# Pottslab

Pottslab is a toolbox for jump-sparse reconstruction based on the Potts model.

The Potts model is given by

$u^* = \arg\min_u \gamma \| \nabla u\|_0 + \| Au - f\|_p^p,$ where $$f$$ is noisy data and $$A$$ a linear operator.

• the regularizing term $$\| \nabla u\|_0$$ enforces jump-sparse minimizers,
• $$\gamma > 0$$ is an empirical parameter which controls the balance between the regularizing term and the data term $$\| Au - f\|_p^p$$, ($$p = 1$$ or $$p = 2$$ )
• also known as piecewise constant Mumford-Shah model (recently also called l0-gradient model)

## Application examples

### Application to segmentation of vector-valued images

• Supports segmentation of vector-valued images (e.g. multispectral images, feature images)
• Linear complexity in number of color channels
• No a-priori label selection required

Left: A natural image; Right: Result using Potts model

### Application to denoising of jump-sparse/piecewise-constant signals, or step/changepoint detection

Top: Noisy signal; Bottom: Minimizer of Potts functional (ground truth in red)