Digital Signal Processing Reference
In-Depth Information
Λ
={
P
N
,σ
N
,
P
S
,λ
S
}
(9.4)
are independent of time and frequency, and can be trained by the EM algorithm (cf.
P
N
·
f
N
(
m
f
,
t
)
p
(
sil
|
m
f
,
t
,Λ)
=
(9.5)
P
N
·
f
N
(
m
f
,
t
)
+
P
S
·
f
S
(
m
f
,
t
)
p
(
act
|
m
f
,
t
,Λ)
=
1
−
p
(
sil
|
m
f
,
t
,Λ).
(9.6)
For the Maximisation step, the moment method is used: An update
σ
N
employing
all data takes place before all data with values above the new
σ
N
help to update
λ
S
.
Two update equations describe the method as follows:
f
,
t
m
2
f
,
t
·
1
2
p
(
sil
|
m
f
,
t
,Λ)
σ
N
=
(9.7)
2
f
,
t
2
p
(
sil
|
m
f
,
t
,Λ)
m
f
,
t
> σ
N
(
m
f
,
t
−
σ
N
)
−
1
·
p
(
act
|
m
f
,
t
,Λ)
λ
S
=
m
f
,
t
> σ
N
.
(9.8)
p
(
act
|
m
f
,
t
,Λ)
Subsequent to the training of all mixture parameters
Λ
={
P
N
,σ
N
,
P
S
,λ
S
}
USS
with the parameter
σ
N
as floor value is applied:
max
1
m
f
,
t
σ
N
m
USS
f
=
,
(9.9)
,
t
Flooring to a non-zero value is required for MFCC or similar features, as zero
magnitude values after spectral subtraction can result in unfavourable dynamics.
Overall, USS is a simple and efficient preprocessing method that allows for unsuper-
vised EM fitting on observed data. As a downside, it requires reliable estimation of
an audio magnitude PDF which is rather challenging. With the PDFs not depending
on frequency and time, USS only handles stationary noises. Further, it only mod-
els large magnitudes of the audio of interest. Low audio magnitudes thus cannot be
distinguished from background noise.
9.2 Feature Enhancement
In feature enhancement, enhancement takes place after the extraction of features to
reduce a potential mismatch between test and training conditions. Popular methods
include CMS [
11
], MVN [
12
], HEQ [
9
], and the Taylor Series approach [
34
] able
to cope with the non-linear effects of noise. There are some further methods tai-
lored to specific types of features, such as in the cepstrum-domain, where a feature
