A new method for reconstructing a High Resolution Orientation Distribution Function (HRODF) from X-ray diffraction data is presented. It is shown that the method is capable of accommodating very localized features, e.g. sharp peaks from recrystallized grains on a background of a texture component from the deformed material. The underlying mathematical formalism supports all crystallographic space groups and reduces the problem to solving a (large) set of linear equations. An implementation on multi-core CPUs and Graphical Processing Units (GPUs) is discussed along with an example on simulated data.