Pseudo-polar reconstruction for tomography

摘要

We propose a stable and fast reconstruction technique for parallel-beam (PB) tomographic X-Ray imaging, relying on the discrete pseudo-polar (PP) Radon and PP Fourier transforms. Our main contribution is a resampling method, based on modern sampling theory, that transforms the 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 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 with SNR measurements. Our approach is shown to achieve superior results over other state-of-the-art solutions, that operate directly on the PB measurements.