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 iterative method 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, 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.
Elias Helou Neto, Eduardo Xavier Miqueles.
Eduardo X Miqueles, Elias S Helou and Alvaro De R Pierro. Generalized Backprojection Operator: Fast Calculation. Journal of Physics: Conference Series 490(1):012148, 2014.
Elias Salomão Helou, Yair Censor, Tai-Been Chen, I-Liang Chern, Álvaro Rodolfo De Pierro, Ming Jiang and Henry Horng-Shing Lu. String-averaging expectation-maximization for maximum likelihood estimation in emission tomography. Inverse Problems 30(5):055003, 2014.