<s>
Shrinkage	B-Algorithm
fields	I-Algorithm
is	O
a	O
random	O
field-based	O
machine	O
learning	O
technique	O
that	O
aims	O
to	O
perform	O
high	O
quality	O
image	B-Algorithm
restoration	I-Algorithm
(	O
denoising	O
and	O
deblurring	B-Algorithm
)	O
using	O
low	O
computational	O
overhead	O
.	O
</s>
<s>
A	O
shrinkage	O
(	O
mapping	O
)	O
function	O
is	O
directly	O
modeled	O
as	O
a	O
linear	O
combination	O
of	O
radial	B-Algorithm
basis	I-Algorithm
function	I-Algorithm
kernels	I-Algorithm
,	O
where	O
is	O
the	O
shared	O
precision	O
parameter	O
,	O
denotes	O
the	O
(	O
equidistant	O
)	O
kernel	O
positions	O
,	O
and	O
M	O
is	O
the	O
number	O
of	O
Gaussian	O
kernels	O
.	O
</s>
<s>
Because	O
the	O
shrinkage	O
function	O
is	O
directly	O
modeled	O
,	O
the	O
optimization	O
procedure	O
is	O
reduced	O
to	O
a	O
single	O
quadratic	O
minimization	O
per	O
iteration	O
,	O
denoted	O
as	O
the	O
prediction	O
of	O
a	O
shrinkage	O
field	O
where	O
denotes	O
the	O
discrete	B-Algorithm
Fourier	I-Algorithm
transform	I-Algorithm
and	O
is	O
the	O
2D	O
convolution	B-Language
with	O
point	O
spread	O
function	O
filter	O
,	O
is	O
an	O
optical	O
transfer	O
function	O
defined	O
as	O
the	O
discrete	B-Algorithm
Fourier	I-Algorithm
transform	I-Algorithm
of	O
,	O
and	O
is	O
the	O
complex	O
conjugate	O
of	O
.	O
</s>
<s>
is	O
learned	O
as	O
for	O
each	O
iteration	O
with	O
the	O
initial	O
case	O
,	O
this	O
forms	O
a	O
cascade	O
of	O
Gaussian	O
conditional	B-General_Concept
random	I-General_Concept
fields	I-General_Concept
(	O
or	O
cascade	O
of	O
shrinkage	B-Algorithm
fields	I-Algorithm
(	O
CSF	O
)	O
)	O
.	O
</s>
<s>
The	O
learning	O
objective	O
function	O
is	O
defined	O
as	O
,	O
where	O
is	O
a	O
differentiable	O
loss	B-Algorithm
function	I-Algorithm
which	O
is	O
greedily	O
minimized	O
using	O
training	O
data	O
and	O
.	O
</s>
<s>
Preliminary	O
tests	O
by	O
the	O
author	O
suggest	O
that	O
RTF5	O
obtains	O
slightly	O
better	O
denoising	O
performance	O
than	O
,	O
followed	O
by	O
,	O
,	O
,	O
and	O
BM3D	B-Algorithm
.	O
</s>
<s>
BM3D	B-Algorithm
denoising	O
speed	O
falls	O
between	O
that	O
of	O
and	O
,	O
RTF	O
being	O
an	O
order	O
of	O
magnitude	O
slower	O
.	O
</s>
<s>
A	O
reference	O
implementation	O
has	O
been	O
written	O
in	O
MATLAB	B-Language
and	O
released	O
under	O
the	O
BSD	O
2-Clause	O
license	O
:	O
</s>
