Mixed noise removal filter for multi‐channel images based on halfspace deepest location

Abstract

In this study, the authors propose a novel method for removing mixed (mixture of impulse and Gaussian) multi-channel noise from multi-channel digital images based on a modified version of the algorithm introduced by Struyf and Rousseeuw (Comput. Stat. Data Anal. (2000), 34, pp. 415–426) for finding approximate halfspace deepest location (Tukey's median). Denoising results of this new nonlinear spatial domain filtering method applied to benchmark images corrupted by multi-channel mixed noise outperform currently used spatial domain filters and state-of-the-art wavelet transform domain filters in terms of both peak signal-to-noise ratio and visual quality. Unlike most of the existing algorithms which remove the noise from multi-channel digital images on each of the channels separately, our method, because of its multivariate/multi-dimensional nature, eliminates the noise on all channels simultaneously without their separation, thus preserving the spectral correlation between channels in a multi-channel image. Proposed denoising method is very effective for removal of very wide range of powers of mixed multi-channel noise, but can be also successfully implemented for reduction of other forms of multi-channel noise since it is independent of the source or distribution of the noise.