Image Processing Reference
In-Depth Information
Ring Algorithm
e
j
ω
Input
: A distance function
D
j
(
P
,
P
)
, an initial power spectrum
P
(
)
,the
e
j
ω
squared sensor frequency responses
G
i
(
)
, and the autocorrelation estimates
R
v
i
(
k
)
for
k
=
,,...,
L
−
and
i
=
,,...,
N
.
e
j
ω
Output
: A power spectrum
P
∗
(
)
.
Procedure
:
, and
P
(
m
)
1. Let
m
=
,
i
=
=
P
.
2. Send
P
(
)
to the
i
th sensor node.
At the
i
th sensor:
m
and define
P
k
P
(
m
)
.
(
i
)
Let
k
=
=
Calculate
P
k
(
ii
)
=
P
[
for
k
=
,,...,
L
−
.
P
k
↦Q
i
,
k
;
D
j
]
−
P
L
,
P
є then let
P
P
L
(
iii
)
If
D
(
)>
=
and go back to item
(
ii
)
.
−
−
Otherwise, let
i
=
i
+
andgotoStep3.
3. If
(
imodN
)=
then set
m
=
m
+
and reset
i
to 1. Otherwise, set
P
L
P
(
m
)
=
and go back to Step 2.
−
P
L
4. Define
P
(
m
)
=
P
(
m
)
,
P
(
m
−
)
)>
.If
D
(
є, go back to Step 2. Otherwise
−
output
P
∗
=
P
(
m
)
and stop.
(
m
)
(
j
ω)
Input
P
(
m
)
(
j
ω)
Output
P
(0)
(
P
j
ω)
(
m
)
(
P
j
ω)
Feasible sets
Q
i
,
k
(
m
)
(
P
j
ω)
Speech
source
x
(
n
)
(
m
)
(
P
j
ω)
(
m
)
(
P
j
ω)
FIGURE .
Graphical depiction of the Ring Algorithm. For illustrative reasons, only three feasible sets
Q
i
,
k
are
shownintheinsidepicture.Also,itisshownthattheoutputspectrum
P
(
m
)
e
j
ω
is obtained from the input
P
(
m
)
e
j
ω
)
only after three projections. In practice, each sensor node has
L
feasible sets and has to repeat the sequence of pro-
jections many times before it can successfully project the input
P
(
(
)
(
m
)
e
j
ω
(
)
into the intersection of its feasible sets.