JP2006146484A - Signal separation system, signal separation method, and signal separation program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a signal separation system capable of accurately performing the process of separating signal source signals under certain conditions. <P>SOLUTION: A wavelet packet transformation part 13 of a signal separation part 12 performs wavelet packet transformation to transform an observation matrix X in a time domain into an observation matrix X' in a time-frequency domain. Next, based on the observation matrix X' in the time-frequency domain, a mixed matrix estimating part 14 estimates a mixed matrix A that specifies the relationship between the observation matrix X' in the time-frequency domain and a signal source matrix S' in a time-frequency domain. Based on the mixed matrix A estimated and the observation matrix X' in the time-frequency domain, the signal source matrix S' in the time-frequency domain is estimated. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a signal separation system that separates (extracts) a specific signal source signal from an observation signal in which a plurality of signal source signals are mixed. In particular, the signal source signal separation process is performed with high accuracy under an arbitrary condition. The present invention relates to a signal separation system, a signal separation method, and a signal separation program.

In many application fields, various observation signals (EEG (electroencephalogram) signal, MEG (magnetoencephalogram) signal, mixed audio signal, image signal, seismic signal, etc.) mixed with a plurality of signal source signals and signal source signals The relationship between is expressed by a linear mixed model such as the following equation (1).
X = AS + V (1)

Here, X = [ x (1),..., X (K)] εRn ^{× K} is an observable matrix, and its column vector x (i) is a set of n observation signals. , X (i) = [x ₁ (i),..., X _n (i)] ^T (i = 1, 2,..., K). S = [ s (1),..., S (K)] ∈R ^{m × K} is a source matrix, and its column vector s (i) is m unspecified signal sources. As a set of signals, s (i) = [s ₁ (i),..., S _m (i)] ^T (i = 1,..., K). Further, AεR ^{n × m} is a mixing matrix (channel parameter), and VεR ^{n × K} is a Gaussian noise matrix. Here, n is the number of observation points such as sensors, m is the number of unspecified signal sources, and K is the total number of available samples. Underlined alphabetic characters represent vectors.

In the above equation (1), the noise matrix V may be negligible in relation to the signal source matrix S. In this case, the linear mixture model of the above equation (1) is a model without noise. Is expressed by the following equation (2). Hereinafter, in order to simplify the description, the linear mixed model of the following equation (2) will be mainly described.
X = AS (2)

  In the linear mixture model like the above equation (1), if the mixing matrix (channel parameter) A can be estimated based on the observation matrix X, the above equation (2) is solved by using an existing arbitrary method. A source matrix (cluster of datasets) S can be estimated. That is, in the linear mixture model such as the above equation (2), a method of estimating the mixing matrix A based on the observation matrix X is very important, and several methods have been proposed for this purpose. ing.

  As such a conventional method, there is an independent component analysis method (ICA: Independent Component Analysis) in which the mixing matrix A is estimated by estimating a de-mixing matrix W that is an inverse matrix of the mixing matrix A. It is known (Non-Patent Document 1).

However, in the independent component analysis method, due to an estimation error (numerical instability / approximation error) due to noise or the like, the matrix W ⁻¹ that is the inverse matrix of the signal separation matrix W cannot be calculated in many cases. There is a problem that a large difference often occurs between the mixing matrix A and the matrix W- ¹ . In addition, in the independent component analysis method, when the mixing matrix A is singular, the linear mixing model of the above equation (2) cannot be solved in the first place. Furthermore, the independent component analysis method must satisfy the constraint that each signal source is statistically independent and the number of signal sources is equal to or smaller than the number of observation points (sensors). There is a problem.

  On the other hand, as a method other than such an independent component analysis method, a standard clustering method (K-means clustering method or the like) is also known.

However, in the standard clustering method, parameters are adjusted by iterative calculation, so whether or not to converge to a globally convergent point cannot be determined uniquely and falls into a locally convergent point. There is a problem that the possibility is high. Further, in the standard clustering method, as a problem caused by iterative calculation, the behavior of adjustment of each component of the mixing matrix A varies greatly depending on how the initial values are given. When the variance (data structure) of each component is not sufficiently sparse, each component of the finally obtained mixing matrix A often deviates significantly from the true value. .
A. Cichocki and S. Amari: Adaptive Blind Signal and Image Processing-Learning Algorithms and Applications, John Wiley & Sons, 2002.

  The present invention has been made in consideration of such points, and a process for separating a signal source signal from various observation signals in which a plurality of signal source signals are mixed (a signal source signal separation process) Regardless of the statistical properties of the signal, the relationship between the number of observed signals and the number of source signals, the nature of the data structure of the signal source matrix including the source signals, etc. An object is to provide a signal separation system, a signal separation method, and a signal separation program.

  As a first solution, the present invention provides an input unit for capturing a plurality of observation signals in a signal separation system that separates a specific signal source signal from an observation signal in which a plurality of signal source signals are mixed, and the input unit A signal separation unit that separates a specific signal source signal from each observation signal captured by the input unit, wherein the signal separation unit includes a number of predetermined samples of each observation signal captured by the input unit. Defines the relationship between the observation matrix and the signal source matrix based on the time-frequency domain observation matrix transformed by the time-frequency domain and the time-frequency domain transformation matrix that transforms the observation matrix into the time-frequency domain observation matrix A mixing matrix estimation unit for estimating a mixing matrix to be performed, a mixing matrix estimated by the mixing matrix estimation unit, an observation matrix in the time-frequency domain converted by the time-frequency conversion unit, Based on a signal source matrix estimator for estimating a time-frequency domain signal source matrix including a predetermined number of signal source signals, and a time-frequency domain signal source matrix estimated by the signal source matrix estimator. An inverse time-frequency conversion unit that converts the signal into a signal source matrix in the region, and the mixing matrix estimation unit of the signal separation unit includes a component between the components included in the observation matrix in the time-frequency region converted by the time-frequency conversion unit. A first process for obtaining a plurality of matrices having a ratio of the above and a plurality of sub-matrices obtained by dividing each matrix obtained by the first process and having a row vector forming a horizontal line in a time-frequency domain coordinate system Performing a second process and a third process for estimating each column vector of the mixing matrix based on a column vector of a specific partial matrix included in the plurality of partial matrices obtained in the second process. To provide a No. separation system.

  In the first solving means described above, the time-frequency conversion unit of the signal separation unit converts the time-domain observation matrix into the time-frequency-domain observation matrix using wavelet packet conversion, and the signal Preferably, the inverse time-frequency transform unit of the separation unit transforms the time-frequency domain signal source matrix into the time-domain signal source matrix using inverse wavelet packet transform.

  Further, in the first solving means described above, the mixing matrix estimation unit of the signal separation unit is a time converted by the time frequency conversion unit as an observation matrix of the time frequency domain that is a target of the first processing. It is preferable to use a vector obtained by removing a column vector whose norm is less than a predetermined value from column vectors included in an observation matrix in the frequency domain.

  Furthermore, in the first solving means described above, the signal source matrix estimation unit estimates the signal matrix of the time frequency domain based on the mixing matrix and the observation matrix of the time frequency domain using linear programming. It is preferable to do.

  As a second solution, the present invention provides a signal separation method for separating a specific signal source signal from an observation signal in which a plurality of signal source signals are mixed. A first step of converting a time-domain observation matrix including only a few minutes into a time-frequency domain observation matrix, and based on the time-frequency domain observation matrix converted in the first step, an observation matrix and a signal source matrix A signal source signal based on a second step of estimating a mixing matrix that defines a relationship between the two, a mixing matrix estimated in the second step, and an observation matrix in the time-frequency domain converted in the first step A third step of estimating a time-frequency domain signal source matrix including a predetermined number of samples, and the time-frequency domain signal source matrix estimated in the third step as a time-domain signal source row A first step of obtaining a plurality of matrices having, as components, a ratio between components included in the observation matrix in the time-frequency domain converted in the first step; , A second process for dividing each matrix obtained in the first process and obtaining a plurality of sub-matrices in which a row vector forms a horizontal line in a time-frequency domain coordinate system; and a plurality of the matrixes obtained in the second process And a third process for estimating each column vector of the mixing matrix based on a column vector of a specific submatrix included in the submatrix.

  In the second solving means described above, the first step converts the time domain observation matrix into the time frequency domain observation matrix using wavelet packet transformation, and the fourth step includes an inverse wavelet. Preferably, the time-frequency domain signal source matrix is transformed into the time-domain signal source matrix using packet transformation.

  Also, in the second solving means described above, the second step is included in the time-frequency domain observation matrix transformed in the first step as the time-frequency domain observation matrix to be subjected to the first processing. It is preferable to use a column vector obtained by removing a column vector whose norm is less than a predetermined value.

  Further, in the second solving means described above, the fourth step estimates the time-frequency domain signal source matrix based on the mixing matrix and the time-frequency domain observation matrix using linear programming. Is preferred.

  As a third solution, the present invention causes a computer to execute a procedure corresponding to the first step to the fourth step included in the signal separation method according to the second solution described above. A signal separation program is provided.

  According to the present invention, when estimating a mixing matrix that defines a relationship between an observation matrix and a signal source matrix based on an observation matrix in the time-frequency domain, between components included in the observation matrix in the time-frequency domain A first process for obtaining a plurality of matrices X having a ratio as a component, and a plurality of sub-matrices X that divide each matrix X obtained by the first process and form a horizontal line in a coordinate system in a time-frequency domain. And a third process for calculating the average of column vectors of a specific partial matrix included in the plurality of partial matrices obtained in the second process and estimating each column vector of the mixing matrix A. As a result, the mixing matrix can be accurately estimated under any condition. Further, by using the mixing matrix estimated in this way, it is possible to accurately estimate the time-frequency domain signal source matrix, that is, the time-domain signal source matrix S under an arbitrary condition. Therefore, the process of separating the signal source signal from the various observation signals mixed with multiple signal source signals (signal source signal separation process) can be performed using the statistical properties of the signal source signal, the number of signals Regardless of the relationship with the number of source signals, the nature of the data structure of the signal source matrix including the signal source signals, etc., it can be performed accurately under arbitrary conditions.

BEST MODE FOR CARRYING OUT THE INVENTION

  Embodiments of the present invention will be described below with reference to the drawings. 1 to 3 are diagrams for explaining an embodiment of a signal separation system according to the present invention.

  As shown in FIG. 1, the signal separation system 10 according to the present embodiment includes an observation signal (EEG (electroencephalogram) signal, MEG (magnetoencephalogram) signal, mixed audio signal, image signal) in which a plurality of signal source signals are mixed. , Seismic signals, etc.) for separating a specific signal source signal, an input unit 11 for capturing a plurality of observation signals, and a signal separation for separating a specific signal source signal from each observation signal captured by the input unit 11 Part 12.

  Among these, the input unit 11 includes n sensors 11 a for detecting observation signals, and n observation signals detected by these sensors 11 a are input to the signal separation unit 12. Yes.

  The signal separation unit 12 estimates an unspecified signal source signal (for example, m signal source signals) based on the n observation signals detected by the sensors 11a of the input unit 11, and the wavelet A packet conversion unit (time frequency conversion unit) 13, a mixing matrix estimation unit 14, a signal source matrix estimation unit 15 and a wavelet packet conversion unit (time frequency conversion unit) 16 are included.

Here, n observation signals detected by the sensors 11a of the input unit 11 are transmitted to the signal separation unit 12 as an observation matrix X in a time domain including the n observation signals by a predetermined number of samples (K). Entered. On the other hand, the data finally output from the signal separation unit 12 is a time-domain signal source matrix S including m signal source signals. More specifically, the time-domain observation matrix X is expressed as X = [ x (1),..., X (K)] ∈Rn ^{× K,} and the column vector x (i) is represented by n A set of observation signals is expressed as x (i) = [x ₁ (i),..., X _n (i)] ^T (i = 1, 2,..., K). Further, the time domain signal source matrix S is expressed as S = [ s (1),..., S (K)] ∈R ^{m × K,} and its column vector s (i) is m unspecified. As a set of signal source signals, s (i) = [s ₁ (i),..., S _m (i)] ^T (i = 1,..., K). Note that the observation matrix X and the signal source matrix S are represented by the linear mixing model of the above equation (2) using the mixing matrix AεR ^{n × m} as described above.

  The signal separation unit 12 is for obtaining the signal source matrix S based on the observation matrix X according to the linear mixture model of the above equation (2), and the processing is (1) the mixing matrix A based on the observation matrix X. A first stage for estimating (blind identification), and (2) a second stage for estimating the signal source matrix S based on the mixing matrix A and the observation matrix X estimated in the first stage. It is roughly divided into

  Hereinafter, details of processing performed in the signal separation unit 12 will be described.

(Basic principle)
First, the basic principle of processing performed by the signal separation unit 12 will be described.

As described above, the time-domain observation matrix X and the signal source matrix S are represented by the linear mixed model of the above equation (2) using the mixing matrix A, but here, the time-domain observation matrix X and the signal The source matrix S is converted into an observation matrix X ′ and a signal source matrix S ′ in the time frequency domain. At this time, in order to obtain a more sparse representation of the time frequency domain, the above equation (2) is subjected to wavelet packet transformation instead of standard wavelet transformation. As a result, a new linear mixed model such as the following equation (3) is obtained for the observation matrix X ′ and the signal source matrix S ′ in the time-frequency domain. The wavelet packet transformation is a kind of linear transformation, and details thereof are described in, for example, Non-Patent Document 2 (G. Strang and T. Nguyen: Wavelets and Filter Banks, Wellesley-Cambridge Press, 1995.). Yes.

  In the above equation (3), each row of the observation matrix X ′ in the time frequency domain is a time frequency representation of the corresponding observation signal in the observation matrix X in the time domain, and each row of the signal source matrix S ′ in the time frequency domain is 4 is a time frequency representation of a corresponding signal source signal of a time domain signal source matrix S.

Here, a mode in which the signal source matrix S ′ in the time-frequency domain has a sufficiently large number of column vectors having only one non-zero component (that is, a column vector having only one component as the main meaning). And sparse. For example, as shown in the following equation (4), only the first component of the L column vectors [ s ′ (i ₁ ),..., S ′ (i _L )] of the signal source matrix S ′ is not 0. Let it be a column vector.

In this case, the column vectors [ x ′ (i ₁ ),..., X ′ (i _L )] of the observation matrix X ′ in the time frequency domain are as shown in the following equation (5).

Here, if q∈ {1,..., N}, each column vector x ′ (i _j ) = [x ₁ ′ (i _j ),..., X _n ′ (i) of the observation matrix X ′ in the time frequency domain. _j )] The ratio between each component of ^T (j = 1,..., L) and x _q ′ (i _j ) is calculated according to the following equation (6).

When the above equation (6) is applied to the above equation (5), the following equation (7) is obtained.

Further, the following equation (8) is obtained from the above equation (7). Thus, it is possible to estimate the row vector a ₁ in a specific scale. Each component of a ₁ represented by the formula (8) can be expressed in the following equation (9).

Here, from the equation of the above equation (7), the n row vectors of the matrix on the left side of the above equation (7) (matrix of the following equation (10)) are all j, x _i ′ (j) and It can be seen that a horizontal line (see FIG. 7) is formed in the coordinate system in the relationship.

Further, the matrix of the above formula (10) is a matrix ([x _i ′ (j) / x _q ′ (j)] _n ) obtained based on the observation signal X ′ in the original time frequency domain. _It can also be seen that it is a submatrix of ( _{× K} ).

In the above equation (11), the following equation (12) is satisfied.

  As described above, a matrix in which each of the n row vectors forms a horizontal line (a matrix of the above equation (11) obtained based on the observation signal X ′ in the original time frequency domain (n × K matrix) )), The column vector of the mixing matrix A can be estimated using the above equation (8), and the mixing matrix A and the signal source matrix S can be estimated finally. .

(Specific processing in the signal separation unit 12)
Next, specific processing (processing for estimating the mixing matrix A and the signal source matrix S) performed by the signal separation unit 12 according to the basic principle described above will be described with reference to FIGS.

<Stage 1>
When a time domain observation matrix XεR ^{n × K} including n observation signals by a predetermined number of samples (K) is input to the signal separation unit 12, first, wavelet packet transformation of the signal separation unit 12 is performed. The unit 13 performs wavelet packet transformation on each row vector of the time domain observation matrix X input from the input unit 11, and converts the time domain observation matrix X into a time frequency domain observation matrix X ′. (Step 101 in FIG. 2).

  Next, based on the time-frequency domain observation matrix X ′ converted by the wavelet / packet conversion unit 13 by the mixing matrix estimation unit 14 of the signal separation unit 12, the time-frequency-domain observation matrix X ′ and the time-frequency-domain observation matrix X ′ A mixing matrix A that defines the relationship with the signal source matrix S ′ is estimated.

<Stage 2>
Specifically, first, the norm of each column vector becomes larger than ξ ₁ (a preset positive constant) based on the time-frequency domain observation matrix X ′ transformed by the wavelet packet transformation unit 13. Such a partial observation matrix X ^{(^)} (same as the notation with “^” added to the top of X) is obtained (step 102 in FIG. 2). The norm of the column vector [x ₁ ′ (i),..., X _n ′ (i)] is defined by the following equation (13).

  Note that the processing in step 102 described above is preferable in terms of reducing the calculation load in the subsequent processing and removing column vectors that are inappropriately affected by noise.

<Stage 3>
Then, for n ₁ = _{1 to} n, the loop including steps 3.1 and 3.2 (steps 104 to 117 in FIG. 2) is repeated.

<Stage 3.1>
Specifically, first, the row vector forms a horizontal line in the coordinate system in the time-frequency domain by taking the ratio between the components included in the partial observation matrix X ^{(^)} obtained in step 2, and the following equation (14 A ratio matrix X ^{(^)} ′ such as ⁾ is calculated (step 104).

In the above equation (14), K ₁ is a number that is equal to or smaller than the number of column vectors of the matrix X ^(＾) . Here, when the component of the n _1st row vector of the matrix X ^{(^)} is small (for example, smaller than a preset positive constant ξ ₂ ⁾ , the matrix X ^{(^)} containing that component corresponds. Ignore column vectors.

Here, the ratio matrix X ^{(^)} ′ of the above equation (14) is a horizontal line in the coordinate system of the time frequency domain in the row vector (its height corresponds to the component of the column vector of the mixing matrix A at a specific scale. And such submatrices are found by the following step 3.2.

<Step 3.2>
Then, for n ₂ = 1 to n (n ₂ ≠ n ₁ ), the loop including stages 3.2.1, 3.2.2 and 3.2.3 (steps 105 to 115 in FIG. 2) is repeated.

<Step 3.2.1>
Specifically, first, the ratio matrix ^X of the equation (14) ^{(^)} 'minimum value of _{n 2-th} row vector of (vector in equation (15)) _{(r' n2)} and a maximum value (R ' _n2 ).

Here, the range of [r ′ _n2 , R ′ _n2 ] is divided into M ₀ (preset positive constant) sub-intervals, and the ratio matrix X ^{(^)} ′ is divided into M sub-matrices X ″ ₁ ,. , X ″ _M0 (step 107 in FIG. 2). At this time, all the components of the n _2nd row vector of each submatrix X ″ _k (k = 1,..., M ₀ ) are in the kth subinterval. Also, each submatrix X ″ _k ( k = 1,..., M ₀ ) includes different column vectors (column vectors corresponding to points in different time frequency regions where only one of the signal source components is not ₀ ) of the ratio matrix X ^{(^)} ′.

<Step 3.2.2>
Next, a portion of the submatrix X ″ _k (k = 1,..., M ₀ ) obtained in step 3.2.1 where the number of column vectors is smaller than J ₁ (a preset positive integer). The matrix is deleted, and a new submatrix X ″ _jk (k = 1,..., N ₁ ) is obtained (step 108 in FIG. 2).

  Through the above steps 3.2.1 and 3.2.2 (steps 107 and 108 in FIG. 2), the above-described partial matrix (the partial matrix in which the row vector forms a horizontal line in the coordinate system of the time-frequency domain) is converted. can be found. Note that all the components of the submatrix (submatrix having substantially the same column vector) obtained in this way form n horizontal lines corresponding to n row vectors of the submatrix. Moreover, the average column vector of such a submatrix corresponds to one column vector of the mixing matrix (that is, the cluster center vector in the clustering method).

  However, with these steps alone, there may be too many sub-matrices used to estimate the mixing matrix, and steps 3.2.1 and 3.2.2 are performed according to step 3.2.3 below. Decrease the number of sub-matrices obtained in.

<Step 3.2.3>
That is, for n ₃ = 1 to n (n ₃ ≠ n ₁ , n ₃ ≠ n ₂ ), the loop including stage 3.2.3.1 (steps 109 to 113 in FIG. 2) is repeated.

<Step 3.2.3.1>
Specifically, for n ₃ = 1 to n (n ₃ ≠ n ₁ , n ₃ ≠ n ₂ ), a plurality of sub-matrices X ″ _jk (k = 1,..., Based on N ₁ ), a vector e _i corresponding to the column vector of the mixing matrix A is obtained (step 111).

That relates to k = 1 to N _1, the loop repeats comprising the following steps 3.2.3.1 (a) ~ (c) ( step 201 to 207 in FIG. 3).

(A) First, the same processing as in the above-described step 3.2.1 (step 107 in FIG. 2) is performed on the submatrix X ″ _jk (step 202 in FIG. 3). Instead of n ₂ and X ^{(^)} ′ in 2.1, n ₃ and X ″ _jk are used. Thus, M ₀ partial matrices X ″ _q ^(jk) (q = 1,..., M ₀ ) are obtained for each partial matrix X ″ _jk .

(B) Next, for the M ₀ sub-matrices X ″ _q ^(jk) (q = 1,..., M ₀ ) thus obtained, the above-described step 3.2.2 (FIG. 2) is performed. After performing the same processing as in step 108) (X ″ _q ^(jk) and J ₂ (preset positive constants are used instead of X ″ _k and J ₁ )) to obtain a new submatrix ( Step 203 in FIG. 3), a submatrix (for example, X ″ _p ^(jk) ) having the smallest total variance of n row vectors is selected from the obtained submatrices (step 204 in FIG. 3).

The above steps 3.2.3.1 (a) and (b) are similar to the above-described steps 3.2.1 and 3.2.2. The number is reduced. Then, according to the submatrix X ″ _p ^(jk) obtained in this way, n distinct horizontal lines (see FIG. 8) are formed by the row vectors.

(C) Finally, the average of all the column vectors of the partial matrix X ″ _p ^(jk) obtained in this way is calculated and normalized, and the vector e _i corresponding to the column vector of the mixing matrix A is estimated. (Step 205).

<Stage 4>
As described above, when four loops relating to n ₁ , n ₂ , n ₃ , and k are repeated, a matrix E = [ e ₁ ,..., E _N0 , which is a set of vectors corresponding to the column vector of the mixing matrix A. ] Is required. Here, since there are four loops, a plurality of vectors are estimated corresponding to one column vector included in the mixing matrix A. However, all these estimated vectors are included in the matrix E. Will be included. That is, the estimated matrix E has more column vectors than the mixing matrix A.

Therefore, in Step 4, redundant ones of the estimated column vectors of the matrix E are deleted. Specifically, if there are column vectors in the estimated matrix E that are almost the same or opposite in direction, these column vectors are converted into one normalized average column vector. replace. Finally, the matrix A _E ∈R ^{n × m0} (m ≦ m ₀ ) obtained in this way is obtained as an estimation of the original mixing matrix A (step 118 in FIG. 2).

<Stage 5>
Thereafter, the signal matrix estimation unit 15 of the signal separation unit 12 observes the mixing matrix A estimated by the mixing matrix estimation unit 14 (that is, the matrix A _E ) and the time frequency domain converted by the wavelet packet conversion unit 13. Based on the matrix X ′, the signal source matrix S ′ in the time-frequency domain including the signal source signal by a predetermined number of samples is estimated using linear programming. Specifically, the signal source matrix S ′ in the time-frequency domain is estimated by solving the linear programming problem defined by the following equation (16).

Note that the matrix A _E estimated by the mixing matrix estimation unit 14 includes a submatrix close to the mixing matrix A if the size and order of non-essential column vectors are ignored. In addition, for analysis of robustness in Non-Patent Document 3 (YQ Li, A. Cichocki and S. Amari, "Analysis of Sparse representation and blind source separation," Neural Computation, vol. 16, pp. 1193-1234.) Therefore, it is known that the estimation of the signal source matrix S ′ in the time-frequency domain is effectively performed if the submatrix included in the matrix A _E is sufficiently close to the mixing matrix A.

  Finally, the inverse wavelet / packet transform unit 16 of the signal separation unit 12 performs inverse wavelet / packet transform on the signal matrix S ′ in the time-frequency domain estimated by the signal source matrix estimation unit 15. To the signal source matrix S.

In the processing in the signal separation unit 12 described above, five parameters (parameters ξ ₁ and ξ ₂ related to the size of the matrix component in the analysis region, the number of partial sections M ₀ , the column of the selected partial matrix are shown. There is a minimum number of vectors J ₁ , J ₂ ), but the values of these parameters depend on the problem to be processed (the total number of samples and the maximum absolute value of the coefficients obtained by wavelet packet transformation). Value or the like).

As described above, according to the present embodiment, in the mixing matrix estimation unit 14 of the signal separation unit 12, a plurality of ratio matrices X ^{(^)} having as a component a ratio between components included in the observation matrix X ′ in the time-frequency domain. And a plurality of sub-matrices X ″ _{k in} which the row vector forms a horizontal line in the coordinate system of the time-frequency domain, by dividing the first process for ^obtaining ′ and each ratio matrix X ^{(^)} ′ obtained by the first process. A second process to be calculated, and a third process to estimate each column vector of the mixing matrix A by calculating an average of the column vectors of a specific partial matrix included in the plurality of partial matrices X ″ _k determined by the second process Therefore, the mixing matrix A can be estimated with high accuracy under an arbitrary condition. Further, by using the mixing matrix A estimated in this way, the time-frequency domain signal source matrix S ′, that is, the time-domain signal source matrix S can be accurately estimated under arbitrary conditions. Therefore, the process of separating the signal source signal from the various observation signals mixed with multiple signal source signals (signal source signal separation process) can be performed using the statistical properties of the signal source signal, the number of signals Regardless of the relationship with the number of source signals, the nature of the data structure of the signal source matrix including the signal source signals, etc., it can be performed accurately under arbitrary conditions.

  More specifically, according to the signal separation method according to the present embodiment, an independent component analysis method or a standard clustering method (K-means clustering method or the like) generally used as a conventional signal separation method. There is no problem like that. Hereinafter, advantages of the signal separation method according to the present embodiment will be described in comparison with the conventional signal separation method.

(1) Comparison with Independent Component Analysis Method The independent component analysis method can be used to estimate the mixing matrix A and the signal source matrix S, similarly to the signal separation method according to the present embodiment. Specifically, in the independent component analysis method, the mixing matrix A and the signal source matrix S are estimated by estimating a signal separation matrix W that is an inverse matrix of the mixing matrix A. On the other hand, the signal source matrix S is estimated by obtaining the product of the estimated signal separation matrix W and the observed signal matrix X by ^obtaining an inverse matrix W ⁻¹ of the estimated signal separation matrix W. Is called.

However, in such an independent component analysis method, the matrix W ⁻¹ that is the inverse matrix of the signal separation matrix W cannot be calculated due to an estimation error due to noise or the like, and even if it can be calculated, the mixing matrix A and Often, large differences occur between the matrices W- ¹ . Further, in the independent component analysis method, when the mixing matrix A is singular, the linear mixing model of the above equation (2) cannot be solved in the first place. Furthermore, the independent component analysis method must satisfy the constraint that each signal source is statistically independent and the number of signal sources is equal to or smaller than the number of observation points (sensors). Therefore, it cannot be applied to many realistic cases (estimation of signal sources in the brain, etc.).

  On the other hand, in the signal separation method according to the present embodiment, the mixing matrix A is estimated more directly rather than indirectly through the inverse matrix. As a result, the mixing matrix A and the signal source matrix S can be estimated more accurately and reliably. In addition, in the signal separation method according to the present embodiment, each signal source does not have to be statistically independent, and there is no restriction on the number of signal sources, so that it is effective for many realistic cases. Can be applied.

(2) Comparison with a standard clustering method A standard clustering method (K-means clustering method, etc.) estimates the mixing matrix A and the signal source matrix S in the same manner as the signal separation method according to this embodiment. Can be used for Specifically, in the standard clustering method, the mixing matrix A and the signal source matrix S are estimated by adjusting parameters by iterative calculation.

  However, in such a standard clustering method, parameters are adjusted by iterative calculation, so whether or not to converge to a global convergence point is not uniquely determined, and there is a high possibility of falling into a local solution. Further, in the standard clustering method, as a problem caused by iterative calculation, the behavior of adjustment of each component of the mixing matrix A varies greatly depending on how the initial values are given. If the variance (data structure) of each component is not sufficiently sparse, each component of the finally obtained mixing matrix A often deviates significantly from the true value.

  On the other hand, the signal separation method according to the present embodiment does not repeatedly perform calculation for parameter adjustment, so there is no problem of not converging to a global convergence point. Further, in the signal separation method according to the present embodiment, there is no problem that the behavior of adjustment of each component of the mixing matrix A greatly changes depending on the selection of the initial value, and each component in the signal source matrix S is not changed. Even if the variance (data structure) is not sufficiently sparse, each component of the finally obtained mixing matrix A does not deviate significantly from the true value.

In the above-described embodiment, in order to obtain a partial matrix forming n horizontal lines, each row of all the n row vectors included in the ratio matrix X ^{(^)} ′ in the above equation (14) is obtained. The range of the vector components is divided into M subspaces, and the row vector ratio matrix X ^{(^)} ′ is divided into M submatrixes X ″ ₁ ,..., X ″ _{M0 based} on the range. However, almost the same result can be obtained only by performing the same processing on the two row vectors of the ratio matrix X ^{(^)} ′. That is, regarding the two row vectors (for example, the first row vector and the second vector) included in the ratio matrix X ^{(^)} ′ in the above equation (14), the range of the components of each row vector is represented by M parts. Dividing into spaces, the row vector ratio matrix X ^{(^)} ′ is divided into M sub-matrices X ″ ₁ ,..., X ″ _M0 (all of the two row vectors included in each of these sub-matrices). May be divided into each of the corresponding two partial sections. As a result of verification by the present inventors through simulation or the like, when all the components of the two row vectors included in the submatrix are within each of the corresponding two subsections (that is, two rows) It is known that the other row vectors also form horizontal lines (if the vectors form two horizontal lines).

In the above-described embodiment, the signal matrix estimation unit 15 of the signal separation unit 12 performs the mixing matrix A (that is, the matrix A _E ) estimated by the mixing matrix estimation unit 14 and the wavelet packet conversion unit 13. As a method for estimating the time-frequency domain signal source matrix S ′ based on the transformed time-frequency domain observation matrix X ′, linear programming is used. However, the present invention is not limited to this, and any optimization problem can be solved. Can be used.

  Furthermore, in the above-described embodiment, each part of the signal separation unit 12 of the signal separation system 10 (wavelet / packet conversion unit 13, mixing matrix estimation unit 14, signal source matrix estimation unit 15 and inverse wavelet packet conversion unit 16) Both can be realized as a program that runs on a computer system. Such a program is stored in a computer-readable recording medium such as a memory, a hard disk, a flexible disk, a CD-ROM, a DVD, and the like, and is sequentially read from a processor of a computer system and executed. Functions or procedures are realized.

  Next, specific examples of the above-described embodiment will be described. In the present embodiment, a case where the mixing matrix A and the signal source matrix S are estimated based on an observation matrix X as artificially prepared mixed signal data will be described as an example.

(Example)
In the present embodiment, the signal source matrix SεR ^{4 × 10000} is composed of components having values having a uniform distribution in the range of [−5, 5], and 800 having only one non-zero component. Of column vectors. Of these 800 column vectors, the first group of 200 column vectors is not zero in the first component, and the second group of 200 column vectors is zero in the second component. Instead, the 200th column vector in the third group has a third component that is not 0, and the 200th column vector in the fourth group has a fourth component that is not 0.

In addition, the mixing matrix AεR ^{3 × 4} has only randomly selected components (normalized components) as in the following equation (17).

Furthermore, the observation matrix X∈R ^{3 × 10000} was obtained by taking the product of the signal source matrix S and the mixing matrix A prepared in advance according to X = AS in the above equation (2).

  In this embodiment, the observation matrix X thus obtained is processed using the signal separation method (steps 1 to 3) described above, and the mixing matrix A is estimated. However, in this example, since the observation matrix X is artificially prepared and has an appropriate sparsity, steps 1 and 5 were not executed.

Here, since the specific procedure of the signal separation method is the same as that described above, detailed description thereof is omitted, but the components of the ratio matrix X ^{(^)} ′ obtained in step 3.1 are shown in FIG. The result is as shown in FIG. 4 shows the three-dimensional dispersion of the components of the ratio matrix X ^{(^)} ′ obtained in step 3.1, and FIG. 5 shows the first row of the ratio matrix X ^{(^)} ′. It is a figure which shows all the components of a vector. As is clear from FIGS. 4 and 5, at this stage, no cluster in which a plurality of components are collected is found. In particular, FIG. 4 does not show any directions of the four column vectors of the mixing matrix. This is because only 2% of all points represent each of these directions.

Further, the components of the first row vector of the matrix X ″ _k obtained in the step 3.2.1 are as shown in FIG. 6, and the components of the matrix X ″ _jk obtained in the step 3.2.2. Was as shown in FIG. In FIG. 6, the solid line extending in the horizontal direction represents several partial sections. As can be seen from FIGS. 6 and 7, at this stage, it can be seen that there are several line segments overlaid with noise.

Furthermore, the components of the matrix X ″ _p ^(jk) obtained in step 3.2.3.1 (b) are as shown in FIG. 8. As is clear from FIG. It can be seen that there are three distinct line segments, these three line segments having a height corresponding to the three components of the first column vector of the mixing matrix A, X ″ _p ^{(jk )} Three row vectors. The normalized average column vector of X ″ _p ^(jk) corresponds to the estimated column vector of the mixing matrix A (one of the column vectors of the estimated matrix E).

As described above, as a result of estimating the matrix E corresponding to the mixing matrix A, a matrix of the following equation (18) was obtained.

  Here, when the column vector of the matrix E estimated in this way is compared with the column vector of the mixing matrix A of the above equation (17), all the column vectors of the mixing matrix A are estimated very well. It can be seen that there are several redundant vectors in the estimated matrix E.

Therefore, finally, by removing redundant vectors existing in the estimated matrix E (step 4 of the signal separation method described above), the final mixing matrix A (matrix A _E ) is estimated. It was.

  From the above, it has been found that the signal separation method described above functions well despite only 8% of the column vectors of the signal source matrix S being sparse (only one component is not 0).

(Comparative example)
As a comparative example, the observation matrix X used in the above-described embodiment was processed using the K-means clustering method to estimate the mixing matrix A. The following equation (18) shows an estimation matrix of the mixing matrix A obtained as a result.

  Comparing the estimation matrix of the above equation (18) and the mixing matrix A of the above equation (17), it can be seen that the mixing matrix is not estimated well by the K-means clustering method.

Industrial application fields

  The signal separation system according to the present invention can be effectively used in fields such as biomedical signal processing, sound processing, image processing, and earthquake signal processing. This will be specifically described below.

(1) Biomedical signal processing Biomedical signals including electroencephalogram (EEG) signals, magnetoencephalogram (MEG) signals, etc. can be used as mixed signals of unspecified multiple brain signal sources, artifacts, noise, etc. (1 ) It appears in the form of the linear mixed model of (2). That is, the observation matrix X including the biomedical signal that is the observation signal is expressed in the form of the product of the unspecified mixing matrix A and the unspecified signal source matrix S.

  According to the signal separation system of the present invention, the mixing matrix A can be estimated based on a biomedical signal observed by an electroencephalograph, a magnetoencephalograph or the like, and a signal source matrix can be combined with other methods. Since S can be estimated, the signal source in the brain can be identified as a result. The intracerebral signal source identified in this way is caused by diseases such as head injury, brain infection, cerebral hemorrhage, Alzheimer's disease, degeneration of brain tissue, stroke, brain tumor and the like. Therefore, finding these brain signal sources is useful for medical diagnosis.

(2) Audio processing The mixed audio signal appears in the form of a linear mixed model of the above equations (1) and (2) as a mixed signal such as a plurality of unspecified audio signal sources and noise. That is, the observation matrix X including the mixed speech signal that is the observation signal is expressed in the form of the product of the unspecified mixing matrix A and the unspecified signal source matrix S.

  According to the signal separation system of the present invention, the mixing matrix A can be estimated based on the mixed speech signal observed by a microphone, sonar, or the like, and the signal source matrix S is estimated by combining with other methods. As a result, it is possible to identify a plurality of unspecified audio signal sources.

(3) Image processing An image digital signal such as a medical image such as a nuclear magnetic resonance functional image (fMRI) or an astronomical image is expressed as a mixed signal such as a plurality of unspecified image signal sources and noise. ) Appears in the form of a linear mixed model. That is, the observation matrix X including the image digital signal that is the observation signal is expressed in the form of a product of the unspecified mixing matrix A and the unspecified signal source matrix S.

  According to the signal separation system of the present invention, the mixing matrix A can be estimated based on an image digital signal observed by a camera, an astronomical telescope, or the like, and the signal source matrix S can be obtained by combining with other methods. As a result, it is possible to specify a plurality of unspecified image signal sources.

(4) Seismic signal processing The seismic signal is in the form of a linear mixed model of the above formulas (1) and (2) as mixed signals such as unspecified multiple seismic signal sources, other signal sources and noise caused by the earthquake. appear. That is, the observation matrix X including the seismic signal as the observation signal is expressed in the form of the product of the unspecified mixing matrix A and the unspecified signal source matrix S.

  According to the signal separation system of the present invention, the mixing matrix A can be estimated based on the seismic signal observed (recorded) by the seismometer, and the signal source matrix S can be estimated by combining with other methods. As a result, a plurality of unspecified earthquake signal sources can be identified.

1 is a block diagram showing a configuration of a signal separation system according to an embodiment of the present invention. The flowchart for demonstrating the process performed in the signal separation part of the signal separation system shown in FIG. The flowchart for demonstrating the process of step 111 shown in FIG. The figure which shows the mode of the three-dimensional dispersion | distribution of the component of the matrix (ratio matrix obtained after the process of step 3.1 (process of step 104 of FIG. 2)) obtained in the middle in the Example. The figure which shows all the components of the 1st row vector of the matrix (The ratio matrix obtained after the process of the step 3.1 (process of step 104 of FIG. 2)) obtained in the middle in an Example. The figure which shows some components of the 1st row vector of the matrix (matrix obtained after the process of step 3.2.1 (process of step 107 of FIG. 2)) obtained in the middle in an Example. The figure which shows all the components of the matrix (The matrix obtained after the process of step 3.2.2 (process of step 108 of FIG. 2)) obtained intermediately in the Example. The figure which shows the component of the matrix (The matrix obtained after the process of step 3.2.3.1 (b) (process of step 203 of FIG. 3)) obtained in the middle in an Example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Signal separation system 11 Input part 11a Sensor 12 Signal separation part 13 Wavelet packet conversion part 14 Mixing matrix estimation part 15 Signal source matrix estimation part 16 Inverse wavelet packet conversion part

Claims (9)

In a signal separation system for separating a specific signal source signal from an observation signal in which a plurality of signal source signals are mixed,
An input unit for capturing a plurality of observation signals;
A signal separation unit for separating a specific signal source signal from each observation signal captured by the input unit;
The signal separator is
A time-frequency conversion unit that converts a time-domain observation matrix including each observation signal captured by the input unit by a predetermined number of samples into a time-frequency domain observation matrix;
A mixing matrix estimation unit that estimates a mixing matrix that defines a relationship between an observation matrix and a signal source matrix based on the observation matrix in the time-frequency domain transformed by the time-frequency transformation unit;
Based on the mixing matrix estimated by the mixing matrix estimation unit and the time-frequency domain observation matrix converted by the time-frequency conversion unit, a signal source in the time-frequency domain including a signal source signal for a predetermined number of samples A signal source matrix estimator for estimating a matrix;
An inverse time-frequency conversion unit that converts the time-frequency domain signal source matrix estimated by the signal source matrix estimation unit into a time-domain signal source matrix;
The mixing matrix estimation unit of the signal separation unit includes a first process for obtaining a plurality of matrices having components as ratios between components included in the observation matrix in the time-frequency domain transformed by the time-frequency transformation unit; Each matrix obtained in one process is divided into a second process for obtaining a plurality of submatrices in which a row vector forms a horizontal line in a coordinate system in a time-frequency domain, and a plurality of submatrices obtained in the second process. And a third process for estimating each column vector of the mixing matrix based on a column vector of a specific partial matrix included.   The time frequency conversion unit of the signal separation unit converts the time domain observation matrix into the time frequency domain observation matrix using wavelet packet transformation, and the inverse time frequency conversion unit of the signal separation unit includes: The system of claim 1, wherein the time-frequency domain source matrix is transformed into the time-domain source matrix using an inverse wavelet packet transform.   The mixing matrix estimation unit of the signal separation unit includes, as an observation matrix of the time frequency domain that is a target of the first processing, a column vector included in the observation matrix of the time frequency domain converted by the time frequency conversion unit. 3. The system according to claim 1, wherein a column vector whose norm is less than a predetermined value is used.   The signal source matrix estimation unit estimates the signal matrix in the time-frequency domain based on the mixing matrix and the observation matrix in the time-frequency domain using linear programming. 4. The system according to any one of 3. In a signal separation method for separating a specific signal source signal from an observation signal in which a plurality of signal source signals are mixed,
A first step of converting a time-domain observation matrix including a predetermined number of samples of each observation signal captured by the input unit into a time-frequency domain observation matrix;
A second step of estimating a mixing matrix defining a relationship between the observation matrix and the signal source matrix based on the observation matrix in the time-frequency domain transformed in the first step;
Based on the mixing matrix estimated in the second step and the time-frequency domain observation matrix transformed in the first step, a time-frequency domain signal source matrix including a predetermined number of samples of signal source signals is obtained. A third step to estimate;
A fourth step of converting the time-frequency domain source matrix estimated in the third step into a time-domain source matrix;
The second step includes a first process for obtaining a plurality of matrices having as a component a ratio between components included in the observation matrix in the time-frequency domain transformed in the first step, and each of the steps obtained in the first process. A second process for dividing a matrix and obtaining a plurality of sub-matrices in which a row vector forms a horizontal line in a time-frequency domain coordinate system; and a specific sub-matrix included in the plurality of sub-matrices obtained in the second process And a third process for estimating each column vector of the mixing matrix based on the column vector.   The first step converts the time domain observation matrix into the time frequency domain observation matrix using a wavelet packet transform, and the fourth step uses the inverse wavelet packet transform to convert the time frequency domain observation matrix. 6. The method of claim 5, wherein the source matrix is transformed into the time domain source matrix.   In the second step, a norm is set to a predetermined value from among column vectors included in the time-frequency domain observation matrix transformed in the first step as the time-frequency domain observation matrix to be subjected to the first processing. The method according to claim 5 or 6, characterized in that a vector obtained by removing a column vector that is less than one is used.   8. The method according to claim 5, wherein the fourth step estimates a signal source matrix in the time-frequency domain based on the mixing matrix and the observation matrix in the time-frequency domain using linear programming. The signal separation method according to any one of claims.   A signal separation program for causing a computer to execute a procedure corresponding to the first step to the fourth step included in the signal separation method according to claim 5.

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