Recent progress in local reconstruction

While classic CT theory targets exact reconstruction of a whole cross-section or of an entire object from complete projections, practical applications often focus on much smaller internal ROIs. Traditional CT methods cannot exactly reconstruct an internal ROI only from local truncated projections associated with x-rays through the ROI, because this interior problem does not have a unique solution. When applying approximate local CT algorithms for interior reconstruction from truncated projection data, features outside the ROI may create artifacts overlapping inside features, rendering the images inaccurate or useless. Recently, novel solutions for the interior problem were published by our group with numerical results demonstrating that the interior problem can be solved in a theoretically exact and numerically stable fashion aided by some prior knowledge, such as a small known sub-region inside the ROI or the ROI can modeled by piecewise constant/polynomial function. In this invited paper, we will review the recent progress in local reconstruction. The topic includes lambda tomography, analytic and iterative interior reconstructions, with an emphasis on total variation minimization based soft-threshold methods and statistical based interior reconstruction algorithms.