The mathematics of computerized tomography
The mathematics of computerized tomography
Estimation of the joint probability of multisensory signals
Pattern Recognition Letters
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Nonparametric estimation of the dependence function for a multivariate extreme value distribution
Journal of Multivariate Analysis
Using continuous features in the maximum entropy model
Pattern Recognition Letters
An Introduction to Copulas
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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 f"1(x) and f"2(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 f"1(x), f"2(y) are the horizontal and vertical line integrals. The problem of determining f(x,y) from f"1(x) and f"2(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.