A Backprojection Slice Theorem for Tomographic Reconstruction

Abstract

Fast image reconstruction techniques are becoming important with the increasing number of scientific cases in high resolution micro and nano tomography. The processing of the large scale 3D data demands new mathematical tools for the tomographic reconstruction. Due to the high computational complexity of most current algorithms, big data sizes demands powerful hardware and more sophisticated numerical techniques. Several reconstruction algorithms are dependent on a mathematical tool called backprojection (a transposition process). A conventional implementation of the backprojection operator has cubic computational complexity. In the present manuscript we propose a new fast backprojection operator for the processing of tomographic data, providing a low-cost algorithm for this task. We compare our formula against other fast transposition techniques, using real and simulated large data sets.

Efficient Bandwidth Estimation in 2D Filtered Backprojection Reconstruction

“…The easy estimation of the filter resolution size and its good performance even at lower emissions rates (which translates to lower signal-noise ratio for other applications) potentially makes it desirable to also use BPF in applications where reconstruction in the form of the 1D filtering step can be begun synchronous with data acquisition at other projection angles also, This would hold especially if the waiting time for data acquisition at all angles is more than compensated by the increased reconstruction accuracy afforded by GCV selection of the bandwidth. Methods speeding up backprojection [59] can further reduce the cost for using BPF.…”

Location of water in fresh sugarcane bagasse observed by synchrotron X-ray microtomography

“…Each 3D reconstruction used 1001 equally spaced projection images acquired by sample rotation from 0° to 180°. 3D image reconstruction used the in-house developed Reconstruction Algorithms for Tomography (RAFT) [11]. A rendered visualization of a bagasse particle is shown in Fig 2 to exemplify the type of object captured by the microtomography analysis.…”

From brittle‐to‐ductile fracture of polymer composites: The incorporation of energy dissipation mechanisms by carbon nanotubes‐based multilayered interface

“…The reconstruction algorithm used was a Filtered Backprojection developed by Miqueles and Helou. [19] Fibers and pores were segmented through the module interactive thresholding of the FEI Avizo 8.1 software. The gray scale values ranges from 0 to 45 (pores) and from 145 to 255 (fibers).…”