What is a Sigma filter and how does it work?

A Sigma Filter, also known as Sigma-Kappa Filter, is a statistical filter used in image noise reduction and signal processing. It is named after the Greek letter 'Sigma' (σ) and was first introduced to filter out cosmic ray hits in astronomical images. The functioning of a Sigma filter is mainly based on mean and standard deviation statistics.

Below is a concise way how Sigma filter works:

1. Set a window around each pixel. The size of the window is usually determined by the user.
2. Calculate the mean (μ) and the standard deviation (σ) of the pixel intensities within the window.
3. If the pixel intensity deviates from the mean by more than a certain factor (k) times the standard deviation, then it's considered as noise.
4. Noise pixels are replaced by the mean of the non-noise pixels in the window.
5. The process is repeated for each pixel in the image or signal.

Through this technique, Sigma filter can effectively line out the unwanted noise and improve the quality of images or signals.

Learn more:

1. What is the difference between sigma filter and median filter in digital image processing? | ResearchGate
2. A Sigma Filter for Fourier Domain Optical Coherence Tomography | OSA Publishing
3. Sigma: A New Image Filter for Anisotropic Diffusion - OSTI.GOV