<s>
In	O
mathematics	O
,	O
the	O
X-ray	B-Algorithm
transform	I-Algorithm
(	O
also	O
called	O
John	B-Algorithm
transform	I-Algorithm
)	O
is	O
an	O
integral	B-Algorithm
transform	I-Algorithm
introduced	O
by	O
Fritz	O
John	O
in	O
1938	O
that	O
is	O
one	O
of	O
the	O
cornerstones	O
of	O
modern	O
integral	O
geometry	O
.	O
</s>
<s>
It	O
is	O
very	O
closely	O
related	O
to	O
the	O
Radon	B-Algorithm
transform	I-Algorithm
,	O
and	O
coincides	O
with	O
it	O
in	O
two	O
dimensions	O
.	O
</s>
<s>
In	O
higher	O
dimensions	O
,	O
the	O
X-ray	B-Algorithm
transform	I-Algorithm
of	O
a	O
function	O
is	O
defined	O
by	O
integrating	O
over	O
lines	O
rather	O
than	O
over	O
hyperplanes	O
as	O
in	O
the	O
Radon	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
The	O
X-ray	B-Algorithm
transform	I-Algorithm
derives	O
its	O
name	O
from	O
X-ray	O
tomography	B-Algorithm
(	O
used	O
in	O
CT	O
scans	O
)	O
because	O
the	O
X-ray	B-Algorithm
transform	I-Algorithm
of	O
a	O
function	O
ƒ	O
represents	O
the	O
attenuation	O
data	O
of	O
a	O
tomographic	B-Algorithm
scan	O
through	O
an	O
inhomogeneous	O
medium	O
whose	O
density	O
is	O
represented	O
by	O
the	O
function	O
ƒ	O
.	O
Inversion	O
of	O
the	O
X-ray	B-Algorithm
transform	I-Algorithm
is	O
therefore	O
of	O
practical	O
importance	O
because	O
it	O
allows	O
one	O
to	O
reconstruct	O
an	O
unknown	O
density	O
ƒ	O
from	O
its	O
known	O
attenuation	O
data	O
.	O
</s>
<s>
The	O
X-ray	B-Algorithm
transform	I-Algorithm
satisfies	O
an	O
ultrahyperbolic	O
wave	O
equation	O
called	O
John	O
's	O
equation	O
.	O
</s>
<s>
The	O
Gauss	O
hypergeometric	O
function	O
can	O
be	O
written	O
as	O
an	O
X-ray	B-Algorithm
transform	I-Algorithm
.	O
</s>
