A Finite Element Mesh Aggregating Approach to Multiple-Source Reconstruction in Bioluminescence Tomography

<table>Top row: regularized solutions by Tikhonov regularization (left) and <svg height="10.8625" id="M83" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 37.200001 10.8625" width="37.200001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8625)">
<g transform="translate(72,-63.31)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑙</tspan>
<tspan style="font-size: 12.50px; " x="3.9759541" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="10.915119" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="20.179842" y="0">𝑙</tspan>
<tspan style="font-size: 12.50px; " x="24.155796" y="0">𝑠</tspan>
</text>
</g>
</g>
</svg> method (right). Middle row: corresponding final reconstruction results by GTS with a threshold of <svg height="14.9" id="M84" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 89.400002 14.9" width="89.400002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.9)">
<g transform="translate(72,-60.08)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="23.955748" y="0">m</tspan>
<tspan style="font-size: 12.50px; " x="33.683083" y="0">a</tspan>
<tspan style="font-size: 12.50px; " x="39.234413" y="0">x</tspan>
<tspan style="font-size: 12.50px; " x="51.737415" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="55.900913" y="0">𝑆</tspan>
</text>
<text transform="matrix(1,0,0,-1,-7.91,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑖</tspan>
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<text transform="matrix(1,0,0,-1,-4.69,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">)</tspan>
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</svg>. Bottom row: final reconstruction results by Tikhonov + MSDS (left) and <svg height="10.8625" id="M85" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 37.200001 10.8625" width="37.200001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8625)">
<g transform="translate(72,-63.31)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑙</tspan>
<tspan style="font-size: 12.50px; " x="3.9759541" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="10.915119" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="20.179842" y="0">𝑙</tspan>
<tspan style="font-size: 12.50px; " x="24.155796" y="0">𝑠</tspan>
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</g>
</g>
</svg> + MSDS (right).</table>

International Journal of Biomedical Imaging

fig4

Figure 4

Figure 4: A Finite Element Mesh Aggregating Approach to Multiple-Source Reconstruction in Bioluminescence Tomography 