Hybrid BM3D and PDE filtering for non-parametric single image denoising

Abstract

The BM3D method achieves excellent denoising performance, but it has artificial effects and bias effects and its performance largely depends on the noise level parameter. To address this, we propose a hybrid BM3D and PDE method for non-parametric single image denoising. First, a non-local Perona–Malik (NLPM) filtering is proposed, and we prove its discontinuity maintaining, mean invariance, convergence, and local continuity. Based on these mathematical properties, an NLPM based noise level estimator (NLPM-NLE) is explored, which involves three steps: preprocessing by NLPM filtering, sample area selection, parameter estimation. And then, we advance a stable-BM3D (SBM3D) method with NLPM filtering to avoid artificial effects and bias effects. Finally, connecting the NLPM-NLE and SBM3D by merging the same part, we develop a non-parametric single image denoising (NPSID) method. Additionally, our proposed BM3D method with NLPM-NLE and the NPSID are compared with other blind denoising methods including PCA + BM3D, WTP + BM3D, and ESM + BM3D on real image denoising. Experiments show that the proposed non-parametric method can automatically and effectively remove noise and preserve details.