<s>
Matching	B-General_Concept
pursuit	I-General_Concept
(	O
MP	O
)	O
is	O
a	O
sparse	O
approximation	O
algorithm	O
which	O
finds	O
the	O
"	O
best	O
matching	O
"	O
projections	O
of	O
multidimensional	O
data	O
onto	O
the	O
span	O
of	O
an	O
over-complete	O
(	O
i.e.	O
,	O
redundant	O
)	O
dictionary	O
.	O
</s>
<s>
Instead	O
,	O
matching	B-General_Concept
pursuit	I-General_Concept
chooses	O
the	O
atoms	O
one	O
at	O
a	O
time	O
in	O
order	O
to	O
maximally	O
(	O
greedily	O
)	O
reduce	O
the	O
approximation	O
error	O
.	O
</s>
<s>
For	O
comparison	O
,	O
consider	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
representation	O
of	O
a	O
signal	O
-	O
this	O
can	O
be	O
described	O
using	O
the	O
terms	O
given	O
above	O
,	O
where	O
the	O
dictionary	O
is	O
built	O
from	O
sinusoidal	O
basis	O
functions	O
(	O
the	O
smallest	O
possible	O
complete	O
dictionary	O
)	O
.	O
</s>
<s>
In	O
1993	O
,	O
Mallat	O
and	O
Zhang	O
proposed	O
a	O
greedy	B-Algorithm
solution	O
that	O
they	O
named	O
"	O
Matching	O
Pursuit.	O
"	O
</s>
<s>
In	O
signal	O
processing	O
,	O
the	O
concept	O
of	O
matching	B-General_Concept
pursuit	I-General_Concept
is	O
related	O
to	O
statistical	O
projection	B-General_Concept
pursuit	I-General_Concept
,	O
in	O
which	O
"	O
interesting	O
"	O
projections	O
are	O
found	O
;	O
ones	O
that	O
deviate	O
more	O
from	O
a	O
normal	O
distribution	O
are	O
considered	O
to	O
be	O
more	O
interesting	O
.	O
</s>
<s>
Matching	B-General_Concept
pursuit	I-General_Concept
has	O
been	O
applied	O
to	O
signal	O
,	O
image	O
and	O
video	O
coding	O
,	O
shape	O
representation	O
and	O
recognition	O
,	O
3D	O
objects	O
coding	O
,	O
and	O
in	O
interdisciplinary	O
applications	O
like	O
structural	O
health	O
monitoring	O
.	O
</s>
<s>
It	O
has	O
been	O
shown	O
that	O
it	O
performs	O
better	O
than	O
DCT	B-General_Concept
based	O
coding	O
for	O
low	O
bit	O
rates	O
in	O
both	O
efficiency	O
of	O
coding	O
and	O
quality	O
of	O
image	O
.	O
</s>
<s>
The	O
main	O
problem	O
with	O
matching	B-General_Concept
pursuit	I-General_Concept
is	O
the	O
computational	O
complexity	O
of	O
the	O
encoder	O
.	O
</s>
<s>
The	O
matching	B-General_Concept
pursuit	I-General_Concept
algorithm	O
is	O
used	O
in	O
MP/SOFT	O
,	O
a	O
method	O
of	O
simulating	O
quantum	O
dynamics	O
.	O
</s>
<s>
MP	O
is	O
also	O
used	O
in	O
dictionary	B-General_Concept
learning	I-General_Concept
.	O
</s>
<s>
A	O
popular	O
extension	O
of	O
Matching	B-General_Concept
Pursuit	I-General_Concept
(	O
MP	O
)	O
is	O
its	O
orthogonal	O
version	O
:	O
Orthogonal	O
Matching	B-General_Concept
Pursuit	I-General_Concept
(	O
OMP	O
)	O
.	O
</s>
<s>
OMP	O
was	O
shown	O
to	O
have	O
stability	O
and	O
performance	O
guarantees	O
under	O
certain	O
restricted	B-Algorithm
isometry	I-Algorithm
conditions	O
.	O
</s>
<s>
An	O
obvious	O
extension	O
of	O
Matching	B-General_Concept
Pursuit	I-General_Concept
is	O
over	O
multiple	O
positions	O
and	O
scales	O
,	O
by	O
augmenting	O
the	O
dictionary	O
to	O
be	O
that	O
of	O
a	O
wavelet	O
basis	O
.	O
</s>
<s>
Matching	B-General_Concept
pursuit	I-General_Concept
is	O
related	O
to	O
the	O
field	O
of	O
compressed	O
sensing	O
and	O
has	O
been	O
extended	O
by	O
researchers	O
in	O
that	O
community	O
.	O
</s>
<s>
Notable	O
extensions	O
are	O
Orthogonal	O
Matching	B-General_Concept
Pursuit	I-General_Concept
(	O
OMP	O
)	O
,	O
Stagewise	O
OMP	O
(	O
StOMP	O
)	O
,	O
compressive	O
sampling	O
matching	B-General_Concept
pursuit	I-General_Concept
(	O
CoSaMP	O
)	O
,	O
Generalized	O
OMP	O
(	O
gOMP	O
)	O
,	O
and	O
Multipath	O
Matching	B-General_Concept
Pursuit	I-General_Concept
(	O
MMP	O
)	O
.	O
</s>
