No subject
Tue Jan 15 14:41:49 EST 2013
signal is precisely the signal that this filter aims to recover.
Nevertheless, it is common for the noise to have a power spectral density
that is flat or decreasing significantly more slowly than the power
spectral density of a typical image as the frequency [image: $\omega$]
increases.
Hence, [image: $P_n(\omega)$] can typically be approximated with a
constant, and this filter makes this assumption (see the NoiseVariance
member variable). [image: $P_f(\omega)$], on the other hand, will vary with
input. This filter computes the power spectral density of the input blurred
image, subtracts the power spectral density of the noise, and uses the
result as the estimate of [image: $P_f(\omega)$].
Yes, the Wiener deconvolution filter makes the assumption of a flat noise
spectrum across all frequencies. This leads to the assumption that the
signal (image) will dominate the low frequencies, 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, but as I understand it,
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, Mar 20, 2013 at 11:57 AM, lena russo <lilli888899 at hotmail.it> wrote:
> Hi Christopher,
>
> thanks for your answer! I'm not very familiar with noise in images, but if
> 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
> its nature but I need to find which kind of noise affected the image?
>
> Many many thanks
>
> Lena
>
> ------------------------------
> Date: Wed, 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_1WienerDeconvolutionImageFilter.html
>
>
> On Wed, Mar 13, 2013 at 10:46 AM, lena russo <lilli888899 at hotmail.it>wrote:
>
> Hi all,
>
> 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 remove this noise. Have
> you got any suggestion?
>
> Many many thanks for your help,
>
> Lena
>
> _____________________________________
> Powered by www.kitware.com
>
> Visit other Kitware open-source projects at
> http://www.kitware.com/opensource/opensource.html
>
> Kitware offers ITK Training Courses, for more information visit:
> http://www.kitware.com/products/protraining.php
>
> Please keep messages on-topic and check the ITK FAQ at:
> http://www.itk.org/Wiki/ITK_FAQ
>
> Follow this link to subscribe/unsubscribe:
> http://www.itk.org/mailman/listinfo/insight-users
>
>
>
>
> --
> Christopher Mullins
> R&D Engineer
> Kitware Inc.,
> 919.869.8871
>
--
Christopher Mullins
R&D Engineer
Kitware Inc.,
919.869.8871
--f46d04426d76eaa51b04d85f5264
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
<div dir=3D"ltr">From [1]:=A0<span style=3D"color:rgb(0,0,0);font-family:&#=
39;Lucida Grande',Verdana,Geneva,Arial,sans-serif;font-size:12px;line-h=
eight:19px">The power spectral densities of the signal and noise are typica=
lly unavailable for a given problem. In particular,=A0</span><img class=3D"=
" alt=3D"$P_f(\omega)$" src=3D"http://www.itk.org/Doxygen/html/form_312.png=
" style=3D"vertical-align: middle; color: rgb(0, 0, 0); font-family: 'L=
ucida Grande', Verdana, Geneva, Arial, sans-serif; font-size: 12px; lin=
e-height: 19px;"><span style=3D"color:rgb(0,0,0);font-family:'Lucida Gr=
ande',Verdana,Geneva,Arial,sans-serif;font-size:12px;line-height:19px">=
=A0cannot be computed from=A0</span><img class=3D"" alt=3D"$f(x)$" src=3D"h=
ttp://www.itk.org/Doxygen/html/form_315.png" style=3D"vertical-align: middl=
e; color: rgb(0, 0, 0); font-family: 'Lucida Grande', Verdana, Gene=
va, Arial, sans-serif; font-size: 12px; line-height: 19px;"><span style=3D"=
color:rgb(0,0,0);font-family:'Lucida Grande',Verdana,Geneva,Arial,s=
ans-serif;font-size:12px;line-height:19px">=A0because this unknown signal i=
s precisely the signal that this filter aims to recover. Nevertheless, it i=
s common for the noise to have a power spectral density that is flat or dec=
reasing significantly more slowly than the power spectral density of a typi=
cal image as the frequency=A0</span><img class=3D"" alt=3D"$\omega$" src=3D=
"http://www.itk.org/Doxygen/html/form_316.png" style=3D"vertical-align: mid=
dle; color: rgb(0, 0, 0); font-family: 'Lucida Grande', Verdana, Ge=
neva, Arial, sans-serif; font-size: 12px; line-height: 19px;"><span style=
=3D"color:rgb(0,0,0);font-family:'Lucida Grande',Verdana,Geneva,Ari=
al,sans-serif;font-size:12px;line-height:19px">=A0increases. Hence,=A0</spa=
n><img class=3D"" alt=3D"$P_n(\omega)$" src=3D"http://www.itk.org/Doxygen/h=
tml/form_313.png" style=3D"vertical-align: middle; color: rgb(0, 0, 0); fon=
t-family: 'Lucida Grande', Verdana, Geneva, Arial, sans-serif; font=
-size: 12px; line-height: 19px;"><span style=3D"color:rgb(0,0,0);font-famil=
y:'Lucida Grande',Verdana,Geneva,Arial,sans-serif;font-size:12px;li=
ne-height:19px">=A0can typically be approximated with a constant, and this =
filter makes this assumption (see the NoiseVariance member variable).=A0</s=
pan><img class=3D"" alt=3D"$P_f(\omega)$" src=3D"http://www.itk.org/Doxygen=
/html/form_312.png" style=3D"vertical-align: middle; color: rgb(0, 0, 0); f=
ont-family: 'Lucida Grande', Verdana, Geneva, Arial, sans-serif; fo=
nt-size: 12px; line-height: 19px;"><span style=3D"color:rgb(0,0,0);font-fam=
ily:'Lucida Grande',Verdana,Geneva,Arial,sans-serif;font-size:12px;=
line-height:19px">, on the other hand, will vary with input. This filter co=
mputes the power spectral density of the input blurred image, subtracts the=
power spectral density of the noise, and uses the result as the estimate o=
f=A0</span><img class=3D"" alt=3D"$P_f(\omega)$" src=3D"http://www.itk.org/=
Doxygen/html/form_312.png" style=3D"vertical-align: middle; color: rgb(0, 0=
, 0); font-family: 'Lucida Grande', Verdana, Geneva, Arial, sans-se=
rif; font-size: 12px; line-height: 19px;"><span style=3D"color:rgb(0,0,0);f=
ont-family:'Lucida Grande',Verdana,Geneva,Arial,sans-serif;font-siz=
e:12px;line-height:19px">.</span><div>
<span style=3D"color:rgb(0,0,0);font-family:'Lucida Grande',Verdana=
,Geneva,Arial,sans-serif;font-size:12px;line-height:19px"><br></span></div>=
<div style><span style=3D"color:rgb(0,0,0);font-family:'Lucida Grande&#=
39;,Verdana,Geneva,Arial,sans-serif;font-size:12px;line-height:19px">Yes, t=
he Wiener deconvolution filter makes the assumption of a flat noise spectru=
m across all frequencies. =A0This leads to the assumption that the signal (=
image) will dominate the low frequencies, while the noise is higher in the =
high frequencies - which is typically the case. =A0A common method to remov=
e noise is to convolve with a Gaussian kernel, but as I understand it, find=
ing the noise variance is a nontrivial problem. =A0Maybe check out some of =
the smoothing filters [2].</span></div>
<div style><span style=3D"color:rgb(0,0,0);font-family:'Lucida Grande&#=
39;,Verdana,Geneva,Arial,sans-serif;font-size:12px;line-height:19px"><br></=
span></div><div style><span style=3D"color:rgb(0,0,0);font-family:'Luci=
da Grande',Verdana,Geneva,Arial,sans-serif;font-size:12px;line-height:1=
9px">[2]=A0</span><a href=3D"http://www.itk.org/Wiki/ITK/Examples#Smoothing=
">http://www.itk.org/Wiki/ITK/Examples#Smoothing</a></div>
</div><div class=3D"gmail_extra"><br><br><div class=3D"gmail_quote">On Wed,=
Mar 20, 2013 at 11:57 AM, lena russo <span dir=3D"ltr"><<a href=3D"mail=
to:lilli888899 at hotmail.it" target=3D"_blank">lilli888899 at hotmail.it</a>>=
</span> wrote:<br>
<blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p=
x #ccc solid;padding-left:1ex">
<div><div dir=3D"ltr">
Hi Christopher,<br><br>thanks for your answer! I'm not very familiar wi=
th noise in images, 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 noi=
se affected the image?<br>
<br>Many many thanks<span class=3D"HOEnZb"><font color=3D"#888888"><br><br>=
Lena<br></font></span><div class=3D"hm HOEnZb"><br></div><div><div class=3D=
"hm HOEnZb"><div></div><hr>Date: Wed, 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" target=3D"_blank">=
christopher.mullins at kitware.com</a><br>To: <a href=3D"mailto:lilli888899 at ho=
tmail.it" target=3D"_blank">lilli888899 at hotmail.it</a><br>CC: <a href=3D"ma=
ilto:insight-users at itk.org" target=3D"_blank">insight-users at itk.org</a></di=
v>
<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? =A0You might consider the im=
plementation of the Wiener deconvolution filter [1].<div><br></div><div>[1]=
=A0<a href=3D"http://www.itk.org/Doxygen/html/classitk_1_1WienerDeconvoluti=
onImageFilter.html" target=3D"_blank">http://www.itk.org/Doxygen/html/class=
itk_1_1WienerDeconvolutionImageFilter.html</a></div>
</div><div><br><br><div>On Wed, Mar 13, 2013 at 10:46 AM, lena russo <span =
dir=3D"ltr"><<a href=3D"mailto:lilli888899 at hotmail.it" target=3D"_blank"=
>lilli888899 at hotmail.it</a>></span> wrote:<br>
<blockquote style=3D"border-left:1px #ccc solid;padding-left:1ex">
<div><div dir=3D"ltr">
Hi all,<br><br>I'm trying to develop a good method to evaluate the leve=
l
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,<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, 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&D Engineer</div><div>Kitware Inc.,</div><div><a href=
=3D"tel:919.869.8871" value=3D"+19198698871" target=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&D Engineer</div><div>Kitware Inc.,</div><div>919.869.8871=
</div>
</div>
--f46d04426d76eaa51b04d85f5264--
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