<s>
Noiselets	B-Algorithm
are	O
functions	O
which	O
gives	O
the	O
worst	O
case	O
behavior	O
for	O
the	O
Haar	O
wavelet	O
packet	O
analysis	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
noiselets	B-Algorithm
are	O
totally	O
incompressible	O
by	O
the	O
Haar	O
wavelet	O
packet	O
analysis	O
.	O
</s>
<s>
Like	O
the	O
canonical	O
and	O
Fourier	O
bases	O
,	O
which	O
have	O
an	O
incoherent	O
property	O
,	O
noiselets	B-Algorithm
are	O
perfectly	O
incoherent	O
with	O
the	O
Haar	O
basis	O
.	O
</s>
<s>
Noiselet	B-Algorithm
can	O
be	O
extended	O
and	O
discretized	O
.	O
</s>
<s>
Use	O
extended	O
noiselet	B-Algorithm
,	O
we	O
can	O
generate	O
the	O
noiselet	B-Algorithm
matrix	O
,	O
where	O
n	O
is	O
a	O
power	O
of	O
two	O
:	O
</s>
<s>
The	O
elements	O
of	O
the	O
noiselet	B-Algorithm
matrices	O
take	O
discrete	O
values	O
from	O
one	O
of	O
two	O
four-element	O
sets	O
:	O
</s>
<s>
2D	O
noiselet	B-Algorithm
transforms	O
are	O
obtained	O
through	O
the	O
Kronecker	O
product	O
of	O
1D	O
noiselet	B-Algorithm
transform	O
:	O
</s>
<s>
Noiselet	B-Algorithm
has	O
some	O
properties	O
that	O
make	O
them	O
ideal	O
for	O
applications	O
:	O
</s>
<s>
The	O
noiselet	B-Algorithm
matrix	O
can	O
be	O
derived	O
in	O
.	O
</s>
<s>
Noiselet	B-Algorithm
completely	O
spread	O
out	O
spectrum	O
and	O
have	O
the	O
perfectly	O
incoherent	O
with	O
Haar	O
wavelets	O
.	O
</s>
<s>
Noiselet	B-Algorithm
is	O
conjugate	O
symmetric	O
and	O
is	O
unitary	O
.	O
</s>
<s>
The	O
complementarity	O
of	O
wavelets	O
and	O
noiselets	B-Algorithm
means	O
that	O
noiselets	B-Algorithm
can	O
be	O
used	O
in	O
compressed	O
sensing	O
to	O
reconstruct	O
a	O
signal	O
(	O
such	O
as	O
an	O
image	O
)	O
which	O
has	O
a	O
compact	O
representation	O
in	O
wavelets	O
.	O
</s>
<s>
MRI	O
data	O
can	O
be	O
acquired	O
in	O
noiselet	B-Algorithm
domain	O
,	O
and	O
,	O
subsequently	O
,	O
images	O
can	O
be	O
reconstructed	O
from	O
undersampled	O
data	O
using	O
compressive-sensing	O
reconstruction	O
.	O
</s>
