<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.</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.

DC-Programming versus ℓ0-Superiorization for Discrete Tomography

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

DC-Programming versus ℓ-Superiorization for Discrete Tomography

In this paper we focus on the reconstruction of sparse solutions to underdetermined systems of linear equations with variable bounds. The problem is motivated...

DC-Programming versus ℓ₀-Superiorization for Discrete Tomography

Published Online: Nov 22, 2018

Page range: 105 - 133

Received: May 01, 2017

Accepted: Oct 01, 2017

DOI: https://doi.org/10.2478/auom-2018-0021

Keywords
DC-Programming, Sparse Regularization, Superiorization, Discrete Tomography, Split Convex Feasibility Problem

© 2018 Aviv Gibali, Stefania Petra, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

DC-Programming versus ℓ0-Superiorization for Discrete Tomography

Published Online: Nov 22, 2018

Page range: 105 - 133

Received: May 01, 2017

Accepted: Oct 01, 2017

DOI: https://doi.org/10.2478/auom-2018-0021

KeywordsDC-Programming, Sparse Regularization, Superiorization, Discrete Tomography, Split Convex Feasibility Problem

© 2018 Aviv Gibali, Stefania Petra, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

DC-Programming versus ℓ₀-Superiorization for Discrete Tomography

Keywords
DC-Programming, Sparse Regularization, Superiorization, Discrete Tomography, Split Convex Feasibility Problem