Reconstruction Method for Nonconcyclic Dual-Source Circular Cone-Beam CT with a Large Field of View

<table>Two DR images under the 100th project angle, (a) DR image from the cone beam formed by the X-ray source <svg height="15.5375" id="M201" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 14.6125 15.5375" width="14.6125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68
l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" id="x1D446"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.225,15.475)"><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>
</svg> and the panel detectors <svg height="15.25" id="M202" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 20.112499 15.25" width="20.112499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M780 372q0 -191 -178 -297q-128 -75 -335 -75h-250l7 27q61 7 77 22t28 76l77 398q11 62 0 76.5t-77 22.5l6 28h292q164 0 258.5 -67.5t94.5 -210.5zM678 375q0 119 -73 180.5t-201 61.5q-62 0 -82 -13q-17 -7 -25 -53l-80 -427q-8 -47 -4 -62t26 -20q24 -6 80 -6
q166 0 262.5 95t96.5 244z" id="x1D437"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.712,15.187)"><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>
</svg>; (b) DR image from the cone beam formed by the X-ray <svg height="15.5125" id="M203" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 14.5125 15.5125" width="14.5125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path d="M409 504l-29 -5q-16 60 -44.5 96t-86.5 36q-54 0 -82.5 -32t-28.5 -77q0 -51 30.5 -82.5t96.5 -65.5l35.5 -18t33 -19.5t33.5 -23.5l27 -25.5t24.5 -32t13.5 -36.5t6 -45q0 -80 -62 -134.5t-160 -54.5q-47 0 -98 15q-22 7 -50 21q-8 23 -27 155l30 7q7 -27 18 -52
t30 -51.5t49 -42.5t67 -16q56 0 88 32.5t32 87.5q0 51 -31.5 82t-98.5 67q-80 44 -110 73q-55 53 -55 124q0 75 56 126.5t150 51.5q53 0 126 -23z" id="x53"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.125,15.45)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg> and the panel detectors <svg height="15.25" id="M204" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 20.112499 15.25" width="20.112499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M780 372q0 -191 -178 -297q-128 -75 -335 -75h-250l7 27q61 7 77 22t28 76l77 398q11 62 0 76.5t-77 22.5l6 28h292q164 0 258.5 -67.5t94.5 -210.5zM678 375q0 119 -73 180.5t-201 61.5q-62 0 -82 -13q-17 -7 -25 -53l-80 -427q-8 -47 -4 -62t26 -20q24 -6 80 -6
q166 0 262.5 95t96.5 244z" id="x1D437"></path></g>
<g transform="matrix(.012,-0,0,-.012,13.712,15.187)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Reconstruction Method for Nonconcyclic Dual-Source Circular Cone-Beam CT with a Large Field of View 