<s>
The	O
Shinnar	O
–	O
Le	O
Roux	O
(	O
SLR	O
)	O
algorithm	O
is	O
a	O
mathematical	O
tool	O
for	O
generating	O
frequency-selective	O
radio	O
frequency	O
(	O
RF	O
)	O
pulses	O
in	O
magnetic	O
resonance	O
imaging	O
(	O
MRI	B-Algorithm
)	O
.	O
</s>
<s>
Frequency	O
selective	O
pulses	O
are	O
used	O
in	O
MRI	B-Algorithm
to	O
isolate	O
a	O
slice	O
through	O
the	O
subject	O
for	O
excitation	O
,	O
inversion	O
and	O
saturation	O
.	O
</s>
<s>
Given	O
a	O
desired	O
magnetization	O
profile	O
,	O
determining	O
the	O
RF	O
pulse	O
that	O
produces	O
it	O
is	O
generally	O
nonlinear	O
,	O
due	O
to	O
the	O
non-linearity	O
of	O
the	O
Bloch	B-Algorithm
equations	I-Algorithm
.	O
</s>
<s>
A	O
direct	O
solution	O
to	O
the	O
pulse	O
design	O
problem	O
was	O
independently	O
proposed	O
by	O
Shinnar	O
and	O
Le	O
Roux	O
based	O
on	O
a	O
discrete	O
approximation	O
to	O
the	O
spin	O
domain	O
version	O
of	O
the	O
Bloch	B-Algorithm
equations	I-Algorithm
.	O
</s>
<s>
The	O
SLR	O
algorithm	O
simplifies	O
the	O
solution	O
of	O
the	O
Bloch	B-Algorithm
equations	I-Algorithm
to	O
the	O
design	O
of	O
two	O
polynomials	O
,	O
which	O
can	O
be	O
solved	O
using	O
well-known	O
digital	O
filter	O
design	O
algorithms	O
.	O
</s>
