<s>
In	O
magnetic	O
resonance	O
imaging	O
(	O
MRI	O
)	O
,	O
k-space	B-Algorithm
is	O
the	O
2D	O
or	O
3D	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
the	O
image	O
measured	O
.	O
</s>
<s>
In	O
MRI	B-Algorithm
physics	I-Algorithm
,	O
complex	O
values	O
are	O
sampled	O
in	O
k-space	B-Algorithm
during	O
an	O
MR	O
measurement	O
in	O
a	O
premeditated	O
scheme	O
controlled	O
by	O
a	O
pulse	O
sequence	O
,	O
i.e.	O
</s>
<s>
In	O
practice	O
,	O
k-space	B-Algorithm
often	O
refers	O
to	O
the	O
temporary	O
image	O
space	O
,	O
usually	O
a	O
matrix	O
,	O
in	O
which	O
data	O
from	O
digitized	O
MR	O
signals	O
are	O
stored	O
during	O
data	O
acquisition	O
.	O
</s>
<s>
When	O
k-space	B-Algorithm
is	O
full	O
(	O
at	O
the	O
end	O
of	O
the	O
scan	O
)	O
the	O
data	O
are	O
mathematically	O
processed	O
to	O
produce	O
a	O
final	O
image	O
.	O
</s>
<s>
Thus	O
k-space	B-Algorithm
holds	O
raw	O
data	O
before	O
reconstruction	O
.	O
</s>
<s>
The	O
concept	O
of	O
k-space	B-Algorithm
is	O
situated	O
in	O
the	O
spatial	O
frequency	O
domain	O
.	O
</s>
<s>
Thus	O
position	O
(	O
x	O
,	O
y	O
)	O
and	O
spatial	O
frequency	O
(	O
,	O
)	O
constitute	O
a	O
Fourier	B-Algorithm
transform	I-Algorithm
pair	O
.	O
</s>
<s>
Typically	O
,	O
k-space	B-Algorithm
has	O
the	O
same	O
number	O
of	O
rows	O
and	O
columns	O
as	O
the	O
final	O
image	O
and	O
is	O
filled	O
with	O
raw	O
data	O
during	O
the	O
scan	O
,	O
usually	O
one	O
line	O
per	O
TR	O
(	O
Repetition	O
Time	O
)	O
.	O
</s>
<s>
Conventional	O
qualitative	O
interpretation	O
of	O
Fourier	O
Analysis	O
asserts	O
that	O
low	O
spatial	O
frequencies	O
(	O
near	O
the	O
center	O
of	O
k-space	B-Algorithm
)	O
contain	O
the	O
signal	O
to	O
noise	O
and	O
contrast	O
information	O
of	O
the	O
image	O
,	O
whereas	O
high	O
spatial	O
frequencies	O
(	O
outer	O
peripheral	O
regions	O
of	O
k-space	B-Algorithm
)	O
contain	O
the	O
information	O
determining	O
the	O
image	O
resolution	O
.	O
</s>
<s>
This	O
is	O
the	O
basis	O
for	O
advanced	O
scanning	O
techniques	O
,	O
such	O
as	O
the	O
keyhole	O
acquisition	O
,	O
in	O
which	O
a	O
first	O
complete	O
k-space	B-Algorithm
is	O
acquired	O
,	O
and	O
subsequent	O
scans	O
are	O
performed	O
for	O
acquiring	O
just	O
the	O
central	O
part	O
of	O
the	O
k-space	B-Algorithm
;	O
in	O
this	O
way	O
,	O
different	O
contrast	O
images	O
can	O
be	O
acquired	O
without	O
the	O
need	O
of	O
running	O
full	O
scans	O
.	O
</s>
<s>
A	O
nice	O
symmetry	O
property	O
exists	O
in	O
k-space	B-Algorithm
if	O
the	O
image	O
magnetization	O
Mxy	O
is	O
prepared	O
to	O
be	O
proportional	O
simply	O
to	O
a	O
contrast-weighted	O
proton	O
density	O
and	O
thus	O
is	O
a	O
real	O
quantity	O
.	O
</s>
<s>
In	O
such	O
a	O
case	O
,	O
the	O
signal	O
at	O
two	O
opposite	O
locations	O
in	O
k-space	B-Algorithm
is	O
:	O
</s>
<s>
Thus	O
k-space	B-Algorithm
information	O
is	O
somewhat	O
redundant	O
then	O
,	O
and	O
an	O
image	O
can	O
be	O
reconstructed	O
using	O
only	O
one	O
half	O
of	O
the	O
k-space	B-Algorithm
,	O
either	O
in	O
the	O
PE	O
(	O
Phase	O
Encode	O
)	O
direction	O
saving	O
scan	O
time	O
(	O
such	O
a	O
technique	O
is	O
known	O
as	O
half	O
Fourier	O
or	O
half	O
scan	O
)	O
or	O
in	O
the	O
FE	O
(	O
Frequency	O
Encode	O
)	O
direction	O
,	O
allowing	O
for	O
lower	O
sampling	O
frequencies	O
and/or	O
shorter	O
echo	O
times	O
(	O
such	O
a	O
technique	O
is	O
known	O
as	O
half	O
echo	O
)	O
.	O
</s>
<s>
MRI	O
k-space	B-Algorithm
is	O
related	O
to	O
NMR	O
time-domainErnst	O
RR	O
,	O
Bodenhausen	O
G	O
and	O
Wokaun	O
A	O
(	O
1987	O
)	O
,	O
Principles	O
of	O
nuclear	O
magnetic	O
resonance	O
in	O
one	O
and	O
two	O
dimensions	O
,	O
Oxford	O
University	O
Press	O
.	O
</s>
<s>
The	O
only	O
difference	O
between	O
the	O
MRI	O
k-space	B-Algorithm
and	O
the	O
NMR	O
time	O
domain	O
is	O
that	O
a	O
gradient	O
G	O
is	O
present	O
in	O
MRI	O
data	O
acquisition	O
,	O
but	O
is	O
absent	O
in	O
NMR	O
data	O
acquisition	O
.	O
</s>
<s>
Due	O
to	O
the	O
presence	O
of	O
the	O
gradient	O
G	O
,	O
the	O
spatial	O
information	O
r	O
(	O
not	O
the	O
spatial	O
frequency	O
information	O
k	O
)	O
is	O
encoded	O
onto	O
the	O
frequency	O
,	O
and	O
at	O
the	O
same	O
time	O
the	O
time-domain	O
is	O
renamed	O
as	O
k-space	B-Algorithm
.	O
</s>
