Reconstruction of linear recurrent sequence over prime residue ring from its image

We consider pseudorandom sequences $v$ over $\mathbb Z_p$, $p\ge3$, obtained from a primitive sequence $u$ over integer residue ring $\mathbb Z_{p^n}$ by means of some compressing map. We study sufficient conditions for the reconstruction of $u$ from known $v$ and suggest some methods of such reconstruction. The review of known results is presented also.