  In 1917 Johann Radon introduced the Radon transform which is used in 1963 by
A. M. Cormack for application in the context of tomographic image
reconstruction. He proposed to reconstruct the spatial variation of the
material density of the body from X-Ray images (radiographies) for different
directions. Independently G. N. Hounsfield derived an algorithm and built the
first medical CT scanner. Basically the idea of the X-ray CT is to get an image
of the interior structure of an object by X-raying the object from many
different directions. The mathematical problem is then estimating a
multivariate function from its line integrals.
  Four year before Cormack's idea, Abe Sklar introduced a theory in the context
of Statistics called copula. Shortly copulas are functions that link
multivariate distributions to theirs univariate marginal functions. It appeared
that copulas captivated all dependence structure concerning the marginal
functions and offer a wide range of parametric family model which could be used
as a model for the joint distribution function. This statistical problem is the
same as in Tomography, because a marginal density is obtained from a line
integral of its joint distribution. In the particular case of only given
horizontal and vertical projections corresponding to a given two marginal
functions, we link the theory of copula to tomography via the Radon transform
and Sklar's theorem. The result we propose seems to be new as mathematical
approach to solve this tomographic inverse problem.

Data Analysis, Statistics and Probability