Reconstructing 3-D FRI shapes from tomographic projections at unknown angles

Kate L.Y. Zhao, Renke Wang, Pier Luigi Dragotti

Session: General

Keywords: multidimensional sampling, exponential approximation, finite rate of innovation, 3-D reconstruction, sampling at unknown locations, unknown view tomography, cryogenic electron microscopy

Abstract: Conventional methods for 3-D reconstruction from 2-D tomographic projections require prior knowledge of projection orientation. Without such information, reconstruction typically becomes a non-convex optimization problem. However, previous work has demonstrated perfect reconstruction of bilevel convex polyhedra from unknown orientations given a minimum number of projections. In this paper, we further extend that theory by generalizing reconstruction to arbitrary shapes. We represent objects and their projections as multidimensional finite rate of innovation (FRI) signals. We retrieve FRI parameters through the use of isotropic, exponential approximating kernels to obtain the signal’s exponential moments, followed by application of 2-D harmonic retrieval methods. FRI parameters are then paired across different projections. Finally, an algebraic method is applied to retrieve the orientation angles of the samples, allowing for successful reconstruction.

Submission Number: 56