Additive and exclusive noise suppression by iterative trimmed and truncated mean algorithm

• A novel iterative trimmed and truncated arithmetic mean (ITTM) algorithm is proposed.
• Three types of ITTM filter outputs are proposed based on the ITTM algorithm.
• The ITTM filter is effective in suppressing the additive and exclusive noise.
• The ITTM filter can effectively preserving the signal structure.
• The ITTM filter has a linear computational complexity O(n)O(n).

An iterative trimmed and truncated arithmetic mean (ITTM) algorithm is proposed, and the ITTM filters are developed. Here, trimming a sample means removing it and truncating a sample is to replace its value by a threshold. Simultaneously trimming and truncating enable the proposed filters to attenuate the mixed additive and exclusive noise in an effective way. The proposed trimming and truncating rules ensure that the output of the ITTM filter converges to the median. It offers an efficient method to estimate the median without time-consuming data sorting. Theoretical analysis shows that the ITTM filter of size n   has a linear computational complexity O(n)O(n). Compared to the median filter and the iterative truncated arithmetic mean (ITM) filter, the proposed ITTM filter suppresses noise more effectively in some cases and has lower computational complexity. Experiments on synthetic data and real images verify the filter's properties.