Abstract: A method is provided for constructing a tomographic reconstruction through the application of statistical inversion. Unknowns associated with points of a reconstruction grid are represented with components of a vector-valued variable. A next version of the vector-valued variable is repeatedly created by drawing for each component a value from a conditional distribution. The components of a so generated version of the vector-valued variable are used as the tomographic reconstruction. The components are divided into sets, so that components in a set represent unknowns associated with mutually independent points of the reconstruction grid, or into independent collections. For at least two components of a set or at least two collections, the drawing of values from a conditional distribution is performed in parallel in a computer-implemented process.