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. Additional substantial speed-tip of those approaches can be obtained utilizing powerful and cheap off-the-shelf FFT processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform or the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform Fast Fourier transform (NUFFT) framework. This approach is particularly well suited to the geometries of PET scanners. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods, and that it is a viable candidate for fast iterative image reconstruction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85805/1/Fessler178.pd

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. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85804/1/Fessler62.pd

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. It is also used to index an experimental serial crystallography dataset from lysozyme microcrystals. The increased number of indexed crystals is shown to result in a better signal-to-noise ratio, and fewer images are needed to achieve the same data quality as when indexing one crystal per image. The relative orientations between the multiple crystals indexed in an image show a slight tendency of the lysozme microcrystals to adhere on $(\overline {1}10)$ facets

Archaeal communities of frozen Quaternary sediments of marine origin on the coast of Western Spitsbergen,

The archaeal composition of permafrost samples taken during drilling of frozen marine sediments in the area of the Barentsburg coal mine on the east coast of Grønfjord Bay of Western Spitsbergen has been studied. The study was based on the analysis of the V4 region of the 16S rRNA gene, carried out using next generation sequencing. This is the second part of the work dedicated to the prokaryotic composition of the Western Spitsbergen, the fi rst part was devoted to the domain of Bacteria. The general phyla of the the Archaea domain were Euryarchaeota, Bathyarchaeota, Thaumarchaeota and Asgardarchaeota. As a result of phylogenetic analysis of the dominant operational taxonomic units, representatives of methanogenic methane- and ammonium-oxidizing archaea, as well as heterotrophic archaea were found. Methanobacteria class of methanogenic archaea was found in the controversial genesis, while methane-oxidizing archaea of the Methanomicrobia class of Methanosarcinales order were found in the marine permafrost of Cape Finneset: ANME-2a, -2b group was found in layers 8.6 and 11.7 m, and a group ANME-2d (Candidatus Methanoperedens) – in a layer of 6.5 m. Ammonium-oxidizing archaea of the phylum Thaumarchaeota was present in all types of permafrost, while Nitrososphaerales was detected in controversial genesis permafrost, and the order-Nitrosopumilales in the marine permafrost or controversial genesis ones. Representatives of phylum Bathyarchaeota were found in the stratigraphicly most ancient samples under this study. Superphylum Asgardarchaeota was met exclusively in the layers of permafrost with marine genesis and was represented by phyla Lokiarchaeota, Thorarchaeota and another group belonging to this superphylum that was not identified by us. The presence in the marine permafrost terrace of Cape Finneset at 11.7 m depth of methane, ethylene and ethane, as well as the composition of the archaeal community gives this layer to assume in it the presence of microbiological processes of the anaerobic oxidation of methane, probably received from Tertiary deposits before freezing. The results obtained are represented the permafrost of Spitsbergen as a rich archive of genetic information of little studied prokaryotic groups

Charge separation relative to the reaction plane in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}= 2.76 TeV

Measurements of charge dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudo-rapidity range $|\eta| < 0.8$ are presented as a function of the collision centrality, particle separation in pseudo-rapidity, and transverse momentum. A clear signal compatible with a charge-dependent separation relative to the reaction plane is observed, which shows little or no collision energy dependence when compared to measurements at RHIC energies. This provides a new insight for understanding the nature of the charge dependent azimuthal correlations observed at RHIC and LHC energies.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio