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This paper proposes a new two-stage method for restoring image corrupted by additive impulsive and Gaussian noise based on local polynomial regression (LPR) and edge preserving regularization. In LPR, the observations are modeled locally by a polynomial using least-squares criterion with a kernel controlled by a certain bandwidth matrix. A refined intersection confidence intervals (RICI) adaptive scale selector for symmetric kernel is applied in LPR to achieve a better bias-variance tradeoff. The method is further extended to steering kernel with local orientation to adapt better to local characteristics of images. The resulting steering-kernel-based LPR with RICI method (SK-LPR-RICI) is applied to smooth images contaminated with Gaussian noise. Furthermore, to remove the impulsive noise in images, an edge-preserving regularization method is employed prior to SK-LPR-RICI and it gives rise to a two-stage method for suppressing both additive impulsive and Gaussian noises. Simulation results show that the proposed method performs satisfactorily and the SK-LPR-RICI method significantly improves the performance after edge-preservation regularization in suppressing the impulsive noise.