Method and apparatus for blind source separation using two sensors

[0001] This application claims the priority of Korean Patent Application No. 2003-20059, filed on Mar. 31, 2003, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein in its entirety by reference.

[0002] 1. Field of the Invention

[0003] The present invention relates to blind source separation, and more particularly, to a method of and apparatus for separating mixture signals received through two microphones into N source signals while eliminating noise from the received signals in real time.

[0004] 2. Description of the Related Art

[0005] Recently, mobile robots have become of particular interest in areas such as health, security, home networking, and entertainment. To operate a mobile robot, human-robot interaction is required. That is, the mobile robot must be able to assess its surroundings using a vision system, detect the presence of humans and possible obstacles, and understand commands given by an operator.

[0006] As such, the mobile robot indispensably requires a sound input system for human-robot interaction and autonomous traveling. Important issues affecting the performance of the sound input system of the mobile robot are factors such as noises, reverberations, and distances to an operator in an indoor environment. In an indoor environment, reverberations exist due to various noise sources, walls, or other objects. Low frequency components of a sound are attenuated more than high frequency components of the sound. The sound input system required for human-robot interaction in an indoor environment must be constructed so that the autonomous traveling mobile robot can receive the operator's voice command from a distance of several meters away and use the received voice command directly for sound recognition including speech recognition.

[0007] Generally, the sound input system uses a microphone array consisting of at least two microphones in order to improve the quality of sound and a sound recognition rate including a speech recognition rate. Also, the sound input system eliminates noise components included in sound signals received from the microphone array, using methods such as a single channel speech enhancement method, an adaptive acoustic noise canceling method, a generalized sidelobe canceling method, or a blind signal separation algorithm.

[0008] The single channel speech enhancement method uses one microphone and can be applied only to a case where a statistical property of noise is not time dependent, for example, stationary background noise. An acoustic noise elimination technique disclosed in the paper “Adaptive Noise Canceling: Principles and Applications,” by B. Widrow et al., Proceedings of IEEE, vol. 63, no.12, pp. 1692-1716, 1975, uses two microphones. One of the two microphones is a reference microphone to receive only specified noise. However, when the reference microphone receives other noise rather than only the predetermine noise, the noise elimination performance is greatly deteriorated. A generalized sidelobe canceling method disclosed in the paper “A Robust Adaptive Beamformer For Microphone Arrays With A Blocking Matrix Using Constrained Adaptive Filters,” by O. Hoshuyama et al., in IEEE Trans. Signal Processing, vol. 47, no. 10, pp. 2677-2684, 1999, is disadvantageous in that a voice activity detector is required and source signals as well as noise signals are eliminated.

[0009] Meanwhile, conventional techniques related to the Degenerate Unmixing Estimation Technique (DUET) as a type of blind signal separation algorithm include “Blind Separation of Disjoint Orthogonal Signals: Demixing n Sources from 2 Mixtures,” by A. Jourjine, S. Rickard, and O. Yilmaz, in Proc. Int. Conf. on Acoust., Speech, Signal Processing, 2000. vol 5, pp. 2985-2988, “Real-time Time-Frequency based Blind Source Separation,” by S. Rickard, R. Balan, and J. Rosca, in Proc. Int. Conf. on Independent Component Analysis and Blind Signal Separation, 2001, pp. 651-656, and “On the Approximate w-Disjoint Orthogonality of Speech,” by S. Richard and O. Yilmaz, in Proc. ICASSP 2002, pp. 529-532. Such conventional techniques have been developed on the basis of the w-disjoint orthogonality by which the frequency components of two sound signals s₁(t) and s₂(t) do not overlapped with each other, that is, at most one sound signal component occupies one frequency band. However, when noise is mixed with a mixture signal and the w-disjoint orthogonality is not satisfied, that is, when white Gaussian noise with spectra over an entire frequency band or fan noise generated by a fan motor with spectra over a relatively wide frequency band is mixed with the mixture signal (sound signal), a signal separation performance is greatly deteriorated.

[0010] The present invention provides a method of separating mixture signals received through two microphones into N source signals while eliminating noise from the received signals in real time.

[0011] The present invention also provides an apparatus for implementing the method.

[0012] According to an aspect of the present invention, there is provided a method of separating first and second mixture signals received through two sensors into source signals, including: (a) calculating a global signal absence probability for each frame of the mixture signal and a local signal absence probability for each frequency band of a frame for at least one of the first and second mixture signals; (b) estimating a spectrum vector for each frequency band in which a noise signal is eliminated using the global signal absence probability calculated in the calculating; (c) determining a plurality of frequency bands including at least one of a noise signal and a source signal using the local signal absence probability, and generating a source label vector which consists of a plurality of frequency bands assigned to each source, using an attenuation parameter and a delay parameter generated for each of the determined frequency bands; and (d) multiplying the spectrum vector estimated for each frequency band obtained in the estimating by the source label vector obtained in the determining, and obtaining signals separated according to the source signals.

[0013] According to another aspect of the present invention, there is provided an apparatus for separating first and second mixture signals received through two sensors into source signals, includng: a signal absence probability calculator, which calculates a global signal absence probability for each frame of the mixture signals and a local signal absence probability for each frequency band of a frame for at least one of the first and second mixture signals; a signal estimation unit, which estimates a spectrum vector in which a noise signal is eliminated for each frequency band using the global signal absence probability calculated by the signal absence probability calculator; a source signal identification unit, which determines a plurality of frequency bands including at least one of a noise signal and a source signal using the local signal absence probability calculated by the signal absence probability calculator, and generates a source label vector which consists of a plurality of frequency bands assigned to each source signal, using an attenuation parameter and a delay parameter generated for each of the determined frequency bands; and a signal separator, which multiplies the spectrum vector estimated for each frequency band generated by the signal estimation unit by the source label vector obtained for each source signal by the source identification unit, and obtains signals separated according to the source signal.

[0014] According to still another aspect of the present invention, there is provided a method of separating first and second mixture signals received through two sensors into source signals, including: (a) calculating a global signal absence probability for each frame of the mixture signals and a local signal absence probability for each frequency band of the frame for at least one of the first and second mixture signals; (b) estimating a spectrum vector in which a noise signal is eliminated for each frequency band using the global signal absence probability calculated in the calculating, and generating first and second mixture signals without noise signals; (c) performing clustering using the first and second mixture signals without noise, and generating a source label vector consisting of a source and a frequency band assigned to each source; and (d) multiplying the source label vector obtained by the source identifying by the spectrum vector obtained by the estimating for each frequency band of the frame, and performing an inverse Fourier transform to separate the received signals into source signals of time domain.

[0015] According to yet another aspect of the present invention, there is provided a method of separating first and second mixture signals received through two microphones into source signals while eliminating noise from the received mixture signals, including: (a) calculating a global signal absence probability for each frame of the mixture signals and a local signal absence probability for each frequency band of a frame for at least one of the first and second mixture signals; (b) estimating a spectrum vector in which a noise signal is eliminated for each frequency band using the global signal absence probability calculated in the calculating; (c) determining a plurality of frequency bands including at least one of a noise signal and a source signal using the local signal absence probability, and generating a source label vector which consists of a plurality of frequency bands assigned to each source, using an attenuation parameter and a delay parameter generated for each of the determined frequency bands; and (d) multiplying the spectrum vector estimated for each frequency band obtained in the estimating by the source label vector obtained in the determining, and obtaining signals separated according to the source signals.

[0026] Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout. The embodiments are described below in order to explain the present invention by referring to the figures.

[0027] Prior to describing a signal separation method and apparatus according to embodiments of the present invention, principles employed in the present invention will be described.

[0028] In an environment characterized by small reverberations, the relationship between source signals s_j(t) and microphone observations x_i(t) (here, i=1, 2) can be expressed by equations 1 and 2.

[0029] $\begin{array}{cc}{x}_1\left(t\right)=\sum _{j=1}^N{s}_j\left(t\right)+n_1\left(t\right)& \left(1\right)\\ x_2\left(t\right)=\sum _{j=1}^N{a}_j{s}_j\left(t-d_j\right)+n_2\left(t\right)& \left(2\right)\end{array}$

[0030] Referring to equations 1 and 2, n₁(t) is a noise component which is added to a first microphone observation x₁(t) from a background source, n₂(t) is a noise component which is added to a second microphone observation x₂(t) due to another propagating channel, a_j is a relative attenuation parameter, and d_j is a relative delay parameter between microphones due to the arrival direction.

[0031] Such time-domain signals x₁(t) and x₂(t) are subjected to a Fourier transform, for example, a Short-Time Fourier Transform to be transformed into frequency-domain signals. In the frequency domain, assuming that the first microphone observation X(m) is a sum of a source signal S(m) and added noise N(m), a statistical model employing global hypothesis, H₀ and H₁, which indicate source signal absence and presence at an m-th frame, respectively, is expressed by the following equation 3.
H₀:X(m)=N(m)
H₁:X(m)=S(m)+N(m)  (3)

[0032] The source signal S(m) in H₁ is a sum of all the individual source signals and is expressed by equation 4.

[0033] $\begin{array}{cc}S\left(m\right)=\sum _{j=1}^N{S}_j\left(m\right)& \left(4\right)\end{array}$

[0034] Moreover, since source signal absence and presence arise in each frequency bin, a statistical model employing local hypothesis H_{0, k} and H_{1, k} for each frequency bin, which indicate source signal absence and presence at k-th frequency bin of the m-th frame, respectively, is expressed by the following equation 5.
H_0,k:X_k(m)=N_k(m)
H_1,k:X_k(m)=S_k(m)+N_k(m)  (5)

[0035] The source signal S_k(m) in H_1,k is a sum of all the individual source signal components and is expressed by equation 6.

[0036] $\begin{array}{cc}{S}_k\left(m\right)=\sum _{j=1}^N{S}_k^{\left(j\right)}\left(m\right)& \left(6\right)\end{array}$

[0037] Here, S_k^(j)(m) represents the j-th source signal component at the k-th frequency bin, that is, the k-th frequency band of the m-th frame. Assuming that the w-disjoint orthogonality is satisfied, at most one source of N sources will dominantly occupy one frequency bin. Therefore, S_k(m)=S_k^(j)(m) for an arbitrary j. The w-disjoint orthogonality is disclosed in detail in the paper “On the Approximate w-Disjoint Orthogonality of Speech,” by S. Rickard and O. Yilmaz, in Proc. Int. Conf. on Acoust., Speech, Signal Processing, 2002, vol.1, pp. 529-532, the disclosure of which is incorporated by reference. Also, it is assumed that X_k(m) and N_k(m) have zero-mean complex Gaussian densities.

[0038] On the basis of the above-described principles, embodiments of the present invention will be described.

[0039] FIG. 1 is a block diagram of a signal separation apparatus according to a first embodiment of the present invention. The signal separation apparatus comprises a signal absence probability calculator 11, a source identification unit 13, a signal estimation unit 15, and a source signal separator 17. The signal separation apparatus separates N independent sources from M microphone observations, where M≦N. Hereinafter, for convenience of description, an exemplary case when M=2 will be described.

[0040] Referring to FIG. 1, the signal absence probability calculator 11 calculates a global signal absence probability p(H₀|X(m)) and a local signal absence probability p(H_0,k|Xk(m)) for each of the frequency bins of an m-th frame, for one of the first and second microphone observations which are received through two sensors, for example, two microphones, and are transformed into frequency-domain signals. Referring to FIG. 2, this calculation is described in more detail as follows.

[0041] Λ k(m) (where k=1, . . . , L/2) represents the likelihood ratio computed for a k-th frequency bin of the m-th frame is calculated using equation 7. L represents the number of points in Fourier transform.

[0042] ${\Lambda }_k\left(m\right)=\frac{p\left(X_k\left(m\right)|H_{1,k}\right)}{p\left(X_k\left(m\right)|H_{0,k}\right)}$
where,

[0043] $\begin{array}{cc}\begin{array}{c}p\left(X_k\left(m\right)|H_{1,k}\right)=\frac{1}{\pi \left({\sigma }_{S_k}^2\left(m\right)+{\sigma }_{N_k}^2\left(m\right)\right)}\exp \left[-\frac{{X_k\left(m\right)}^2}{\left({\sigma }_{S_k}^2\left(m\right)+{\sigma }_{N_k}^2\left(m\right)\right)}\right]\\ p\left(X_k\left(m\right)|H_{0,k}\right)=\frac{1}{\pi {\sigma }_{N_k}^2\left(m\right)}\exp \left[-\frac{{X_k\left(m\right)}^2}{{\sigma }_{N_k}^2\left(m\right)}\right]\end{array}& \left(7\right)\end{array}$

[0044] Here, p(X_k(m)|H_1,k) is a probability value of the k-th frequency bin of the m-th frame according to local signal presence hypothesis H_1,k, and p(X_k(m)|H_0,k) is a probability value of the k-th frequency bin of the m-th frame according to local signal absence hypothesis H_0,k, wherein p(X_k(m)|H_1,k) and p(X_k(m)|H_0,k) can be calculated using a source signal power σ_Sk² and a noise signal power σ_N², respectively.

[0045] Next, the likelihood ratios are multiplied by a specified a priori probability q_k expressed by equation 8, respectively.

[0046] $\begin{array}{cc}{q}_k=\frac{p\left(H_{1,k}\right)}{p\left(H_{0,k}\right)}& \left(8\right)\end{array}$

[0047] Here, p(H1,k) is a probability that noise and source signals will coexist at the k-th frequency bin and p(H0,k) is a probability that only noise will exist at the k-th frequency bin.

[0048] Next, a specified value, for example, ‘1’, is respectively added to the multiplied results.

[0049] Then, local signal absence probabilities p(Ho,k|Xk(m)) for the L/2 frequency bins of the m-th frame are calculated as the reciprocals of the added results calculated, as in equation 9.

[0050] $\begin{array}{cc}p\left(H_{0,k}|X_k\left(m\right)\right)=\frac{1}{1+q_k{\Lambda }_k\left(m\right)}& \left(9\right)\end{array}$

[0051] Next, by multiplying all the individual values of the L/2 local signal absence probabilities p(H_0,k|X_k(m)) using equation 10, a global signal absence probability p(H₀|X(m)) at the m-th frame is calculated.

[0052] $\begin{array}{cc}\begin{array}{c}p\left(H_0|X\left(m\right)\right)=\frac{p\left(H_0,X\left(m\right)\right)}{p\left(X\left(m\right)\right)}\\ =\frac{1}{\prod _{k=1}^M\left[1+q_k{\Lambda }_k\left(m\right)\right]}\end{array}& \left(10\right)\end{array}$

[0053] The above equation 10 can be derived using the following equations 11 and 12.

[0054] $\begin{array}{cc}p\left(H_0|X\left(m\right)\right)=\prod _{k=1}^M\left[p\left(X_k\left(m\right)|H_{0,k}\right)p\left(H_{0,k}\right)\right]& \left(11\right)\\ p\left(X\left(m\right)\right)=\prod _{k=1}^{M}p\left(X_k\left(m\right)\right)& \left(12\right)\\ =\prod _{k=1}^M[p\left(X_k\left(m\right)|H_{0,k}\right)p\left(H_{0,k}\right)+& \\ p\left(X_k\left(m\right)|H_{1,k}\right)p\left(H_{1,k}\right)]& \end{array}$

[0055] Here, since short-time Fourier transform coefficients are not correlated, it is assumed that the spectral component in each of frequency bins, that is, X_k(m), is statistically independent.

[0056] Returning to FIG. 1, the source identification unit 13 receives the local signal absence probabilities for respective frames of the first or second microphone observations, which are calculated by the signal absence probability calculator 11, compares the local signal absence probabilities with a predefined first threshold value, and determines whether a source signal exists at a corresponding frequency bin of each frame, that is, a corresponding frequency band, according to the compared result. Thereafter, the source identification unit 13 generates attenuation and delay parameters for the signal value of the frequency band at which it is determined that a source signal exists. The source identification unit 13 recognizes the number of sources and identifies respective frequency bands assigned to respective sources through mixing parameters consisting of the attenuation and delay parameters. The source identification unit 13 performs the above-described source identification process for each frame. Referring to FIG. 3, this operation will be described in more detail as follows.

[0057] Referring to FIG. 3, the local signal absence probability of the m-th frame is compared with the first threshold value and a frequency band in which a source signal exists is identified. That is, assuming that a source satisfies the w-disjoint orthogonality, only one source signal component among N sources exists at the k-th frequency band. Accordingly, by comparing the local signal absence probability calculated by equation 9 with the first threshold value, it can be determined which frequency band includes the source signal. For example, if the local signal absence probability exceeds the first threshold value, it is determined that no source signal exists at the corresponding frequency band. If the local signal absence probability does not exceed the first threshold value, it is determined that a source signal exists at the corresponding frequency band. The frequency band in which the source signal exists satisfies the following equation 13 for an arbitrary source j.

[0058] $\begin{array}{cc}\left[\begin{array}{c}{X}_{1,k}\left(m\right)\\ X_{2,k}\left(m\right)\end{array}\right]\approx \left[\begin{array}{c}1\\ a_j{e}^{-iw{d}_j}\end{array}\right]S_k^{\left(j\right)}\left(m\right)& \left(13\right)\end{array}$

[0059] Here, ω=2πk/L and L is the number of Fourier transform points.

[0060] Next, the attenuation and delay parameters at each of the frequency bands including the source signals can be computed by analyzing a ratio of X_1,k(m), and X_2,k(m). A mixing parameter μ^(k) consisting of the attenuation and delay parameters can be expressed by equation 14.

[0061] $\begin{array}{cc}\begin{array}{c}{\mu }^{\left(k\right)}=\left(a\left(k,m\right),d\left(k,m\right)\right)\\ =\left(\frac{X_{2,k}\left(m\right)}{X_{1,k}\left(m\right)},-\frac{1}{\omega }\angle \frac{X_{2,k}\left(m\right)}{X_{1,k}\left(m\right)}\right)\end{array}& \left(14\right)\end{array}$

[0062] Therefore, the frequency bands in which the source signals exist in the m-th frame, for example, P mixing parameters can be obtained using equation 14.

[0063] To cluster the P mixing parameters using a soft K-means clustering algorithm, it is determined whether the present frame is a first frame. When the present fame is the first frame, the respective centers μ_j (where j=1, . . . , K) of K clusters are initialized to random values. When the present frame is not the first frame, the respective centers of the K clusters, i.e., respective average values of mixing parameters which belong to the respective clusters, are initialized into the respective cluster centers of the previous frame. Meanwhile, the number K of clusters is set to 2 through N, and then a specified clustering algorithm is performed. For each of the K values, R values proposed in definition 5 in the paper “A Cluster Separation Measure,” by David L. Davies and Donald W. Bouldin, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-1, no.2, April 1979, are calculated, the disclosure of which is incorporated by reference. K with a smallest R value corresponds to the number of actually existing clusters.

[0064] Next, ‘responsibility’ r_j^(k) is calculated. The responsibility r_j^(k), that is, the probability with which the k-th frequency band belongs to the j-th cluster (where j=1, . . . , K), is clustered using mixing parameters μ^(k) (where k=1 through P) and cluster centers μ_j (where j=1, . . . , K), as in equation 15. The k-th frequency band is assigned to a cluster having the greatest responsibility.

[0065] $\begin{array}{cc}{r}_j^{\left(k\right)}=\frac{\exp \left(-\beta d\left({\mu }_j,{\mu }^{\left(k\right)}\right)\right)}{\sum \exp \left(-\beta d\left({\mu }_j,{\mu }^{\left(k\right)}\right)\right)}& \left(15\right)\end{array}$

[0066] Here, d(μ_j,μ^(k)) is a distance operator between the center of the cluster and the mixing parameter and β is a decaying parameter which is inversely proportional to the noise variance.

[0067] When each of frequency bands is assigned to one of K clusters according to the responsibilities calculated by equation 15, the center μ_j of each cluster j is updated according to equation 16.

[0068] $\begin{array}{cc}{\mu }_j=\frac{\sum _k{r}_j^{\left(k\right)}{\mu }^{\left(k\right)}}{\sum _k{r}_j^{\left(k\right)}}\equiv \left(a_j\left(m\right),d_j\left(m\right)\right)& \left(16\right)\end{array}$

[0069] Here, a_j(m) and d_j(m) represent the attenuation and delay parameters of the j-th source at the m-th frame, respectively.

[0070] Next, it is determined whether the processed algorithm converges. The responsibility calculation and the cluster center updating are performed for a specified iteration number or until the responsibilities do not change anymore. When it is determined that the algorithm does not converge, the process returns to perform responsibility calculation and cluster center updating using the center of cluster updated by equation 16.

[0071] When it is determined that the algorithm converges, the number of the clusters is considered as the number of sources and a source label vector for each of sources is generated.

[0072] FIGS. 4a and 4b are graphs respectively showing 2-dimensional and 3-dimensional results of clusters obtained by the source identification unit 13, respectively. Here, since three clusters are generated, three sources exist.

[0073] If the center of each cluster for the present frame is estimated using moving averages, tracking the target sources is possible when the target sources are slowly moving. An initial guess of the cluster centers for the next frame is the cluster centers obtained in the current frame, thereby capable of speeding up the convergence of the clustering algorithm.

[0074] Alternately, a hard K-means clustering algorithm, as another possibility of clustering P mixing parameters, can be used. In the hard K-means clustering algorithm, the responsibility r_j^(k) is represented as 0 or 1. As a result, since a process of computing the exponential function for all data points is unnecessary, the computational burden is reduced. However, in this case, the responsibility r_j^(k) is assigned to a value proportional to the magnitude of the spectral component necessary to compute the data point μ_j only when the cluster means are calculated after the algorithm has converged. This is because spectral components of large magnitude are less vulnerable to corrupting noise.

[0075] Returning to FIG. 1 again, the signal estimation unit 15 compares the global signal absence probability calculated by the signal absence probability calculator 11 with a second threshold value, and determines that only a noise signal exists for a frame in which the global signal absence probability exceeds the second threshold value. Then, the signal estimation unit 15 updates the noise signal power and updates the source signal power for all frames to thereby generate a source signal component without noise signals. This process will be described in more detail with reference to FIG. 5 as follows.

[0076] Referring to FIG. 5, a posteriori signal-to-noise ratios (SNRs) for the m-th frame are calculated by equation 26, using the first through M-th a priori SNRs for the previous (m−1)-th frame calculated by equation 25.

[0077] Next, the global signal absence probability for the m-th frame calculated by the signal absence probability calculator 11 is compared with the second threshold value and it is determined whether only a noise signal exists in the present m-th frame. That is, when the global signal absence probability for the m-th frame exceeds the second threshold value, it is determined that only a noise signal exists.

[0078] When it is determined that only a noise signal exists at the m-th frame, the noise signal power σ_Nk² is updated according to equation 17.
σ_Nk²(m)=ζ_Nkσ_Nk²(m−1)+(1−ζ_Nk)|N_k(m)|₂  (17)

[0079] In the equation 17, ζ_Nk is a smoothing parameter (0≦ζ_Nk≦1).

[0080] Next, spectral component values for each of the frequency bands for the frame in which only the noise signal exists and the noise signal power is updated, or for the frame in which the noise signal and the source signal coexist are estimated. At this time, to eliminate the noise, a Minimum Mean-Square Error (MMSE) estimation algorithm is used.

[0081] That is, in a case where the signal absence probability calculator 11 calculates the signal absence probability for the first microphone observation, assuming that X_k(m) denotes the k-th spectral component in m-th frame of the first mixture x₁(t) and S_k(m) and N_k(m) denote the source and noise component therein, equation 18 is satisfied.
X_k(m)=S_k(m)+N_k(m)
where, X_k(m)=R_ke^iθk and S_k(m)=A_ke^iαk  (18)

[0082] In equation 18, R_k and A_kare the short-time spectral magnitude of the X_k(m) and S_k(m), respectively.

[0083] By using the MMSE estimation algorithm, estimating A_k from X_k is possible, because the short-time spectral amplitude rather than its waveform is of major importance in human perception. The constrained complex exponential estimator is found to be a complex exponential of the noisy phase, i.e. α_k=θ_k. This is disclosed in detail in the paper “Speech Enhancement Using a Minimum Mean-square Error Short-time Spectral Amplitude Estimator,” by Y. Ephraim and D. Malah, IEEE Trans. Acoust, Speech, Signal Processing, vol. 32, no.6, pp.1109-1121, 1984, the disclosure of which is incorporated by reference.

[0084] Since the spectral component values in the respective frequency bands are assumed to be statistically independent, the MMSE estimator Â_k of A_k is obtained by equations 19 and 20.

[0085] $\begin{array}{cc}{\hat{A}}_k=E\left\{A_k|X\right\}& \left(19\right)\\ =E\left\{A_k|X_k\right\}& \\ =p\left(H_{1,k}|X_k\right)E\left\{A_k|X_k,H_{1,k}\right\}& \\ =(1-p\left(H_{0,k}|X_k\right)E\left\{A_k|X_k,H_{1,k}\right\}& \\ =\frac{q_k{\Lambda }_k}{1+q_k{\Lambda }_k}E\left\{A_k|X_k,H_{1,k}\right\}& \\ E\left\{A_k|X_k,H_{1,k}\right\}=\frac{{\int }_0^{\infty }{\int }_0^{2\pi }{A}_{k}p\left(X_k|A_k,{\alpha }_k\right)d{\alpha }_{k}d{A}_k}{{\int }_0^{\infty }{\int }_0^{2\pi }p\left(X_k|A_k,{\alpha }_k\right)d{\alpha }_{k}d{A}_k}& \left(20\right)\end{array}$
where the probability density function p(X_k|A_k,α_k) is given by equation 21.

[0086] $\begin{array}{cc}p\left(X_k|A_k,{\alpha }_k\right)=\frac{1}{\pi {\sigma }_{N_k}^2}\exp \left(-\frac{1}{{\sigma }_{N_k}^2}{X_k-A_k{e}^{i\alpha k}}^2\right)& \left(21\right)\end{array}$

[0087] Since complex Gaussian probability density is assumed for the probability density function of the signal, the probability density function of its magnitude p(A_k) becomes a Rayleigh distribution, and p(α_k) is independent of p(A_k) and is uniform over [−π,π]. Accordingly, p(A_k,α_k) is expressed by equation 22.

[0088] $\begin{array}{cc}p\left(A_k,{\alpha }_k\right)=p\left(A_k\right)p\left({\alpha }_k\right)=\frac{A_k}{\pi {\sigma }_{S_k}^2}\exp \left(-\frac{A_k^2}{{\sigma }_{S_k}^2}\right)& \left(22\right)\end{array}$

[0089] After some calculations disclosed in the paper “Speech Enhancement Using a Minimum Mean-square Error Short-time Spectral Amplitude Estimator,” by Y. Ephraim and D. Malah, IEEE Trans. Acoust, Speech, Signal Processing, vol. 32, no.6, pp.1109-1121, 1984, the disclosure of which is incorporated by reference, the following equation 23 is obtained.

[0090] $\begin{array}{cc}\begin{array}{c}{\hat{A}}_k=\frac{q_k{\Lambda }_k}{1+q_k{\Lambda }_k}·\Gamma \left(1.5\right)\frac{\sqrt{v_k}}{{\gamma }_k}\exp \left(-\frac{v_k}{2}\right)·\\ \left[\left(1+v_k\right)I_0\left(\frac{v_k}{2}\right)+v_k{I}_1\left(\frac{v_k}{2}\right)\right]R_k\end{array}& \left(23\right)\end{array}$

[0091] In the above equation 23, Γ(·) is the gamma function with Γ(1.5)=√{square root over (π)}/2; I₀(·) and I₁(·) denote the modified Bessel functions of zero and first order, respectively, and v_k is defined by equation 24.

[0092] $\begin{array}{cc}{v}_k=\frac{{\xi }_k}{1+{\xi }_k}\left({\gamma }_k+1\right)& \left(24\right)\end{array}$

[0093] Here, ξ_k and γ_k are defined by equations 25 and 26.

[0094] $\begin{array}{cc}{\xi }_k=\frac{{\sigma }_{S_k}^2}{{\sigma }_{N_k}^2}& \left(25\right)\\ {\gamma }_k=\frac{R_k^2}{{\sigma }_{N_k}^2}-1& \left(26\right)\end{array}$

[0095] ξ_k and γ_k are known as the a priori and a posteriori SNR, respectively. If the a priori SNR is very great, the MMSE short-time spectral amplitude estimator Â_k converges to the Wiener amplitude estimator as in Equation 27.

[0096] $\begin{array}{cc}{\hat{A}}_k\approx \frac{{\xi }_k}{1+{\xi }_k}{R}_k& \left(27\right)\end{array}$

[0097] Next, the source signal power σ_sk² is updated according to equation 28 using the MMSE amplitude estimator Â_k for the spectral magnitude A_k of each frequency band.
σ_sk²=|Â_k|²  (28)

[0098] The real acoustic environment is continuously changing. To adapt the time-varying nature of source and noise signals, the signal variances are updated for every frame using equations 28 and 17. The a posteriori SNR γ_k of equation 26 can be easily updated using such an updated noise signal power σ_Nk².

[0099] For abruptly changing source signals, the a priori SNR is updated using equation 29.

[0100] $\begin{array}{cc}{\xi }_k\left(m\right)={\zeta }_{\mathrm{SNR}}\frac{{\hat{A}}_k^2\left(m-1\right)}{{\sigma }_{N_k}^2\left(m-1\right)}+\left(1-{\zeta }_{\mathrm{SNR}}\right)P\left({\gamma }_k\left(m\right)\right)& \left(29\right)\end{array}$

[0101] In the above equation 29, _ζSNR is a smoothing parameter (0≦_ζSNR≦1), Â_k (m−1) is an amplitude estimator of the k-th spectral component at the (m−1)-th frame, and P(·) is an operator which is defined by equation 30.

[0102] $\begin{array}{cc}P\left(x\right)=\{\begin{array}{cc}x& \mathrm{if}x\ge 0\\ 0& \mathrm{otherwise}\end{array}& \left(30\right)\end{array}$

[0103] P(·) is used to ensure the positiveness of the proposed estimator Â_k in case γ_k (m) is negative. As γ_k defined by equation 26 is not necessary positive, the operator P, it is ensured that the a priori SNR is always a non-negative value by using P(·) defined by equation 30. By doing so, the smoothing effect of the a priori SNR is achieved when the a posteriori SNR is fluctuating. If there is an abrupt change in the a posteriori SNR, the a priori SNR can follow it with a one frame delay. This property of the a priori SNR helps it to reduce the musical noise effect. This process is disclosed in detail in the paper “Elimination of the Musical Noise Phenomenon With the Ephraim and Malah Noise Suppressor,” by O. Cappé, IEEE Trans. Speech and Audio Pressing, vol 2, pp. 345-349,1994, the disclosure of which is incorporated by reference.

[0104] Next, a spectrum vector estimated for each frequency band is generated according to equation 31, using the amplitude estimator for each frequency band.
Ŝ_k(m)={circumflex over (S_k^(j))}(m)  (31)
where, {circumflex over (α)}_k=θ_k  (31)

[0105] Returning to FIG. 1 again, after the signal separator 17 multiplies the source vector of the m-th frame provided from the source identification unit 13 by the spectrum vector estimated for each frequency band of the m-th frame provided by the signal estimation unit 15, the signal separator 17 performs inverse Fourier transform and separates the received signals into source signals of time domain. This process is described in more detail with reference to FIG. 6.

[0106] Referring to FIG. 6, the source label vector expressed by “1” or “0” according to the number of clusters provided by the source identification unit 13 and the index of the frequency band assigned to each cluster, and the spectrum vector estimated for each frequency band of the m-th frame provided by the signal estimation unit 15, are received.

[0107] The source label vector and the estimated spectrum vector received are multiplied to each other and signals separated according to sources are obtained.

[0108] Thereafter, an inverse Fourier transform is performed for the signals separated according to the sources to transform the signals into signals of time domain.

[0109] Source signal separation using the spectrum vector estimated for each frequency band of the m-th frame provided by the signal estimation unit 15, is done with appropriate pairing of k and S_k{circumflex over (()}m). On the basis of equation 4, the k-th spectral component of the signal estimate at the m-th frame is rewritten as equation 32.
Ŝ_k(m)=Ŝ_k^(l)(m)+ . . . +Ŝ_k^(N)(m)  (32)

[0110] Also, the above equation 32 is simplified in equation 33 on the basis of the w-disjoint orthogonality.
Ŝ_k(m)=Ŝ_(k)^(j)(m)  (33)

[0111] To separate the sources, source label vectors corresponding to each of sources are generated. The each source label vector is applied to the estimated spectrum vectors Ŝ(m) to produce the separated source spectrum. First, a source label vector £_j(m), which maps the relationship between the support of source j and Ŝ_k^(j)(m) is defined. Each component of the source label vector has the value “0” or “1”. Then, a spectrum vector Ŝ_j(m) of the j-th source at the m-th frame can be obtained by equation 34.
Ŝ_j(m)=£_j(m)⊙Ŝ(m)  (34)

[0112] In the above equation 34, ⊙ represents the component-wise multiplication of vectors.

[0113] FIG. 7 is a block diagram of a signal separation apparatus according to a second embodiment of the present invention, wherein the source separation apparatus comprises a signal absence probability calculator 71, a signal estimation unit 73, a source identification unit 75, and a source signal separator 77.

[0114] Referring to FIG. 7, the signal absence probability calculator 71 calculates the global signal absence probabilities p(Ho|X1(m)) and p(Ho|X2(m)) for the m-th frame and the local signal absence probabilities p(Ho,k|X1,k(m)) and p(Ho,k|X2,k(m)) at each of frequency bins of the m-th frame, for the first and second microphone observations X1(m) and X2(m).

[0115] The signal estimation unit 73 estimates a spectrum vector in which noise signals are eliminated for each frequency band per frames using the global signal absence probabilities calculated by the signal absence probability calculator 71, for the first and second microphone observations, and generates first and second microphone observations X1(m) and X2(m) without noise signals.

[0116] The source identification unit 75 performs clustering using the first and second microphone observations X1(m) and X2(m) without noise signals, as in the above-described first embodiment, and generates a source label vector consisting of a source and a frequency band assigned to each source.

[0117] The source signal separator 77 multiplies the source label vector for the m-th frame provided by the source identification unit 75 by the spectrum vector estimated for each frequency band of the m-th frame provided by the signal estimation unit 73, and then performs inverse Fourier transform to thereby separate the received signals into source signals of time domain.

[0118] That is, the above-described configuration may be applicable especially in a case where the SNR of the first and second microphone observations X1(m) and X2(m) is large.

[0119] To verify the performance of the proposed noisy, underdetermined blind source separation algorithm, experiments on speech signals have been performed. Clean speech data were previously recorded at 16 kHz in an anechoic room. 40 words for computer commands and Korean names uttered by four male speakers were used for making the target signals. 40 words pronounced by each speaker were split into 10 files, each file consisting of four words. Thus, 10 sets of target sources were prepared. White Gaussian noise (WGN) was used as a broad-band noise. According to the SNR, WGN was simply added sample by sample after adjusting the signal levels by the method described in the ITU-T recommendation P.830. Source identification and signal estimation were done frame by frame.

[0120] FIG. 8 and FIGS. 9a through 9c are views for describing experimental results of the proposed algorithm according to the present invention. When first and second microphones Mic1 and Mic2 and first through fourth sources Source 1 through Source 4 are used as in FIG. 8, FIG. 9a shows the first through fourth source signals s1 through s4, FIG. 9b shows the first and second microphone observations x1 and x2, and FIG. 9c shows signals u1 through u4 separated according to sources by the source separation algorithm of the present invention. Referring to the above-mentioned drawings, when the source separation algorithm according to the present invention is used, it is possible to significantly reduce noise in real time and correctly separate signals according to sources.

[0121] The present invention may be embodied as a program stored on a computer readable medium that can be run on a general computer. Here, the computer readable medium includes but is not limited to storage media such as magnetic storage media (e.g., ROM's, floppy disks, hard disks, etc.), optically readable media (e.g., CD-ROMs, DVDs, etc.), and carrier waves (e.g., transmission over the Internet). The present invention may also be embodied as a computer readable program code unit stored on a computer readable medium, for causing a number of computer systems connected via a network to affect distributed processing.

[0122] Also, the source separation method and apparatus according to the present invention is applicable to an environment in which a terminal is kept as distant as possible from a user's device, such as PDA (Personal Digital Assistant), WebPad, or a mobile phone for a vehicle with the smaller number of microphones, as well as an autonomous traveling robot including a microphone array. The present invention can significantly improve the performance of a sound recognizer in such an environment. Also, the present invention is applicable to sound input systems requiring high-quality sound and can be used for a sound source separation system capable of separating respective sound sources in a case where a plurality of sound sources exist in the same environment. Also, the present invention can be used in all fields using conventional sensor arrays, such as a communication field and a radar field.

[0123] As described above, according to the present invention, it is possible to separate signals received through two microphones into N source signals while eliminating noise from the received signals in real time. Also, by calculating the signal absence probabilities for the respective frequency bands considering the attenuation and delay parameters, the present invention is applicable even to a case where a white Gaussian noise not satisfying the w-disjoint orthogonality is mixed, thereby improving the tone quality of the restored sound. Also, it is possible to estimate source signals with difficulty in being recognized due to background noise, by using the signal absence probabilities.

[0124] Although a few embodiments of the present invention have been shown and described, the present invention is not limited to the described embodiments. Instead, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.