Numerically robust tetrahedron-based tomographic forward and backward projectors on parallel architectures

Fourier-based forward and back projectors for iterative tomographic image reconstruction

Forward projectors are needed for iterative image reconstruction algorithms for CT or PET image reconstruction. The major cost of iterative reconstruction algorithms is computing the forward and backward projections. Conventionally, this is done in the image domain as computing the lengths of intersections between each X-ray ray and each image voxel. These operations are the major computational...

Parallel Complexity of Forward and Backward Propagation

We show that the forward and backward propagation can be formulated as a solution of lower and upper triangular systems of equations. For standard feedforward (FNNs) and recurrent neural networks (RNNs) the triangular systems are always block bi-diagonal, while for a general computation graph (directed acyclic graph) they can have a more complex triangular sparsity pattern. We discuss direct an...

Forward and Backward Uncertainty Quantification in Optimization

This contribution gathers some of the ingredients presented during the Iranian Operational Research community gathering in Babolsar in 2019.It is a collection of several previous publications on how to set up an uncertainty quantification (UQ) cascade with ingredients of growing computational complexity for both forward and reverse uncertainty propagation.

Fast orthogonalization algorithm and parallel architecture for AR spectral estimation based on forward-backward linear prediction

Fourier-Based Forward and Back-Projectors for Iterative Image Reconstruction

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the co...