JP6808597B2 - Signal separation device, signal separation method and program - Google Patents

Description

The present invention relates to a signal separation device, a signal separation method and a program.

In the situation where there is no information on how the source signals are mixed, the target source signal can be accurately obtained from the mixed signals observed by a plurality of sensors (hereinafter referred to as "observed signals"). As a method of extracting, a method called blind signal separation is known.

As a method of blind signal separation utilizing the non-stationarity of a signal, a method of simultaneously diagonalizing a correlation matrix of a plurality of time intervals has been conventionally known. Hereinafter, this conventional method will be described.

The discrete time is represented by j = 1, ..., J. The M observation signals x _jm (m = 1, ..., M) are collectively referred to as a vector representation x _j = [x _j1 , ..., x _jM ] ^T. In addition, T represents transposition.

At this time, if N source signals having non-stationarity are s _jn = [s _j ] _n (n = 1, ..., N), the observed signals x _j are linear as shown in the following equation 1. Expressed as a mixture.

Here, A is a mixed matrix of M × N.

The purpose of blind signal separation is to obtain the separation matrix W of N × M from only the observed signal x _{jm, and the} separation signal y _jn = [y _j ] _n (n = 1, ..., N) as close as possible to the source signal s _jn. ) Is calculated by the following equation 2.

In the blind signal separation method by simultaneous diagonalization of the correlation matrix, J times are time intervals.

Divide into.

That is,

And.

At this time, in each time interval p, the correlation matrix X _p (correlation matrix of the observed signal) shown in the following equation 3 and the correlation matrix Y _p (correlation matrix of the separation signal) shown in the following equation 4 are considered, and P Diagonalize the correlation matrices Y _p (p = 1, ..., P) at the same time (that is, make the off-diagonal component [Y _p ] _nm (n ≠ m) of the correlation matrix Y _p close to 0). Find the separation matrix W.

In addition, H represents conjugate transpose (complex number conjugate is taken and transpose is performed).

When P = 2, it is possible to diagonalize strictly (set the off-diagonal component to 0) by using generalized eigenvalue decomposition or the like. FIG. 1 shows an example of simultaneous diagonalization of the correlation matrix Y _p in the case of P = 2. The waveforms of the _two source signals s ₁ and s ₂ are shown in FIG. 1 (a). Time interval from 0 to 0.2 seconds

And the time interval is 0.2 to 0.4 seconds.

And. At this time, a scatter plot corresponding to the correlation matrices X ₁ and X ₂ is shown in FIG. 1 (b), and a scatter plot corresponding to the simultaneous diagonalized correlation matrices Y ₁ and Y ₂ is shown in FIG. 1 (c). From this, it can be seen that signal separation has been achieved.

When P ≧ 3, an exact solution is generally not obtained. Therefore, after defining the distance scale d shown in the following equations 5 and 6, the cost function C shown in the following equation 7 which is the sum of them is minimized.

Here, diag (Y) is an operation in which the diagonal component of the matrix Y is left as it is and the off-diagonal component is set to 0. In the above equation 6, since the correlation matrix Y is a Hermitian matrix, setdiag (Y) ≧ detY holds. Various optimization algorithms have been proposed for minimizing the cost function C shown in the above equation 7 with respect to the distance scale d shown in the above equations 5 and 6.

Nobutaka Ono. Stable and fast update rules for independent vector analysis based on auxiliary function technique. In Applications of Signal Processing to Audio and Acoustics (WASPAA), 2011 IEEE Workshop on, pages 189-192. IEEE, 2011.

In the above-mentioned conventional method, one separation matrix W is calculated by simultaneous diagonalization of the correlation matrix Y _p . This was valid when the entire source signal was mixed by the same mixing matrix A.

On the other hand, the source signal may be mixed by a plurality of mixing matrices _Ai (i = 1, ..., I). For example, mixing of the sound source with delayed and reverberation in a real environment, when viewed in the time frequency domain, source signals at different mixing matrix A _i for each frequency bin i is mixed. In such a case, the blind signal separation by the conventional method has a problem that the permutation problem needs to be solved separately. This issue will be described below.

i = 1, ..., I represent different mixed systems such as frequency bins. The discrete time is represented by j = 1, ..., J. The M observation signals x _ijm (m = 1, ..., M) are collectively referred to as a vector representation x _ij = [x _ij1 , ..., x _ijM ] ^T. At this time, if N source signals having non-stationarity are s _ijn = [s _ij ] _n (n = 1, ..., N), the observed signal x _ij is linear as shown in the following equation 8. Expressed as a mixture.

Here, it is assumed that A _i is a mixed matrix of M × N and is different for each mixed system i.

The purpose of the blind signal separation is only sought separation matrix _{W i} of N × M from the observation signals _{x ijm,} the source signal _{s ijn} possible to the separated signal _{y ijn = [y ij] n} (n = 1, ···, N) is calculated by the following equation 9.

At this time, even when the above-mentioned plurality of different mixed systems exist, it is possible to achieve signal separation by applying the conventional method for each mixed system i. However, when applying the conventional method, as described above, it is necessary to separately solve the permutation problem peculiar to the blind method. That is, in the simultaneous diagonalization, for example, even if the two source signals s _ij1 and s _ij2 can be separated, the separated signals may be obtained by _exchanging them as y _ij1 = s _ij2 , y _ij2 = s _ij1. .. This replacement differs for each mixed system i, for example, in the mixed system i ₁ and the mixed system i ₂ .

If the result is obtained, either mixed system (for example, mixed system i ₂ )

It is necessary to replace the separated signals as in.

The present invention has been made in view of the above points, and achieves blind signal separation by simultaneous diagonalization without solving the permutation problem even when a plurality of different mixed systems exist. The purpose is.

In order to solve the above problem, a signal separator that separates a source signal from a plurality of observation signals including a plurality of different mixed systems and obtains a plurality of separation signals indicating the source signal obtains the plurality of observation signals. A frequency region conversion unit that converts to one time-frequency representation, a first correlation matrix calculation unit that calculates a first correlation matrix from the first time-frequency representation, and the plurality of separation signals from the plurality of observation signals. The linear conversion unit that calculates the second time-frequency representation obtained by linearly converting the first time-frequency representation and the second correlation matrix are calculated from the second time-frequency representation using the separation matrix for obtaining. A second correlation matrix calculation unit, a non-stationarity calculation unit that calculates a predetermined parameter independent of the mixed system from the second correlation matrix, the first correlation matrix, and the second correlation. Having a matrix, a matrix optimization unit that updates the separation matrix based on the predetermined parameters, and a time region conversion unit that converts the second time-frequency representation into the plurality of separation signals. It is a feature.

Even when a plurality of different mixed systems exist, blind signal separation by simultaneous diagonalization can be achieved without solving the permutation problem.

It is a figure explaining an example of simultaneous diagonalization of the correlation matrix in the case of P = 2. It is a figure which shows an example of the structure of the signal separation apparatus in embodiment of this invention. It is a figure which schematically explains the simultaneous diagonalization of this invention. It is a figure which shows an example of the hardware composition of the signal separation apparatus in embodiment of this invention. It is a figure which shows an example of the functional structure of the signal separation apparatus in embodiment of this invention. It is a flowchart which shows an example of the whole processing executed by the signal separation apparatus in embodiment of this invention. It is a figure explaining an example of the effect of this invention.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the embodiment of the present invention described below, it is assumed that the observed signal is a signal having non-stationarity. Examples of signals having non-stationarity include voice, noise, brain waves, radio signals and the like. In addition, non-stationarity is a property that the power of a signal changes with the passage of time.

<Structure of signal separation device 10>
First, the configuration of the signal separation device 10 according to the embodiment of the present invention will be described with reference to FIG. FIG. 2 is a diagram showing an example of the configuration of the signal separation device 10 according to the embodiment of the present invention.

The signal separation device 10 shown in FIG. 2 is a computer that obtains a separation signal from an observation signal in which a plurality of different mixed systems exist. The signal separation program 100 is installed in the signal separation device 10 shown in FIG. The signal separation program 100 may be a program group composed of a plurality of modules.

Signal separating apparatus 10 according to the embodiment of the present invention, the signal separating program 100, by calculating the separation matrix W _i simultaneously diagonalizing the correlation matrix of the separation signal, calculates a separation signal from the input observation signal Then, the calculated separation signal is output.

The configuration of the signal separation device 10 shown in FIG. 2 is an example, and may be another configuration. For example, the signal separation device 10 may be composed of a plurality of computers.

<Simultaneous diagonalization of the correlation matrix of separated signals>
Here, the method of simultaneous diagonalization (simultaneous diagonalization of the correlation matrix of the separated signals) by the signal separation device 10 in the embodiment of the present invention will be described.

When there are a plurality of different mixed systems (ie, when Equation 1 above is extended to Equation 8 and the separation signal is calculated by Equation 9 instead of Equation 2 above), the correlation matrix of the observed signals is: From the above equation 3 to the following equation 10.

Further, the correlation matrix of the separated signals is changed from the above equation 4 to the following equation 11.

At this time, as shown in FIG. 3, in the conventional method, P correlation matrices _Yip are diagonalized at the same time for each frequency (mixed system) i, whereas signal separation in the embodiment of the present invention is performed. In the device 10, the average power v _pn of the signal n in the time interval p is calculated, and the correlation matrix Y _ip is diagonalized at the same time so as to approach the diagonal matrix having this v _pn as a diagonal component.

That is, the signal separation device 10 according to the embodiment of the present invention is a diagonal matrix defined by the following equation 12.

By making the correlation matrix Y _ip as close as possible to, the correlation matrix Y _ip is diagonalized at the same time.

According to the definition shown in Equation 12 above, the non-stationarity of the source signal can be modeled as a parameter that depends only on the signal and time (in other words, as a parameter that does not depend on the mixed system i). Thereby, in the signal separation device 10 according to the embodiment of the present invention, the permutation problem is solved.

Diagonal matrix of the correlation matrix Y _ip of the separation signal

In order to get as close as possible, consider defining the difference between these two matrices and minimizing the difference. The cost function C for evaluating the difference between the matrices is defined by using the multichannel IS divergence shown in Equation 13 below.

Equation 13 above is

Then, since it becomes the same as the equation 6, it can be said that the multi-channel Itakura Saito distance d _IS shown in the above equation 13 is an extension of the distance scale shown in the above equation 6.

Let V be a P × N matrix, and let v _pn = [V] _pn . The signal separation device 10 according to the embodiment of the present invention minimizes the total cost shown in the following equation 14 that summarizes all the mixing systems i and all the time intervals p.

When the equation of the above equation 14 is rearranged and the constant term is removed, the following equation 15 is the cost function C to be minimized.

<Hardware configuration of signal separator 10>
Next, the hardware configuration of the signal separation device 10 according to the embodiment of the present invention will be described with reference to FIG. FIG. 4 is a diagram showing an example of the hardware configuration of the signal separation device 10 according to the embodiment of the present invention.

The signal separation device 10 shown in FIG. 4 includes an input device 11, a display device 12, an external I / F 13, a RAM (Random Access Memory) 14, a ROM (Read Only Memory) 15, and a CPU (Central Processing Unit). It has 16, a communication I / F 17, and an auxiliary storage device 18. Each of these hardware is connected so as to be able to communicate with each other via the bus B.

The input device 11 is, for example, a keyboard, a mouse, a touch panel, or the like, and is used for a user to input various operations. The display device 12 is, for example, a display or the like, and displays various screens or the like. The signal separation device 10 does not have to have at least one of the input device 11 and the display device 12.

The external I / F 13 is an interface with an external device. The external device includes a recording medium 13a and the like. The signal separation device 10 can read or write the recording medium 13a or the like via the external I / F 13. The signal separation program 100 or the like may be recorded on the recording medium 13a.

The recording medium 13a includes, for example, a flexible disk, a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), a USB (Universal Serial Bus) memory card, and the like.

The RAM 14 is a volatile semiconductor memory that temporarily holds programs and data. The ROM 15 is a non-volatile semiconductor memory capable of holding programs and data even when the power is turned off. The ROM 15 stores, for example, OS (Operating System) settings, network settings, and the like.

The CPU 16 is an arithmetic unit that reads a program or data from the ROM 15 or the auxiliary storage device 18 or the like onto the RAM 14 and executes processing.

The communication I / F 17 is an interface for connecting the signal separation device 10 to the network. The signal separation program 100 may be acquired (downloaded) from a predetermined server or the like via the communication I / F17.

The auxiliary storage device 18 is, for example, an HDD (Hard Disk Drive), an SSD (Solid State Drive), or the like, and is a non-volatile storage device that stores programs and data. The programs and data stored in the auxiliary storage device 18 include, for example, an OS, an application program that realizes various functions on the OS, a signal separation program 100, and the like.

The signal separation device 10 according to the embodiment of the present invention can realize various processes described later by having the hardware configuration shown in FIG.

<Functional configuration of signal separation device 10>
Next, the functional configuration of the signal separation device 10 according to the embodiment of the present invention will be described with reference to FIG. FIG. 5 is a diagram showing an example of the functional configuration of the signal separation device 10 according to the embodiment of the present invention.

The signal separation device 10 shown in FIG. 5 includes a frequency domain conversion unit 110, a linear conversion unit 120, a first correlation matrix calculation unit 130, a second correlation matrix calculation unit 140, and a non-stationarity calculation unit 150. , A matrix optimization unit 160 and a time domain conversion unit 170. Each of these parts is realized by a process in which the signal separation program 100 causes the CPU 16 to execute.

The frequency domain transform unit 110 applies a short-time Fourier transform (STFT) to the observed signal to represent the time frequency x _ij (i = 1, ..., I, j = 1,). ..., J) is obtained.

The linear conversion unit 120 obtains the time-frequency representation y _ij (i = 1, ..., I, j = 1, ..., J) by the above equation 9.

The first correlation matrix calculation unit 130 calculates the correlation matrix X _ip (i = 1, ..., I, p = 1, ..., P) of the observed signal by the above equation 10. The number P of the time interval is predetermined by the user or the like to be an arbitrary number of J or less.

The second correlation matrix calculation unit 140 calculates the correlation matrix Y _ip (i = 1, ..., I, p = 1, ..., P) of the separated signal by the above equation 11.

The non-stationarity calculation unit 150 calculates a _VPN for minimizing the above equation 15.

Matrix optimization unit 160, the separation matrix _W i to minimize the equation 15 described above (i = 1, ···, I ) was calculated, and updates the separating matrix _{W i.}

And linear transformation by the linear transformation unit 120, the calculation of the correlation matrix _{Y ip} according to the second correlation matrix calculation section 140, of _{v pn} by unsteadiness calculating unit 150 calculates and, of the separation matrix _{W i} by the matrix optimization unit 160 The update is repeatedly executed until a predetermined condition is satisfied. The case where the predetermined condition is satisfied, for example, if the number of repetitions is equal to or greater than a predetermined number of times, if the separating matrix W _i converges (i.e., the variation of the separation matrix W _i several times is less than a minute value Case) and the like. Thus, the separation matrix W _i is optimized. The separation matrix _Wi (i = 1, ..., I) is initialized to, for example, an identity matrix.

The time domain transform section 170, by applying the inverse transformation of short-time Fourier transform on the time-frequency representation y _ij obtained using the optimized separating matrix W _i, to obtain the separated signals. As a result, a separation signal is output.

<Details of processing>
Next, the details of the processing executed by the signal separation device 10 according to the embodiment of the present invention will be described with reference to FIG. FIG. 6 is a flowchart showing an example of the overall processing executed by the signal separation device 10 according to the embodiment of the present invention. In the following, it is assumed that the separation matrix _Wi (i = 1, ..., I) is initialized to the unit matrix. Further, it is assumed that the number P of the time interval is determined in advance by the user or the like as the number P of J or less.

Step S101: The frequency domain conversion unit 110 applies a short-time Fourier transform to the observed signal to represent the time frequency x _ij (i = 1, ..., I, j = 1, ..., J). To get.

Step S102: The first correlation matrix calculation unit 130 uses the above equation 10 to express the correlation matrix X _ip of the observed signal from the time frequency representation x _ij (i = 1, ..., I, p = 1, ...・, P) is calculated.

Step S103: The linear conversion unit 120 linearly transforms the time-frequency representation x _{ij according} to the above equation 9, and the time-frequency representation y _ij (i = 1, ..., I, j = 1, ..., Get J).

Step S104: The second correlation matrix calculation unit 140 uses the above equation 11 to express the correlation matrix Y _ip of the separated signal from the time frequency representation y _ij (i = 1, ..., I, p = 1, ...・, P) is calculated.

Step S105: The non-stationarity calculation unit 150 calculates a _VPN for minimizing the above equation 15. The non-stationarity calculation unit 150 calculates the v _pn for minimizing the above equation 15 by the following equation 16.

This is derived as a solution in which the partial differential shown in the following equation 17 (that is, the partial derivative with respect to v _pn of the above equation 15) becomes 0.

Step S106: The matrix optimization unit 160 calculates and updates the separation matrix _Wi (i = 1, ..., I) for minimizing the above equation 15.

The matrix optimization unit 160 updates the matrix shown in the following equation 18 for each frequency (mixed system) i by using the auxiliary function method. The auxiliary function method is disclosed in, for example, Non-Patent Document 1.

First, the weighted average of the correlation matrix X _ip of the observed signals shown in the following equation 19 is calculated for all signals n = 1, ..., N.

Above the N matrix _{U in} hybrid simultaneous diagonalized: to update the _{W i} as (HEAD Hybrid Exact-Approximate Joint Diagonalization ) to matrix. As the procedure, the following equation 20 is calculated.

Here, e _n in only 1 n th element, a vector is any other element is 0.

Then, the scale is normalized by the following equation 21.

As a result, the separation matrix _Wi is updated.

As described above, step S103~ step S106 described above, until a predetermined condition is satisfied (for example, until the number of repetitions or until the separating matrix W _i equal to or greater than a predetermined number of times to converge) is repeatedly executed. Thus, the separation matrix W _i is optimized.

Step S107: the linear transformation unit 120 uses the optimized separating matrix _{W i,} the equation 9 above, and a linear transformation of the time-frequency representation _{x ij,} obtaining a time-frequency representation _{y ij.}

Step S108: The time domain transform unit 170 applies the inverse transform of the short-time Fourier transform to the time-frequency representation y _ij to obtain a separated signal.

As described above, in the signal separation device 10 according to the embodiment of the present invention, the separation signal can be obtained from the observation signal in which a plurality of different mixed systems exist by using the blind separation signal method by simultaneous diagonalization of the correlation matrix. it can. Moreover, in the signal separation device 10 according to the embodiment of the present invention, the separation signal can be obtained without separately solving the permutation problem.

<Effect of the present invention>
Here, the effect of the present invention using the signal separation device 10 in the embodiment of the present invention will be described with reference to FIG. 7. FIG. 7 is a diagram illustrating an example of the effect of the present invention.

FIG. 7 shows an example in which two audio signals mixed in a real environment are separated. FIGS. 7 (a) shows the two observation signals x ₁ and x ₂ are observed in the course of 2 seconds at the microphone. This 2 seconds was divided into a time interval of P = 20, and a separated signal was obtained using the signal separation device 10 according to the embodiment of the present invention.

FIG. 7B shows the separation signals y ₁ and y ₂ obtained by using the signal separation device 10 according to the embodiment of the present invention. As shown in FIG. 7B, it can be seen that the separation of the source signal is satisfactorily achieved according to the signal separation device 10 according to the embodiment of the present invention.

FIG. 7 (c) shows the v _pn calculated by the non-stationarity calculation unit 150 for two signals n (that is, y ₁ and y ₂ ) and 20 time intervals p. FIG. 7 (c) is the result of estimating in which time interval each signal has average power (in terms of time and frequency). This solved the permutation problem.

The present invention is not limited to the above-described embodiment disclosed specifically, and various modifications and modifications can be made without departing from the scope of claims.

10 Signal separation device 100 Signal separation program 110 Frequency domain conversion unit 120 Linear conversion unit 130 First correlation matrix calculation unit 140 Second correlation matrix calculation unit 150 Non-stationarity calculation unit 160 Matrix optimization unit 170 Time domain conversion unit

Claims (5)

A signal separation device that separates a source signal from a plurality of observation signals including a plurality of different mixed systems and obtains a plurality of separated signals indicating the source signal.
A frequency domain converter that converts the plurality of observed signals into a first time-frequency representation, and
A first correlation matrix calculation unit that calculates a first correlation matrix from the first time-frequency representation, and
A linear conversion unit that calculates a second time-frequency representation obtained by linearly converting the first time-frequency representation using a separation matrix for obtaining the plurality of separation signals from the plurality of observation signals.
A second correlation matrix calculation unit that calculates a second correlation matrix from the second time-frequency representation, and
From the second correlation matrix, a non-stationarity calculation unit that calculates a predetermined parameter independent of the mixed system, and
A matrix optimization unit that updates the separation matrix based on the first correlation matrix, the second correlation matrix, and the predetermined parameters.
A time domain conversion unit that converts the second time-frequency representation into the plurality of separated signals, and
Have a,
The plurality of observation signals are divided into a predetermined number of time intervals determined in advance.
The signal separation device, characterized in that the predetermined parameter is the average power for each time interval . The linear conversion unit, the second correlation matrix calculation unit, the non-stationarity calculation unit, and the matrix optimization unit calculate the second time-frequency representation until a predetermined condition is satisfied. The signal separation apparatus according to claim 1, wherein the calculation of the second correlation matrix, the calculation of the predetermined parameters, and the update of the separation matrix are repeatedly executed. The signal separation device according to claim 2, wherein the repetition is executed using the initial value of the separation matrix as a unit matrix. A signal separator that separates a source signal from a plurality of observation signals including a plurality of different mixed systems and obtains a plurality of separated signals indicating the source signal.
A frequency domain conversion procedure for converting the plurality of observed signals into a first time-frequency representation, and
The first correlation matrix calculation procedure for calculating the first correlation matrix from the first time-frequency representation, and
A linear conversion procedure for calculating a second time-frequency representation obtained by linearly converting the first time-frequency representation using a separation matrix for obtaining the plurality of separation signals from the plurality of observation signals.
A second correlation matrix calculation unit that calculates a second correlation matrix from the second time-frequency representation, and
A non-stationarity calculation procedure for calculating a predetermined parameter independent of the mixed system from the second correlation matrix, and
A matrix optimization procedure for updating the separation matrix based on the first correlation matrix, the second correlation matrix, and the predetermined parameters.
A time domain conversion procedure for converting the second time-frequency representation into the plurality of separated signals, and
The execution,
The plurality of observation signals are divided into a predetermined number of time intervals determined in advance.
A signal separation method, characterized in that the predetermined parameter is the average power for each time interval . In a signal separation device that separates a source signal from a plurality of observation signals including a plurality of different mixed systems and obtains a plurality of separated signals indicating the source signal.
A frequency domain conversion procedure for converting the plurality of observed signals into a first time-frequency representation, and
The first correlation matrix calculation procedure for calculating the first correlation matrix from the first time-frequency representation, and
A linear conversion procedure for calculating a second time-frequency representation obtained by linearly converting the first time-frequency representation using a separation matrix for obtaining the plurality of separation signals from the plurality of observation signals.
A second correlation matrix calculation unit that calculates a second correlation matrix from the second time-frequency representation, and
A non-stationarity calculation procedure for calculating a predetermined parameter independent of the mixed system from the second correlation matrix, and
A matrix optimization procedure for updating the separation matrix based on the first correlation matrix, the second correlation matrix, and the predetermined parameters.
A time domain conversion procedure for converting the second time-frequency representation into the plurality of separated signals, and
To execute ,
The plurality of observation signals are divided into a predetermined number of time intervals determined in advance.
A program characterized in that the predetermined parameter is an average power for each time interval .