Backward Moving Median

Local Algorithm - One-Dimensional Algorithm

Backward Moving Median algorithm replaces each original data value by the Median over its neighbor values. The choice of filter width has a great impact on the final results. The basic formula (for filter width \(L = M+1\)) is stated as follows:

\[\hat{x}[n] = \text{Median}\{x[n-M], \ldots, x[n] \} \, \text{,}\]

where \(x[n]\) and \(\hat{x}[n]\) denote raw data and processed data, respectively.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
\(x[n]\)	\(x[n] \in \mathbb R^N\)	\(N \in \mathbb{N}\)	Input data sequence of length \(N\)
\(L\)	\(L \in \mathbb N\)	\(L = M + 1, \quad M \in \mathbb{N}\)

Output Parameters

Parameter	Type	Constraint	Description	Remarks
\(\hat{x}[n]\)	\(\hat{x}[n] \in \mathbb R^N\)	\(N \in \mathbb{N}\)	Output data sequence of length \(N\)

Tool Support

• Matlab

Single Steps using the Algorithm

• Data Denoising with Backward Moving Median

References

• G.R. Arce, Nonlinear Signal Processing: A Statistical Approach, Wiley:New Jersey, USA, 2005.