This paper studies nonparametric estimation of the integrated
volatility of Poisson jump-diffusion processes with noisy high-frequency data. We
propose jump-robust two-scale and multi-scale estimators. The estimators are based on
a combination of the multi-scale method and threshold technique, which serves to remove
microstructure noise and jumps, respectively. Furthermore, asymptotic properties of the
proposed estimators, such as consistency, are established.