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Advances in Visual Data Compression and Communication
book

Advances in Visual Data Compression and Communication

by Feng Wu
July 2014
Intermediate to advanced content levelIntermediate to advanced
513 pages
16h 40m
English
Auerbach Publications
Content preview from Advances in Visual Data Compression and Communication
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1.2 Source Coding 13
I(S;
ˆ
S) = h(S) h(S |
ˆ
S), (1.33)
=
1
2
log(2πe)σ
2
s
h(S
ˆ
S |
ˆ
S), (1.34)
1
2
log(2πe)σ
2
s
h(S
ˆ
S), (1.35)
1
2
log(2πe)σ
2
s
h(N(0,E(S
ˆ
S)
2
)), (1.36)
=
1
2
log(2πe)σ
2
s
1
2
log(2πe)E(S
ˆ
S)
2
, (1.37)
1
2
log(2πe)σ
2
s
1
2
log(2πe)D, (1.38)
=
1
2
log
σ
2
s
D
, (1.39)
where Eq. (1.35) follows from the fact that conditioning reduces entropy and Eq.
(1.36) follows from the fact that normal distribution maximizes entropy for a given
second moment. Hence
R(D)
1
2
log
σ
2
s
D
. (1.40)
To find the conditional density f ( ˆs | s) that achieves this lower bound Eq. (1.40),
it is usually more convenient to look at the conditional density f (s | ˆs), which is
sometimes called ...
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Publisher Resources

ISBN: 9781482234138