System and method for non-square blind source separation under coherent noise by beamforming and time-frequency masking
View Patent ↗A system and method for non-square blind source separation (BSS) under coherent noise. The system and method for non-square BSS estimates the mixing parameters of a mixed source signal and filters the estimated mixing parameters so that output noise is reduced and the mixed source signal is separated from the noise. The filtering is accomplished by a linear filter that performs a beamforming for reducing the noise and another linear filter that solves a source separation problem by selecting time-frequency points where, according to a W-disjoint orthogonality assumption, only one source is active.
1. A method for non-square blind source separation (BSS) under coherent noise, comprising:
estimating mixing parameters of a mixed source signal;
first filtering the estimated mixing parameters so that output noise is reduced; and
second filtering the estimated mixing parameters so that the mixed source signal is separated from the output noise,
wherein the step of estimating the mixing parameters comprises:
computing a partition and selection map by using the following equation
Σ
^
(
k
,
ω
)
=
argmax
l
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
X
(
k
,
ω
)
2
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
Z
Σ
(
k
,
ω
)
,
with α l =α l s and τ l =τ l s ; and
computing mixing parameters by applying a gradient descent to the following equation
(
α
l
^
,
τ
l
^
)
=
argmax
α
l
,
τ
l
∑
(
k
,
ω
)
∈
Ω
l
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
X
(
k
,
ω
)
2
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
Z
Σ
(
k
,
ω
)
until it converges to a local optimum α l s+l , τ l s+l for each 1≦l≦L and subset of time-frequency points Ω l s+l .
2. The method of claim 1 , wherein the step of estimating the mixing parameters further comprises:
computing an alignment criterion.
3. The method of claim 2 , wherein the alignment criterion are computed by
J s =J(A s , Σ s ) after setting s=s+1.
4. The method of claim 3 , wherein the computation of the alignment criterion is iterated until (J s−J s−1 )/J s <∈.
5. The method of claim 1 , wherein a first filter is used for the first filtering, the first filter is
S
^
=
Z
l
*
Γ
n
-
1
X
Z
l
*
Γ
n
-
1
Z
l
.
6. The method of claim 5 , wherein the first filter is applied across spatial channels.
7. The method of claim 5 , wherein the first filter performs a beamforming.
8. The method of claim 1 , wherein a second filter is used for the second filtering, the second filter is
S l (k, w)=S(k, w)1 Ωi (k, w).
9. The method of claim 8 , wherein the second filter is applied across the time-frequency domain.
10. The method of claim 8 , wherein the second filter performs a time-frequency masking to select time frequency points where only one source is active according to a W-disjoint orthogonality assumption.
11. The method of claim 1 , further comprising:
converting filtered data from a time-frequency domain to a time-domain.
12. The method of claim 11 , further comprising:
outputting the converted data.
13. A system for non-square blind source separation (BSS) under coherent noise, comprising:
an estimator for estimating mixing parameters of a mixed source signal;
a first filter for filtering the estimated mixing parameters so that output noise is reduced; and
a second filter for filtering the estimated mixing parameters so that the mixed source signal is separated from the output noise,
wherein the mixing parameters are estimated by:
computing a partition and selection man by using the following equation
Σ
^
(
k
,
ω
)
=
argmax
l
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
X
(
k
,
ω
)
2
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
Z
Σ
(
k
,
ω
)
,
with α l =α l s and τ l =τ l s ; and
computing mixing parameters by applying a gradient descent to the following equation
(
α
l
^
,
τ
l
^
)
=
argmax
α
l
,
τ
l
∑
(
k
,
ω
)
∈
Ω
l
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
X
(
k
,
ω
)
2
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
Z
Σ
(
k
,
ω
)
until it converges to a local optimum α l s+l , τ l s+l for each 1≦l≦L and subset of time-frequency points Ω l s+l .
14. The system of claim 13 , wherein the mixing parameters are further estimated by:
computing an alignment criterion by calculating the following
J s =J(A s , Σ s ).
15. The system of claim 13 , wherein the first filter is
S
^
=
Z
l
*
Γ
n
-
1
X
Z
l
*
Γ
n
-
1
Z
l
.
16. The system of claim 13 , wherein the second filter is
S i (k, w)=S(k, w)1 Ωi (k, w).
17. A computer program product comprising a computer useable medium having computer program logic recorded thereon for non-square blind source separation (BSS) under coherent noise, the computer program logic comprising:
program code for estimating mixing parameters of a mixed source signal;
program code for first filtering the estimated mixing parameters so that output noise is reduced; and
program code for second filtering the estimated mixing parameters so that the mixed source signal is separated from the output noises,
wherein the mixing parameters are estimated by:
computing a partition and selection man by using the following equation
Σ
^
(
k
,
ω
)
=
argmax
l
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
X
(
k
,
ω
)
2
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
Z
Σ
(
k
,
ω
)
,
with α l =α l s and τ l =τ l s ; and
computing mixing parameters by applying a gradient descent to the following equation
(
α
l
^
,
τ
l
^
)
=
argmax
α
l
,
τ
l
∑
(
k
,
ω
)
∈
Ω
l
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
X
(
k
,
ω
)
2
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
Z
Σ
(
k
,
ω
)
until it converges to a local optimum α l s+l , τ l s+l for each 1≦l≦L and subset of time-frequency points Ω l s+l .
18. The computer program product of claim 17 , the program code for estimating mixing parameters further comprising:
program code for computing an alignment criterion.
19. The computer program product of claim 18 , wherein the alignment criterion are computed by the following
J s =J(A s , Σ s ) after setting s=s+1.
20. The computer program product of claim 19 , wherein the computation of the alignment criterion is iterated until (J s −J s−1 )/J s <∈.
21. The computer program product of claim 17 , wherein the first filtering is computed by the following
S
^
=
Z
l
*
Γ
n
-
1
X
Z
l
*
Γ
n
-
1
Z
l
.
22. The computer program product of claim 17 , wherein the second filtering is computed by the following
S i (k, w)=S(k, w)1 Ωi (k, w).
23. The system of claim 13 , wherein the first filter is applied across spatial channels and performs a beamforming.
24. The system of claim 13 , wherein the second filter is applied across the time-frequency domain and performs time-frequency masking to select time frequency points where only one source is active according to a W-disjoint orthogonality assumption.
25. A method for non-square blind source separation (BSS) under coherent noise, comprising:
initializing mixing parameters with random values;
setting a source signal and alignment value to zero;
choosing a stopping threshold;
computing an optimal partition and selection map by using the following equation
Σ
^
(
k
,
ω
)
=
argmax
l
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
X
(
k
,
ω
)
2
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
Z
Σ
(
k
,
ω
)
,
with α l =α l s and τ l =τ l s ;
computing the mixing parameters by applying a gradient descent to the following equation
(
α
l
^
,
τ
l
^
)
=
argmax
α
l
,
τ
l
∑
(
k
,
ω
)
∈
Ω
l
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
X
(
k
,
ω
)
2
Z
Σ
(
k
,
ω
)
*
Γ
n
-
1
Z
Σ
(
k
,
ω
)
until it converges to a local optimum α l s+l , τ l s+l for each 1≦l≦L and subset of time-frequency points Ω l s+l ;
computing an alignment criterion;
first filtering the mixing parameters so that output noise is reduced;
second filtering the mixing parameters so that a mixed source signal is separated from the output noise;
converting filtered data from a time-frequency domain to a time-domain; and
outputting the converted data.