Copula and Tomography

Abstract: An important problem in statistics is determining a joint probability distribution from its marginals. In 2D case, the marginal probability density functions f1(x) and f2(y) are related to their joint distribution f (x,y) via the horizontal and vertical line integrals. So, the problem of determining f (x,y) from f1(x) and f2(y) is an ill-posed inverse problem. In statistics the notion of copula is exactly introduced to obtain a solution to this problem. Interestingly, this is also a problem encountered in X ray tomography image reconstruction where f (x,y) is an image representing the distribution of the material density and f1(x) and f2(y) are the horizontal and vertical line integrals. In this paper, we try to link the notion of copula to X ray Computed Tomography (CT) and to see if we can use the methods used in each domain to the other one.