JP2018136368A - Signal analyzer, method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a signal analyzer capable of learning a base spectrum using an algorithm with convergence guaranteed.SOLUTION: The signal analyzer includes: an auxiliary variable update part 42 that updates an auxiliary variable; a parameter update part 44 that updates a base spectrum and an activation parameter of each constituent sound so that an auxiliary function as an upper bound function which represents the magnitude of an error between an extraction spectrogram of a constituent sound signal of the constituent sound extracted from a spectrogram of a mixed signal and a spectrogram of a constituent sound signal of the constituent sound gets smaller; and a convergence determination part 46 that causes the auxiliary variable update part 42 and the parameter update part 44 to repeat the update until a predetermined convergence condition is satisfied.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a signal analysis apparatus, method, and program, and more particularly, to a signal analysis apparatus, method, and program for estimating parameters.

  In recent years, non-negative matrix factorization (NMF) has attracted attention as a promising technique for monophonic acoustic signal processing problems (Non-patent Document 1). Approximating the amplitude or power spectrum observed at each time with a non-negative combination of the base spectrum is equivalent to considering the observation spectrogram as a matrix and approximating it with the product of two matrices (base matrix and activation matrix). Since each matrix element is non-negative, it is called NMF because matrix decomposition is performed on the observed spectrogram under non-negative constraints. In the problem setting for supervised or semi-supervised sound source separation, NMF is first performed on the spectrogram of the learning sample of each sound source, and the base matrix is pre-learned. On the other hand, during the test, the learned base matrix is fixed and only the activation matrix is estimated. By using the power spectrogram of each sound source thus obtained, the target sound source signal can be obtained from the mixed signal by the Wiener filter.

  In the above approach (Non-Patent Document 1), the error between the spectrogram of the learning sample and the matrix product is used as an optimization criterion in the base learning, but the criterion is not such that the separated signal itself is optimal. Focusing on this point, discriminative non-negative matrix factorization (DNMF) that performs base learning using the error between the output signal of the Wiener filter and the learning sample of the target sound source as an optimization criterion directly (non-patent literature) A framework called 2) has been proposed. In this method, since the optimization criteria used at the time of learning and testing are the same, it is expected that a base spectrum having higher separation ability can be obtained by learning.

P. Smaragdis, R. Bhiksha, and S. Madhusudana, “Supervised and semi-supervised separation of sounds from single-channel mixture.”, In Proc. ICA, pp. 414-421, 2007. F. Weninger, J. L. Roux, J. R. Hershey, and S. Watanabe, “Discriminative NMF and its application to single-channel source separation.”, In Proc. INTERSPEECH, pp. 865-869, 2014.

  However, discriminative NMF learning criteria (discussed below) are analytically more complex than conventional NMF optimization criteria. For this reason, Non-Patent Document 2 proposes an optimization algorithm using a general-purpose method called a multiplicative update algorithm, but convergence to a stopping point is not guaranteed and the potential of DNMF can be fully demonstrated. I couldn't say.

  The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a signal analysis apparatus, method, and program that can learn a base spectrum using an algorithm that guarantees convergence.

  In order to achieve the above object, a signal analyzing apparatus according to the present invention includes time-series data of mixed signals obtained by mixing the constituent sounds, time-series data of constituent sound signals for the constituent sounds obtained by separating the mixed signals, and For the mixed signal and each component sound signal of each component sound, a time frequency expansion unit that outputs a spectrogram representing a signal component of each time and each frequency, and the time frequency expansion unit output An activation parameter representing a base spectrum for each component sound signal of each component sound and a sound volume at each base and each time based on a spectrogram for each component sound signal of the mixed signal and each component sound The extracted spectrogram of the component sound signal extracted from the spectrogram of the mixed signal using A parameter learning unit that estimates a base spectrum of each component sound and an activation parameter of each component sound so as to reduce a criterion that represents a magnitude of an error with a spectrogram of the component sound signal of the component sound; The parameter learning unit includes a parameter updating unit that updates a base spectrum of each constituent sound and an activation parameter of each constituent sound so as to reduce an auxiliary function that is an upper bound function of the criterion, A convergence determination unit that repeats updating by the parameter updating unit until a convergence condition is satisfied.

In the signal analysis method according to the present invention, the time-frequency expansion unit inputs time-series data of a mixed signal obtained by mixing each component sound and time-series data of the component sound signal for each component sound obtained by separating the mixed signal. For each of the mixed signal and each component sound signal of each component sound, a spectrogram representing a signal component of each time and each frequency is output, and a parameter learning unit is output by the time frequency expansion unit, Based on the mixed signal and the spectrogram for each constituent sound signal of each constituent sound, the base spectrum for each constituent sound signal of each constituent sound and the activation parameter representing the volume at each base and each time are used. The extracted spectrogram of the component sound signal extracted from the spectrogram of the mixed signal, and the configuration A signal analysis method for estimating a base spectrum of each component sound and an activation parameter of each component sound so as to reduce a criterion representing an error magnitude with respect to a spectrogram of the component sound signal, wherein the parameter learning The parameter updating unit updates the base spectrum of each constituent sound and the activation parameter of each constituent sound so as to reduce the auxiliary function that is the upper bound function of the criterion, and determines the convergence Including repeating the updating by the parameter updating unit until a predetermined convergence condition is satisfied.
The extraction spectrogram of the constituent sound signal of the constituent sound is extracted from the spectrogram of the mixed signal by the Wiener filter.

  Moreover, the program of this invention is a program for functioning a computer as each part which comprises said signal analysis apparatus.

  As described above, according to the signal analysis apparatus, method, and program of the present invention, the activation spectrum representing the base spectrum and the sound volume at each base and each time for each of the constituent sound signals of each constituent sound is obtained. An auxiliary function that is a standard upper bound function representing the magnitude of an error between the extracted spectrogram of the constituent sound signal of the constituent sound and the spectrogram of the constituent sound signal of the constituent sound, which is extracted from the spectrogram of the mixed signal By repeatedly updating the base spectrum of each constituent sound and the activation parameter of each constituent sound so as to reduce the function, the base spectrum can be learned by an algorithm with guaranteed convergence.

It is a block diagram which shows the functional structure of the signal analyzer which concerns on embodiment of this invention. It is a flowchart figure which shows the learning process routine in the signal analyzer which concerns on embodiment of this invention. It is a figure which shows an experimental result.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Existing method>
<Sound source separation by supervised NMF>
A power spectrogram of a mixed signal consisting of L sound sources

And

Where ω and t are frequency and time indexes. In supervised NMF, the base spectrum of each sound source trained in advance

Using the observation spectrogram

The basis matrix

And activation matrix

The objective is to obtain an estimated power spectrogram value for extracting each sound source signal from the mixed signal by the Wiener filter.

In Non-Patent Document 1,

Spectrogram of the training sample of the sound source l

And error

Is used as an optimization criterion. However,

Is the spectrogram of the training sample of sound source l

And matrix product

It is a function that measures the error of. At the time of testing, pre-trained basis matrix

Fixed,

Activation matrix to minimize

By estimating

Components of the power spectrogram of each sound source included in

Can be estimated. Error function

When I divergence is used as

It becomes. However, [·] ij represents the {i, j} -th element of the matrix. Power spectrogram of each sound source

If you want a Wiener filter

And without contradiction

A spectrogram of each sound source signal guaranteed to be obtained can be obtained. However,

When

Represents the multiplication and division for each element. However, in the above-mentioned approach (Non-patent Document 1), since the equation (1) is used in the basis learning criterion, the criterion for optimizing the separation signal according to the equation (4) was not established.

<Distinguishing NMF and multiplicative update algorithm>
The discriminative NMF (Non-patent Document 2) is the error between the Wiener filter output and the spectrogram of the training sample instead of (1).

It is a framework for sound source separation by supervised NMF that performs basic learning with reference to. However, although α _l ≧ 0 is a parameter representing the importance of the l-th separated signal.

In the following, for simplification of explanation, consider a sound source separation problem consisting of two types of sound sources (L = 2), speech and noise. When speech enhancement is intended, the accuracy of speech signal separation is more important, so the importance α is 1 for speech and 0 for noise. Therefore, the spectrogram of the clean speech learning sample

Spectrogram of noise learning sample

And the spectrogram of the mixed signal

Then, the basic learning problem of discriminative NMF is

It is formulated as an optimization problem such as However, the basis matrix

Consists of K ^s speech basis spectra and K ⁿ noise basis spectra.

Weninger et al. Proposed an optimization algorithm using a multiplicative update method for the above optimization problem (Non-patent Document 2). In the Weninger et al. Algorithm, the activation matrix is first calculated using normal NMF (ie, equation (2)).

Seeking

With the basis matrix W

The method of updating is taken. The above update formula is

of

The quotient of the negative and positive terms of the partial derivative of

, But it is not guaranteed that the objective function decreases with each update. For this reason, the convergence of the iterative algorithm based on these update equations is not guaranteed.

<Proposed method>
<Basic learning algorithm by auxiliary function method>
The embodiment of the present invention is an optimization algorithm that is derived based on the principle of the auxiliary function method and in which convergence of the optimization problem of Equation (6) to the stationary point is guaranteed.

<Auxiliary function method>
Assuming that F (θ) is an objective function to be minimized with respect to θ,

A function that satisfies

Is called an auxiliary function, and α is called an auxiliary variable. If you can design such an auxiliary function,

When

By alternately repeating the above, a stationary point of the objective function F (θ) can be obtained. This optimization method is called an auxiliary function method.

<Auxiliary function design>
The objective function

Design auxiliary functions for. First, the objective function

In

Is designed using the following inequality.

(Lemma 1)
any

Inequality

And

The equality holds when

(Proof)
any

Against

Since M _{ω and t} are non-negative values, from Lemma 1,

Holds. However, = ^c represents an equal sign for only the term depending on the parameter. Also,

age,

And The equal sign of (12) is

This holds true. Next, the auxiliary function for each term in Eq. (12) is designed.

Is a positive value, and the negative logarithmic function is a convex function, Jensen's inequality

Holds. However,

Is

And the equal sign in (14) is

This holds true.

Since is a positive value, the logarithmic function of the second term in Eq. (12) is a concave function. Since the concave function can be suppressed from above by the tangent at any point,

Holds. here,

Is a positive variable,

In this case, the equal sign in equation (16) holds. continue,

Design auxiliary functions for. Since quadratic functions are convex, Jensen's inequality

Holds. However,

Is

And the equal sign in (18) is

It is established when Finally,

Design auxiliary functions for. The function 1 / x ² is convex for x> 0, so Jensen's inequality

Holds. However,

Is

It is a variable that satisfies The equal sign in equation (20) is

This holds true.

(12), (14), (16), (18) and (20)

Auxiliary functions

Can be obtained. here,

Is an auxiliary variable

D is a constant term. The point of deriving this auxiliary function is

When

The global optimal solution for can be obtained analytically.

<Parameter update formula>
The condition of the auxiliary variable that minimizes the above auxiliary function is none other than the condition for establishing the equality of each inequality, so in Equation (13), Equation (15), Equation (17), Equation (19), Equation (21) Given. Also minimize auxiliary functions

Is

When

That is,

It can be obtained by solving positive number solutions of quartic and cubic equations such as Since the constant term and the coefficient of the quadratic equation of the above quartic equation are both negative values, it is always shown that there is only one positive solution.

<Configuration of Signal Analysis Device according to Embodiment of the Present Invention>
Next, the configuration of the signal analysis apparatus according to the embodiment of the present invention will be described. As shown in FIG. 1, a signal analyzing apparatus 100 according to an embodiment of the present invention includes a CPU, a RAM, and a ROM that stores a program for executing a learning processing routine described later and various data. Can be configured. Functionally, the signal analyzing apparatus 100 includes an input unit 10, an arithmetic unit 20, and an output unit 90 as shown in FIG.

  The input unit 10 receives time-series data of a mixed signal in which each component sound is mixed and time-series data of an acoustic signal for each component sound from which the mixed signal is separated.

  The calculation unit 20 includes a time frequency expansion unit 24 and a parameter learning unit 36.

The time frequency expansion unit 24 is a power spectrogram that represents a signal component of each frequency at each time based on the time-series data of the mixed signal.

Calculate Also, based on the time-series data of each component sound signal, a power spectrogram representing the signal components of each frequency at each time

Calculate In this embodiment, time frequency expansion such as short-time Fourier transform and wavelet transform is performed.

Based on the power spectrogram of the mixed signal and the power spectrogram of each component sound signal calculated by the time-frequency expansion unit 24, the parameter learning unit 36, for each component sound signal of each component sound, Using the activation parameters representing the base and the volume at each time, the magnitude of the error between the extracted spectrogram of the constituent sound extracted from the spectrogram of the mixed signal and the spectrogram of the constituent sound of the constituent sound is determined. Representing the base spectrum of each component sound so as to reduce the criterion of the above formula (5)

And activation of each component sound

Is estimated.

  Specifically, the parameter learning unit 36 includes an initial value setting unit 40, an auxiliary variable update unit 42, a parameter update unit 44, and a convergence determination unit 46.

The initial value setting unit 40 has a base spectrum of speech and noise.

And voice and noise activation

Set the initial value to. For example, an initial value is set at random.

Auxiliary variable updating unit 42 is an initial value or last updated base spectrum of speech and noise

And voice and noise activation

And γ _{k, ω,} for each base k, each frequency ω, and each time t according to the above formulas (13), (15), (17), (19), and (21) _. Update λ _{ω, t} and η _{ω, t} for _t , β _{k, ω, t} , θ _{k, ω, t} , each frequency ω, and each time t.

The parameter update unit 44 is a power spectrogram of the mixed signal output by the time frequency expansion unit 24.

And the power spectrogram of the audio signal

Γ _{k, ω, t} , β _{k, ω, t} , θ _{k, ω, t} , each frequency ω and each frequency k updated for each base k, each frequency ω, and each time t by the auxiliary variable updating unit 42. Λ _{ω, t} , η _{ω, t} with respect to time t _, and initial values, last updated, initial values, or last updated base spectrum of speech and noise

And voice and noise activation

Based on the above, by solving the quaternary equation and the cubic equation shown in the above equations (23) to (26), the base spectrum of speech and noise which is an initial value or updated last time

And voice and noise activation

Is estimated.

  The convergence determination unit 46 determines whether or not the convergence condition is satisfied, and repeats the update process in the auxiliary variable update unit 42 and the update process in the parameter update unit 44 until the convergence condition is satisfied.

  As the convergence condition, for example, the fact that the number of repetitions has reached the upper limit number can be used. Alternatively, as the convergence condition, it can be used that the difference between the value of the criterion of the above formula (6) and the value of the previous criterion is equal to or less than a predetermined threshold value.

The output unit 90 is a speech and noise base spectrum finally acquired by the parameter learning unit 36.

And voice and noise activation

Is output.

<Operation of Signal Analysis Device According to Embodiment of the Present Invention>
Next, the operation of the signal analyzing apparatus 100 according to the embodiment of the present invention will be described. First, when receiving the time-series data of the mixed signal in which the constituent sounds are mixed in the input unit 10 and the time-series data of the acoustic signal for each of the constituent sounds from which the mixed signals are separated, the signal analysis apparatus 100 receives the signal in FIG. The learning process routine shown in FIG.

First, in step S100, a power spectrogram representing a signal component of each frequency at each time based on the time series data of the mixed signal in the input unit.

Calculate Also, based on the time-series data of each component sound signal, a power spectrogram representing the signal components of each frequency at each time

Calculate

Next, in step S102, the base spectrum of speech and noise

And voice and noise activation

Set the initial value to.

In step S104, the base spectrum of speech and noise, which is an initial value or updated last time

And voice and noise activation

And γ _{k, ω,} for each base k, each frequency ω, and each time t according to the above formulas (13), (15), (17), (19), and (21) _. Update λ _{ω, t} and η _{ω, t} for _t , β _{k, ω, t} , θ _{k, ω, t} , each frequency ω, and each time t.

Next, in step S106, the power spectrogram of the mixed signal output by the time-frequency expansion unit 24.

And the power spectrogram of the audio signal

Γ _{k, ω, t} , β _{k, ω, t} , θ _{k, ω, t} , each frequency ω and each frequency k updated for each base k, each frequency ω, and each time t by the auxiliary variable updating unit 42. Λ _{ω, t} , η _{ω, t} with respect to time t _, and initial values, last updated, initial values, or last updated base spectrum of speech and noise

And voice and noise activation

Based on the above, by solving the quartic equation and the cubic equation shown in the above equations (23) to (26), a base spectrum of speech and noise is obtained.

And voice and noise activation

Is estimated.

  Next, in step S108, it is determined whether a convergence condition is satisfied. If the convergence condition is satisfied, the process proceeds to step S110. If the convergence condition is not satisfied, the process proceeds to step S104, and the processes in steps S104 to S106 are repeated.

In step S110, the base spectrum of speech and noise finally updated in step S106 above.

And voice and noise activation

Is output from the output unit 90 and the learning process routine is terminated.

<Experimental example>
In order to verify the speech enhancement effect according to the method of this embodiment, evaluation is performed using speech data of the ATR speech database 503 sentences (see Non-Patent Document 3) and ATR environmental sound database (two types of department noise and subway station noise). The experiment was conducted. Compared to the conventional supervised NMF method (SNMF) and discriminative NMF multiplicative update algorithm (DNMF MU), the signal-to-distortion ratio (SDR) and signal-to-interference ratio (SIR) before and after processing (non- The improvement value of Patent Document 4) was evaluated.

[Non-Patent Document 3] A. Kurematsu, K. Takeda, Y. Sagisaka, S. Katagiri, H. Kuwabara, and K. Shikano, "ATR Japanese speech database as a tool of speech recognition and synthesis," Speech Communication, vol 9, pp. 357-363, 1990.
[Non-Patent Document 4] E. Vincent, R. Gribonval, and C. Fevotte, "Performance measurement in blind audio source separa-tion.", IEEE transactions on audio, speech, and language processing, vol. 14, no. 4 , Pp. 1462-1469, 2016.

The test data was created by superimposing each noise on clean speech with a signal-to-noise ratio (SNR) of -6, -3, 0, 3dB. The acoustic signal used in the experiment was a monaural signal with a sampling frequency of 16 kHz, and a Fourier transform was performed for a short time with a frame length of 32 ms and a frame shift of 16 ms.

Was calculated. In base learning, speech base learning was performed using a total of 200 sentences from two male and two female speakers. The basis number was 40 for both speech and noise. Figure 3 shows a plot of the mean and variance of SDR improvement values when the iteration algorithm is tried 5 times with randomly determined initial values, and the number of iterations in each trial is 0, 10, 25, 50, 100, 200. is there. According to the results of FIG. 3, the number of iterations was set to 25 in the following experiment. The test data set was created by superimposing noise on 40 sentences of voice data randomly selected from the ATR503 sentence database. Tables 1 and 2 show the average of the improved SDR and SIR values obtained by trying the proposed method (DNMF AU) and the conventional method (SNMF, DNMF MU) five times under the above conditions. In any evaluation scale, it was confirmed that the proposed method was able to obtain higher improvement values in all cases.

  Table 1 above shows the average SDR improvement [dB] obtained by trying each method five times. The top row is the speech enhancement result for Department noise, and the bottom row is the speech enhancement result for Subway station noise.

  Table 2 above shows the average SIR improvement [dB] obtained by trying each method five times. The top row is the speech enhancement result for Department noise, and the bottom row is the speech enhancement result for Subway station noise.

As described above, according to the signal analysis device according to the embodiment of the present invention, the base spectrum and the activation parameter for each component sound signal of each component sound are extracted from the spectrogram of the mixed signal. The base of each component sound is reduced so as to reduce the auxiliary function that is the upper bound function of the standard representing the magnitude of the error between the component spectrogram of the component sound and the spectrogram of the component sound signal of the component sound. By repeatedly updating the spectrum and the activation parameter of each component sound, the base spectrum can be learned by an algorithm with guaranteed convergence.
Further, in the supervised sound source separation method using non-negative matrix factorization, the base spectrum can be learned by an algorithm that guarantees convergence by using the reconstruction error of the separated signal as a criterion.

  Note that the present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the gist of the present invention.

  For example, in the present specification, the program has been described as an embodiment in which the program is installed in advance. However, the program can be provided by being stored in a computer-readable recording medium or provided via a network. It is also possible to do.

DESCRIPTION OF SYMBOLS 10 Input part 20 Calculation part 24 Time frequency expansion part 36 Parameter learning part 40 Initial value setting part 42 Auxiliary variable update part 44 Parameter update part 46 Convergence determination part 90 Output part 100 Signal analysis apparatus

Claims (7)

Using the time series data of the mixed signal in which each component sound is mixed and the time series data of the component sound signal for each component sound separated from the mixture signal as inputs, the mixed signal and the component sound signal of each component sound For each, a time-frequency expansion unit that outputs a spectrogram representing a signal component at each time and frequency,
Based on the mixed signal and the spectrogram for each component sound signal of each component sound output by the time-frequency expansion unit, the base spectrum for each component sound signal of each component sound, and each base and The magnitude of error between the extraction spectrogram of the component sound signal extracted from the spectrogram of the mixed sound and the spectrogram of the component sound signal of the component sound, which is extracted from the spectrogram of the mixed signal using an activation parameter representing the volume at each time A parameter learning unit that estimates a base spectrum of each component sound and an activation parameter of each component sound,
Including
The parameter learning unit
A parameter updating unit that updates the base spectrum of each component sound and the activation parameter of each component sound so as to reduce the auxiliary function that is the upper bound function of the criterion;
A convergence determination unit that repeats the update by the parameter update unit until a predetermined convergence condition is satisfied;
Including a signal analysis device.   The signal analysis apparatus according to claim 1, wherein an extraction spectrogram of the constituent sound signal of the constituent sound is extracted from the spectrogram of the mixed signal by a Wiener filter. Each component sound is voice and noise,
The signal analysis apparatus according to claim 2, wherein the criterion is an I divergence criterion represented by the following expression.

Where W ^s represents a speech base spectrum, H ^s represents a speech activation parameter, W represents a base matrix composed of a speech base spectrum and a noise base spectrum, and H represents a speech activation spectrum. Represents an activation matrix consisting of an activation parameter and a noise activation parameter, S ^s represents a spectrogram of a speech component sound signal, M represents a spectrogram of a mixed signal, W _{ω, k} represents a frequency ω and a basis represents the power spectrum of k. The time-frequency expansion unit receives as input the time-series data of the mixed signal in which each component sound is mixed and the time-series data of the component sound signal for each component sound separated from the mixed signal, and the mixed signal and each component For each of the sound signals constituting the sound, a spectrogram representing the signal components at each time and each frequency is output,
Based on the mixed signal and the spectrogram for each constituent sound signal of each constituent sound, which is output by the time-frequency expanding section, the parameter learning unit, the base spectrum for each constituent sound signal of each constituent sound And an extraction spectrogram of the component sound signal of the component sound, and a spectrogram of the component sound signal of the component sound, which are extracted from the spectrogram of the mixed signal using an activation parameter representing the volume at each base and each time, and A signal analysis method for estimating a base spectrum of each component sound and an activation parameter of each component sound so as to reduce a criterion representing the magnitude of the error of
By the parameter learning unit estimating,
The parameter update unit updates the base spectrum of each component sound and the activation parameter of each component sound so as to reduce the auxiliary function that is the upper bound function of the criterion,
A signal analysis method comprising: causing a convergence determination unit to repeat updating by the parameter updating unit until a predetermined convergence condition is satisfied.   The signal analysis method according to claim 4, wherein an extraction spectrogram of the constituent sound signal of the constituent sound is extracted from the spectrogram of the mixed signal by a Wiener filter. Each component sound is voice and noise,
The signal analysis method according to claim 4, wherein the criterion is an I divergence criterion expressed by the following equation.

Where W ^s represents a speech base spectrum, H ^s represents a speech activation parameter, W represents a base matrix composed of a speech base spectrum and a noise base spectrum, and H represents a speech activation spectrum. Represents an activation matrix consisting of an activation parameter and a noise activation parameter, S ^s represents a spectrogram of a speech component sound signal, M represents a spectrogram of a mixed signal, W _{ω, k} represents a frequency ω and a basis represents the power spectrum of k.   The program for functioning a computer as each part of the signal analyzer of any one of Claims 1-3.