<s>
An	O
anamorphic	B-General_Concept
stretch	I-General_Concept
transform	I-General_Concept
(	O
AST	O
)	O
also	O
referred	O
to	O
as	O
warped	O
stretch	O
transform	B-Algorithm
is	O
a	O
physics-inspired	O
signal	O
transform	B-Algorithm
that	O
emerged	O
from	O
time	O
stretch	O
dispersive	O
Fourier	O
transform	B-Algorithm
.	O
</s>
<s>
The	O
transform	B-Algorithm
can	O
be	O
applied	O
to	O
analog	O
temporal	O
signals	O
such	O
as	O
communication	O
signals	O
,	O
or	O
to	O
digital	O
spatial	O
data	O
such	O
as	O
images	O
.	O
</s>
<s>
The	O
transform	B-Algorithm
reshapes	O
the	O
data	O
in	O
such	O
a	O
way	O
that	O
its	O
output	O
has	O
properties	O
conducive	O
for	O
data	B-General_Concept
compression	I-General_Concept
and	O
analytics	B-General_Concept
.	O
</s>
<s>
An	O
anamorphic	B-General_Concept
stretch	I-General_Concept
transform	I-General_Concept
(	O
AST	O
)	O
is	O
a	O
mathematical	O
transformation	O
in	O
which	O
analog	O
or	O
digital	O
data	O
is	O
stretched	O
and	O
warped	O
in	O
a	O
context-aware	O
manner	O
,	O
such	O
that	O
it	O
results	O
in	O
nonuniform	O
Fourier	O
domain	O
sampling	O
.	O
</s>
<s>
The	O
resulting	O
non-uniform	O
sampling	O
,	O
where	O
information	O
rich	O
portions	O
of	O
the	O
signal	O
are	O
sampled	O
at	O
a	O
higher	O
rate	O
than	O
the	O
sparse	O
regions	O
,	O
can	O
be	O
exploited	O
for	O
data	B-General_Concept
compression	I-General_Concept
.	O
</s>
<s>
As	O
any	O
other	O
data	B-General_Concept
compression	I-General_Concept
method	O
,	O
the	O
maximum	O
compression	O
that	O
can	O
be	O
achieved	O
using	O
AST	O
is	O
signal	O
dependent	O
.	O
</s>
<s>
The	O
reconstruction	O
accuracy	O
and	O
lossy	B-Algorithm
nature	O
of	O
this	O
compression	O
method	O
have	O
been	O
analyzed	O
previously	O
.	O
</s>
<s>
Because	O
of	O
the	O
limited	O
bandwidth	O
and	O
the	O
limited	O
resolution	O
of	O
the	O
digitizer	O
,	O
as	O
measured	O
by	O
its	O
effective	O
number	O
of	O
bits	O
(	O
ENOB	O
)	O
,	O
the	O
reconstruction	O
will	O
never	O
be	O
ideal	O
,	O
and	O
therefore	O
,	O
this	O
is	O
a	O
lossy	B-Algorithm
compression	I-Algorithm
method	O
.	O
</s>
<s>
Reconstruction	O
(	O
inverse	O
mapping	O
)	O
of	O
the	O
spatial	O
image	O
via	O
Fourier	O
transform	B-Algorithm
require	O
knowledge	O
of	O
phase	O
in	O
addition	O
to	O
amplitude	O
of	O
the	O
warped	O
image	O
.	O
</s>
<s>
Finite	O
SNR	O
will	O
compromise	O
the	O
quality	O
of	O
phase	O
recovery	O
and	O
data	B-General_Concept
compression	I-General_Concept
.	O
</s>
<s>
Because	O
of	O
this	O
challenge	O
,	O
practical	O
implementation	O
of	O
anamorphic	O
data	B-General_Concept
compression	I-General_Concept
is	O
not	O
achieved	O
yet	O
.	O
</s>
<s>
In	O
this	O
alternative	O
data	B-General_Concept
compression	I-General_Concept
method	O
,	O
information-rich	O
portions	O
of	O
the	O
data	O
are	O
dilated	O
in	O
a	O
process	O
that	O
emulates	O
the	O
effect	O
of	O
group	O
velocity	O
dispersion	O
on	O
temporal	O
signals	O
.	O
</s>
<s>
The	O
phase	B-Algorithm
stretch	I-Algorithm
transform	I-Algorithm
or	O
PST	O
is	O
a	O
computational	O
approach	O
to	O
signal	O
and	O
image	O
processing	O
.	O
</s>
<s>
Both	O
phase	B-Algorithm
stretch	I-Algorithm
transform	I-Algorithm
and	O
AST	O
transform	B-Algorithm
the	O
image	O
by	O
emulating	O
propagation	O
through	O
a	O
diffractive	O
medium	O
with	O
engineered	O
3D	O
dispersive	O
property	O
(	O
refractive	O
index	O
)	O
.	O
</s>
<s>
The	O
difference	O
between	O
the	O
two	O
mathematical	O
operations	O
is	O
that	O
AST	O
uses	O
the	O
magnitude	O
of	O
the	O
complex	O
amplitude	O
after	O
transformation	O
but	O
phase	B-Algorithm
stretch	I-Algorithm
transform	I-Algorithm
employs	O
the	O
phase	O
of	O
the	O
complex	O
amplitude	O
after	O
transformation	O
.	O
</s>
<s>
Anamorphic	O
(	O
warped	O
)	O
stretch	O
transform	B-Algorithm
is	O
a	O
physics-based	O
mathematical	O
operation	O
that	O
reduces	O
the	O
signal	O
bandwidth	O
without	O
proportionally	O
increasing	O
the	O
size	O
of	O
the	O
signal	O
,	O
thus	O
providing	O
space-bandwidth	O
product	O
compression	O
.	O
</s>
<s>
This	O
operation	O
may	O
be	O
used	O
as	O
a	O
pre-processing	O
operation	O
that	O
may	O
enhance	O
conventional	O
image	O
compression	B-General_Concept
techniques	I-General_Concept
.	O
</s>
<s>
This	O
lossy	B-Algorithm
transformation	O
may	O
make	O
it	O
possible	O
to	O
capture	O
and	O
digitize	O
signals	O
that	O
are	O
faster	O
than	O
the	O
speed	O
of	O
the	O
sensor	O
and	O
the	O
digitizer	O
,	O
and	O
also	O
to	O
minimize	O
the	O
volume	O
of	O
the	O
data	O
generated	O
in	O
the	O
process	O
.	O
</s>
