Modelling and Simulation of Compton Scatter Image Formation in Positron Emission Tomography.

We present the comparative study of the analytical forward model and the statistical simulation of the Compton single scatter in the Positron Emission Tomography. The formula of the forward model has been obtained using the Single Scatter Simulation approximation under simplified assumptions and therefore we calculate scatter projections using independent Monte Carlo simulation mimicking the scatter physics. The numerical comparative study has been performed using a digital cylindrical phantom filled in with water and containing spherical sources of emission activity located at the central and several displaced positions.

FELIX: an algorithm for indexing multiple crystallites in X-ray free-electron laser snapshot diffraction images.

A novel algorithm for indexing multiple crystals in snapshot X-ray diffraction images, especially suited for serial crystallography data, is presented. The algorithm, FELIX, utilizes a generalized parametrization of the Rodrigues-Frank space, in which all crystal systems can be represented without singularities. The new algorithm is shown to be capable of indexing more than ten crystals per image in simulations of cubic, tetragonal and monoclinic crystal diffraction patterns.

Fully three-dimensional defocus-gradient corrected backprojection in cryoelectron microscopy.

Recognizing that the microscope depth of field is a significant resolution-limiting factor in 3D cryoelectron microscopy, Jensen and Kornberg proposed a concept they called defocus-gradient corrected backprojection (DGCBP) and illustrated by computer simulations that DGCBP can effectively eliminate the depth of field limitation. They did not provide a mathematical justification for their concept. Our paper provides this, by showing (in the idealized case of noiseless data being available for all projection directions) that the reconstructions obtained based on DGCBP from data produced with distance-dependent blurring are essentially the same as what is obtained by a classical method of reconstruction of a 3D object from its line integrals.

Fourier-based reconstruction for fully 3-D PET: optimization of interpolation parameters.

Fourier-based approaches for three-dimensional (3-D) reconstruction are based on the relationship between the 3-D Fourier transform (FT) of the volume and the two-dimensional (2-D) FT of a parallel-ray projection of the volume. The critical step in the Fourier-based methods is the estimation of the samples of the 3-D transform of the image from the samples of the 2-D transforms of the projections on the planes through the origin of Fourier space, and vice versa for forward-projection (reprojection). The Fourier-based approaches have the potential for very fast reconstruction, but their straightforward implementation might lead to unsatisfactory results if careful attention is not paid to interpolation and weighting functions.

Iterative tomographic image reconstruction using Fourier-based forward and back-projectors.

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 computation time in iterative reconstruction.