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

<table>Reconstruction kernel <svg height="19.375" id="M223" style="vertical-align:-5.76988pt" version="1.1" viewbox="0 0 68.712502 19.375" width="68.712502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> for <svg height="15.35" id="M224" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 64.574997 15.35" width="64.574997" 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> associated to the scalar cone beam transform <svg height="15.8375" id="M225" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 18.737499 15.8375" width="18.737499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><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,-.012,12.337,15.637)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg> according to [<a href="/journals/ijbi/2008/174283/#B12">12</a>].</table>

International Journal of Biomedical Imaging

fig5

Figure 5

Figure 5: A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography 