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.
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