MMSE Reconstruction for 3D Freehand Ultrasound Imaging

<table>Two synthetic 3D ultrasound image sets <svg height="15.7" id="M104" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.075 15.7" width="13.075" 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="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" id="x1D408"></path></g>
<g transform="matrix(.012,-0,0,-.012,6.675,15.637)"><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 <svg height="15.7" id="M105" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.075 15.7" width="13.075" 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="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" id="x1D408"></path></g>
<g transform="matrix(.012,-0,0,-.012,6.675,15.637)"><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>. <svg height="15.7" id="M106" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.075 15.7" width="13.075" 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="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" id="x1D408"></path></g>
<g transform="matrix(.012,-0,0,-.012,6.675,15.637)"><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 <svg height="15.7" id="M107" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.075 15.7" width="13.075" 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="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" id="x1D408"></path></g>
<g transform="matrix(.012,-0,0,-.012,6.675,15.637)"><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> are imaged the same region but with different
speckle pattern: (a) <svg height="15.7" id="M108" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.075 15.7" width="13.075" 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="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" id="x1D408"></path></g>
<g transform="matrix(.012,-0,0,-.012,6.675,15.637)"><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> cross-sectional view, (b) <svg height="15.7" id="M109" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.075 15.7" width="13.075" 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="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" id="x1D408"></path></g>
<g transform="matrix(.012,-0,0,-.012,6.675,15.637)"><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> sagittal view, (c) <svg height="15.7" id="M110" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.075 15.7" width="13.075" 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="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" id="x1D408"></path></g>
<g transform="matrix(.012,-0,0,-.012,6.675,15.637)"><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> cross-sectional view, (d) <svg height="15.7" id="M111" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.075 15.7" width="13.075" 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="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" id="x1D408"></path></g>
<g transform="matrix(.012,-0,0,-.012,6.675,15.637)"><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> sagittal view.</table>

International Journal of Biomedical Imaging

MMSE Reconstruction for 3D Freehand Ultrasound Imaging

Figure 6