Target source signal generation apparatus, target source signal generation method, and program
View Patent ↗A sound source signal generation technology based on an optimization algorithm that enables high-speed processing of sound source extraction is provided. A sound source signal generation device includes an optimization unit that optimizes a separation matrix W(f)=[w 1 (f), . . . , w K (f), W Z (f)] using an observed signal x(f, t), the optimization unit includes an auxiliary function calculation unit that calculates an auxiliary function V i (f) (i=1, . . . , K) according to a predetermined equation, a first separation filter calculation unit that calculates a separation filters w i (f) (i=1, . . . , K) using auxiliary functions V i (f) (i=1, . . . , K) and V z (f), and a second separation filter calculation unit that calculates a separation filter W Z (f) according to a predetermined equation when a convergence condition is satisfied.
1. A sound source signal generation device in which K and M are integers satisfying 1≤K<M, x(f, t) (f=1, . . . , F, t=1, . . . , T, and F and T are integers satisfying 1≤F and 1≤T) (where f is an index indicating a frequency bin and t is an index indicating a time frame) is an observed signal of mixed sound from K sound sources observed using M microphones, x i (f, t) (i=1, . . . , K, f=1, . . . , F, t=1, . . . , T) is an i-th sound source signal, the i-th sound source signal being an estimation signal of an i-th sound source, W(f)=[w 1 (f), . . . , w K (f), W Z (f)] (where C is a set of complex numbers, w i (f)∈C M (i=1, . . . , K) is a separation filter for the i-th sound source signal, z represents noise signal, and W Z (f)∈C M×(M−K) is a separation filter for a noise signal) is a separation matrix, V i (f) (i=1, . . . , K) is an auxiliary function of the i-th sound source signal, and V Z (f) is an auxiliary function of the noise signal,
the sound source signal generation device comprising
an initialization circuitry configured to initialize a separation matrix W(f) and an auxiliary function V Z (f);
an optimization circuitry configured to optimize the separation matrix W(f) using the observed signal x(f, t); and
a sound source signal generation circuitry configured to generate an i-th sound source signal x i (f, t) from the observed signal x(f, t) using the separation matrix W(f),
wherein the optimization circuitry includes
an auxiliary function calculation circuitry configured to calculate the auxiliary function V i (f) (i=1, . . . , K) using the following equations;
s
l
(
f
,
t
)
←
w
l
(
f
)
h
×
(
f
,
t
)
(where h represents complex conjugate transpose and s i (f, t) is a complex number)
r
l
(
t
)
←
s
i
(
t
)
(where s i (t)=[s i (1, t), . . . , s i (F, t)] T is a vector and r i (t) is a real number)
α
i
β
←
β
2
F
(
1
T
∑
t
r
i
(
t
)
β
)
(where β is a predetermined constant and α i β is a real number)
ϕ
i
(
t
)
←
β
2
1
α
i
β
r
i
(
t
)
2
-
β
(where φ i (t) is a real number)
V
l
(
f
)
←
1
T
∑
t
ϕ
i
(
t
)
×
(
f
,
t
)
×
(
f
,
t
)
h
a first separation filter calculation circuitry configured to calculate the separation filters w i (f) (i=1, . . . , K) using auxiliary functions V i (f) (i=1, . . . , K) and V z (f); and
a second separation filter calculation circuitry configured to calculate a separation filter W Z (f) according to a predetermined equation when a convergence condition is satisfied.
2. The sound source signal generation device according to claim 1 ,
wherein I M−K is an (M−K)-dimensional unit matrix, e j (M) (j=1, . . . , M) is an M-dimensional unit vector in which a j-th element is 1 and other elements are 0, E s =[e 1 (M), . . . , e K (M) ] is a matrix, and E z =[e K+1 (M) , . . . , e M (M) ] is a matrix, and
the first separation filter calculation circuitry calculates a separation filter w 1 (f) using the following equation when K=1,
w
1
(
f
)
←
u
(
u
h
V
1
(
f
)
u
)
-
1
2
(where the vector u is a vector corresponding to a maximum eigenvalue λ max satisfying V z (f)u=λ max V 1 (f)u), and
calculates the separation filters w i (f) (i=1, . . . , K) using the following equation when K>1
P
k
(
f
)
←
(
W
(
f
)
h
V
k
(
f
)
)
-
1
[
e
l
(
M
)
,
E
z
]
(
k
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i
,
z
)
(where P k (f) is a matrix)
G
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(
f
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←
P
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(
f
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h
V
k
(
f
)
P
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(
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k
=
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(where G k (f) is a matrix)
w
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(
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←
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b
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b
h
G
i
(
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b
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-
1
2
(where the vector b is a vector corresponding to a maximum eigenvalue λ max satisfying G i (f)b=λ max G z (f)b), and
a predetermined equation used by the second separation filter calculation circuitry is the following equation
W
z
(
f
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←
[
(
W
s
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h
V
z
(
f
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E
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-
1
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W
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I
M
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(
where
W
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=
[
w
1
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…
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w
K
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]
)
.
3. The sound source signal generation device according to claim 1 ,
wherein L is an integer satisfying 1≤L≤K,
a i (f)∈C M (i=1, . . . , L) is an acoustic transfer function from the i-th sound source to the M microphones,
A 1 (f)=[a 1 (f), . . . , a L (f)] is a matrix,
I M−K is an (M−K)-dimensional unit matrix,
e j (d) (j=1, . . . , d) is a d-dimensional unit vector in which a j-th element is 1 and other elements are 0, E 2 =[e L+1 (M) , . . . , e M (M) ] is a matrix,
W 2 ′(f)=[A 1 (f), E 2 ] −h E 2 is a matrix,
− V z (f)=W 2 ′(f) h V z (f)W 2 ′(f) is a matrix,
− W(f)=[ − w L+1 (f), . . . , − w K (f), − W Z (f)] (where − w i (f)∈C (M−L) (i=L+1, . . . , K) is a separation filter for an i-th sound source signal, and a matrix − W Z (f)∈C (M−L)×(M−K) is a separation filter for a noise signal) is a matrix,
− E s =[e 1 (M−L) , . . . , e K−L (M−L) ] is a matrix,
− E z =[e K−L+1 (M−L) , . . . , e M−L (M−L) ] is a matrix,
the first separation filter calculation circuitry calculates the separation filters w i (f) (i=1, . . . , K) using the following equation when L=K, and
w
l
(
f
)
←
V
i
(
f
)
-
1
A
1
(
f
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(
A
1
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)
h
V
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f
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A
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-
1
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(
K
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calculates the separation filter w i (f) (i=1, . . . , K−1) using the following equation
w
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(
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←
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1
A
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A
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A
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and calculates a separation filter w K (f) using the following equation when L=K−1,
V
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←
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V
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W
2
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(
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(where − V k (f) is a matrix)
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_
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_
)
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(where vector − u is a vector corresponding to a maximum eigenvalue λ max that satisfies − V z (f) − u=λ max − V k (f) − u), and
calculates a separation filter w i (f) (i=1, . . . , L) using the following equation
w
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(
f
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←
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1
A
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(
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A
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V
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A
1
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)
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1
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(
l
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and calculates a separation filter w i (f) (i=L+1, . . . , K) using the following equation when L<K−1,
V
_
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(
f
)
←
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2
′
(
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(
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W
2
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(
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(
i
=
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1
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…
,
K
)
(where − V i (f) is a matrix)
P
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k
(
f
)
←
(
W
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(
f
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h
V
_
k
(
f
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)
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1
[
e
l
(
M
-
1
)
,
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_
z
]
(
k
=
i
,
z
)
(where − P k (f) is a matrix)
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_
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(
f
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←
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_
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(
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)
h
V
_
k
(
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)
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k
(
f
)
(
k
=
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,
z
)
(where − G k (f) is a matrix)
w
i
(
f
)
←
W
2
′
(
f
)
P
_
i
(
f
)
b
_
(
b
_
h
G
_
i
(
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)
b
_
)
-
1
2
(where vector − b is a vector corresponding to the maximum eigenvalue λ max that satisfies − G i (f) − b=λ max − G z (f) − b), and
a predetermined equation used by the second separation filter calculation circuitry is the following equation
W
2
(
f
)
←
W
2
′
(
f
)
[
(
W
_
s
(
f
)
h
V
_
z
(
f
)
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)
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1
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s
(
f
)
h
V
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z
(
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z
)
-
I
M
-
K
]
(where − W s (f)=[ − w L+1 (f), . . . , − w K (f)] is a matrix).
4. A sound source signal generation method in which K and M are integers satisfying 1≤K<M, x(f, t) (f=1, . . . , F, t=1, . . . , T, where F and T are integers satisfying 1≤F and 1≤T) (where f is an index indicating a frequency bin, and t is an index indicating a time frame) is an observed signal of mixed sound from K sound sources observed using M microphones, x i (f, t) (i=1, . . . , K, f=1, . . . , F, t=1, . . . , T) is an i-th sound source signal, the i-th sound source signal being an estimation signal of an i-th sound source, W(f)=[w 1 (f), . . . , w K (f), W Z (f)] (where C is a set of complex numvbers, w i (f)∈C M (i=1, . . . , K) is a separation filter for the i-th sound source signal, z represents noise signal, and W Z (f)∈C M×(M−K) is a separation filter for a noise signal) is a separation matrix, V i (f) (i=1, . . . , K) is an auxiliary function of the i-th sound source signal, and V Z (f) is an auxiliary function of the noise signal, and
the sound source signal generation method comprises
an initialization step of initializing, by a sound source signal generation device, a separation matrix W(f) and an auxiliary function V Z (f);
an optimization step of optimizing, by the sound source signal generation device, the separation matrix W(f) using the observed signal x(f, t); and
a sound source signal generation step of generating, by the sound source signal generation device, an i-th sound source signal x i (f, t) from the observed signal x(f, t) using the separation matrix W(f),
wherein the optimization step includes
an auxiliary function calculation step of calculating the auxiliary function V i (f) (i=1, . . . , K) using the following equation,
s
l
(
f
,
t
)
←
w
i
(
f
)
h
x
(
f
,
t
)
(where h represents complex conjugate transpose and s i (f, t) is a complex number)
r
i
(
t
)
←
s
i
(
t
)
(where s i (t)=[s i (1, t), . . . , s i (F, t) T is a vector and r i (t) is a real number]
α
i
β
←
β
2
F
(
1
T
∑
t
T
i
(
t
)
β
)
(where β is a predetermined constant and α i β is a real number)
ϕ
i
(
t
)
←
β
2
1
α
i
β
r
i
(
t
)
2
-
β
(where φ i (t) is a real number)
V
i
(
f
)
←
1
T
∑
t
ϕ
i
(
t
)
x
(
f
,
t
)
x
(
f
,
t
)
h
a first separation filter calculation step of calculating the separation filters w i (f) (i=1, . . . , K) using auxiliary functions V i (f) (i=1, . . . , K) and V z (f); and
a second separation filter calculation step of calculating a separation filter W Z (f) according to a predetermined equation when a convergence condition is satisfied.
5. A non-transitory computer-readable recording medium storing a program for causing a computer to function as the sound source signal generation device according to claim 1 .