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

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.