Abstract: An image is produced of a target region from tomographic measurements through statistical inversion. The target region is mapped with a grid of voxels. Unknowns in the voxels are the components of a vector-valued variable. A next version of the vector-valued variable is repeatedly generated by drawing for each component a value from a conditional distribution. Elements of a theory matrix indicate, what is the contribution of each voxel in the grid to a detection result. The non-zero elements of the theory matrix are stored in a compressed form. A proper subset of the elements of the theory matrix is decompressed for either updating the quantity Ax and/or calculating the quantity AjT(Ax), where A is the theory matrix, x is the vector-valued variable and AjT is the transpose of the j:th column of the theory matrix.

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.

Abstract: An image is produced of a target region from tomographic measurements through statistical inversion. The target region is mapped with a grid of voxels. Unknowns in the voxels are the components of a vector-valued variable. A next version of the vector-valued variable is repeatedly generated by drawing for each component a value from a conditional distribution. Elements of a theory matrix indicate, what is the contribution of each voxel in the grid to a detection result. The non-zero elements of the theory matrix are stored in a compressed form. A proper subset of the elements of the theory matrix is decompressed for either updating the quantity Ax and/or calculating the quantity AjT(Ax), where A is the theory matrix, x is the vector-valued variable and AjT is the transpose of the j:th column of the theory matrix.

Abstract: A method and apparatus are disclosed for performing tomographic reconstruction. An object to be examined is represented with a tomographic model that includes grid points. A set of measurement data represents attenuation experienced by radiation that propagated through parts of the object to be examined. Statistical inversion is applied to convert the set of measurement data into a calculated distribution of attenuation values associated with at least a number of the grid points. Applying statistical inversion includes associating values of a prior with the grid points, which prior includes at least one regularization parameter. The values of the prior for different grid points come from using different values of the regularization parameter. The method includes producing an image representation of the calculated distribution of attenuation values.