<s>
Embedded	B-Data_Structure
Zerotrees	I-Data_Structure
of	I-Data_Structure
Wavelet	I-Data_Structure
transforms	I-Data_Structure
(	O
EZW	B-Data_Structure
)	O
is	O
a	O
lossy	O
image	B-General_Concept
compression	I-General_Concept
algorithm	O
.	O
</s>
<s>
By	O
considering	O
the	O
transformed	O
coefficients	O
as	O
a	O
tree	O
(	O
or	O
trees	O
)	O
with	O
the	O
lowest	O
frequency	O
coefficients	O
at	O
the	O
root	O
node	O
and	O
with	O
the	O
children	O
of	O
each	O
tree	O
node	O
being	O
the	O
spatially	O
related	O
coefficients	O
in	O
the	O
next	O
higher	O
frequency	O
subband	B-Algorithm
,	O
there	O
is	O
a	O
high	O
probability	O
that	O
one	O
or	O
more	O
subtrees	O
will	O
consist	O
entirely	O
of	O
coefficients	O
which	O
are	O
zero	O
or	O
nearly	O
zero	O
,	O
such	O
subtrees	O
are	O
called	O
zerotrees	O
.	O
</s>
<s>
In	O
zerotree	O
based	O
image	B-General_Concept
compression	I-General_Concept
scheme	O
such	O
as	O
EZW	B-Data_Structure
and	O
SPIHT	O
,	O
the	O
intent	O
is	O
to	O
use	O
the	O
statistical	O
properties	O
of	O
the	O
trees	O
in	O
order	O
to	O
efficiently	O
code	O
the	O
locations	O
of	O
the	O
significant	O
coefficients	O
.	O
</s>
<s>
Since	O
most	O
of	O
the	O
coefficients	O
will	O
be	O
zero	O
or	O
close	O
to	O
zero	O
,	O
the	O
spatial	O
locations	O
of	O
the	O
significant	O
coefficients	O
make	O
up	O
a	O
large	O
portion	O
of	O
the	O
total	O
size	O
of	O
a	O
typical	O
compressed	B-General_Concept
image	I-General_Concept
.	O
</s>
<s>
EZW	B-Data_Structure
uses	O
four	O
symbols	O
to	O
represent	O
(	O
a	O
)	O
a	O
zerotree	O
root	O
,	O
(	O
b	O
)	O
an	O
isolated	O
zero	O
(	O
a	O
coefficient	O
which	O
is	O
insignificant	O
,	O
but	O
which	O
has	O
significant	O
descendants	O
)	O
,	O
(	O
c	O
)	O
a	O
significant	O
positive	O
coefficient	O
and	O
(	O
d	O
)	O
a	O
significant	O
negative	O
coefficient	O
.	O
</s>
<s>
In	O
practical	O
implementations	O
,	O
it	O
would	O
be	O
usual	O
to	O
use	O
an	O
entropy	O
code	O
such	O
as	O
arithmetic	B-Algorithm
code	I-Algorithm
to	O
further	O
improve	O
the	O
performance	O
of	O
the	O
dominant	O
pass	O
.	O
</s>
<s>
The	O
coding	O
performance	O
of	O
EZW	B-Data_Structure
has	O
since	O
been	O
exceeded	O
by	O
SPIHT	O
and	O
its	O
many	O
derivatives	O
.	O
</s>
<s>
Embedded	B-Data_Structure
zerotree	I-Data_Structure
wavelet	I-Data_Structure
algorithm	O
(	O
EZW	B-Data_Structure
)	O
as	O
developed	O
by	O
J	O
.	O
Shapiro	O
in	O
1993	O
,	O
enables	O
scalable	O
image	O
transmission	O
and	O
decoding	O
.	O
</s>
<s>
It	O
is	O
based	O
on	O
four	O
key	O
concepts	O
:	O
first	O
,	O
it	O
should	O
be	O
a	O
discrete	O
wavelet	B-Algorithm
transform	I-Algorithm
or	O
hierarchical	O
subband	B-Algorithm
decomposition	O
;	O
second	O
,	O
it	O
should	O
predict	O
the	O
absence	O
of	O
significant	O
information	O
when	O
exploring	O
the	O
self-similarity	O
inherent	O
in	O
images	O
;	O
third	O
,	O
it	O
has	O
entropy-coded	O
successive-approximation	O
quantization	O
,	O
and	O
fourth	O
,	O
it	O
is	O
enabled	O
to	O
achieve	O
universal	O
lossless	O
data	O
compression	O
via	O
adaptive	O
arithmetic	B-Algorithm
coding	I-Algorithm
.	O
</s>
<s>
Besides	O
,	O
the	O
EZW	B-Data_Structure
algorithm	O
also	O
contains	O
the	O
following	O
features	O
:	O
</s>
<s>
(	O
1	O
)	O
A	O
discrete	O
wavelet	B-Algorithm
transform	I-Algorithm
which	O
can	O
use	O
a	O
compact	O
multiresolution	O
representation	O
in	O
the	O
image	O
.	O
</s>
<s>
(	O
4	O
)	O
A	O
prioritization	O
protocol	O
which	O
the	O
importance	O
is	O
determined	O
by	O
the	O
precision	O
,	O
magnitude	O
,	O
scale	O
,	O
and	O
spatial	O
location	O
of	O
the	O
wavelet	B-Algorithm
coefficients	I-Algorithm
in	O
order	O
.	O
</s>
<s>
(	O
5	O
)	O
Adaptive	O
multilevel	O
arithmetic	B-Algorithm
coding	I-Algorithm
which	O
is	O
a	O
fast	O
and	O
efficient	O
method	O
for	O
entropy	O
coding	O
strings	O
of	O
symbols	O
.	O
</s>
<s>
Using	O
this	O
scanning	O
on	O
EZW	B-Data_Structure
transform	O
is	O
to	O
perform	O
scanning	O
the	O
coefficients	O
in	O
such	O
way	O
that	O
no	O
child	O
node	O
is	O
scanned	O
before	O
its	O
parent	O
node	O
.	O
</s>
<s>
Also	O
,	O
all	O
positions	O
in	O
a	O
given	O
subband	B-Algorithm
are	O
scanned	O
before	O
it	O
moves	O
to	O
the	O
next	O
subband	B-Algorithm
.	O
</s>
<s>
In	O
this	O
method	O
,	O
it	O
will	O
visit	O
the	O
significant	O
coefficients	O
according	O
to	O
the	O
magnitude	O
and	O
raster	O
order	O
within	O
subbands	B-Algorithm
.	O
</s>
