Median Filter

Non-linear filter excellent for removing salt-and-pepper noise while preserving edges.

Definition

Replace each sample with the median of its neighborhood:

$$ y[n] = \text{median}{x[n-k], \ldots, x[n], \ldots, x[n+k]} $$

Implementation

1from scipy import signal, ndimage
2import numpy as np
3
4# 1D median filter
5window_size = 5
6y = signal.medfilt(x, kernel_size=window_size)
7
8# 2D median filter (images)
9filtered_image = ndimage.median_filter(image, size=3)

Advantages

• Preserves edges
• Removes impulse noise effectively
• No ringing artifacts

Disadvantages

• Non-linear (no frequency response)
• Slower than linear filters
• Can remove fine details

Use Cases

• Salt-and-pepper noise removal
• Image preprocessing
• Outlier removal in sensor data

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