A Network Flow Algorithm for Binary Image Reconstruction from Few Projections

Abstract

Tomography deals with the reconstruction of images from their projections. In this paper we focus on tomographic reconstruction of binary images (i.e., black-and-white) that do not have an intrinsic lattice structure from a small number of projections. We describe how the reconstruction problem from only two projections can be formulated as a network flow problem in a graph, which can be solved efficiently. When only two projections are used, the reconstruction problem is severely underdetermined and many solutions may exist. To find a reconstruction that resembles the original image, more projections must be used. We propose an iterative algorithm to solve the reconstruction problem from more than two projections. In every iteration a network flow problem is solved, corresponding to two of the available projections. Different pairs of projection angles are used for consecutive iterations. Our algorithm is capable of computing high quality reconstructions from very few projections. We evaluate its performance on simulated projection data and compare it to other reconstruction algorithms.