No subject
Tue Jan 15 14:41:49 EST 2013
y unavailable for a given problem. In particular=2C cannot be computed fro=
m because this unknown signal is precisely the signal that this filter aim=
s to recover. Nevertheless=2C it is common for the noise to have a power sp=
ectral density that is flat or decreasing significantly more slowly than th=
e power spectral density of a typical image as the frequency increases. He=
nce=2C can typically be approximated with a constant=2C and this filter ma=
kes this assumption (see the NoiseVariance member variable). =2C on the oth=
er hand=2C will vary with input. This filter computes the power spectral de=
nsity of the input blurred image=2C subtracts the power spectral density of=
the noise=2C and uses the result as the estimate of .
Yes=2C the Wiener deconvolution filter makes the assumption of a flat noise=
spectrum across all frequencies. This leads to the assumption that the si=
gnal (image) will dominate the low frequencies=2C while the noise is higher=
in the high frequencies - which is typically the case. A common method to=
remove noise is to convolve with a Gaussian kernel=2C but as I understand =
it=2C finding the noise variance is a nontrivial problem. Maybe check out =
some of the smoothing filters [2].
[2] http://www.itk.org/Wiki/ITK/Examples#Smoothing
On Wed=2C Mar 20=2C 2013 at 11:57 AM=2C lena russo <lilli888899 at hotmail.it>=
wrote:
Hi Christopher=2C
thanks for your answer! I'm not very familiar with noise in images=2C but i=
f I understand correctly the Wiener deconvolution filter requires knowledge=
about the nature of the noise itself. Am I correct? What if I don't know i=
ts nature but I need to find which kind of noise affected the image?
Many many thanks
Lena
Date: Wed=2C 13 Mar 2013 10:57:25 -0400
Subject: Re: [Insight-users] Level of noise in an image
From: christopher.mullins at kitware.com
To: lilli888899 at hotmail.it
CC: insight-users at itk.org
Are you looking for the power spectral densities of the signal and noise? =
You might consider the implementation of the Wiener deconvolution filter [1=
].
[1] http://www.itk.org/Doxygen/html/classitk_1_1WienerDeconvolutionImageFil=
ter.html
On Wed=2C Mar 13=2C 2013 at 10:46 AM=2C lena russo <lilli888899 at hotmail.it>=
wrote:
Hi all=2C
I'm trying to develop a good method to evaluate the level
of noise in an image in order to filter the image accordingly and=20
remove this noise. Have you got any suggestion?
Many many thanks for your help=2C
Lena =20
_____________________________________
Powered by www.kitware.com
Visit other Kitware open-source projects at
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--=20
Christopher MullinsR&D EngineerKitware Inc.=2C919.869.8871
=20
--=20
Christopher MullinsR&D EngineerKitware Inc.=2C919.869.8871
=
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<body class=3D'hmmessage'><div dir=3D'ltr'>
Thanks a million Christopher.<br><br>Lena<br><br><div><div id=3D"SkyDrivePl=
aceholder"></div><hr id=3D"stopSpelling">Date: Wed=2C 20 Mar 2013 15:23:51 =
-0300<br>Subject: Re: [Insight-users] Level of noise in an image<br>From: c=
hristopher.mullins at kitware.com<br>To: lilli888899 at hotmail.it<br>CC: insight=
-users at itk.org<br><br><div dir=3D"ltr">From [1]: =3B<span style=3D"colo=
r:rgb(0=2C0=2C0)=3Bfont-family:'Lucida Grande'=2CVerdana=2CGeneva=2CArial=
=2Csans-serif=3Bfont-size:12px=3Bline-height:19px">The power spectral densi=
ties of the signal and noise are typically unavailable for a given problem.=
In particular=2C =3B</span><img class=3D"ecx" alt=3D"$P_f(\omega)$" sr=
c=3D"http://www.itk.org/Doxygen/html/form_312.png" style=3D"vertical-align:=
middle=3Bcolor:rgb(0=2C 0=2C 0)=3Bfont-family:'Lucida Grande'=2C Verdana=2C=
Geneva=2C Arial=2C sans-serif=3Bfont-size:12px=3Bline-height:19px"><span s=
tyle=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Lucida Grande'=2CVerdana=2CGene=
va=2CArial=2Csans-serif=3Bfont-size:12px=3Bline-height:19px"> =3Bcannot=
be computed from =3B</span><img class=3D"ecx" alt=3D"$f(x)$" src=3D"ht=
tp://www.itk.org/Doxygen/html/form_315.png" style=3D"vertical-align:middle=
=3Bcolor:rgb(0=2C 0=2C 0)=3Bfont-family:'Lucida Grande'=2C Verdana=2C Genev=
a=2C Arial=2C sans-serif=3Bfont-size:12px=3Bline-height:19px"><span style=
=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Lucida Grande'=2CVerdana=2CGeneva=
=2CArial=2Csans-serif=3Bfont-size:12px=3Bline-height:19px"> =3Bbecause =
this unknown signal is precisely the signal that this filter aims to recove=
r. Nevertheless=2C it is common for the noise to have a power spectral dens=
ity that is flat or decreasing significantly more slowly than the power spe=
ctral density of a typical image as the frequency =3B</span><img class=
=3D"ecx" alt=3D"$\omega$" src=3D"http://www.itk.org/Doxygen/html/form_316.p=
ng" style=3D"vertical-align:middle=3Bcolor:rgb(0=2C 0=2C 0)=3Bfont-family:'=
Lucida Grande'=2C Verdana=2C Geneva=2C Arial=2C sans-serif=3Bfont-size:12px=
=3Bline-height:19px"><span style=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Luc=
ida Grande'=2CVerdana=2CGeneva=2CArial=2Csans-serif=3Bfont-size:12px=3Bline=
-height:19px"> =3Bincreases. Hence=2C =3B</span><img class=3D"ecx" =
alt=3D"$P_n(\omega)$" src=3D"http://www.itk.org/Doxygen/html/form_313.png" =
style=3D"vertical-align:middle=3Bcolor:rgb(0=2C 0=2C 0)=3Bfont-family:'Luci=
da Grande'=2C Verdana=2C Geneva=2C Arial=2C sans-serif=3Bfont-size:12px=3Bl=
ine-height:19px"><span style=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Lucida =
Grande'=2CVerdana=2CGeneva=2CArial=2Csans-serif=3Bfont-size:12px=3Bline-hei=
ght:19px"> =3Bcan typically be approximated with a constant=2C and this=
filter makes this assumption (see the NoiseVariance member variable). =
=3B</span><img class=3D"ecx" alt=3D"$P_f(\omega)$" src=3D"http://www.itk.or=
g/Doxygen/html/form_312.png" style=3D"vertical-align:middle=3Bcolor:rgb(0=
=2C 0=2C 0)=3Bfont-family:'Lucida Grande'=2C Verdana=2C Geneva=2C Arial=2C =
sans-serif=3Bfont-size:12px=3Bline-height:19px"><span style=3D"color:rgb(0=
=2C0=2C0)=3Bfont-family:'Lucida Grande'=2CVerdana=2CGeneva=2CArial=2Csans-s=
erif=3Bfont-size:12px=3Bline-height:19px">=2C on the other hand=2C will var=
y with input. This filter computes the power spectral density of the input =
blurred image=2C subtracts the power spectral density of the noise=2C and u=
ses the result as the estimate of =3B</span><img class=3D"ecx" alt=3D"$=
P_f(\omega)$" src=3D"http://www.itk.org/Doxygen/html/form_312.png" style=3D=
"vertical-align:middle=3Bcolor:rgb(0=2C 0=2C 0)=3Bfont-family:'Lucida Grand=
e'=2C Verdana=2C Geneva=2C Arial=2C sans-serif=3Bfont-size:12px=3Bline-heig=
ht:19px"><span style=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Lucida Grande'=
=2CVerdana=2CGeneva=2CArial=2Csans-serif=3Bfont-size:12px=3Bline-height:19p=
x">.</span><div>
<span style=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Lucida Grande'=2CVerdana=
=2CGeneva=2CArial=2Csans-serif=3Bfont-size:12px=3Bline-height:19px"><br></s=
pan></div><div><span style=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Lucida Gr=
ande'=2CVerdana=2CGeneva=2CArial=2Csans-serif=3Bfont-size:12px=3Bline-heigh=
t:19px">Yes=2C the Wiener deconvolution filter makes the assumption of a fl=
at noise spectrum across all frequencies.  =3BThis leads to the assumpt=
ion that the signal (image) will dominate the low frequencies=2C while the =
noise is higher in the high frequencies - which is typically the case. &nbs=
p=3BA common method to remove noise is to convolve with a Gaussian kernel=
=2C but as I understand it=2C finding the noise variance is a nontrivial pr=
oblem.  =3BMaybe check out some of the smoothing filters [2].</span></d=
iv>
<div><span style=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Lucida Grande'=2CVe=
rdana=2CGeneva=2CArial=2Csans-serif=3Bfont-size:12px=3Bline-height:19px"><b=
r></span></div><div><span style=3D"color:rgb(0=2C0=2C0)=3Bfont-family:'Luci=
da Grande'=2CVerdana=2CGeneva=2CArial=2Csans-serif=3Bfont-size:12px=3Bline-=
height:19px">[2] =3B</span><a href=3D"http://www.itk.org/Wiki/ITK/Examp=
les#Smoothing" target=3D"_blank">http://www.itk.org/Wiki/ITK/Examples#Smoot=
hing</a></div>
</div><div class=3D"ecxgmail_extra"><br><br><div class=3D"ecxgmail_quote">O=
n Wed=2C Mar 20=2C 2013 at 11:57 AM=2C lena russo <span dir=3D"ltr"><=3B<=
a href=3D"mailto:lilli888899 at hotmail.it">lilli888899 at hotmail.it</a>>=3B</=
span> wrote:<br>
<blockquote class=3D"ecxgmail_quote" style=3D"border-left:1px #ccc solid=3B=
padding-left:1ex">
<div><div dir=3D"ltr">
Hi Christopher=2C<br><br>thanks for your answer! I'm not very familiar with=
noise in images=2C but if I understand correctly the Wiener deconvolution =
filter requires knowledge about the nature of the noise itself. Am I correc=
t? What if I don't know its nature but I need to find which kind of noise a=
ffected the image?<br>
<br>Many many thanks<span class=3D"ecxHOEnZb"><font color=3D"#888888"><br><=
br>Lena<br></font></span><div class=3D"ecxhm ecxHOEnZb"><br></div><div><div=
class=3D"ecxhm ecxHOEnZb"><div></div><hr>Date: Wed=2C 13 Mar 2013 10:57:25=
-0400<br>Subject: Re: [Insight-users] Level of noise in an image<br>
From: <a href=3D"mailto:christopher.mullins at kitware.com">christopher.mullin=
s at kitware.com</a><br>To: <a href=3D"mailto:lilli888899 at hotmail.it">lilli888=
899 at hotmail.it</a><br>CC: <a href=3D"mailto:insight-users at itk.org">insight-=
users at itk.org</a></div>
<div><div class=3D"h5"><br><br><div dir=3D"ltr">Are you looking for the pow=
er spectral densities of the signal and noise?  =3BYou might consider t=
he implementation of the Wiener deconvolution filter [1].<div><br></div><di=
v>[1] =3B<a href=3D"http://www.itk.org/Doxygen/html/classitk_1_1WienerD=
econvolutionImageFilter.html" target=3D"_blank">http://www.itk.org/Doxygen/=
html/classitk_1_1WienerDeconvolutionImageFilter.html</a></div>
</div><div><br><br><div>On Wed=2C Mar 13=2C 2013 at 10:46 AM=2C lena russo =
<span dir=3D"ltr"><=3B<a href=3D"mailto:lilli888899 at hotmail.it">lilli8888=
99 at hotmail.it</a>>=3B</span> wrote:<br>
<blockquote style=3D"border-left:1px #ccc solid=3Bpadding-left:1ex">
<div><div dir=3D"ltr">
Hi all=2C<br><br>I'm trying to develop a good method to evaluate the level
of noise in an image in order to filter the image accordingly and=20
remove this noise. Have you got any suggestion?<br><br>Many many thanks for=
your help=2C<br><br>Lena </div></div>
<br>_____________________________________<br>
Powered by <a href=3D"http://www.kitware.com" target=3D"_blank">www.kitware=
.com</a><br>
<br>
Visit other Kitware open-source projects at<br>
<a href=3D"http://www.kitware.com/opensource/opensource.html" target=3D"_bl=
ank">http://www.kitware.com/opensource/opensource.html</a><br>
<br>
Kitware offers ITK Training Courses=2C for more information visit:<br>
<a href=3D"http://www.kitware.com/products/protraining.php" target=3D"_blan=
k">http://www.kitware.com/products/protraining.php</a><br>
<br>
Please keep messages on-topic and check the ITK FAQ at:<br>
<a href=3D"http://www.itk.org/Wiki/ITK_FAQ" target=3D"_blank">http://www.it=
k.org/Wiki/ITK_FAQ</a><br>
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Follow this link to subscribe/unsubscribe:<br>
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ank">http://www.itk.org/mailman/listinfo/insight-users</a><br>
<br></blockquote></div><br><br clear=3D"all"><div><br></div>-- <br>Christop=
her Mullins<div>R&=3BD Engineer</div><div>Kitware Inc.=2C</div><div><a t=
arget=3D"_blank">919.869.8871</a></div>
</div></div></div></div> </div></div>
</blockquote></div><br><br clear=3D"all"><div><br></div>-- <br>Christopher =
Mullins<div>R&=3BD Engineer</div><div>Kitware Inc.=2C</div><div>919.869.=
8871</div>
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