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| Author(s): |
Camila de Lima
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2017-06-09 |
| Examining board members: |
Elias Salomão Helou Neto;
Alvaro Rodolfo de Pierro;
Moacir Antonelli Ponti;
Jose Hiroki Saito
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| Advisor: | Elias Salomão Helou Neto |
| Abstract | |
Incremental methods belong to a class of iterative methods that divide the data set into ordered subsets, and which update the image when processing each subset (sub-iterations). It accelerates the reconstruction convergence and quality images are obtained in fewer iterations. However, it is necessary to compute the projection and backprojection operators in each sub-iteration, resulting in the computational cost of O(n3) flops for × images. On the other hand, some alternatives based on interpolation over a regular grid on the Fourier space or on nonequispaced fast transforms, among other ideas, were developed in order to alleviate the computational cost. In addition, several approaches substantially speed up the computation of the iterations of classical algorithms, but the incremental methods had not been benefited from these techniques. In this work, a new approach is proposed in which the nonequispaced fast Fourier transform (NFTT) is used in each subiteration of incremental methods in order to perform the numerically intensive calculations efficiently: the projection and backprojection, resulting in incremental methods with complexity O(n2 log n ). The proposed methods are applied to the synchrotron radiation tomography and the results show a good performance. (AU) | |
| FAPESP's process: | 13/16762-7 - Fast Computation of the Backprojection Operator with Applications in Tomographic Image Reconstruction |
| Grantee: | Camila de Lima |
| Support Opportunities: | Scholarships in Brazil - Doctorate |