  We propose a stable and fast reconstruction technique for parallel-beam (PB)
tomographic X-ray imaging, relying on the discrete pseudo-polar (PP) Radon
transform. Our main contribution is a resampling method, based on modern
sampling theory, that transforms the acquired PB measurements to a PP grid. The
resampling process is both fast and accurate, and in addition, simultaneously
denoises the measurements, by exploiting geometrical properties of the
tomographic scan. The transformed measurements are then reconstructed using an
iterative solver with total variation (TV) regularization. We show that
reconstructing from measurements on the PP grid, leads to improved recovery,
due to the inherent stability and accuracy of the PP Radon transform, compared
with the PB Radon transform. We also demonstrate recovery from a reduced number
of PB acquisition angles, and high noise levels. Our approach is shown to
achieve superior results over other state-of-the-art solutions, that operate
directly on the given PB measurements. The proposed method can benefit fan-beam
and/or cone-beam projections by coupling it with a rebinning process.
