Stability in Discrete Tomography: Linear Programming, Additivity and Convexity
نویسندگان
چکیده
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 image processing, data security, electron microscopy. In this paper we focus on the stability of the reconstruction problem for some lattice sets. First we show some theoretical bounds for additive sets, and a numerical experiment is made by using linear programming to deal with stability for convex sets. keywords: Discrete Tomography, Linear Programming, Additivity.
منابع مشابه
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.
متن کاملSOME PROPERTIES FOR FUZZY CHANCE CONSTRAINED PROGRAMMING
Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...
متن کاملNon-linear Analysis of Stability in the Islamic Banking Industry
Stability analysis is one of the most important fields of study in the Islamic banking and finance industry. For measuring stability in Islamic banking, we introduced, for the first time, an Islamic banking stability index (IBS) during 2013 to 2016 which use all CAMEL factors and so seems to be more comprehensive than Z-score stability index which dominantly used in the existing literatures. To...
متن کاملStability 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...
متن کاملReconstruction of Discrete Sets from Two or More Projections in Any Direction
During the workshop entitled “Discrete Tomography”, held in Volkrange on March 22, 1999, A. Kuba presented the open problem of reconstructing discrete sets satisfying the properties of connectivity and convexity by projections taken along many directions. In this paper, we study this problem, considering a similar property of discrete sets: the Q-convexity. In fact this property contains a cert...
متن کامل