A Forward Regridding Method With Minimal Oversampling for Accurate and Efficient Iterative Tomographic Algorithms

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Filippo ArcaduFederica Marone

Abstract

Reconstruction of underconstrained tomographic data sets remains a major challenge. Standard analytical techniques frequently lead to unsatisfactory results due to insufficient information. Several iterative algorithms, which can easily integrate a priori knowledge, have been developed to tackle this problem during the last few decades. Most of these iterative algorithms are based on an implementation of the Radon transform that acts as forward projector. This operator and its adjoint, the backprojector, are typically called few times per iteration and represent the computational bottleneck of the reconstruction process. Here, we present a Fourier-based forward projector, founded on the regridding method with minimal oversampling. We show that this implementation of the Radon transform significantly outperforms in efficiency other state-of-the-art operators with O(N2log2N) complexity. Despite its reduced computational cost, this regridding method provides comparable accuracy to more sophisticated projectors and can, therefore, be exploited in iterative algorithms to substantially decrease the time required for the reconstruction of underconstrained tomographic data sets without loss in the quality of the results.

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Citations

Jul 15, 2016·Optics Express·Michael T McCannMichael Unser
Dec 24, 2016·Journal of Synchrotron Radiation·F ArcaduM Stampanoni
Dec 23, 2016·Advanced Structural and Chemical Imaging·Zdeněk MatějDarren Spruce
Dec 23, 2017·Journal of Synchrotron Radiation·Camila de Lima, Elias Salomão Helou

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