<s>
This	O
article	O
is	O
about	O
Compressed	B-Application
sensing	I-Application
in	I-Application
speech	I-Application
signals	I-Application
.	O
</s>
<s>
In	O
communications	B-General_Concept
technology	I-General_Concept
,	O
the	O
technique	O
of	O
compressed	O
sensing	O
(	O
CS	O
)	O
may	O
be	O
applied	O
to	O
the	B-Algorithm
processing	I-Algorithm
of	I-Algorithm
speech	I-Algorithm
signals	I-Algorithm
under	O
certain	O
conditions	O
.	O
</s>
<s>
In	O
particular	O
,	O
CS	O
can	O
be	O
used	O
to	O
reconstruct	O
a	O
sparse	B-Algorithm
vector	I-Algorithm
from	O
a	O
smaller	O
number	O
of	O
measurements	O
,	O
provided	O
the	O
signal	O
can	O
be	O
represented	O
in	O
sparse	O
domain	O
.	O
</s>
<s>
This	O
reconstructed	O
sparse	B-Algorithm
vector	I-Algorithm
can	O
be	O
used	O
to	O
construct	O
back	O
the	O
original	O
signal	O
if	O
the	O
sparse	O
domain	O
of	O
signal	O
is	O
known	O
.	O
</s>
<s>
Consider	O
a	O
speech	O
signal	O
,	O
which	O
can	O
be	O
represented	O
in	O
a	O
domain	O
such	O
that	O
,	O
where	O
speech	O
signal	O
,	O
dictionary	B-General_Concept
matrix	I-General_Concept
and	O
the	O
sparse	O
coefficient	O
vector	O
.	O
</s>
<s>
This	O
speech	O
signal	O
is	O
said	O
to	O
be	O
sparse	O
in	O
domain	O
,	O
if	O
the	O
number	O
of	O
significant	O
(	O
non	O
zero	O
)	O
coefficients	O
in	O
sparse	B-Algorithm
vector	I-Algorithm
is	O
,	O
where	O
.	O
</s>
<s>
If	O
measurement	O
matrix	O
satisfies	O
the	O
restricted	B-Algorithm
isometric	I-Algorithm
property	I-Algorithm
(	O
RIP	O
)	O
and	O
is	O
incoherent	O
with	O
dictionary	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
Estimating	O
the	O
sparsity	B-Algorithm
of	O
a	O
speech	O
signal	O
is	O
a	O
problem	O
since	O
the	O
speech	O
signal	O
varies	O
greatly	O
over	O
time	O
and	O
thus	O
sparsity	B-Algorithm
of	O
speech	O
signal	O
also	O
varies	O
highly	O
over	O
time	O
.	O
</s>
<s>
If	O
sparsity	B-Algorithm
of	O
speech	O
signal	O
can	O
be	O
calculated	O
over	O
time	O
without	O
much	O
complexity	O
that	O
will	O
be	O
best	O
.	O
</s>
<s>
If	O
this	O
is	O
not	O
possible	O
then	O
worst-case	O
scenario	O
for	O
sparsity	B-Algorithm
can	O
be	O
considered	O
for	O
a	O
given	O
speech	O
signal	O
.	O
</s>
<s>
Sparse	B-Algorithm
vector	I-Algorithm
(	O
)	O
for	O
a	O
given	O
speech	O
signal	O
is	O
reconstructed	O
from	O
as	O
small	O
as	O
possible	O
a	O
number	O
of	O
measurements	O
(	O
)	O
using	O
minimization	O
.	O
</s>
<s>
Then	O
original	O
speech	O
signal	O
is	O
reconstructed	O
form	O
the	O
calculated	O
sparse	B-Algorithm
vector	I-Algorithm
using	O
the	O
fixed	O
dictionary	B-General_Concept
matrix	I-General_Concept
as	O
as	O
=	O
.	O
</s>
<s>
Estimation	O
of	O
both	O
the	O
dictionary	B-General_Concept
matrix	I-General_Concept
and	O
sparse	B-Algorithm
vector	I-Algorithm
from	O
random	O
measurements	O
only	O
has	O
been	O
done	O
iteratively	O
.	O
</s>
<s>
The	O
speech	O
signal	O
reconstructed	O
from	O
estimated	O
sparse	B-Algorithm
vector	I-Algorithm
and	O
dictionary	B-General_Concept
matrix	I-General_Concept
is	O
much	O
closer	O
to	O
the	O
original	O
signal	O
.	O
</s>
<s>
Some	O
more	O
iterative	B-Algorithm
approaches	O
to	O
calculate	O
both	O
dictionary	B-General_Concept
matrix	I-General_Concept
and	O
speech	O
signal	O
from	O
just	O
random	O
measurements	O
of	O
speech	O
signal	O
have	O
been	O
developed	O
.	O
</s>
<s>
The	O
application	O
of	O
structured	O
sparsity	B-Algorithm
for	O
joint	O
speech	O
localization-separation	O
in	O
reverberant	O
acoustics	O
has	O
been	O
investigated	O
for	O
multiparty	O
speech	O
recognition	O
.	O
</s>
<s>
Further	O
applications	O
of	O
the	O
concept	O
of	O
sparsity	B-Algorithm
are	O
yet	O
to	O
be	O
studied	O
in	O
the	O
field	O
of	O
speech	B-Algorithm
processing	I-Algorithm
.	O
</s>
<s>
The	O
idea	O
behind	O
applying	O
CS	O
to	O
speech	O
signals	O
is	O
to	O
formulate	O
algorithms	O
or	O
methods	O
that	O
use	O
only	O
those	O
random	O
measurements	O
(	O
)	O
to	O
carry	O
out	O
various	O
forms	O
of	O
application-based	O
processing	O
such	O
as	O
speaker	B-Application
recognition	I-Application
and	O
speech	B-Application
enhancement	I-Application
.	O
</s>
