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Region-of-Interest reconstruction from truncated cone-beam projections by Azencott, Robert; Bodmann, Bernhard G.; Chowdhury, Tasadduk; Labate, Demetrio; Sen, Anando; Vera, Daniel is a scholarly article available to read on EtoBox.

What is Region-of-Interest reconstruction from truncated cone-beam projections about?

Region-of-Interest (ROI) tomography aims at reconstructing a region of interest $C$ inside a body using only x-ray projections intersecting $C$ with the goal to reduce overall radiation exposure when only a small specific region of the body needs to be examined. We consider x-ray acquisition from sources located on a smooth curve $\Gamma$ in $\mathbb{R}^3$ verifying classical Tuy's condition. In this situation, the {\it non-trucated} cone-beam transform $D f$ of smooth densities $f$ admits an explicit inverse $Z$; however $Z$ cannot directly reconstruct $f$ from ROI-truncated projections. To deal with the ROI tomography problem, we introduce a novel reconstruction approach. For densities $f$ in $L^{\infty}(B)$ where $B$ is a bounded ball in $\mathbb{R}^3$, our method iterates an operator $U$ combining ROI-truncated projections, inversion by the operator $Z$ and appropriate regularization operators. Assuming only knowledge of projections corresponding to a spherical ROI $C \subset B$, given $\epsilon >0$, we prove that if $C$ is sufficiently large our iterative reconstruction algorithm converges uniformly to an $\epsilon$-accurate approximation of $f$, where the accuracy depends on

Author

Azencott, Robert; Bodmann, Bernhard G.; Chowdhury, Tasadduk; Labate, Demetrio; Sen, Anando; Vera, Daniel

Published

2015

Language

EN