Reconstructing Convex Matrices by Integer Programming Approaches

A simulated annealing for reconstructing hv-convex binary matrices

We consider a variant of the NP-hard problem of reconstructing hv-convex binary matrices from two projections. This variant is reformulated as an integer programming problem and approximated by simulated annealing approach.

DISCRETE TOMOGRAPHY AND FUZZY INTEGER PROGRAMMING

We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions.

Interior Point and Semidefinite Approaches in Combinatorial Optimization

Conic programming, especially semidefinite programming (SDP), has been regarded as linear programming for the 21st century. This tremendous excitement was spurred in part by a variety of applications of SDP in integer programming (IP) and combinatorial optimization, and the development of efficient primal-dual interior-point methods (IPMs) and various first order approaches for the solution of ...

Integer Programming Approaches for Some Non-convex and Stochastic Optimization Problems

Stability in Discrete Tomography: some positive results

The problem of reconstructing finite subsets of the integer lattice from X-rays has been studied in discrete mathematics and applied in several fields like data security, electron microscopy, medical imaging. In this paper we focus on the stability of the reconstruction problem for some special lattice sets. First we prove that if the sets are additive, then a stability result holds for very sm...