Fast Computation of the Backprojection Operator with Applications in Tomographic Image Reconstruction

• Grant number: 13/16762-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2014
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Elias Salomão Helou Neto
• Grantee: Camila de Lima
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Alternatives to alleviate the computationally intense part of each iteration of iterative methods in tomographic reconstruction have all been based in interpolation over a regular grid on the Fourier space or in fast nonuniform Fourier transforms. Both approaches substantially speed up the computation of the iterations of classical algorithms, but are not suitable to be used with a wide range of more advanced and faster algorithms: incremental methods such as OS-EM, BRAMLA and BSREM, among others, cannot benefit from these techniques. This project's proposal is to study the application of the interpolation of the Radon transform in a log-polar grid, where FFT algorithms can be used in order to compute efficiently projections/backprojections of parts of the data, in order to speed up each iteration of incremental methods in tomography, with applications to synchrotron tomography.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DE LIMA, CAMILA; HELOU, ELIAS SALOMAO. Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction. JOURNAL OF SYNCHROTRON RADIATION, v. 25, n. 1, p. 248-256, JAN 2018. (13/07375-0, 13/16762-7, 13/16508-3, 16/24286-9)

DE LIMA, CAMILA; HELOU, ELIAS SALOMAO. Fast projection/backprojection and incremental methods applied to synchrotron light tomographic reconstruction. JOURNAL OF SYNCHROTRON RADIATION, v. 25, p. 9-pg., 2018-01-01. (13/07375-0, 13/16762-7, 16/24286-9, 13/16508-3)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

LIMA, Camila de. Fast computation of the backprojection operator with applictions in tomographic image reconstruction. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.