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.

The iterative proportional fitting procedure (IPFP) was introduced formally by Deming and Stephan in 1940. For bivariate densities, this procedure has been investigated by Kullback and Rüschendorf. It is well known that the IPFP is a sequence of successive I-projections onto sets of probability measures with fixed marginals. However, when finding the I-projection onto the intersection of arbitr...

The iterative proportional fitting procedure (IPFP) was introduced formally by Deming and Stephan in 1940. For bivariate densities, this procedure has been investigated by Kullback and Rüschendorf. It is well known that the IPFP is a sequence of successive I-projections onto sets of probability measures with fixed marginals. However, when finding the I-projection onto the intersection of arbitr...

We derive a dual-primal recursive algorithm based on the Fenchel duality framework, extending Dykstra’s successive projections and Csiszar’s I-projections schemes, to handle Tsallis MaxEnt. The Tsallis entropy Sq(p) is a one-parameter extension of Shannon’s entropyH(p) in the sense that Sq→1(p) = H(p). The solution of the Tsallis MaxEnt falls under a q-deformed Gibbs distribution which is a pow...

The proof of Proposition 1 and Theorem 2 in [3] is incorrect. Indeed, §2.5 and §2.7 in op.cit contain a vicious circle: the definition of the filtration Vi, 1 ≤ i ≤ n, in §2.5 depends on the choice of the integers ni, when the definition of the integers ni in §2.7 depends on the choice of the filtration (Vi). Thus, only Theorem 1 and Corollary 1 in [3] are proved. We shall prove below another r...

1 Introduction Filtered Back-Projection (FBP) is a well-known algorithm for reconstruction of tomographic images from projections [1-3]. Some of FBP's highlights are: (i) allows agile software implementations , and; (ii) production of images of good quality, i. e., relatively free of artifacts. Our goal is to reconstruct images from fan beam projections collected by detectors set in a linear ar...