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Image processing transforms recorded image signal data to remove noise, recover detail or extract structure. Variational image processing describes desired reconstructions through energies, while diffusion image processing describes filtering through evolution equations.

A grey-value image signal is a scalar function on an image signal domain or an array of pixel values. Continuous image processing models use spaces such as $L^2$, Sobolev spaces or the BV space, while discrete models use finite-dimensional arrays. The chosen representation distinguishes smooth transitions, noise and image edges.