In some applications,there are signals with piecewise structure to be recovered.In this paper,we propose a piecewise_ISS (P_ISS) method which aims to preserve the piecewise sparse structure (or the small-scaled entries) of piecewise signals.In order to avoid selecting redundant false small-scaled elements,we also implement the piecewise_ISS algorithm in parallel and distributed manners equipped with a deletion rule.Numerical experiments indicate that compared with aISS,the P_ISS algorithm is more effective and robust for piecewise sparse recovery.