3D Analytic Cone-Beam Reconstruction for Multiaxial CT Acquisitions

A conventional 3rd generation Computed Tomography (CT) system with a single circular source trajectory is limited in terms of longitudinal scan coverage since extending the scan coverage beyond 40 mm results in significant cone-beam artifacts. A multiaxial CT acquisition is achieved by combining multiple sequential 3rd generation axial scans or by performing a single axial multisource CT scan with multiple longitudinally offset sources. Data from multiple axial scans or multiple sources provide complementary information. For full-scan acquisitions, we present a window-based 3D analytic cone-beam reconstruction algorithm by tessellating data from neighboring axial datasets. We also show that multi-axial CT acquisition can extend the axial scan coverage while minimizing cone-beam artifacts. For half-scan acquisitions, one cannot take advantage of conjugate rays. We propose a cone-angle dependent weighting approach to combine multi-axial half-scan data. We compute the relative contribution from each axial dataset to each voxel based on the X-ray beam collimation, the respective cone-angles, and the spacing between the axial scans. We present numerical experiments to demonstrate that the proposed techniques successfully reduce cone-beam artifacts at very large volumetric coverage

Maximum likelihood three-dimensional virus reconstruction from projections of unknown orientation and cryo electron microscopy application

Biological spherical viruses are nanometer (10–100nm) objects of roughly spherical shape where in many species each example of the species is identical. Cryo electron microscopy of such viruses provides images that are essentially 2-D tomographical projections of the 3-D virus scattering intensity. Three key problems are that the projection angles are not known, the projections are modified by a contrast transfer function with zeros, and the signal to noise ratio is less than 1. The goal is to compute a 3-D reconstruction of the virus scattering intensity. Motivated by the low signal to noise ratio, we developed statistical approaches. In particular, we developed a statistical model of the image formation process which forms the basis for a maximum likelihood estimation problem. We developed expectation maximization algorithms to solve the maximum likelihood problem. These algorithms are unusual because the maximization step is easy but the expectation step is hard because multi-dimensional numerical integrations are required. To incorporate the uncertainty in the image origin offset, 5-D integration rules are necessary and have been introduced. Several examples of 3D virus reconstruction from image data, which include classification and reconstruction using synthetic mixed particle data and single particle reconstruction using experimental data, successfully demonstrate the use of the proposed algorithms