Generalized support constraint for three-dimensional reconstruction from incomplete Fourier spectra

Abstract

Many imaging systems involve a loss of information that requires the incorporation of prior knowledge in the restoration/reconstruction process. We focus on the typical case of 3D reconstruction from an incomplete set of projections. An approach based on constrained optimization is introduced. This approach provides a powerful mathematical framework for selecting a specific solution from the set of feasible solutions; this is done by minimizing some criteria depending on prior densitometric information that can be interpreted through a generalized support constraint. We propose a global optimization scheme using a deterministic relaxation algorithm based on Bregman's algorithm associated with half-quadratic minimization techniques. When used for 3D vascular reconstruction from 2D digital subtracted angiography (DSA) data, such an approach enables the reconstruction of a well-contrasted 3D vascular network in comparison with results obtained using standard algorithms.