DC-Programming versus ℓ0-Superiorization for Discrete Tomography
2018 ◽
Vol 26
(2)
◽
pp. 105-133
◽
Keyword(s):
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 ℓ0-minimization problem we consider two approaches: DC-programming and ℓ0-superiorization. We show that ℓ0-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, ℓ0-superiorization yields comparable results at significantly lower costs.
1977 ◽
Vol 20
(1)
◽
pp. 57-69
◽
2006 ◽
Vol 59
(6)
◽
pp. 797-829
◽
1984 ◽
Vol 5
(4)
◽
pp. 988-997
◽
2012 ◽
Vol 58
(2)
◽
pp. 1094-1121
◽
2019 ◽
Vol 51
(10)
◽
pp. 1-22