DC-Programming versus ℓ 0 -Superiorization for Discrete Tomography
Aviv Gibali, Stefania Petra · Analele Universităţii "Ovidius" Constanţa. Seria Matematică · 2018
Abstract In this paper we focus on the reconstruction of sparse solutions to underdetermined systems of linear equations with variable bounds. The problem is motivated by sparse and gradient-sparse reconstruction in binary and discrete tomography from limited data. To address the ℓ 0 -minimization problem we consider two approaches: DC-programming and ℓ 0 -superiorization. We show that ℓ 0 -minimization over bounded polyhedra can be equivalently formulated as a DC program. Unfortunately, standard DC algorithms based on convex programming often get trapped in local minima. On the other hand, ℓ 0 -superiorization yields comparable results at significantly lower costs.