Fast computation of the generalized Backprojection operator with applications in tomographic image reconstruction

• Grant number: 13/16508-3
• Support Opportunities: Regular Research Grants
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Elias Salomão Helou Neto
• Grantee: Elias Salomão Helou Neto
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated researchers: Alvaro Rodolfo de Pierro ; Eduardo Xavier Miqueles ; Marcelo Victor Wüst Zibetti

Abstract

Reduction of computational time in high resolution image reconstruction is essential in basic research and applications as well. This reduction is important for different types of traditional non diffractive tomography in medical diagnosis as well as for applications in nanomaterials research, related to modern technologies.Alternatives to alleviate the computationally intense part of each iteration of iterative methods in tomographic reconstruction have all been based on interpolation over a regular grid in the Fourier domain or in fast nonuniform Fourier transforms. Both approaches speed up substantially the computation of each iteration of classical algorithms, but are not suitable for being used in a large class of more advanced faster algorithms: incremental methods such as OS-EM, BRAMLA or BSREM, among others, cannot benefit from these techniques.This proposal aims at developing the application of the Radon transform over a log-polar grid, where FFT algorithms can be used in order to execute projections/backprojections of parts of the data efficiently, in order to speed up each iteration of incremental methods in tomographic image reconstruction. Apart from classical tomographic inversion, we will also study the application of the generalized projection/backprojection operators that appear in more recent acquisition techniques. (AU)

Scientific publications

(9)

(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)

HELOU, ELIAS SALOMAO; CENSOR, YAIR; CHEN, TAI-BEEN; CHERN, I-LIANG; DE PIERRO, ALVARO RODOLFO; JIANG, MING; LU, HENRY HORNG-SHING. String-averaging expectation-maximization for maximum likelihood estimation in emission tomography. INVERSE PROBLEMS, v. 30, n. 5, MAY 2014. (13/16508-3)

OLIVEIRA, R. M.; HELOU, E. S.; COSTA, E. F.. String-averaging incremental stochastic subgradient algorithms. OPTIMIZATION METHODS & SOFTWARE, v. 34, n. 3, p. 665-692, MAY 4 2019. (15/10171-2, 13/19380-8, 13/07375-0, 13/16508-3, 17/20934-9)

HELOU, ELIAS S.; SIMOES, LUCAS E. A.. epsilon-subgradient algorithms for bilevel convex optimization. INVERSE PROBLEMS, v. 33, n. 5, MAY 2017. (13/07375-0, 11/02219-4, 13/14615-7, 13/16508-3)

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)

HELOU, ELIAS S.; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. A fast gradient and function sampling method for finite-max functions. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 71, n. 3, p. 673-717, DEC 2018. (13/05475-7, 13/07375-0, 16/22989-2, 13/16508-3, 13/14615-7)

HELOU, ELIAS SALOMAO; SANTOS, SANDRA A.; SIMOES, LUCAS E. A.. On the differentiability check in gradient sampling methods. OPTIMIZATION METHODS & SOFTWARE, v. 31, n. 5, p. 983-1007, OCT 2016. (13/16508-3, 13/05475-7, 13/14615-7, 13/07375-0)

DE OLIVEIRA, RAFAEL MASSAMBONE; HELOU, ELIAS SALOMAO; COSTA, EDUARDO FONTOURA. String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images. INVERSE PROBLEMS, v. 32, n. 11, NOV 2016. (13/07375-0, 15/10171-2, 13/19380-8, 13/16508-3)

PONTI, MOACIR; HELOU, ELIAS S.; FERREIRA, PAULO JORGE S. G.; MASCARENHAS, NELSON D. A.. Image Restoration Using Gradient Iteration and Constraints for Band Extrapolation. IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING, v. 10, n. 1, p. 71-80, FEB 2016. (13/16508-3, 13/07375-0, 11/22749-8)

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)