in the table 1 only represents the time of estimated parameter process need, and by Fig. 1,2 as can be known, the method for the invention has also been omitted the process of reconstruct mixed signal, and promptly generally speaking, this method is more than the time that the method for prior art is saved.

Claims (6)

1. the hybrid parameter method of estimation under the multichannel compressed sensing framework is characterized in that it comprises the steps:
Step 1: gather mixed signal x iThe compression observation signal be y i, 1≤i≤m;
Wherein, x iBe i mixed signal, m is the number of mixed signal, mixed signal x iLength be N, observation signal y iLength be M, promptly
Figure FDA000029745442000110
, and M＜＜N;
If: the real number array that matrix W is the capable m row of m is closed in back mixing, promptly
Measuring matrix is that Ф is the real number matrix of the capable N row of M, promptly
The initial value of algorithm iteration number of times l is 1, and total iterations is L, and it is W that the matrix initial value is closed in back mixing 0, the renewal step-length is η;
Step 2, in (0,1) interior monotonically increasing function, choose any nonlinear function g ();
Step 3, set the yW that is input as of function g () L-1, be output as Y, i.e. Y=g (yW L-1), y=[y wherein 1, y 2..., y m], y iThe compression measured value of representing i mixed signal;
The entropy of step 4, calculating Y H ( Y ) = H ( y ) + E [ Σ i = 1 m ln g ′ ( y W l - 1 ) ] + ln | W l - 1 | ,
Wherein H (Y) represents the entropy of Y, the entropy of H (y) expression mixed signal measured value y, and function ln is a logarithmic function, the first derivative of g ' expression g,
Figure FDA00002974544200012
Expression ln g ' (yW L-1) average;
The gradient of step 5, calculating entropy H (Y)
Figure FDA00002974544200013
Figure FDA00002974544200014
Wherein
Figure FDA00002974544200015
Matrix W is closed in the back mixing that is the l-1 time cycle calculations L-1Each element,
Figure FDA00002974544200016
Be that entropy is about variable
Figure FDA00002974544200017
Partial derivative,
Figure FDA00002974544200018
It is the gradient of entropy;
Step 6, upgrade back mixing along the gradient direction of entropy H (Y) and close matrix, make entropy H (Y) increase gradually, the formula that matrix is closed in described renewal back mixing is: W l = W l - 1 + η * ▿ h ;
Step 7, judge iterations l whether more than or equal to the total iterations L that sets, judged result is for being, then execution in step eight, and judged result is for denying, and then the value with iterations l adds 1, and l=l+1 returns step 3;
Matrix W is closed in step 8, the back mixing that L iteration renewal obtains according to process L, calculate hybrid parameter
Figure FDA00002974544200021
For:
A ^ = ( W L ) - 1
Described hybrid parameter
Figure FDA00002974544200023
A wherein IjExpression produces mixed signal x iThe time, the weight of j source signal;
Above-mentioned mixed signal x iBe meant the mixed signal of i multichannel source signal that collects.
2. the hybrid parameter method of estimation under a kind of multichannel compressed sensing framework according to claim 1 is characterized in that described m mixed signal x iForm be
Figure FDA00002974544200025
M observation signal y then iForm be
Figure FDA00002974544200026
3. the hybrid parameter method of estimation under a kind of multichannel compressed sensing 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 ) + · · · + a m 1 s 2 ( t ) · · · x m ( t ) = a 1 m s 1 ( t ) + a 2 m s 2 ( t ) + · · · + a mm s 2 ( t )
To mixed signal x iCompress observation, x i(t) i mixed signal of expression, t=1 wherein, 2 ..., N, the discrete value of express time; With x i(t) form of the matrix of being write as is expressed as x is i(t) i source signal of expression;
The model of compressed sensing processing signals is:
y i＝Фx i。
4. the hybrid parameter method of estimation under a kind of multichannel compressed sensing framework according to claim 1 is characterized in that described measurement matrix Ф Gaussian distributed.
5. the hybrid parameter method of estimation under a kind of multichannel compressed sensing framework according to claim 1 is characterized in that described total iterations is 100, and iteration step length is 0.25.
6. the hybrid parameter method of estimation under a kind of multichannel compressed sensing framework according to claim 1 is characterized in that described nonlinear function g () selects the tanh function for use.
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