A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography

<table>(a) Original vector field <svg height="17.700001" id="M255" style="vertical-align:-2.3205pt" version="1.1" viewbox="0 0 108.6125 17.700001" width="108.6125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,96.075,6.587)"><path d="M619 498h-254v-498h-58v498h-254v50h566v-50z" id="x22A4"></path></g>
<g transform="matrix(.017,-0,0,-.017,104.675,14.738)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g>
</svg> (b) Reconstruction with the described
algorithm for <svg height="15.35" id="M256" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 72.737503 15.35" width="72.737503" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5
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</svg> using exact, simulated data <svg height="15.95" id="M257" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 28.262501 15.95" width="28.262501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.813)"><path d="M14 651v25h312q172 0 267 -88q97 -88 97 -243q0 -77 -30.5 -147t-84.5 -117q-93 -81 -252 -81h-309v25q83 1 83 73v486q0 34 -17.5 48t-65.5 19zM259 598v-498q0 -36 12.5 -50.5t45.5 -14.5q98 0 149 72q23 33 36.5 94t13.5 129q0 138 -41 211q-59 101 -163 101
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<g transform="matrix(.012,-0,0,-.012,12.337,15.888)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
<g transform="matrix(.017,-0,0,-.017,18.675,11.813)"><path d="M14 417v44h57q0 132 40 179q42 51 135 51q64 0 103.5 -28t39.5 -72q0 -28 -17 -46t-45 -18q-25 0 -42.5 17t-17.5 40q0 12 5.5 25t11 22t5.5 10q0 19 -29 19q-27 0 -38.5 -17.5t-11.5 -61.5v-120h86v-44h-86v-310q0 -49 15 -66q14 -15 67 -17v-24h-278v24q34 4 45.5 16.5
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</svg></table>

International Journal of Biomedical Imaging

fig8

Figure 8

Figure 8: A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography 