<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:Consolas;
panose-1:2 11 6 9 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman",serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p
{mso-style-priority:99;
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
font-size:12.0pt;
font-family:"Times New Roman",serif;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
font-size:12.0pt;
font-family:"Times New Roman",serif;}
span.EmailStyle20
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri",sans-serif;
mso-fareast-language:EN-US;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:3.0cm 2.0cm 3.0cm 2.0cm;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="DA" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Hi,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Thank you for the input and reference! <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">You previously mentioned that there was a method to use the iterative reconstructions for fanbeam measurements. What is exactly needed?
And is it similar for the ADMM wavelet reconstruction? <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Best regards,
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Jacob<o:p></o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> simon.rit@gmail.com [mailto:simon.rit@gmail.com]
<b>On Behalf Of </b>Simon Rit<br>
<b>Sent:</b> 17. maj 2017 16:42<br>
<b>To:</b> Jacob Frøsig <jafs@force.dk><br>
<b>Cc:</b> rtk-users@openrtk.org<br>
<b>Subject:</b> Re: [Rtk-users] Reconstructing from fan-beam projections<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<div>
<div>
<div>
<p class="MsoNormal">I guess the extreme negative values are due to truncation. I have never worked on the interior problem before so I don't have experience with this but I'm not surprised that you reconstruct bad values.<br>
The implemented correction is<br>
<span style="font-family:"Arial",sans-serif">Ohnesorge, B.; Flohr, T.; Schwarz, K.; Heiken, J. & Bae, K.<br>
Efficient correction for CT image artifacts caused by objects extending outside the scan field of view<br>
<em><span style="font-family:"Arial",sans-serif">Med Phys, </span></em><b>2000</b><i>, 27</i>, 39-46</span>
<o:p></o:p></p>
</div>
<p class="MsoNormal">The parameter is the ratio of extension (between 0 and 1).<o:p></o:p></p>
</div>
<p class="MsoNormal">Simon<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p class="MsoNormal">On Wed, May 17, 2017 at 3:41 PM, Jacob Frøsig <<a href="mailto:jafs@force.dk" target="_blank">jafs@force.dk</a>> wrote:<o:p></o:p></p>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">Hi,
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Thank you, it is a great help! Attached is a report describing the project where the beginning of chapter
5 describes the data acquisition. <br>
The investigated object is an oil pipe. Yes, the reconstruction contains the expected interior part of the oil pipe along with the ring artefact</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">which is characteristic for the interior problem.<br>
What puzzles me is that I get a few extreme negative values, -1.5884e+38 , in the bottom of the reconstruction using
</span><span lang="EN-US" style="font-size:9.5pt;font-family:Consolas;color:#2B91AF;background:white">FDKConeBeamReconstructionFilter</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">. I have attached the truncated reconstruction
without negative values and the reconstruction with negative values. What exactly is your truncation correction?
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Have you seen something similar before?
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Best regards,
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Jacob</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">
<a href="mailto:simon.rit@gmail.com" target="_blank">simon.rit@gmail.com</a> [mailto:<a href="mailto:simon.rit@gmail.com" target="_blank">simon.rit@gmail.com</a>]
<b>On Behalf Of </b>Simon Rit<br>
<b>Sent:</b> 17. maj 2017 15:03</span><o:p></o:p></p>
<div>
<div>
<p class="MsoNormal"><br>
<b>To:</b> Jacob Frøsig <<a href="mailto:jafs@force.dk" target="_blank">jafs@force.dk</a>><br>
<b>Cc:</b> <a href="mailto:rtk-users@openrtk.org" target="_blank">rtk-users@openrtk.org</a><br>
<b>Subject:</b> Re: [Rtk-users] Reconstructing from fan-beam projections<o:p></o:p></p>
</div>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Hi,<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Here is what I obtain. I have no clue what you expect but that's how I would translate the geometric information that you provided. The interior problem is obviously an issue here
(our truncation correction does not help for interior CT) but maybe you can tell us if you recognize your object. There are clear ring artefacts as well in your sinogram.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">I hope this helps,<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Simon<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">On Tue, May 16, 2017 at 7:22 PM, Jacob Frøsig <<a href="mailto:jafs@force.dk" target="_blank">jafs@force.dk</a>> wrote:<o:p></o:p></p>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<div>
<div id="m_1176708237412262271m_-3655530790667089488divtagdefaultwrapper">
<p><span style="font-family:"Calibri",sans-serif;color:black">Hi, </span><o:p></o:p></p>
<p><span style="font-family:"Calibri",sans-serif;color:black"> </span><o:p></o:p></p>
<p><span style="font-family:"Calibri",sans-serif;color:black">yes, it is indeed an interior- / region of interest problem in the sense that we only are interested in the fully illuminated centre region. <br>
I have previously had success in getting good reconstructions from interior data using variational formulation with tailored penalty term. However, this is implemented in Matlab and the aim is to use your implementation to get a C++ implementation of this method. </span><o:p></o:p></p>
<p><span style="font-family:"Calibri",sans-serif;color:black">But for now, I am just figuring how to do a simple reconstruction to get a grasp on the library. </span><o:p></o:p></p>
<p><span style="font-family:"Calibri",sans-serif;color:black"> </span><o:p></o:p></p>
<p><span style="font-family:"Calibri",sans-serif;color:black">Best regards, </span><o:p></o:p></p>
<p><span style="font-family:"Calibri",sans-serif;color:black"> </span><o:p></o:p></p>
<p><span style="font-family:"Calibri",sans-serif;color:black">Jacob</span><o:p></o:p></p>
<p style="margin-bottom:12.0pt"><span style="font-family:"Calibri",sans-serif;color:black"> </span><o:p></o:p></p>
<p><span style="font-family:"Calibri",sans-serif;color:black"> </span><o:p></o:p></p>
</div>
<div class="MsoNormal" align="center" style="text-align:center">
<hr size="3" width="98%" align="center">
</div>
<div id="m_1176708237412262271m_-3655530790667089488divRplyFwdMsg">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">Fra:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">
<a href="mailto:simon.rit@gmail.com" target="_blank">simon.rit@gmail.com</a> <<a href="mailto:simon.rit@gmail.com" target="_blank">simon.rit@gmail.com</a>> på vegne af Simon Rit <<a href="mailto:simon.rit@creatis.insa-lyon.fr" target="_blank">simon.rit@creatis.insa-lyon.fr</a>><br>
<b>Sendt:</b> 16. maj 2017 16:59:12<br>
<b>Til:</b> Jacob Frøsig<br>
<b>Cc:</b> <a href="mailto:rtk-users@openrtk.org" target="_blank">rtk-users@openrtk.org</a><br>
<b>Emne:</b> Re: [Rtk-users] Reconstructing from fan-beam projections</span> <o:p>
</o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Hi,<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">If this is true, then the sinogram indicates that you are dealing with an interior problem since you have high line integrals at the border (see enclosed profile). Is that indeed
the case? If yes, that's a difficult problem...<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Simon<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">On Tue, May 16, 2017 at 3:16 PM, Jacob Frøsig <<a href="mailto:jafs@force.dk" target="_blank">jafs@force.dk</a>> wrote:<o:p></o:p></p>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">Hi,
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-top:12.0pt;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">The attached sinogram consist of line integral values, i.e., sinogram(i,j) = -ln[
<b>I(i,j)/I_0(i)</b> </span><span lang="EN-US" style="font-size:13.0pt;font-family:"Calibri",sans-serif">]</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> where
<b>I </b>and <i></i><b>I_0 </b>are the measured intensities with and without an object, respectively.
<br>
Since we are measuring with a line detector, the “zero” (<b>I_0</b>) is in this case just an array.</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-top:12.0pt;mso-margin-bottom-alt:auto;text-align:justify">
<b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">j</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> is the index for the projections, i.e.,
<b>j</b> </span><span lang="EN-US" style="font-size:10.5pt;font-family:"Cambria Math",serif;color:black;background:#F8F9FA">∈ {</span><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">1,2,…,360} since we take one projection for each
whole angle. </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-top:12.0pt;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">I hope this explains the sinogram and again; thank you for your time!
</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-top:12.0pt;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Best regards,
</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-top:12.0pt;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Jacob</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-top:12.0pt;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">
<a href="mailto:simon.rit@gmail.com" target="_blank">simon.rit@gmail.com</a> [mailto:<a href="mailto:simon.rit@gmail.com" target="_blank">simon.rit@gmail.com</a>]
<b>On Behalf Of </b>Simon Rit<br>
<b>Sent:</b> 16. maj 2017 14:54<br>
<b>To:</b> Jacob Frøsig <<a href="mailto:jafs@force.dk" target="_blank">jafs@force.dk</a>><br>
<b>Cc:</b> <a href="mailto:rtk-users@openrtk.org" target="_blank">rtk-users@openrtk.org</a></span><o:p></o:p></p>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><br>
<b>Subject:</b> Re: [Rtk-users] Reconstructing from fan-beam projections<o:p></o:p></p>
</div>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Hi Jacob,<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Thanks for the image of the sinogram. I don't understand this sinogram. Do you know how to convert each pixel value to a line integral? I.e., if it's x-ray imaging, do you have
an image without object?<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Thanks,<o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Simon<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">On Tue, May 16, 2017 at 2:24 PM, Jacob Frøsig <<a href="mailto:jafs@force.dk" target="_blank">jafs@force.dk</a>> wrote:<o:p></o:p></p>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Hi again,</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">and thank you for the example!
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">I have some trouble getting a proper reconstruction. If you have the time, any help would be appreciated.
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Attached is my fan-beam sinogram as a .tif file. Here, projections are taken for 360 degrees and the
detector has 507 pixels. <br>
I believe the issue lies in setting the geometry and maybe the spacing between the pixels. The measurement geometry is as follows</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Source to centre: 590 mm</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Source to detector: 1000 mm</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Detector length: 411mm</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Best regards,
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Jacob</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> Rtk-users
[mailto:<a href="mailto:rtk-users-bounces@public.kitware.com" target="_blank">rtk-users-bounces@public.kitware.com</a>]
<b>On Behalf Of </b>Simon Rit<br>
<b>Sent:</b> 15. maj 2017 17:32<br>
<b>To:</b> <a href="mailto:rtk-users@openrtk.org" target="_blank">rtk-users@openrtk.org</a></span><o:p></o:p></p>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><br>
<b>Subject:</b> Re: [Rtk-users] Reconstructing from fan-beam projections<o:p></o:p></p>
</div>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
<div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Hi,</span><o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">I have added an example here:<br>
</span><a href="http://wiki.openrtk.org/index.php/FanBeam" target="_blank"><span lang="EN-US">http://wiki.openrtk.org/index.php/FanBeam</span></a><o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">The values in the first and the third rows are not used, as illustrated in this example. We add them to do a 2D interpolation but we do this 2D interpolation
exactly on the second row so that's not a problem.</span><o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Note that it's a bit more tricky for iterative recon but we also have a solution for this if you need it.</span><o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Best regards,</span><o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Simon</span><o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">On Mon, May 15, 2017 at 4:31 PM, Jacob Frøsig <</span><a href="mailto:jafs@force.dk" target="_blank"><span lang="EN-US">jafs@force.dk</span></a><span lang="EN-US">>
wrote:</span><o:p></o:p></p>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Hi again,
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Thank you for the quick answer! An example would be great, thanks. I have one concern about copying
the fan-beam data: </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"><br>
Then we would have 2D projections for which each column is the same fan-beam projection. By this, values of the same row are equal even though the cone-beam geometry indicates the outer columns correspond to intensities of rays with longer travel time through
the object and hence should have attenuated more. Is this neglectable? </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Again, thanks!
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Best regards,
</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">Jacob</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">
</span><a href="mailto:simon.rit@gmail.com" target="_blank"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">simon.rit@gmail.com</span></a><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> [mailto:</span><a href="mailto:simon.rit@gmail.com" target="_blank"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">simon.rit@gmail.com</span></a><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">]
<b>On Behalf Of </b>Simon Rit<br>
<b>Sent:</b> 15. maj 2017 16:05<br>
<b>To:</b> louie L <</span><a href="mailto:ghostcz@hotmail.com" target="_blank"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">ghostcz@hotmail.com</span></a><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">><br>
<b>Cc:</b> Jacob Frøsig <</span><a href="mailto:jafs@force.dk" target="_blank"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">jafs@force.dk</span></a><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">>;
</span><a href="mailto:rtk-users@public.kitware.com" target="_blank"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">rtk-users@public.kitware.com</span></a><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"><br>
<b>Subject:</b> Re: [Rtk-users] Reconstructing from fan-beam projections</span><o:p></o:p></p>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Hi,</span><o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">I agree. What I do is do a 3 slice sinogram from the fan-beam projections by copying the same data in each slice but reconstruct one 2D slice. If you need an
example, I can quickly demonstrate this in a short Python script.</span><o:p></o:p></p>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Simon</span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">On Mon, May 15, 2017 at 4:01 PM, louie L <</span><a href="mailto:ghostcz@hotmail.com" target="_blank"><span lang="EN-US">ghostcz@hotmail.com</span></a><span lang="EN-US">>
wrote:</span><o:p></o:p></p>
<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Hi,</span><o:p></o:p></p>
</div>
<div id="m_1176708237412262271m_-3655530790667089488m_-2204890646387654464m_-3903298939416454343m_-5086680236978975922m_2009876589595851285m_4474899766812565281AppleMailSignature">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
</div>
<div id="m_1176708237412262271m_-3655530790667089488m_-2204890646387654464m_-3903298939416454343m_-5086680236978975922m_2009876589595851285m_4474899766812565281AppleMailSignature">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">I think you can carefully pad zeros to your projections. Reconstruct as if it is a 3d object. Take the middle slice as your fanbeam result. </span><o:p></o:p></p>
</div>
<div id="m_1176708237412262271m_-3655530790667089488m_-2204890646387654464m_-3903298939416454343m_-5086680236978975922m_2009876589595851285m_4474899766812565281AppleMailSignature">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Let me know if it helps. </span><o:p></o:p></p>
</div>
<div id="m_1176708237412262271m_-3655530790667089488m_-2204890646387654464m_-3903298939416454343m_-5086680236978975922m_2009876589595851285m_4474899766812565281AppleMailSignature">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
</div>
<div id="m_1176708237412262271m_-3655530790667089488m_-2204890646387654464m_-3903298939416454343m_-5086680236978975922m_2009876589595851285m_4474899766812565281AppleMailSignature">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Best regards,</span><o:p></o:p></p>
</div>
<div id="m_1176708237412262271m_-3655530790667089488m_-2204890646387654464m_-3903298939416454343m_-5086680236978975922m_2009876589595851285m_4474899766812565281AppleMailSignature">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Louie<br>
<br>
Sent from my iOS </span><o:p></o:p></p>
</div>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span lang="EN-US"><br>
Am 15.05.2017 um 15:55 schrieb Jacob Frøsig <</span><a href="mailto:jafs@force.dk" target="_blank"><span lang="EN-US">jafs@force.dk</span></a><span lang="EN-US">>:</span><o:p></o:p></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Dear Rtk-users</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">I was wandering if Rtk includes an implementation of a reconstruction method to reconstruct a 2D representation of an object given fan-beam projections.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">Or, if anyone has experience using e.g.
</span><span lang="EN-US" style="font-size:9.5pt;font-family:Consolas;color:#2B91AF;background:white">FDKConeBeamReconstructionFilter</span><span lang="EN-US"> on projections from line-detectors (fan-beam instead of cone-beam).</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">I hope you guys can help.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma",sans-serif">Yours sincerely</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma",sans-serif">Jacob Frøsig
</span></b><span lang="EN-US"><br>
</span><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif"><br>
Project Manager <br>
Sensor Innovation <br>
<br>
FORCE Technology <br>
Park Allé 345 <br>
2605 Brøndby <br>
Denmark <br>
<br>
Phone: </span><a href="tel:+45%2043%2025%2000%2000" target="_blank"><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">+45 43 25 00 00</span></a><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">
<br>
Direct: </span><a href="tel:+45%2043%2025%2016%2043" target="_blank"><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">+45 43 25 16 43</span></a><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">
<br>
Skype for Business: </span><a href="mailto:jafs@forcetechnology.com" target="_blank"><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">jafs@forcetechnology.com</span></a><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif"><br>
Fax: </span><a href="tel:+45%2043%2025%2000%2010" target="_blank"><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">+45 43 25 00 10</span></a><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">
<br>
e-mail: </span><a href="mailto:jafs@force.dk" target="_blank"><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">jafs@force.dk</span></a><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif"><br>
www: </span><a href="https://forcetechnology.com?utm_source=mail-signature&utm_medium=email&utm_campaign=EmployeeBranding" target="_blank"><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">forcetechnology.com</span></a><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif"><br>
<br>
************************************************************************* <br>
This email and any files transmitted with it may contain confidential <br>
information intended for the addressee(s) only. The information is not to be <br>
surrendered or copied to unauthorised persons. If you have received <br>
this communication in error, please notify us immediately by email at: </span><a href="mailto:info@forcetechnology.com" target="_blank"><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">info@forcetechnology.com</span></a><span lang="EN-US" style="font-size:7.5pt;font-family:"Tahoma",sans-serif">
<br>
************************************************************************* </span>
<o:p></o:p></p>
</div>
</div>
</blockquote>
</div>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US">_______________________________________________<br>
Rtk-users mailing list<br>
</span><a href="mailto:Rtk-users@public.kitware.com" target="_blank"><span lang="EN-US">Rtk-users@public.kitware.com</span></a><span lang="EN-US"><br>
</span><a href="http://public.kitware.com/mailman/listinfo/rtk-users" target="_blank"><span lang="EN-US">http://public.kitware.com/mailman/listinfo/rtk-users</span></a><o:p></o:p></p>
</div>
</blockquote>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span lang="EN-US"><br>
_______________________________________________<br>
Rtk-users mailing list<br>
</span><a href="mailto:Rtk-users@public.kitware.com" target="_blank"><span lang="EN-US">Rtk-users@public.kitware.com</span></a><span lang="EN-US"><br>
</span><a href="http://public.kitware.com/mailman/listinfo/rtk-users" target="_blank"><span lang="EN-US">http://public.kitware.com/mailman/listinfo/rtk-users</span></a><o:p></o:p></p>
</blockquote>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span lang="EN-US"> </span><o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</div>
</body>
</html>