While classic computed tomography (CT) theory targets exact reconstruction of a whole cross-section or entire volume from complete projections, biomedical applications often focus on relatively small internal region-of-interests (ROIs). However, traditional CT theory cannot exactly reconstruct an internal ROI only from truncated projections associated with x-rays through the ROI because this interior problem does not have a unique solution in an unconstrained setting. In 2007, the PI and his collaborators proved that the interior problem can be exactly and stably solved if a sub-region is known inside the ROI. Inspired by the compressive sensing (CS) theory, in 2009 the PI proposed the concept of CS-based interior tomography and proved that exact interior reconstruction is achievable with an interior scan if the ROI is piecewise constant, which is subsequently extended to the case of piecewise polynomial ROI.
The goal of this CAREER proposal is to advance the CS-based interior tomography theory and algorithms, and make a paradigm shift from traditional global filtered back-projection (FBP) to contemporary interior reconstruction.
The three objectives are to 1) perform mathematical analysis on a general scarcity constraint model to establish uniqueness, exactness and stability, as well as the properties of the corresponding discrete scheme; 2) develop and optimize novel interior reconstruction algorithms in a general POCS framework incorporating the split-Bregman and statistical reconstruction methods; 3) verify the theoretical findings and validate the proposed algorithms via numerical simulation, and demonstrate its utility by solving the big patient problem.
The research will be closely integrated with educational and outreach activities including creating a Medical Image Reconstruction course at both graduate and undergraduate levels at the Virginia Tech-Wake Forest University School of Biomedical Engineering and Sciences (SBES).
