  Binary tomography is concerned with the recovery of binary images from a few
of their projections (i.e., sums of the pixel values along various directions).
To reconstruct an image from noisy projection data, one can pose it as a
constrained least-squares problem. As the constraints are non-convex, many
approaches for solving it rely on either relaxing the constraints or
heuristics. In this paper we propose a novel convex formulation, based on the
Lagrange dual of the constrained least-squares problem. The resulting problem
is a generalized LASSO problem which can be solved efficiently. It is a
relaxation in the sense that it can only be guaranteed to give a feasible
solution; not necessarily the optimal one. In exhaustive experiments on small
images (2x2, 3x3, 4x4) we find, however, that if the problem has a unique
solution, our dual approach finds it. In case of multiple solutions, our
approach finds the commonalities between the solutions. Further experiments on
realistic numerical phantoms and an experiment on X-ray dataset show that our
method compares favourably to Total Variation and DART.
