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.

Application examples

Segmentation of vector-valued images

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

Texture segmentation using highdimensional curvelet-based feature vectors

Joint image reconstruction and segmentation

Left: Shepp-Logan phantom; Center: Filtered backprojection from 7 angular projections; Right: Joint reconstruction and segmentation using the Potts model from 7 angular projections

Left: Blurred noisy image; Right: Joint deconvolution and segmentation using the Potts model

Denoising of jump-sparse/piecewise-constant signals, or step detection/changepoint detection

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