JP5509481B2 - Blind signal separation method and apparatus - Google Patents

Description

  The present invention relates to a blind signal separation method for estimating unknown signal source signals that are statistically independent from each other mixed by an unknown convolutional mixing system from only observed signals, and in particular, a method for solving a least-squares simultaneous diagonalization problem. The present invention relates to a backward model type blind signal separation method and a backward model type blind signal separation device that can separate signals with high accuracy using.

  When a plurality of unknown signal source signals are mixed and observed by an unknown convolutional mixing system, the process of separating the observation signals and estimating the unknown signal source signals before mixing is called blind signal separation. Blind signal separation is a method of estimating an unknown signal source signal from an observation signal only on the condition of statistical independence between unknown signal source signals, and it is not always necessary to estimate the position of the signal source or the arrival direction of the observation signal. It is a way not to.

  Non-Patent Document 1 proposes a frequency domain signal separation method based on the gradient method. After separating the observation signal for each frequency bin based on the gradient method, the signal source is assigned by solving the permutation problem.

  Non-Patent Document 2 proposes a method combining signal separation based on singular value decomposition of a correlation matrix of an observation signal and linear prediction analysis. This method aims to improve the signal separation accuracy by a linear prediction filter.

  Non-Patent Document 3 proposes a forward model type blind signal separation method using a method of solving the least square simultaneous diagonalization problem. This method consists of estimation of the mixing matrix by solving the least square simultaneous diagonalization problem, estimation of the separation matrix from the mixing matrix using the least square generalized inverse matrix, solving the scaling problem, permutation problem It consists of four procedures.

  S. Araki, R.A. Mukai, S.M. Makino, T .; Nishikawa, and H.K. Saruwatari, “The Fundamental Limitation of Frequency Domain Blind Source Separation for Convotional Measures of Spec.” 11, no. 2, pp. 109-116, Mar. 2003   Nakagawa, Takahashi, “BSS post-processing method with emphasis on prevention of crosstalk speech”, IEICE Transactions, vol. J90-A, no. 8, pp. 633-645, 2007   K. Rahbar and J.M. P. Reilly, "A frequency domain method for blind source separation of convenient audio mixtures", IEEE Transactions on Audio and Proceeding and Audio. 13, no. 5, pp. 832-844, Sept, 2005

  Although the gradient method used in the conventional blind signal separation method has a small amount of calculation, convergence is slow and sufficient signal separation performance cannot be obtained in an actual environment.

  Also, in the method combining signal separation by singular value decomposition and linear prediction analysis, there is a trade-off relationship between the quality of the unknown signal source signal and the signal separation performance, so that it is difficult to achieve both.

  Furthermore, in the forward model type blind signal separation method using the solution of the least squares type simultaneous diagonalization problem, additive noise is considered in estimating the separation matrix using the least squares type generalized inverse matrix of the mixing matrix. The effect of noise cannot be ignored.

  In the conventional solution of the permutation problem using the fact that there is a correlation between adjacent frequency bins of signals generated from the same signal source, once an error occurs, the probability that the subsequent solution will continue to be very high becomes very high.

  The present invention has been made in view of such circumstances, and improves the signal separation performance and halves the procedure by making the inverse matrix of the spatial correlation matrix of the observed signal the subject of the least-squares simultaneous diagonalization problem. In addition, the object is to adaptively solve the permutation problem using the correlation of adjacent frequency bins, except for frequency bins with low signal separation accuracy.

In order to meet such an object, the blind signal separation method according to the present invention (the invention according to claim 1) is configured to extract unknown signal source signals that are statistically independent from each other mixed only by an unknown convolutional mixture system from only observation signals. a method of estimating a blind observed signal after it has been multiplied by a window function, this number K of short discrete Fourier transform exponentially for each frequency bin by forgetting factor applied observation signal vector obtained by the After weighting, the inverse matrix of the spatial correlation matrix of the observation signal is obtained for each block based on the block processing from the weighted vector, normalized, and then one block or a plurality of blocks are least squared of the frequency bin. As a target of the type simultaneous diagonalization problem, the solution of the least square type simultaneous diagonalization problem is obtained by using a solution by a combination of the least square method, the power method, and the iterative method. And obtaining a high separation matrix of the signal separation accuracy by solving adaptively based permutation problem signal separation accuracy by utilizing a correlation in adjacent frequency bins of the signal generated from the issue source Blind signal separation method.

The blind signal separation method according to the present invention (the invention according to claim 2 ) is characterized in that the scaling problem of normalizing each column vector of the separation matrix can be substituted by normalization included in the power method.

The blind signal separation method according to the present invention (the invention described in claim 3 ) is an exponential function for each frequency bin when the calculation amount of the inverse matrix for each block is large in an application with a short block length and a large number of sensors. The inverse matrix lemma is used instead of the calculation of the spatial correlation matrix of the observation signal weighted to and the inverse matrix calculation for each block.

The blind signal separation method according to the present invention (the invention described in claim 4 ) is a method of applying a solution of the least square simultaneous diagonalization problem in which the block length is L and M blocks are target sections n times. After estimating the separation matrix, based on the correlation of each separation signal in the same frequency bin, the square of the inverse of the periodogram of the N separation signals in the frequency bin ω _k (k = 0, 1,..., K−1). The signal separation accuracy μ (ω _k ) ⁽ⁿ⁾ in the frequency bin is _obtained by Expression (4) using normalization by the square root of the sum. Tr (·) represents a matrix trace. Q is a set of matrices in which one element is 1 in each row of the matrix, the other elements are 0, and the position of the element that is 1 does not overlap with other rows. Matrix E (omega _k) ⁽ⁿ⁾ and the matrix _{^{Γ -1 (ω k, nΨL +}} τL) , respectively formula (5), given by (6), tau = 1, 2, ..., in M Γ ^-1 (ω _k , NΨL + τL) is a matrix _obtained by normalizing a diagonal matrix Λ ⁻¹ (ω _k , nΨL + τL) whose diagonal element is the inverse of the periodogram λ _j (ω _k , nΨL + τL) of the separated signal, and the diagonal element γ _j ⁻¹ (ω _k , nΨL + τL). Since M blocks are target sections of the least square simultaneous diagonalization problem, Ψ is an overlapping shift size of two consecutive sets of target sections.

The blind signal separation method according to the present invention (invention 5 ) detects frequency bins with extremely low signal separation accuracy, thins out the corresponding frequency bins, and then packs these frequency bins to cause a permutation problem. Is adaptively solved.

In the blind signal separation method according to the present invention (invention of claim 6 ), there is a correlation between adjacent frequency bins or adjacent frequency bins of signals generated from the same signal source in a state where frequency bins with extremely low signal separation accuracy are packed. It is characterized by adaptively solving the permutation problem.

The blind signal separation method according to the present invention (invention according to claim 7 ) is characterized in that the permutation of the adjacent frequency bin is copied to the permutation corresponding to the frequency bin with extremely low signal separation accuracy.

  That is, according to the present invention, the least square method is obtained by combining the least square method, the power method, and the iterative method by making the inverse matrix of the spatial correlation matrix of the observation signal the object of the least square type simultaneous diagonalization problem. An approximate solution of the simultaneous diagonalization problem, that is, a separation matrix can be obtained adaptively, and both improvement in signal separation performance and reduction in the amount of computation are achieved without solving the scaling problem.

  In addition, according to the present invention, the permutation problem is solved by using the correlation of adjacent frequency bins except for frequency bins with low signal separation accuracy, and the signal separation performance is improved.

  According to the present invention, the inverse matrix of the spatial correlation matrix of the observation signal weighted exponentially using the forgetting factor is obtained, and this is applied to the least square simultaneous diagonalization problem. In the solution of the least square simultaneous diagonalization problem, an approximate solution of the least square simultaneous diagonalization problem by combining the least square method, the power method, and the iterative method without solving the scaling problem, that is, a separation matrix Is determined adaptively. Conventional forward model blind signal separation using least squares simultaneous diagonalization problem is estimation of mixing matrix, estimation of separation matrix using least square generalized inverse matrix of mixing matrix, solution of scaling problem, The blind signal separation method and blind signal separation apparatus according to the present invention, which consists of four procedures for solving the permutation problem, is a scaling that normalizes each column vector of the separation matrix using a backward model type. By substituting the solution of the problem with the normalization included in the power method, there is an effect that the number of steps can be halved to two steps of estimating the separation matrix and solving the permutation problem.

  In addition, before solving the permutation problem by utilizing the fact that there is a correlation between adjacent frequency bins of signals generated from the same signal source, frequency bins with extremely low signal separation accuracy are detected and the frequency bins are thinned out. After that, these frequency bins are packed to solve the permutation problem adaptively. By copying the permutation of the adjacent frequency bin to the permutation corresponding to the frequency bin with a very low signal separation accuracy, the blind signal separation method and the blind signal separation device according to the present invention can be used for the unknown signal source signal. There is an effect of improving the signal separation performance without affecting the quality.

  Furthermore, in the blind signal separation method and the blind signal separation apparatus according to the present invention, the separation matrix that minimizes the influence of noise by making the inverse matrix of the spatial correlation matrix of the observation signal the subject of the least squares type simultaneous diagonalization problem. There is an effect that can be estimated.

  An embodiment of a blind signal separation method according to the present invention will be described with reference to the drawings.

1. As shown in FIG. 1, the signal source signals s _j (t) emitted from N signal sources 11, 12,..., 1N at time t are convolved and observed as x _i (t). The s _j (t) are non-stationary signals that are 0 on average and statistically independent of each other. Further, n _i (t) is a Gaussian white noise having an average of 0 and a variance σ ² applied to the sensor 2 i and is statistically independent of s _j (t). The observation signal x _i (t) observed by the J sensors 21, 22,..., 2J at time t is expressed by Expression (7). Here, J ≧ N ≧ 2.

ここで、＊は畳み込み演算、ｈ_ｉｊ（ｔ）は信号源１ｊからセンサ２ｉまでの信号経路のインパルス応答、Ａはインパルス応答長をそれぞれ表す。観測信号ｘ_ｉ（ｔ）を連続して３１で短時間離散フーリエ変換すると、フレームｍにおける観測信号は式（８）により表される。

Here, * represents a convolution operation, h _ij (t) represents an impulse response of a signal path from the signal source 1j to the sensor 2i, and A represents an impulse response length. When the observation signal x _i (t) is continuously subjected to short-time discrete Fourier transform at 31, the observation signal in the frame m is expressed by Expression (8).

上式（８）において、ｗｉｎ（ｔ）は窓関数、Ｋは短時間離散フーリエ変換の点数、Ｔ_ｂ５は２つの重複窓間のシフトサイズ、ω_ｋ＝２πｋ／Ｋ、ｋ＝０，１，…，Ｋ−１、をそれぞれ表す。ｈｉｊ（ｔ）のＫ点離散フーリエ変換をｈ_ｉｊ（ω_ｋ）、ｓ_ｊ（ｔ）に窓関数を乗算した後、Ｋ点短時間離散フーリエ変換で周波数領域に変換したフレームｍの信号源信号をｓ_ｊ（ω_ｋ，ｍ）、同様に、ｎ_ｉ（ｔ）に窓関数を乗算した後、Ｋ点短時間離散フーリエ変換で周波数領域に変換したフレームｍの雑音をｎ_ｉ（ω_ｋ，ｍ）とそれぞれ表記すると、点数Ｋがｈ_ｉｊ（ｔ）のインパルス応答長Ａより十分に大きいとき観測信号は式（９）により近似される。

In the above equation (8), win (t) is a window function, K is the number of short-time discrete Fourier transform points, T _b 5 is a shift size between two overlapping windows, ω _k = 2πk / K, k = 0, 1 , ..., K-1, respectively. The K-point discrete Fourier transform of _{hij (t) h ij (ω} k), s j after it has been multiplied by the window function (t), a signal source signal for frame m transformed into the frequency domain with a K-point short discrete Fourier transform S _j (ω _k , m), and similarly, n _i (t) is multiplied by a window function, and then the noise of frame m converted to the frequency domain by K-point short-time discrete Fourier transform is converted to n _i (ω _k , m), when the score K is sufficiently larger than the impulse response length A of h _ij (t), the observed signal is approximated by equation (9).

上式（９）において、Ｓ（ω_ｋ，ｍ）はフレームｍに各信号源から出力される信号ベクトルである。信号ベクトルＳ（ω_ｋ，ｍ）、混合ベクトルｈ_ｉ（ω_ｋ）はそれぞれ式（１０）、（１１）により表される。

In the above equation (9), S (ω _k , m) is a signal vector output from each signal source in the frame m. The signal vector S (ω _k , m) and the mixed vector h _i (ω _k ) are expressed by equations (10) and (11), respectively.

If the observed signal vector X (ω _k , m), the mixing matrix H (ω _k ), and the noise vector N (ω _k , m) are defined by equations (12), (13), and (14), respectively, X (ω _k , M) is represented by equation (15).

In order to separate the signals, a separation matrix W (ω _k ) satisfying Equation (16) is estimated for each frequency bin at 51, 52,..., 5K, and a permutation matrix 定 め る (60) that determines the signal source assignment at 60 ω _k ) is determined. Even if the permutation matrix Π (ω _k ) is determined independently for each frequency bin, there is no guarantee that the signal will be completely separated, and the fact that there is a correlation between adjacent or adjacent frequency bins of signals generated from the same signal source is used. Then, the permutation matrix ω (ω _k ) is determined.

上式（１６）においてＤ（ω_ｋ）は周波数ビン毎に異なる任意の対角行列である。

In the above equation (16), D (ω _k ) is an arbitrary diagonal matrix that differs for each frequency bin.

After solving the scaling problem and the permutation problem in order, the separation signal Y in the frequency bin ω _k is _obtained by multiplying X (ω _k , m) by 71, 72,..., 7K from the left with the separation matrix W (ω _k ). (Ω _k , m) is expressed by equation (17). A method for solving the scaling problem will be described later.

上式（１７）を８０で逆離散フーリエ変換と重複加算によって時間領域に変換すると分離信号ｙ_ｉ（ｔ）が求められる。雑音の分散σ^２が十分に小さいとき、ｙ_ｉ（ｔ）≒ｓ_ｉ（ｔ）になる。尚、分離信号ベクトルＹ（ω_ｋ，ｍ）は式（１８）により表される。

When the above equation (17) is converted into the time domain by inverse discrete Fourier transform and overlap addition at 80, a separated signal y _i (t) is obtained. When the noise variance σ ² is sufficiently small, y _i (t) ≈s _i (t). Note that the separated signal vector Y (ω _k , m) is expressed by Expression (18).

  The blind signal separation method according to the present invention will be described in detail with reference to FIGS. 2 to 4 show the calculation procedure of the separation matrix estimated for each frequency bin by the blind signal separation system 40 after the short-time discrete Fourier transform 31 in FIG. FIG. 4 shows a procedure for calculating a permutation matrix according to the present invention in the blind signal separation system 40 after the separation matrix is calculated.

2. Least-squares simultaneous diagonalization problem When the block length L is short and the number of sensors J is large, the inverse matrix computation and the inverse matrix computation frequency increase, and the computation amount per frame increases. Therefore, if L is short and J is large in step S101, an inverse matrix P ⁻¹ (ω _k , m) is recursively obtained using the inverse matrix lemma in equation (19) in step S102, and L is based on block processing. P ⁻¹ (ω _k , nΨL + τL) stored for each frame is normalized by equation (21) in step S105. Here, I is a unit matrix, c is a positive constant, and P ⁻¹ (ω _k , 0) = c ⁻¹ I. The value of the forgetting factor β is selected from 0 <β ≦ 1. If M blocks are the target sections of the least square simultaneous diagonalization problem, Ψ represents the overlapping shift size of two consecutive sets of target sections, and is selected from [1, M]. Further, τ = 1, 2,..., M, n represents the number of times of application of the least square simultaneous diagonalization problem, and n = 0, 1, 2,.

If L is long or J is small in step S101, the forgetting factor β is introduced, X (ω _k , m) X ^H (ω _k , m) is weighted exponentially, and the matrix P (ω _k , m) Is obtained based on the equation (20) in step S103.

ここで、上付き添字^Ｈは複素共役転置をそれぞれ表す。また、初期値をＰ（ω_ｋ，０）＝ｃＩのように設定する。ステップＳ１０４においてブロック処理に基づきＬフレーム毎にＰ（ω_ｋ，ｎΨＬ＋τＬ）の逆行列Ｐ^−１（ω_ｋ，ｎΨＬ＋τＬ）を求め、ステップＳ１０５で式（２１）によって正規化する。

Here, the superscript ^H represents a complex conjugate transpose. Further, the initial value is set as P (ω _k , 0) = cI. _{P (ω k, nΨL + τL} ) for each L frames based on block processing in step S104 inverse matrix _{^{P -1 (ω k, nΨL +}} τL) of the calculated, normalized by equation (21) in step S105.

ここで、‖・‖_Ｆはフロベニウスノルムを表す。

Here, ‖ / ‖ _F represents the Frobenius norm.

2.1 Solving Diagonalization Matrix Block processing is introduced, and the block length is L frames, and M blocks are set as the target section of the least square simultaneous diagonalization problem.

‖W _i (ω _k ) ⁽ⁿ⁾ Diagonalized matrix W (ω _k ) ⁽ⁿ⁾ , that is, the separation matrix and M pieces so that the evaluation function of Equation (22) is minimized on the condition of ‖ ₂ = 1 The diagonal matrix [Lambda] < ^-1 > ([omega] _k , n [Psi] L + [tau] L) is obtained using a least square method, a power method, and an iterative method. However, W _i (ω _k ) ⁽ⁿ⁾ represents the i-th column vector of W ^H (ω _k ) ⁽ⁿ⁾ , and ‖ · ‖ ₂ represents the Euclidean norm. Equation (22) is known as a least-squares simultaneous diagonalization problem. The superscript ⁽ⁿ⁾ represents the number of times the method of solving the least square simultaneous diagonalization problem is applied.

Solving the least squares type simultaneous diagonalization problem on condition that ‖W _i (ω _k ) ⁽ⁿ⁾ ‖ ₂ = 1 as in equation (22), the separation matrix W ^H (ω _k ) ⁽ⁿ⁾ This is equivalent to simultaneously executing the solution of the scaling problem that normalizes each column vector W _i (ω _k ) ⁽ⁿ⁾ , and there is no need to solve the scaling problem separately. The condition ‖ W _i (ω _k ) ⁽ⁿ⁾ ‖ ₂ = 1 is satisfied by the normalization of the power method used in the solution of the least square simultaneous diagonalization problem.

When vector expression is used, the evaluation function of Expression (22) can be expressed as Expression (23). Here, r- ¹ ([omega] _k , n [Psi] L + [tau] L), G ([omega] _k ) ⁽ⁿ⁾ , d ([omega] _k , ^{n [} Psi] L + [tau] L), G ([omega] _k ) ⁽ⁿ⁾ d ([omega] _k , ⁿ [Psi] L + [tau] L) are respectively expressed by the formula (24). ) To (27). Where vec {A} is obtained by stacking the columns of matrix A

g _i (omega _k) ⁽ⁿ⁾ to the evaluation function of equation (23) minimizing the condition ^{_{∈Ω G (ω k) (n}} ) and _{d (ω k, nΨL + τL} ) , the evaluation function of equation (22) Is equal to a separation matrix W (ω _k ) ⁽ⁿ⁾ and a diagonal matrix Λ ⁻¹ (ω _k , nΨL + τL). Here, g _i (ω _k ) ⁽ⁿ⁾ is the i-th column vector of G (ω _k ) ⁽ⁿ⁾ . Further, the space Ω is expressed by the equation (28). Here, C ^{J × 1} represents a J × 1 complex space.

In order to obtain the separation matrix W (ω _k ) ⁽ⁿ⁾ and the diagonal matrix Λ ⁻¹ (ω _k , nΨL + τL) by an iterative method, z _i (ω _k ) ⁽ⁿ⁾ and T (ω _k ) ⁽ⁿ⁾ are It is defined by (29) and (30).

When z _i (ω _k ) ⁽ⁿ⁾ and T (ω _k ) ⁽ⁿ⁾ are used, Expression (23) can be expressed as Expression (31).

In step S106, g _i (ω _k ) ⁽ⁿ⁾ and z _i (ω _k ) ⁽ⁿ⁾ are initialized by equations (32) and (34).

ただし、ｇ_ｊ（ω_ｋ）^（ｎ）は最小２乗型同時対角化問題の解法をｎ回適用して求められた近似解である。また、初期値ｇ_ｊ（ω_ｋ）^（０）は式（３３）で設定する。

However, g _j (ω _k ) ⁽ⁿ⁾ is an approximate solution obtained by applying the solution of the least square simultaneous diagonalization problem n times. The initial value g _j (ω _k ) ⁽⁰⁾ is set by the equation (33).

ここで、ａを任意の実数定数、１_Ｊ＝［１，１，…，１］^Ｔである。

Here, a is an arbitrary real constant, 1 _J = [1, 1,..., 1] ^T.

ただし、ｚ_ｊ（ω_ｋ）^（ｎ）は最小２乗型同時対角化問題の解法をｎ回適用して求められた近似解である。また、初期値ｚ_ｊ（ω_ｋ）^（０）は式（３５）で設定する。

However, z _j (ω _k ) ⁽ⁿ⁾ is an approximate solution obtained by applying the solution of the least square simultaneous diagonalization problem n times. Further, the initial value z _j (ω _k ) ⁽⁰⁾ is set by Expression (35).

ここで、ｂを任意の実数定数、１_Ｍ＝［１，１，…，１］^Ｔである。

Here, b is an arbitrary real number constant, 1 _M = [1, 1,..., 1] ^T.

When determining g _j (ω _k ) ⁽ⁿ⁾ , g _j (ω _k ) ⁽ⁿ⁾ (j ≠ i) is ^expressed by equation (32), and z _j (ω _k ) ⁽ⁿ⁾ is ^expressed by equation (34). As shown below, F _j (ω _k ) ⁽ⁿ⁾ is calculated as a constant.

When calculating the approximate solution g _j (ω _k ) ^{(n, φ)} that minimizes the evaluation function of Expression (37), g _j (ω _k ) ⁽ⁿ⁾ and z _i (ω _k ) that are not the target in step S107. ^(N) (i ≠ j) is fixed as a constant. Since the approximate solution g _j (ω _k ) ^{(n, φ)} is obtained by iteration, the number of iterations φ is indicated by a superscript in the iteration target g _j (ω _k ) ⁽ⁿ⁾ .

ｇ_ｊ（ω_ｋ）^{（ｎ，φ）}∈Ωを条件に式（３７）を最小化する。条件ｇ_ｊ（ω_ｋ）^{（ｎ，φ）}∈Ω

はステップＳ１０８において式（３８）により求められる。

Equation (37) is minimized on condition that g _j (ω _k ) ^{(n, φ)} ∈Ω. Condition g _j (ω _k ) ^{(n, φ)} ∈Ω

Is obtained by equation (38) in step S108.

空間Ωで最小２乗法により式（３８）の解を求めると、ｇ_ｊ（ω_ｋ）^{（ｎ，φ）}∈Ωを条件に式（３７）を最小化する解ｇ_ｊ（ω_ｋ）^{（ｎ，φ）}と一致する。

When solving equation (38) by the least square method in the space _{Ω, g j (ω k)} (n, φ) ∈Ω minimizes equation (37) to condition the solution _{g j} (omega _k) ^{(n , Φ)} .

上式（３９）においてＶ（ω_ｋ）^{（ｎ，φ）}、Ｗ_ｊ（ω_ｋ）^{（ｎ，φ）}Ｗ_ｊ ^Ｈ（ω_ｋ）^{（ｎ，φ）}はそれぞれ式（４０）、（４１）により表される。

In the above equation (39), V (ω _k ) ^{(n, φ)} , W _j (ω _k ) ^{(n, φ)} W _j ^H (ω _k ) ^{(n, φ)} are the equations (40) and (41), respectively. It is represented by

ここで、ｍａｔ｛Ａ｝は、Ｊ^２×１の列ベクトルＡをＪ×Ｊの行列に変換することを表す。

Here, mat {A} represents that the J ² × 1 column vector A is converted into a J × J matrix.

Ｗ_ｊ（ω_ｋ）^{（ｎ，φ）}Ｗ_ｊ ^Ｈ（ω_ｋ）^{（ｎ，φ）}の列ベクトルによって張られる空間の次元はｄｉｍ（Ｗ_ｊ（ω_ｋ）^{（ｎ，φ）}Ｗ_ｊ ^Ｈ（ω_ｋ）^{（ｎ，φ）}）＝１であるので、ステップＳ１０９において、累乗法によって求めたＶ_ｊ（ω_ｋ）^{（ｎ，φ）}の第１固有ベクトルはＷ_ｊ（ω_ｋ）^{（ｎ，φ）}に一致する。

The dimension of the space spanned by the column vector of W _j (ω _k ) ^{(n, φ)} W _j ^H (ω _k ) ^{(n, φ)} is dim (W _j (ω _k ) ^{(n, φ)} W _j ^H ( Since ω _k ) ^{(n, φ)} ) = 1, the first eigenvector of V _j (ω _k ) ^{(n, φ)} obtained by the power method is W _j (ω _k ) ^{(n, φ} ) in step S109. ⁾ .

If the initial value of the power method is expressed as u ⁽⁰⁾ , the power of the equations (42) to (44) is repeated from l = 1 until the error limit ε _P satisfies the equation (44), and the approximate solution W _j (ω _k ) ^{(n, φ)} = u ⁽¹⁾ is obtained.

まれる正規化によって分離行列の各列ベクトルを正規化するスケーリング問題を解いていることになる。

This means that the scaling problem that normalizes each column vector of the separation matrix is solved.

In step S110, j is changed in the order of j = 1, 2,..., N, and the calculation of the first eigenvector of V _j (ω _k ) ^{(n, φ)} by the formulas (36) and (38) and the power method is repeated.

In order to obtain an approximate solution with an error limit ε _G in step S111, j is changed in the order of j = 1, 2,..., N until Expression (45) is satisfied, and Expressions (36) and (38) are satisfied. The calculation of the first eigenvector of V _j (ω _k ) ⁽ⁿ⁾ by the power method is repeated.

2.2 Diagonal matrix solution The diagonal matrix is obtained by minimizing the equation (46).

  When Expressions (24), (26), and (27) are used, Expression (46) is expressed as Expression (47) by vector expression.

  The least square method is applied to the evaluation function of equation (47), and a solution is obtained by equation (48) in step S112.

ここで、Ｇ^＋（ω_ｋ）^（ｎ）は行列Ｇ（ω_ｋ）^（ｎ）の擬似逆行列である。

Here, G ⁺ (ω _k ) ⁽ⁿ⁾ is a pseudo inverse matrix of the matrix G (ω _k ) ⁽ⁿ⁾ .

In step S113, in order to obtain an approximate solution in which the error limit is ε _J , g _j by the first eigenvector of equations (36), (38), V _j (ω _k ) ⁽ⁿ⁾ until equation (49) is satisfied. The calculation of (ω _k ) ^{(n) and} the calculation of d (ω _k , nΨL + τL) according to the equation (48) are repeated. However, | · | represents an absolute value.

3. Solution of Permutation Problem In order to evaluate the signal separation accuracy in the frequency bin ω _k , Λ ⁻ using the inverse λ _j ⁻¹ (ω _k , nΨL + τL) of the periodogram λ _j (ω _k , nΨL + τL) of the separated signal ¹ (ω _k , nΨL + τL) is constructed in step S114 according to equation (50). However, diag (•) represents a diagonal matrix.

Since the frequency component of the separated signal is different for each frequency bin, in order to reduce this influence, Λ ⁻¹ (ω _k , nΨL + τL) is normalized by Equation (51) in step S115. γ _j ⁻¹ (ω _k , nΨL + τL) is a diagonal element of j rows and j columns of Γ ⁻¹ (ω _k , nΨL + τL).

In order to evaluate the signal separation accuracy based on the correlation between the frequency bins, E (ω _k ) ⁽ⁿ⁾ is calculated in step S116 according to the equation (52).

In step S117, the signal separation accuracy μ (ω _k ) ⁽ⁿ⁾ in the frequency bin ω _k is calculated by the equation (53).

ここで、Ｔｒ（・）は行列のトレースを表す。また、Ｑは行列の各行に１となる要素が１箇所、その他の要素は０で、１となる要素の位置が他の行と重複しない行列の集合である。

Here, Tr (•) represents a matrix trace. Q is a set of matrices in which one element is 1 in each row of the matrix, the other elements are 0, and the position of the element that is 1 does not overlap with other rows.

In step S118, the signal separation accuracy μ (ω _k ) ⁽ⁿ⁾ is obtained for all frequency bins using the equation (53), and the lower x% of the signal separation accuracy is detected.

  In step S119, the frequency bin corresponding to the lower x% is thinned out, and the corresponding frequency bin is shortened.

In the thinned-out state, the signal source allocation result E _η (ω _{η ± | φ |} ) ⁽ⁿ⁾ already determined in the adjacent frequency bin is obtained by the equation (54) in step S120. Note that the permutation matrix in the reference frequency bin ω _η is set to Π (ω _η ) ⁽ⁿ⁾ = I.

The permutation matrix に お け^る (ω _{η ± | φ + 1 |} ) ⁽ⁿ⁾ in the adjacent frequency bin ω _{η ± | φ + 1 |} is determined in step S121 by equation (55).

In step S122, Expressions (54) and (55) are repeated for all other frequency bins except for the lower x% frequency bins to obtain Π ( _{ωη ± | φ + 1 |} ) ⁽ⁿ⁾ .

  The permutation matrix of the frequency bin corresponding to the lower x% of the signal separation accuracy is copied in step S123.

In step S124, the observation signal X (ω _k , m) is multiplied from the left by the separation matrix W (ω _k ) ⁽ⁿ⁾ as shown in the equation (56), and then the permutation matrix Π (ω _k ) ⁽ⁿ⁾ Is obtained from the left to obtain a separated signal Y (ω _k , m).

4.1 Evaluation Data As shown in FIG. 5, three signal sources (speakers) 11, 12, 13 are reverberated on the circumference of three sensors (microphones) 21, 22, 23 and a circle having a radius of 1.5 m. Placed in a meeting room with time. 5 is a plan view showing the positional relationship between the three signal sources (speakers) 11, 12, and 13 and the three sensors (microphones) 21, 22, and 23. FIG. The transfer function h _ij (t) between the signal source 1j and the sensor 2i was measured by setting the reverberation time to 100 ms and receiving the TSP signal emitted from the signal source (speaker) with the sensor (microphone). As voice data, three different men were selected from three men and two women, and two sets of mixed data for 3 minutes were created. The experimental conditions are that the number of signal sources (speakers) and sensors (microphones) is J = N = 3, sampling frequency 8 kHz, quantization bit number 16 bits, short-time discrete Fourier transform score K = 2048, shift size T _b = 30, window function is Hanning window. Forgetting factor β = 0.99, block length L = 32 frames, Ψ = 1 block, and M = 1500 block are the targets of the least-squares simultaneous diagonalization problem. In the blind signal separation method according to the present invention, initial values a = b = 1, ε _G = 10 ⁻⁵ , ε _J = 10 ⁻⁵ , and ε _P = 10 ⁻¹⁵ are used. In the solution of the permutation problem, the reference frequency bin is set to f _η = 1.5 kHz. Further, frequency bins corresponding to the lower 20% or lower 50% of the signal separation accuracy are thinned out. The SNR was varied in the range of 10 to 30 dB at 10 dB intervals. Here, the SNRs of the sensors 21, 22, and 23 were calculated by the equation (57), respectively. Here, E [•] represents an expected value.

4.2 Evaluation index The signal separation performance of the blind signal separation method was evaluated by the following method. After calculating the ratio of the power of the desired signal source signal and the interference signal in the observation signal by Expression (58) and the ratio of the power of the desired signal source signal and the interference signal in the output signal by Expression (59), respectively, Thus, the signal separation performance of each output of the blind signal separation device is obtained by the difference between SIR _yi and SIR _xi . The average of each output according to Equation (61) was defined as the signal separation performance. C of c _ij ^{(t) (n)} is the formula (62) (ω _k) the elements of the ^{_{(n), w ij (t}} ) (n) is W ^{(ω _k) (n)} elements inverse discrete Fourier each It is converted.

4.3 Evaluation object The forward model type blind signal separation method (Non-patent Document 3) using the method of solving the least-squares simultaneous diagonalization problem is a comparison object. Incidentally, the non-Patent Document _{3 N S = 32, M =} 1500 epoch targeted minimum squares joint diagonalization problem.

4.4 Evaluation Results As is apparent from the signal separation performance of FIG. 6, the blind signal separation method according to the present invention was able to obtain a higher SIR than the conventional forward model type blind signal separation method. This factor introduces a forgetting factor β to reflect the statistical properties of the signal and minimizes the effects of noise by applying a least-squares simultaneous diagonalization problem to the inverse of the spatial correlation matrix, This is because the separation matrix can be estimated with high accuracy and the correct answer rate of the permutation problem is high.

5.1 Evaluation Data Two signal sources (speakers) 12 and 14 and two sensors (microphones) 21 and 22 were arranged in a reverberant conference room as shown in FIG. FIG. 5 is a plan view showing the positional relationship between the two signal sources (speakers) 12 and 14 and the two sensors (microphones) 21 and 22. The two signal sources (speakers) 12 and 14 are arranged on a straight line. Three minutes of speech by two men was used as speech data. The experimental conditions are that the number of signal sources (speakers) and sensors (microphones) is J = N = 2, sampling frequency 8 kHz, quantization bit number 16 bits, short-time discrete Fourier transform score K = 4096, shift size T _b = 60, window function is Hanning window. Forgetting factor β = 0.99, block length L = 40 frames, Ψ = 1 block, and M = 500 blocks are the targets of the least-squares simultaneous diagonalization problem. In the blind signal separation method according to the present invention, initial values a = b = 1, ε _G = 10 ⁻⁴ , ε _J = 10 ⁻⁴ , and ε _P = 10 ⁻¹⁵ are used. The transfer function h _ij (t) between the signal source 1j and the sensor 2i was measured by setting the reverberation time to 300 ms and receiving the TSP signal emitted from the signal source (speaker) by the sensor (microphone). In the solution of the permutation problem, the reference frequency bin is set to f _η = 1.5 kHz. Further, frequency bins corresponding to the lower 17.4% of the signal separation accuracy are thinned out.

5.2 Evaluation Index Optimum permutation matrix Π _opt (ω _k ) ^{(n) is} _obtained by Expression (63), and permutation matrix Π (ω _k ) ⁽ⁿ⁾ is obtained by the blind signal separation method according to the present invention. The error ‖Π _opt (ω _k ) ⁽ⁿ⁾ −Π (ω _k ) ⁽ⁿ⁾ _{Ｆ F} is calculated. When the error is zero, the permutation problem is correctly solved by the blind signal separation method according to the present invention. When the error is not zero, the correct permutation matrix is not obtained.

5.3 Evaluation Target The solution to the permutation problem (Non-patent Document 3) using the fact that there is a correlation between adjacent frequency bins of signals generated from the same signal source is the comparison target.

5.4 Evaluation results error ^{_{‖Π opt (ω k) (n}} ) -Π (ω k) (n) || _F white frequency bins becomes zero, and draw a frequency bins that do not become zero in black FIGS. 7 and 8 Get the top graph. Gray is an area where white and black appear alternately. 7 and 8, the vertical axis represents the frequency, and the horizontal axis represents the number of applications n of the method of solving the least square simultaneous diagonalization problem. As the area of white in the figure increases, the percentage of correct answers to permutation questions increases. When the permutation problem is adaptively solved by the blind signal separation method according to the present invention, the white area increases as the number of applications increases. From the lower graph of FIG. 7, it can be seen that the error rate decreases with the increase in the number n of application of the method of solving the least square simultaneous diagonalization problem, and thus the correct answer rate of the permutation problem increases. On the other hand, in the conventional solution of the permutation problem, even if the number of applications is increased from the upper graph in FIG. 8, the white area does not increase or decrease, and there are many gray areas, and the blind signal separation according to the present invention is performed. It is unstable compared to the method. Moreover, the error rate is about 50% from the lower graph of FIG. Since this is not different from the result of randomly assigning a permutation matrix, it can be seen that the correct answer rate of the permutation problem does not improve as compared with the blind signal separation method according to the present invention.

6.1 Evaluation Data Two signal sources (speakers) 12 and 14 and two sensors (microphones) 21 and 22 were arranged in a reverberant conference room as shown in FIG. FIG. 5 is a plan view showing the positional relationship between the two signal sources (speakers) 12 and 14 and the two sensors (microphones) 21 and 22. A 3-minute voice by one man was used as voice data, and a 3-minute classical music was used as music data. The experimental conditions are that the number of signal sources (speakers) and sensors (microphones) is J = N = 2, sampling frequency 8 kHz, quantization bit number 16 bits, short-time discrete Fourier transform score K = 4096, shift size T _b = 40, window function is Hanning window. Forgetting factor β = 0.99, block length L = 40 frames, Ψ = 1 block, and M = 900 blocks are the targets of the least-squares simultaneous diagonalization problem. In the blind signal separation method according to the present invention, initial values a = b = 1, ε _G = 10 ⁻⁴ , ε _J = 10 ⁻⁴ , and ε _P = 10 ⁻¹⁵ are used. The transfer function h _ij (t) between the signal source 1j and the sensor 2i was measured by setting the reverberation time to 300 ms and receiving the TSP signal emitted from the signal source (speaker) by the sensor (microphone). In the solution of the permutation problem, the reference frequency bin is set to f _η = 1.5 kHz. Further, frequency bins corresponding to the lower 20% of the signal separation accuracy are thinned out.

6.2 Evaluation index Signal source signals s ₁ (t) and s ₂ (t) in the range of 5 to 9 seconds, observation signals x ₁ (t) and x ₂ (t), in the blind signal separation method according to the present invention Signals y ₁ (t) and y ₂ (t) obtained by separating observed signals x ₁ (t) and x ₂ (t) are displayed as spectrograms, respectively. As for the signal source signals s ₁ (t) and s ₂ (t) and the separated signals y ₁ (t) and y ₂ (t), the sound generation contents and signal waveforms are also shown.

6.3 Evaluation Results The upper part of FIG. 9 shows the signal source signal, the middle part shows the observed signal, and the lower part shows the spectrogram of the separated signal. The spectrograms y ₁ (ω _k , m) and y ₂ (ω _k , m) of the separated signal by the blind signal separation method according to the present invention are respectively the spectrogram s ₁ (ω _k , m) of the delayed signal source signal and It is similar to s ₂ (ω _k , m), and it can be confirmed that the signal is separated.

  It is a figure which shows embodiment of the blind signal separation method which concerns on this invention.   5 is a flowchart for explaining a method of solving a diagonalization matrix of a least square simultaneous diagonalization problem in the blind signal separation method according to the present invention.   6 is a flowchart for explaining a method of solving a diagonal matrix of the least square simultaneous diagonalization problem in the blind signal separation method according to the present invention.   6 is a flowchart for explaining a method of solving a permutation matrix of the blind signal separation method according to the present invention.   It is a top view showing the positional relationship of the signal source (speaker) and sensor (microphone) in Examples 1-3 of the signal separation method which concerns on this invention.   It is a figure which shows the signal separation performance in Example 1 of the signal separation method which concerns on this invention.   It is a figure which shows the solution result and error rate of the permutation problem in Example 2 of the signal separation method which concerns on this invention.   It is a figure which shows the solution result and error rate of the conventional permutation problem in Example 2.   It is a figure which shows the pronunciation content, signal waveform, and spectrogram in Example 3 of the signal separation method based on this invention.

11 to 1N ... signal source, 21 to 2J ... sensor, 31 ... short-time discrete Fourier transform, 40 ... blind signal separation system, 51, 52, ..., 5K ... solution of least squares simultaneous diagonalization problem, 60 ... Solution of permutation problem, 71, 72,..., 7K ... convolution operation, 80 ... inverse discrete Fourier transform and overlap addition

Claims (8)

A method of blindly estimating unknown signal source signals that are statistically independent from each other mixed by an unknown convolutional mixing system from an observation signal only, and after multiplying the observation signal by a window function, this is a short time of K points The observation signal vector obtained by applying the discrete Fourier transform is weighted exponentially with a forgetting factor for each frequency bin, and the inverse matrix of the spatial correlation matrix of the observation signal is calculated for each block based on block processing from the weighted vector. After obtaining and normalizing this, one block or a plurality of blocks are subjected to the least squares type simultaneous diagonalization problem of the frequency bin, and a solution by a combination of the least square method, the power method, and the iterative method is used. Find a solution to the least-squares type diagonalization problem and solve the permutation problem by using the correlation between adjacent frequency bins of signals generated from the same signal source. Blind signal separation method characterized by obtaining high separation matrix of the signal separation accuracy by solving adaptively based on No. separation accuracy. The blind signal separation method using the least square simultaneous diagonalization problem solving method according to claim 1 , wherein a scaling problem for normalizing each column vector of the separation matrix by normalization included in the power method is substituted. A blind signal separation method characterized in that it is possible. A blind signal separation method using the least squares simultaneous diagonalization problem solving method according to any one of claims 1 to 2 , wherein the inverse for each block is applied in an application with a short block length and a large number of sensors. When the amount of calculation of the matrix is large, it is characterized by using the inverse matrix lemma instead of calculating the spatial correlation matrix of the observation signal exponentially weighted for each frequency bin and calculating the inverse matrix for each block. Blind signal separation method. The blind signal separation method using the method of solving the least square simultaneous diagonalization problem according to any one of claims 1 to 3 , wherein the minimum block length is L and M blocks are target sections. After applying the solution of the square-type simultaneous diagonalization problem n times to estimate the separation matrix, the frequency bin ω _k (k = 0, 1,..., K−) based on the correlation of each separation signal in the same frequency bin. The signal separation accuracy μ (ω _k ) ⁽ⁿ⁾ in the frequency bin is _obtained by Expression (1) using normalization by the square root of the square sum of the reciprocal of the periodogram of the N separated signals in 1). A blind signal separation method. Tr (·) represents a matrix trace. Q is a set of matrices in which one element is 1 in each row of the matrix, the other elements are 0, and the position of the element that is 1 does not overlap with other rows. Matrix E (omega _k) ⁽ⁿ⁾ and the matrix _{^{Γ -1 (ω k, nΨL +}} τL) , respectively formula (5), given by (6), tau = 1, 2, ..., in M Γ ^-1 (ω _k , NΨL + τL) is a matrix _obtained by normalizing a diagonal matrix Λ ⁻¹ (ω _k , nΨL + τL) whose diagonal element is the inverse of the periodogram λ _j (ω _k , nΨL + τL) of the separated signal, and the diagonal element γ _j ⁻¹ (ω _k , nΨL + τL). Since M blocks are target sections of the least square simultaneous diagonalization problem, Ψ is an overlapping shift size of two consecutive sets of target sections.

The blind signal separation method using a solution of least-squares joint diagonalization problem according to any one of claims 1 to 4, detects a significantly low frequency bins signal separation accuracy, the corresponding frequency A blind signal separation method characterized by adaptively solving the permutation problem by thinning out the bins and then filling these frequency bins. 6. The blind signal separation method using the method of solving the least square simultaneous diagonalization problem according to any one of claims 1 to 5 , wherein the same signal is packed with frequency bins with extremely low signal separation accuracy. A blind signal separation method, wherein a permutation problem is adaptively solved by using a correlation between adjacent frequency bins of a signal generated from a source. The blind signal separation method using the method of solving the least square simultaneous diagonalization problem according to any one of claims 1 to 6 , wherein a permutation corresponding to a frequency bin with extremely low signal separation accuracy is used. A blind signal separation method characterized by copying permutations of adjacent frequency bins. A blind signal separation device using a blind signal separation method, wherein the blind signal separation method is configured to perform signal source separation using the blind signal separation method according to any one of claims 1 to 7 .

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