Link between copula and tomography

Doriano-Boris Pougaza (1) , Ali Mohammad-Djafari (1) , Jean-François Bercher (1, 2)

1 L2S - Laboratoire des signaux et systèmes
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

An important problem in statistics is to determine a joint probability distribution from its marginals and an important problem in Computed Tomography (CT) is to reconstruct an image from its projections. In the bivariate case, the marginal probability density functions f1(x) and f2(y) are related to their joint distribution f(x, y) via horizontal and vertical line integrals. Interestingly, this is also the case of a very limited angle X-ray CT problem where f(x, y) is an image representing the distribution of the material density and f1(x), f2(y) are the horizontal and vertical line integrals. The problem of determining f(x, y) from f1(x) and f2(y) is an ill-posed undetermined inverse problem. In statistics the notion of copula is exactly introduced to characterize all the possible solutions to the problem of reconstructing a bivariate density from its marginals. In this paper, we elaborate on the possible link between copula and CT and try to see whether we can use the methods used in one domain into the other.

Mots clés: Copula; Tomography; Joint and marginal distributions; Image reconstruction; Additive and multiplicative backprojection; Maximum entropy

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Doriano-Boris Pougaza, Ali Mohammad-Djafari, Jean-François Bercher. Link between copula and tomography. Pattern Recognition Letters, 2010, 31 (14), pp.2258-2264. ⟨10.1016/j.patrec.2010.05.001⟩. ⟨hal-00509705⟩