The median-type filter is an effective technique to remove salt and pepper (SAP) noise; however, such a mechanism cannot always effectively remove noise and preserve details due to the local diversity singularity and local non-stationarity. In this paper, a two-step SAP removal method was proposed based on the analysis of the median-type filter errors. In the first step, a median-type filter was used to process the image corrupted by SAP noise. Then, in the second step, a novel-designed adaptive nonlocal bilateral filter is used to weaken the error of the median-type filter. By building histograms of median-type filter errors, we found that the error almost obeys Gaussian–Laplacian mixture distribution statistically. Following this, an improved bilateral filter was proposed to utilize the nonlocal feature and bilateral filter to weaken the median-type filter errors. In the proposed filter, (1) the nonlocal strategy is introduced to improve the bilateral filter, and the intensity similarity is measured between image patches instead pixels; (2) a novel norm based on half-quadratic estimation is used to measure the image patch- spatial proximity and intensity similarity, instead of fixed L1
norms; (3) besides, the scale parameters, which were used to control the behavior of the half-quadratic norm, were updated based on the local image feature. Experimental results showed that the proposed method performed better compared with the state-of-the-art methods.
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