Region-of-interest tomography using exponential radial sampling

The authors combine several ideas, including nonuniform sampling and circular harmonic expansions, into a new procedure for reconstructing a small region of interest (ROI) of an image from a set of its projections that are densely sampled in the ROI and coarsely sampled outside the ROI. Specifically, the radial sampling density of both the projections and the reconstructed image decreases exponentially with increasing distance from the ROI. The problem and data are reminiscent of the recently formulated local tomography problem; however, the authors' algorithm reconstructs the ROI of the image itself, not the filtered version of it obtained using local tomography. The new algorithm has the added advantages of speed (it can be implemented entirely using the FFT) and parallelizability (each image harmonic is computed independently). Numerical examples compare the new algorithm to filtered backprojection.