An interpolation filter based on natural neighbor Galerkin method for salt and pepper noise restoration with adaptive size local filtering window

In this paper, we present a new interpolation filter for salt and pepper noise (SPN) restoration in digital images. The proposed filter is established on decision-based filters (DBF) and consists of two units: noise detection and noise restoration. In noise restoration unit, the natural neighbor Galerkin method (NNGM), which is a two-dimensional scattered data interpolation, is adopted for estimating the intensities of noisy pixels. For each detected noisy pixel, an adaptive size local filtering window is considered and NNGM interpolation is applied locally. Compared to the other state-of-the-art DBFs for SPN removal, which are based on interpolation methods, our proposed method has better performance in terms of both objective and subjective assessments. In our proposed method, the noise restoration unit requires no manual parameter tuning. Numerous experiments results demonstrate that our proposed filter removes SPN effectively and preserves the details and edges well.