System and method for nonlinear signal enhancement that bypasses a noisy phase of a signal
View Patent ↗A system and method for nonlinear signal enhancement is provided. The method comprises: performing a linear transformation on a measured signal comprising a source component and a noise component; determining a modulus of the linear transformed signal; estimating a noise-free part of the linear transformed signal; and reconstructing the source component of the measured signal using the noise-free part of the linear transformed signal.
1. A method for nonlinear signal enhancement, comprising:
performing a linear transformation on a measured signal comprising a source component and a noise component;
determining a modulus of the linear transformed signal;
estimating a noise-free part of the linear transformed signal; and
reconstructing the source component of the measured signal using the noise-free part of the linear transformed signal.
2. The method of claim 1 , wherein the step of reconstructing the source component of the measured signal, comprises:
performing a nonlinear transformation on the noise-free part of the linear transformed signal;
determining a sign of the source component of the measured signal;
determining a product of the nonlinear transformed signal and the sign; and
performing an overlap-add procedure using the product of the nonlinear transformed signal and the sign.
3. The method of claim 1 , wherein the linear transformation is one of a Fourier transform and a wavelet transform.
4. The method of claim 1 , wherein the noise-free part of the linear transformed signal is estimated using one of a Wiener filtering technique and an Ephraim-Malah estimation technique.
5. The method of claim 1 , wherein the noise-free part of the linear transformed signal is estimated by solving:
Y
(
k
,
ω
)
=
{
X
(
k
,
ω
)
-
R
n
(
k
,
ω
)
if
X
(
k
,
ω
)
2
≥
R
n
(
k
,
ω
)
0
if
otherwise
,
where
R
n
(
k
,
ω
)
=
min
k
-
W
≤
k
′
<
k
R
x
(
k
′
,
ω
)
and
R
x
(
k
,
ω
)
=
(
1
-
β
)
R
x
(
k
-
1
,
ω
)
+
β
X
(
k
,
ω
)
2
.
6. The method of claim 1 , wherein the step of reconstructing the source component of the measured signal, comprises:
defining a three layer neural network by:
q
k
=
σ
(
∑
f
=
1
F
a
k
f
Z
f
+
θ
k
)
,
1
≤
k
≤
L
and
z
m
=
σ
(
∑
k
=
1
L
b
mk
q
k
+
τ
m
)
,
1
≤
m
≤
M
;
performing a nonlinear transformation on the noise-free part of the linear transformed signal by solving:
u
m
=
z
m
Y
1
2
+
⋯
+
Y
F
2
z
1
2
+
⋯
+
z
M
2
;
determining a sign of the source component of the measured signal by solving:
ρ
=
{
+
1
if
∑
k
=
1
M
x
k
-
u
k
2
≤
∑
k
=
1
M
x
k
+
u
k
2
-
1
if
otherwise
;
determining a product of the nonlinear transformed signal and the sign; and
performing an overlap-add procedure using the product of the nonlinear transformed signal and the sign.
7. The method of claim 6 , further comprising:
iterating:
π
t
+
1
=
π
t
-
α
∂
∂
π
∑
m
=
1
M
u
m
-
s
m
2
until π converges, wherein π=(A, B, θ, τ).
8. The method of claim 1 , wherein the noise-free part of the linear transformed signal is estimated by solving:
min
0
≤
α
k
<
2
π
,
2
≤
k
≤
F
∑
k
=
1
F
Y
k
′
-
TU
(
Y
′
)
)
k
2
,
Y
′
=
(
ⅇ
jα
k
Y
k
)
1
≤
k
≤
F
,
α
1
=
0
;
and the step of reconstructing the source component of the measured signal, comprises:
performing a nonlinear transformation on the noise-free part of the linear transformed signal by solving:
z=U ( Y o ), Y k o =e ja k o Y k ;
determining a sign of the source component of the measured signal by solving:
ρ
=
{
+
1
if
∑
k
=
1
M
x
k
-
u
k
2
≤
∑
k
=
1
M
x
k
+
u
k
2
-
1
if
otherwise
;
determining a product of the nonlinear transformed signal and the sign; and
performing an overlap-add procedure using the product of the nonlinear transformed signal and the sign.
9. The method of claim 1 , wherein the step of reconstructing the source component of the measured signal, comprises:
(i) setting k=0, Y 0 =Y;
(ii) computing z k =UY k ;
(iii) computing W=Tz k ;
(iv) computing Y 0 using:
Y
k
+
1
(
n
)
=
Y
(
n
)
W
(
n
)
W
(
n
)
,
n
=
1
,
2
,
…
,
F
,
wherein if ∥Y k −Y k+1 ∥>ε:
incrementing k=k+1, repeating steps (i-iv); and
estimating the source component of the measured signal using Z k .
10. The method of claim 1 , further comprising:
outputting the reconstructed source component of the measured signal.
11. A system for nonlinear signal enhancement, comprising:
a memory device for storing a program;
a processor in communication with the memory device, the processor operative with the program to:
perform a linear transformation on a measured signal comprising a source component and a noise component;
determine a modulus of the linear transformed signal;
estimate a noise-free part of the linear transformed signal; and
reconstruct the source component of the measured signal using the noise-free part of the linear transformed signal.
12. The system of claim 11 , wherein when the source component of the measured signal is reconstructed the processor is further operative with the program code to:
perform a nonlinear transformation on the noise-free part of the linear transformed signal;
determine a sign of the source component of the measured signal;
determine a product of the nonlinear transformed signal and the sign; and
perform an overlap-add procedure using the product of the nonlinear transformed signal and the sign.
13. The system of claim 11 , wherein the measured signal is received using one of a microphone and a database comprising one of audio signals and image signals.
14. The method of claim 11 , wherein when the source component of the measured signal is reconstructed the processor is further operative with the program code to:
define a three layer neural network by:
q
k
=
σ
(
∑
f
=
1
F
a
kf
Z
f
+
θ
k
)
,
1
≤
k
≤
L
and
z
m
=
σ
(
∑
k
=
1
L
b
mk
q
k
+
τ
m
)
,
1
≤
m
≤
M
;
perform a nonlinear transformation on the noise-free part of the linear transformed signal by solving:
u
m
=
z
m
Y
1
2
+
…
+
Y
F
2
z
1
2
+
…
+
z
M
2
;
determine a sign of the source component of the measured signal by solving:
ρ
=
{
+
1
if
∑
k
=
1
M
x
k
-
u
k
2
≤
∑
k
=
1
M
x
k
+
u
k
2
-
1
if
otherwise
;
determine a product of the nonlinear transformed signal and the sign; and
perform an overlap-add procedure using the product of the nonlinear transformed signal and the sign.
15. The method of claim 11 , wherein the noise-free part of the linear transformed signal is estimated by solving:
min
0
≤
α
k
<
2
π
,
2
≤
k
≤
F
∑
k
=
1
F
Y
k
′
-
TU
(
Y
′
)
)
k
2
,
Y
′
=
(
ⅇ
jα
k
Y
k
)
1
≤
k
≤
F
,
α
1
=
0
;
and
when the source component of the measured signal is reconstructed the processor is further operative with the program code to:
perform a nonlinear transformation on the noise-free part of the linear transformed signal by solving:
z=U ( Y o ), Y k o =e ja k o Y k ;
determine a sign of the source component of the measured signal by solving:
ρ
=
{
+
1
if
∑
k
=
1
M
x
k
-
u
k
2
≤
∑
k
=
1
M
x
k
+
u
k
2
-
1
if
otherwise
;
determine a product of the nonlinear transformed signal and the sign; and
perform an overlap-add procedure using the product of the nonlinear transformed signal and the sign.
16. The method of claim 11 , wherein when the source component of the measured signal is reconstructed the processor is further operative with the program code to:
(i) set k=0, Y 0 =Y;
(ii) compute z k =UY k ;
(iii) compute W=Tz k ;
(iv) compute Y 0 using:
Y
k
+
1
(
n
)
=
Y
(
n
)
W
(
n
)
W
(
n
)
,
n
=
1
,
2
,
…
,
F
,
wherein if ∥Y k −Y k+1 ∥>ε:
increment k=k+1, repeat steps (i-iv); and
estimate the source component of the measured signal using z k .
17. The system of claim 11 , wherein the processor is further operative with the program code to:
output the reconstructed source component of the measured signal.
18. The system of claim 17 , wherein the reconstructed source component of the measured signal is output to one of a loudspeaker and an automatic speech recognition system.
19. A method for nonlinear signal enhancement, comprising:
receiving a signal comprising a source component and a noise component;
performing a linear transformation on the received signal;
determining an absolute value of the linear transformed signal;
estimating a noise-free part of the linear transformed signal;
performing a nonlinear transformation on the noise-free part of the linear transformed signal;
determining a sign of the source component of the received signal;
determining a product of the nonlinear transformed signal and the sign; and
performing an overlap-add procedure on the product of the nonlinear transformed signal and the sign to form a reconstructed signal of the source component of the received signal, wherein the reconstructed signal does not comprise the noise component of the received signal; and
outputting the reconstructed signal.
20. The method of claim 19 , wherein the received signal is one of a speech signal and an image signal.