  We suggest new modification (we call it a noise reduction procedure) for
Steinhardt parameters which are often used for detecting crystalline structures
in computer simulation of solids and soft matter systems. We have also
developed a new methodology how to reconstruct "ideal" lattice structure in the
whole simulation box that would be most close to a real noisy crystalline
symmetry, when it is defined locally and then averaged over the whole box. For
this second procedure, which we call lattice reconstruction procedure, we have
developed an algorithm for finding the lattice vectors from the values of
Steinhardt parameters obtained after the noise reduction procedure. We apply
noise to the classical crystalline structures (sc, bcc, fcc, hcp), and use both
procedures to detect the crystalline structures in these classical but noisy
systems. We demonstrate advantages of our procedures in comparison with
existing methods and discuss their applicability limits.
